y = 3x + 5 y = ax + b What values for a and b make the system inconsistent? What values for a and b make the system consistent and dependent? Explain.

Answers

Answer 1

Answer:

inconsistent: a=3, b≠5dependent: a=3, b=5

Step-by-step explanation:

Given the following system of equations, you want to know values of 'a' and 'b' that (i) make the system inconsistent, and (ii) make the system consistent and dependent.

y = 3x +5y = ax +b

(i) Inconsistent

The system is inconsistent when it describes lines that are parallel and have no point of intersection. A solution to one of the equations cannot be a solution to the other.

Parallel lines have the same slope, but different y-intercepts. The system will be inconsistent when a=3 and b≠5.

(ii) Consistent, dependent

The system is consistent when a solution to one equation can be found that is also a solution to the other equation. The system is dependent if the two equations describe the same line (there are infinitely many solutions).

Here, the y-coefficients are the same in both equations, so the system will be dependent only if the values of 'a' and 'b' match the corresponding terms in the first equation:

The system is dependent when a=3, b=5.

__

Additional comment

Dependent systems are always consistent.

<95141404393>


Related Questions

Use the Sum and Difference formulas to evaluate.

cos (tan-¹(4/3)-sin-¹(3/5))

(Your answer should be a fraction. Show Your Work)

Answers

The value of cos(tan^(-1)(4/3) - sin^(-1)(3/5)) is 24/25.

To evaluate the expression cos(tan^(-1)(4/3) - sin^(-1)(3/5)), we can use the sum and difference formulas for trigonometric functions.

Let's start by applying the tangent inverse (tan^(-1)) and sine inverse (sin^(-1)) functions to their respective arguments:

Let angle A = tan^(-1)(4/3) and angle B = sin^(-1)(3/5).

Using the tangent inverse formula, we have:

tan(A) = 4/3

This means that the opposite side of angle A is 4, and the adjacent side is 3. Therefore, the hypotenuse can be found using the Pythagorean theorem:

hypotenuse = sqrt((opposite side)^2 + (adjacent side)^2) = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

So, the values of the sides of angle A are: opposite = 4, adjacent = 3, hypotenuse = 5.

Similarly, using the sine inverse formula, we have:

sin(B) = 3/5

This means that the opposite side of angle B is 3, and the hypotenuse is 5. The adjacent side can be found using the Pythagorean theorem:

adjacent side = sqrt((hypotenuse)^2 - (opposite side)^2) = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt(16) = 4

So, the values of the sides of angle B are: opposite = 3, adjacent = 4, hypotenuse = 5.

Now, we can apply the sum and difference formulas for cosine (cos) to the given expression:

cos(A - B) = cos(A) * cos(B) + sin(A) * sin(B)

Plugging in the values we obtained for angles A and B:

cos(tan^(-1)(4/3) - sin^(-1)(3/5)) = cos(A - B) = cos(tan^(-1)(4/3)) * cos(sin^(-1)(3/5)) + sin(tan^(-1)(4/3)) * sin(sin^(-1)(3/5))

Using the values of the sides we found earlier, we can evaluate the cosine and sine of angles A and B:

cos(A) = adjacent / hypotenuse = 3 / 5

sin(A) = opposite / hypotenuse = 4 / 5

cos(B) = adjacent / hypotenuse = 4 / 5

sin(B) = opposite / hypotenuse = 3 / 5

Substituting these values into the formula:

cos(tan^(-1)(4/3) - sin^(-1)(3/5)) = (3 / 5) * (4 / 5) + (4 / 5) * (3 / 5)

Evaluating the expression:

cos(tan^(-1)(4/3) - sin^(-1)(3/5)) = (12 / 25) + (12 / 25) = 24 / 25

for such more question on inverse

https://brainly.com/question/15066392

#SPJ8

Problem 1 . Prove the following proposition. Proposition 1 Let I⊆R be an interval and f,g two real-valued functions defined on I. Assume that f and g are convex. Then: (a) The function f+g is convex. (b) If c≥0, then cf is convex. (c) If c≤0, then cf is concave.

Answers

It is shown that: (a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex. (c) If c ≤ 0, then cf is concave. The proposition is proven.

How did we prove the proposition?

To prove the proposition, we'll need to show that each part (a), (b), and (c) holds true. Let's start with part (a).

(a) The function f+g is convex:

To prove that the sum of two convex functions is convex, we'll use the definition of convexity. Let's consider two points, x and y, in the interval I, and a scalar λ ∈ [0, 1]. We need to show that:

[tex](f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)[/tex]

Now, since f and g are both convex, we have:

[tex]f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) \: (1) \\

g(λx + (1-λ)y) ≤ λg(x) + (1-λ)g(y) \: (2)[/tex]

Adding equations (1) and (2), we get:

[tex]f(λx + (1-λ)y) + g(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) + λg(x) + (1-λ)g(y) \\

(f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)[/tex]

This shows that

[tex](f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y),[/tex]

which means that f+g is convex.

(b) If c ≥ 0, then cf is convex:

To prove this, let's consider a scalar λ ∈ [0, 1] and two points x, y ∈ I. We need to show that:

[tex](cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)[/tex]

Since f is convex, we know that:

[tex]f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y)[/tex]

Now, since c ≥ 0, multiplying both sides of the above inequality by c gives us:

[tex]cf(λx + (1-λ)y) ≤ c(λf(x) + (1-λ)f(y))

\\ (cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)

[/tex]

This shows that cf is convex when c ≥ 0.

(c) If c ≤ 0, then cf is concave:

To prove this, we'll consider the negative of the function cf, which is (-cf). From part (b), we know that (-cf) is convex when c ≥ 0. However, if c ≤ 0, then (-c) ≥ 0, so (-cf) is convex. Since the negative of a convex function is concave, we conclude that cf is concave when c ≤ 0.

In summary, we have shown that:

(a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex.

(c) If c ≤ 0, then cf is concave.

Therefore, the proposition is proven.

learn more about convex function: https://brainly.com/question/26093364

#SPJ4

a) This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex, b) This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is conve, c) Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

To prove Proposition 1, we will demonstrate each part individually:

(a) To prove that the function f + g is convex, we need to show that for any x, y in the interval I and any λ ∈ [0, 1], the following inequality holds:

(f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y))

Since f and g are convex functions, we know that for any x, y in I and λ ∈ [0, 1], we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

g(λx + (1 - λ)y) ≤ λg(x) + (1 - λ)g(y)

By adding these two inequalities together, we obtain:

f(λx + (1 - λ)y) + g(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) + λg(x) + (1 - λ)g(y)

This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex.

(b) To prove that cf is convex when c ≥ 0, we need to show that for any x, y in I and any λ ∈ [0, 1], the following inequality holds:

(cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y))

Since f is a convex function, we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

By multiplying both sides of this inequality by c (which is non-negative), we obtain:

cf(λx + (1 - λ)y) ≤ c(λf(x)) + c((1 - λ)f(y))

This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is convex when c ≥ 0.

(c) To prove that cf is concave when c ≤ 0, we can use a similar approach as in part (b). By multiplying both sides of the inequality f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) by c (which is non-positive), we obtain the inequality (cf)(λx + (1 - λ)y) ≥ λ(cf(x)) + (1 - λ)(cf(y)), showing that cf is concave when c ≤ 0.

Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

Learn more about concave here:

https://brainly.com/question/27841226

#SPJ11

matrix: Proof the following properties of the fundamental (1)-¹(t₁, to) = $(to,t₁);

Answers

The property (1)-¹(t₁, t₀) = $(t₀,t₁) holds true in matrix theory.

In matrix theory, the notation (1)-¹(t₁, t₀) represents the inverse of the matrix (1) with respect to the operation of matrix multiplication. The expression $(to,t₁) denotes the transpose of the matrix (to,t₁).

To understand the property, let's consider the matrix (1) as an identity matrix of appropriate dimension. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. When we take the inverse of the identity matrix, we obtain the same matrix. Therefore, (1)-¹(t₁, t₀) would be equal to (1)(t₁, t₀) = (t₁, t₀), which is the same as $(t₀,t₁).

This property can be understood intuitively by considering the effect of the inverse and transpose operations on the identity matrix. The inverse of the identity matrix simply results in the same matrix, and the transpose operation also leaves the identity matrix unchanged. Hence, the property (1)-¹(t₁, t₀) = $(t₀,t₁) holds true.

The property (1)-¹(t₁, t₀) = $(t₀,t₁) in matrix theory states that the inverse of the identity matrix, when transposed, is equal to the transpose of the identity matrix. This property can be derived by considering the behavior of the inverse and transpose operations on the identity matrix.

Learn more about matrix

brainly.com/question/29000721

#SPJ11

Q2) C: The probability that a randomly selected elementary or secondary school teacher from a city is a female is 0.68, holds a second job is 0.38, and is a female and holds a second job is 0.29. Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job. a. 0.77 b. 0.99 c. 0.66 d. 0.88

Answers

The probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.77, the correct answer is a.

To find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job, we can use the inclusion-exclusion principle.

Let's denote:

P(F) = Probability of being a female

P(S) = Probability of holding a second job

From the given information:

P(F) = 0.68

P(S) = 0.38

P(F ∩ S) = 0.29 (Probability of being a female and holding a second job)

Using the inclusion-exclusion principle, the probability of the union (female or holding a second job) is given by:

P(F ∪ S) = P(F) + P(S) - P(F ∩ S)

Substituting the values:

P(F ∪ S) = 0.68 + 0.38 - 0.29

P(F ∪ S) = 0.77

Therefore, the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.77. Hence, the correct answer is a. 0.77.

Learn more about probability at https://brainly.com/question/15244723

#SPJ11



Solve each proportion.

3/4 = 5/x

Answers

The value of x in the proportion 3/4 = 5/x is 20/3.

To solve the proportion 3/4 = 5/x, we can use cross multiplication. Cross multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction and vice versa.

In this case, we have (3 * x) = (4 * 5), which simplifies to 3x = 20. To isolate x, we divide both sides of the equation by 3, resulting in x = 20/3.

Therefore, the value of x in the given proportion is 20/3.

Learn more about Proportion

brainly.com/question/33460130

#SPJ11

Write the equation of a function whose parent function, f(x) = x 5, is shifted 3 units to the right. g(x) = x 3 g(x) = x 8 g(x) = x − 8 g(x) = x 2

Answers

The equation of the function that results from shifting the parent function three units to the right is g(x) = x + 8.

To shift the parent function f(x) = x + 5 three units to the right, we need to subtract 3 from the input variable x. This will offset the graph horizontally to the right. Therefore, the equation of the shifted function, g(x), can be written as g(x) = (x - 3) + 5, which simplifies to g(x) = x + 8. The constant term in the equation represents the vertical shift. In this case, since the parent function has a constant term of 5, shifting it to the right does not affect the vertical position, resulting in g(x) = x + 8. This equation represents a function that is the same as the parent function f(x), but shifted three units to the right along the x-axis.

Learn more about function here :

brainly.com/question/30721594?

#SPJ11

The complete question is : Write the equation of a function whose parent function, f(x)=x+5, is shifted 3 units to the right. g(x)=x+3 g(x)=x+8 g(x)=x-8 g(x)=x-2

For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.

If x = 9, then x2 = 81.

Answers

The converse is "If x² = 81, then x = 9." which is true hence, these statements can be combined as: x = 9 if and only if   x² = 81.

A conditional statement is of the form "if p, then q." The statement p is called the hypothesis or premise, while the statement q is known as the conclusion.

For the given conditional statement "if x = 9, the x²  = 81," the converse is: "If x²  = 81, then x = 9."

This is an example of a true biconditional statement.

This means that the original conditional statement and its converse are both true. Therefore, they can be combined to form a biconditional statement.

Let's combine the statements:

If x = 9, then x² = 81. If x² = 81, then x = 9.

These statements can be combined as: x = 9 if and only if x² = 81.

For more such questions on converse  visit:

https://brainly.com/question/5598970

#SPJ8



What is the sum of the solutions of |5 x-4|=x-8 ?

Answers

The sum of the solutions of the equation |5x - 4| = x - 8 is 1.

To find the sum of the solutions of the equation |5x - 4| = x - 8, we need to solve the equation and then sum the solutions.

Let's consider the two cases when the expression inside the absolute value is positive and negative.

Case 1: (5x - 4) is positive

In this case, the equation simplifies to:

5x - 4 = x - 8

Solving for x:

5x - x = -8 + 4

4x = -4

x = -4/4

x = -1

Case 2: (5x - 4) is negative

In this case, we change the sign of the expression inside the absolute value, and the equation becomes:

-(5x - 4) = x - 8

Simplifying and solving for x:

-5x + 4 = x - 8

-5x - x = -8 - 4

-6x = -12

x = -12 / -6

x = 2

So the two solutions are x = -1 and x = 2.

To find the sum of the solutions:

Sum = (-1) + 2

Sum = 1

Therefore, the sum of the solutions of the equation |5x - 4| = x - 8 is 1.

Learn more about linear equations from the given link!

https://brainly.com/question/28307569

#SPJ11

Help please!! On edmentum

Answers

both functions are linear and increasing

4. Express the following algebraic expression in the rectangular (Z = X +iY) form, 2 2 (x+iy 4)² – (x-x)², where x, X and y, Y are - x-iy r+iy/ real numbers.

Answers

To express the algebraic expression [tex]$(x + iy)^2 - (x - x)^2$[/tex] in the rectangular form [tex]$(Z = X + iY)$[/tex] where [tex]$x$[/tex], [tex]$X$[/tex],[tex]$y$[/tex], [tex]$Y$[/tex]are real numbers, we can expand and simplify the expression.

First, let's expand [tex]$(x + iy)^2$[/tex]:

[tex]\[(x + iy)^2 = (x + iy)(x + iy) = x(x) + x(iy) + ix(y) + iy(iy) = x^2 + 2ixy - y^2\][/tex]

Next, let's simplify [tex]$(x - x)^2$[/tex]:

[tex]\[(x - x)^2 = 0^2 = 0\][/tex]

Now, we can substitute these results back into the original expression:

[tex]\[2(x + iy)^2 - (x - x)^2 = 2(x^2 + 2ixy - y^2) - 0 = 2x^2 + 4ixy - 2y^2\][/tex]

Therefore, the algebraic expression [tex]$(x + iy)^2 - (x - x)^2$[/tex] can be expressed in the rectangular form as [tex]$2x^2 + 4ixy - 2y^2$[/tex].

In this form, [tex]$X = 2x^2$[/tex][tex]$Y = 4xy - 2y^2$[/tex], representing the real and imaginary parts respectively.

learn more about real and imaginary parts

https://brainly.com/question/13389642

#SPJ11



Assume a and b are positive integers. Determine whether each statement is true or false. If it is true, explain why. If it is false, give a counterexample.

(a !)^b=a^(b!)

Answers

The statement (a!)^b = a^(b!) is not true for all values of a and b, where they are positive integers. Hence, the given statement is false.

Given: a and b are positive integers.

To determine whether the given statement, (a!)^b = a^(b!) is true or false, we have to apply mathematical logic.  Let us test this statement for some random values of a and b.

Example 1: Let a = 2 and b = 3.

(a!)^b = (2!)^3 = 8^3 = 512

a^(b!) = 2^(3!) = 2^6 = 64

Here, (a!)^b ≠ a^(b!). So, the statement (a!)^b = a^(b!) is false.

Example 2: Let a = 3 and b = 2.

(a!)^b = (3!)^2 = 6^2 = 36

a^(b!) = 3^(2!) = 3^2 = 9

Here, (a!)^b ≠ a^(b!) So, the statement (a!)^b = a^(b!) is false.

Therefore, the statement (a!)^b = a^(b!) is not true for all values of a and b. Hence, the given statement is false.

To know more about positive integers, refer here:

https://brainly.com/question/18380011

#SPJ11

25 points

Mark has purchased 2000 bottles of shampoo at $3. 97/piece for his

barber shop. He sells each bottle of shampoo to each client for

$25. 32/each. How much was Mark's profit from the sale of this shampoo?

Your answer

Answers

Mark's profit from the sale of the shampoo is $42700.

To calculate Mark's profit from the sale of shampoo, we need to consider the total cost of purchasing the shampoo and the total revenue generated from selling it.

Total Cost:

Mark purchased 2000 bottles of shampoo at a cost of $3.97 per bottle. To find the total cost, we multiply the number of bottles (2000) by the cost per bottle ($3.97).

Total Cost = 2000 * $3.97 = $7,940.

Total Revenue:

Mark sells each bottle of shampoo for $25.32 to each client. To find the total revenue, we multiply the selling price per bottle ($25.32) by the number of bottles (2000).

Total Revenue = 2000 * $25.32 = $50,640.

Profit:

To calculate the profit, we subtract the total cost from the total revenue.

Profit = Total Revenue - Total Cost

Profit = $50,640 - $7,940 = $42,700.

Therefore, Mark's profit from the sale of shampoo is $42,700.

It's important to note that profit represents the financial gain obtained after deducting the cost of purchasing the goods from the revenue generated by selling them. In this case, Mark's profit indicates the earnings he achieved by selling the shampoo bottles in his barber shop. It signifies the positive difference between the revenue received from customers and the cost incurred to acquire the shampoo inventory.

Learn more about profit here :-

https://brainly.com/question/32864864

#SPJ11

A regular pentagon and a regular hexagon are both inscribed in the circle below. Which shape has a bigger area? Explain your reasoning.

Answers

Answer:

Hexagon

Step-by-step explanation:

Since the hexagon has more sides it should cover more space

A new project will have an intial cost of $14,000. Cash flows from the project are expected to be $6,000, $6,000, and $10,000 over the next 3 years, respectively. Assuming a discount rate of 18%, what is the project's discounted payback period?
2.59
2.87
2.76
2.98
03.03

Answers

The project's discounted payback period is approximately 4.5 years.

The discounted payback period is a measure of the time it takes for a company to recover its initial investment in a new project, considering the time value of money.

The formula for the discounted payback period is as follows:

Discounted Payback Period = (A + B) / C

Where:

A is the last period with a negative cumulative cash flow

B is the absolute value of the cumulative discounted cash flow at the end of period A

C is the discounted cash flow in the period after A

The formula for discounted cash flow (DCF) is as follows:

DCF = FV / (1 + r)^n

Where:

FV is the future value of the investment

n is the number of years

r is the discount rate

Initial cost of the project, P = $14,000

Cash flow for Year 1, CF1 = $6,000

Cash flow for Year 2, CF2 = $6,000

Cash flow for Year 3, CF3 = $10,000

Discount rate, r = 18%

Discount factor for Year 1, DF1 = 1 / (1 + r)^1 = 0.8475

Discount factor for Year 2, DF2 = 1 / (1 + r)^2 = 0.7185

Discount factor for Year 3, DF3 = 1 / (1 + r)^3 = 0.6096

Discounted cash flow for Year 1, DCF1 = CF1 x DF1 = $6,000 x 0.8475 = $5,085

Discounted cash flow for Year 2, DCF2 = CF2 x DF2 = $6,000 x 0.7185 = $4,311

Discounted cash flow for Year 3, DCF3 = CF3 x DF3 = $10,000 x 0.6096 = $6,096

Cumulative discounted cash flow at the end of Year 3, CF3 = $5,085 + $4,311 + $6,096 = $15,492

Since the cumulative discounted cash flow at the end of Year 3 is positive, we need to find the discounted payback period between Year 2 and Year 3.

DCFA = -$9,396 (CF1 + CF2)

DF3 = 0.6096

DCF3 = CF3 x DF3 = $6,096 x 0.6096 = $3,713

Payback Period = A + B/C = 2 + $9,396 / $3,713 = 4.53 years ≈ 4.5 years

Therefore, The discounted payback period for the project is roughly 4.5 years.

Learn more about Cash flows

https://brainly.com/question/27994727

#SPJ11



For each equation, find all the roots.

3 x⁴ - 11 x³+15 x²-9 x+2=0

Answers

The roots of the equation 3x⁴ - 11x³ + 15x² - 9x + 2 = 0 can be found using numerical methods or software that can solve polynomial equations.

To find all the roots of the equation 3x⁴ - 11x³ + 15x² - 9x + 2 = 0, we can use various methods such as factoring, synthetic division, or numerical methods.

In this case, numerical like the Newton-Raphson method is used to approximate the roots. Using the Newton-Raphson method, we can iteratively find better approximations for the roots. Let's start with an initial guess for a root and perform the iterations until we find the desired level of precision.

Let's say x₁ = 1.

Perform iterations using the following formula until the desired precision is reached:

x₂ = x₁ - (f(x₁) / f'(x₁))

Where:

f(x) represents the function value at x, which is the polynomial equation.

f'(x) represents the derivative of the function.

Repeat the iterations until the desired level of precision is achieved.

Let's proceed with the iterations:

Iteration 1:

x₂ = x₁ - (f(x₁) / f'(x₁))

Substituting x₁ = 1 into the equation:

f(x₁) = 3(1)⁴ - 11(1)³ + 15(1)² - 9(1) + 2

= 3 - 11 + 15 - 9 + 2

= 0

To find f'(x₁), we differentiate the equation with respect to x:

f'(x) = 12x³ - 33x² + 30x - 9

Substituting x₁ = 1 into f'(x):

f'(x₁) = 12(1)³ - 33(1)² + 30(1) - 9

= 12 - 33 + 30 - 9

= 0

Since f'(x₁) = 0, we cannot proceed with the Newton-Raphson method using x₁ = 1 as the initial guess.

We need to choose a different initial guess and repeat the iterations until we find a root. By analyzing the graph of the equation or using other numerical methods, we can find that there are two real roots and two complex roots for this equation.

Learn more about Newton-Raphson method from the given link!

https://brainly.com/question/30648237

#SPJ11

Ali went to a store that sells T-shirts. It’s offering $ 180 for 6 T-shirts or $270 for 9 T-shirts.
Find the constant of proportionality.
Write the equation of proportionality.
What will be the price of 15 T- shirts.
If the price of a T-shirt changed to $43. What will be the price of 7 T- shirts.

Answers

Step-by-step explanation:

To find the constant of proportionality, we can set up a ratio between the number of T-shirts and their respective prices.

Let's denote the number of T-shirts as 'n' and the price as 'p'.

Given that the store offers $180 for 6 T-shirts and $270 for 9 T-shirts, we can set up the following ratios:

180/6 = p/n

270/9 = p/n

We can simplify these ratios by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 180 and 6 is 6, and the GCD of 270 and 9 is also 9. Simplifying the ratios, we get:

30 = p/n

30 = p/n

Since the ratios are equal, we can write the equation of proportionality as:

p/n = 30

The constant of proportionality is 30.

To find the price of 15 T-shirts, we can use the equation of proportionality:

p/n = 30

Substituting the values, we get:

p/15 = 30

Solving for 'p', we find:

p = 30 * 15 = 450

Therefore, the price of 15 T-shirts will be $450.

If the price of a T-shirt changed to $43, we can use the equation of proportionality to find the price of 7 T-shirts:

p/n = 30

Substituting the values, we get:

43/n = 30

Solving for 'n', we find:

n = 43 / 30 * 7 = 10.77 (rounded to two decimal places)

Therefore, the price of 7 T-shirts, when each T-shirt costs $43, will be approximately $10.77.

2) Solve x" + 6x' + 5x = 0, x'(0) = 1,x(0) = 2 I

Answers

The solution to the given differential equation is x(t) = 2e^(-t) - e^(-5t).

We start by finding the characteristic equation associated with the given differential equation. The characteristic equation is obtained by replacing the derivatives with algebraic variables, resulting in the equation r^2 + 6r + 5 = 0.

Next, we solve the characteristic equation to find the roots. Factoring the quadratic equation, we have (r + 5)(r + 1) = 0. Therefore, the roots are r = -5 and r = -1.

Step 3: The general solution of the differential equation is given by x(t) = c1e^(-5t) + c2e^(-t), where c1 and c2 are constants. To find the particular solution that satisfies the initial conditions, we substitute the values of x(0) = 2 and x'(0) = 1 into the general solution.

By plugging in t = 0, we get:

x(0) = c1e^(-5(0)) + c2e^(-0)

2 = c1 + c2

By differentiating the general solution and plugging in t = 0, we get:

x'(t) = -5c1e^(-5t) - c2e^(-t)

x'(0) = -5c1 - c2 = 1

Now, we have a system of equations:

2 = c1 + c2

-5c1 - c2 = 1

Solving this system of equations, we find c1 = -3/4 and c2 = 11/4.

Therefore, the particular solution to the given differential equation with the initial conditions x(0) = 2 and x'(0) = 1 is:

x(t) = (-3/4)e^(-5t) + (11/4)e^(-t)

Learn more about: differential equation

brainly.com/question/16663279

#SPJ11

In a city with a population of 75,000 .people, the number of people P(t) exposed to a rumor in t hours is given by the function P(t)=75,000(1−e−0.0009t). (Round your answers to the nearest hour) (a) Find the number of hours until 10% of the population have heard the rumor. h (b) Find the number of hours until 50% of the population have heard the rumor. h

Answers

Rounding to the nearest hour, it takes approximately 768 hours until 50% of the population have heard the rumor.

(a) To find the number of hours until 10% of the population have heard the rumor, we need to solve the equation P(t) = 0.10 * 75,000.

P(t) = 75,000(1 - e^(-0.0009t))

0.10 * 75,000 = 75,000(1 - e^(-0.0009t))

7,500 = 75,000 - 75,000e^(-0.0009t)

e^(-0.0009t) = 1 - (7,500 / 75,000)

e^(-0.0009t) = 0.90

Taking the natural logarithm of both sides:

-0.0009t = ln(0.90)

t = ln(0.90) / -0.0009

t ≈ 3028

Rounding to the nearest hour, it takes approximately 3028 hours until 10% of the population have heard the rumor.

(b) To find the number of hours until 50% of the population have heard the rumor, we need to solve the equation P(t) = 0.50 * 75,000.

P(t) = 75,000(1 - e^(-0.0009t))

0.50 * 75,000 = 75,000(1 - e^(-0.0009t))

37,500 = 75,000 - 75,000e^(-0.0009t)

e^(-0.0009t) = 1 - (37,500 / 75,000)

e^(-0.0009t) = 0.50

Taking the natural logarithm of both sides:

-0.0009t = ln(0.50)

t = ln(0.50) / -0.0009

t ≈ 768

Know more about logarithm here:

https://brainly.com/question/30226560

#SPJ11

Natalie went to store A and bought 3 4/5 pounds of pistachios for $17. 75. Nicholas went to a store B and brought 4 7/10 pounds of pistachios for $ 19.50.

Answers

Natalie bought pistachios at a lower price per pound compared to Nicholas.

To compare the prices of pistachios at store A and store B, we need to calculate the price per pound for each store based on the given information.

Natalie's purchase at store A:

Weight of pistachios = 3 4/5 pounds

Cost of pistachios = $17.75

To calculate the price per pound at store A, we divide the total cost by the weight:

Price per pound at store A = $17.75 / (3 4/5) pounds.

To simplify the calculation, we can convert the mixed fraction 3 4/5 to an improper fraction:

3 4/5 = (3 [tex]\times[/tex] 5 + 4) / 5 = 19/5

Substituting the values, we have:

Price per pound at store A = $17.75 / (19/5) pounds

Price per pound at store A = $17.75 [tex]\times[/tex] (5/19) per pound

Price per pound at store A = $3.947 per pound (rounded to three decimal places).

Nicholas's purchase at store B:

Weight of pistachios = 4 7/10 pounds

Cost of pistachios = $19.50

To calculate the price per pound at store B, we divide the total cost by the weight:

Price per pound at store B = $19.50 / (4 7/10) pounds

Converting the mixed fraction 4 7/10 to an improper fraction:

4 7/10 = (4 [tex]\times[/tex] 10 + 7) / 10 = 47/10

Substituting the values, we have:

Price per pound at store B = $19.50 / (47/10) pounds

Price per pound at store B = $19.50 [tex]\times[/tex] (10/47) per pound

Price per pound at store B = $4.149 per pound (rounded to three decimal places).

Comparing the prices per pound, we find that the price per pound at store A ($3.947) is lower than the price per pound at store B ($4.149).

For similar question on lower price.

https://brainly.com/question/7303679  

#SPJ8

Elementary linear algebra (Linear Transformations) (Please explain in non-mathematical language as best you can)
Let R[x] be the set of all real polynomials in the variable x. As noted earlier, R[x] is a real vector space.
Let V be the subspace of all polynomials of degree no more than four. Also as noted earlier, differentiation defines a linear
transformation on R[x] , and so, by restriction, a linear transformation T : V →V . Find the 5 × 5 real matrix associated
with this linear transformation with respect to the basis 1,x,x2,x3,x4.

Answers

Linear transformations are operations that take in vectors and produce new vectors in a way that maintains certain properties. They are commonly used in linear algebra to study how vectors change or are mapped from one space to another.

Think of a linear transformation as a machine that takes in objects (vectors) and processes them according to certain rules. Just like a machine that transforms raw materials into finished products, a linear transformation transforms input vectors into output vectors.

These transformations preserve certain properties. For example, they preserve the concept of lines and planes. If a straight line is input into a linear transformation, the result will still be a straight line, although it may be in a different direction or position. Similarly, if a plane is input, the transformation will produce another plane.

Linear transformations can also scale or stretch vectors, rotate them, or reflect them across an axis. They can compress or expand space, but they cannot create new space or change its overall shape.

learn more about Linear transformations

https://brainly.com/question/13595405

#SPJ11

The least number by which 3² x 7² x 5 should be multiplied to make the resulting product a perfect cube is ​

Answers

Answer: 525

Step-by-step explanation:

To determine the least number by which 3² x 7² x 5 should be multiplied to make the resulting product a perfect cube, we need to factorize the given expression and identify the missing factors.

3² x 7² x 5 can be written as (3 x 3) x (7 x 7) x 5 = 3² x 7² x 5

To make it a perfect cube, we need to identify the missing factors. In a perfect cube, each prime factor must have an exponent that is a multiple of 3.

Let's analyze the given expression:

Prime factor 3 appears with an exponent of 2, which is not a multiple of 3. So, we need to multiply it by 3 to make it a perfect cube.

Prime factor 7 appears with an exponent of 2, which is also not a multiple of 3. So, we need to multiply it by 7 to make it a perfect cube.

Prime factor 5 appears with an exponent of 1, which is not a multiple of 3. So, we need to multiply it by 5² to make it a perfect cube.

The least number by which 3² x 7² x 5 should be multiplied to make it a perfect cube is:

3 x 7 x 5² = 3 x 7 x 25 = 525.

Therefore, the expression 3² x 7² x 5 should be multiplied by 525 to make the resulting product a perfect cube.

Final answer:

To make the product 3² x 7² x 5 a perfect cube, we need to factorize it and check for any missing powers. The least number by which it should be multiplied is 21.

Explanation:

To make the product 3² x 7² x 5 a perfect cube, we need to find the least number that can be multiplied with it. In order to do this, we need to factorize the given expression and check for any missing powers.

Factoring 3² x 7² x 5, we have (3 x 3) x (7 x 7) x 5. Now, we check for any missing powers. We need one more factor of 3 and one more factor of 7 to make it a perfect cube.

So, the least number by which 3² x 7² x 5 should be multiplied to make the resulting product a perfect cube is 3 x 7 = 21.

Learn more about perfect cube here:

https://brainly.com/question/32533771

#SPJ2

pls help if you can asap!!!!

Answers

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

1. Transform the following f(x) using the Legendre's polynomial function (i). (ii). 4x32x² 3x + 8 x³ 2x²-x-3 -

Answers

The answer cannot be provided in one row as the specific transformation steps and calculations are not provided in the question.

Transform the given function f(x) using Legendre's polynomial function.

The given problem involves transforming the function f(x) using Legendre's polynomial function.

Legendre's polynomial function is a series of orthogonal polynomials used to approximate and transform functions.

In this case, the function f(x) is transformed using Legendre's polynomial function, which involves expressing f(x) as a linear combination of Legendre polynomials.

The specific steps and calculations required to perform this transformation are not provided, but the result of the transformation will be a new representation of the function f(x) in terms of Legendre polynomials.

Learn more about steps and calculations

brainly.com/question/29162034

#SPJ11

what is one half note multiplied by x one whole note minus two eighth notes?

Answers

One-half note multiplied by x one whole note minus two eighth notes will give

How to determine the amount

To determine what one-half note multiplied by x one whole note minus two eighth notes will give, the figures would be expressed first as follows:

One-half note = 2 quarter notes

One whole note = x(2 half notes) or four quarter notes

Two eight notes = 1 quarter notes

Now, we will sum up all of the quarter notes to have

2 + 4 + 1 = 7 quarter notes.

So the correct option is 7 quarter notes.

Learn more about multiplication here:

https://brainly.com/question/10873737

#SPJ1

Finney Appliances past accounting data shows that their expenses average 8% of an iteris regular selling price. They want to make a 22% profit based on selling price. If Finney Appliances purchases a refngerator for $1,030, answer the following questions For full marks your answer(s) should be rounded to the nearest cent a) What is the reqular sellina pnice? b) What is the amount of

Answers

a) The regular selling price for the refrigerator is approximately $1,471.43.

b) The amount of profit based on the selling price is approximately $441.43.

a) To calculate the regular selling price, we need to consider the expenses and the desired profit.

Let's denote the regular selling price as "P."

Expenses average 8% of the regular selling price, which means expenses amount to 0.08P.

The desired profit based on selling price is 22% of the regular selling price, which means profit amounts to 0.22P.

The total cost of the refrigerator, including expenses and profit, is the purchase price plus expenses plus profit: $1,030 + 0.08P + 0.22P.

To find the regular selling price, we set the total cost equal to the regular selling price:

$1,030 + 0.08P + 0.22P = P.

Combining like terms, we have:

$1,030 + 0.30P = P.

0.30P - P = -$1,030.

-0.70P = -$1,030.

Dividing both sides by -0.70:

P = -$1,030 / -0.70.

P ≈ $1,471.43.

Therefore, the regular selling price is approximately $1,471.43.

b) To calculate the amount of profit, we can subtract the cost from the regular selling price:

Profit = Regular selling price - Cost.

Profit = $1,471.43 - $1,030.

Profit ≈ $441.43.

Therefore, the amount of profit is approximately $441.43.

Please note that the values are rounded to the nearest cent.

To know more about profit, refer to the link below:

https://brainly.com/question/32673662#

#SPJ11

Un, Un+1 € Rª be a collection of vectors such that if i ‡ j 9 Question 5. (a) Let 7₁, V₂ Vj = 0. Show that at least one of the vectors is 0. (b) Let 7₁, , Un E Rn be a collection of non-zero vectors such that if i ‡ j v₁ · Vj = 0. Let W₁, W₂ € Rn be such that for i = 1, ..., n, V¡ · W₁ = V₁ · W₂. Show that w₁ = W₂.

Answers

(a) If v₁, v₂, ..., vn are vectors in Rⁿ and vᵢ · vⱼ = 0 for all i ≠ j, then at least one of the vectors is the zero vector.

(b) If v₁, v₂, ..., vn are nonzero vectors in Rⁿ such that vᵢ · vⱼ = 0 for all i ≠ j, and W₁, W₂ are vectors in Rⁿ such that vᵢ · W₁ = vᵢ · W₂ for all i = 1, ..., n, then W₁ = W₂.

(a) Let's prove that if v₁, v₂, ..., vn are nonzero vectors in Rⁿ such that vᵢ · vⱼ = 0 for all i ≠ j, then at least one of the vectors is the zero vector.

Assume that all vectors v₁, v₂, ..., vn are nonzero. Since the dot product of two vectors is zero if and only if the vectors are orthogonal, this means that all pairs of vectors vᵢ and vⱼ are orthogonal to each other.

Consider the orthogonal complement of each vector vᵢ. The orthogonal complement of a nonzero vector is a subspace orthogonal to that vector. Since all vectors vᵢ are nonzero and pairwise orthogonal, the orthogonal complements of each vector are distinct subspaces.

Now, let's consider the intersection of all these orthogonal complements. Since the orthogonal complements are distinct, their intersection must be the zero vector (the only vector that is orthogonal to all subspaces).

However, if all vectors v₁, v₂, ..., vn were nonzero, their orthogonal complements would not intersect at the zero vector. This leads to a contradiction.

Therefore, at least one of the vectors v₁, v₂, ..., vn must be the zero vector.

(b) Now, let's prove that if v₁, v₂, ..., vn are nonzero vectors in Rⁿ such that vᵢ · vⱼ = 0 for all i ≠ j, and W₁, W₂ are vectors in Rⁿ such that vᵢ · W₁ = vᵢ · W₂ for all i = 1, ..., n, then W₁ = W₂.

Let's assume that W₁ ≠ W₂ and aim to derive a contradiction.

Since W₁ ≠ W₂, their difference vector, let's call it D = W₁ - W₂, is nonzero.

Now, consider the dot product of D with each vector vᵢ:

D · vᵢ = (W₁ - W₂) · vᵢ

       = W₁ · vᵢ - W₂ · vᵢ

       = vᵢ · W₁ - vᵢ · W₂   (by commutativity of dot product)

       = 0   (given condition)

This implies that the dot product of D with every vector vᵢ is zero. However, since D is nonzero and vᵢ are nonzero, this contradicts the given condition that vᵢ · vⱼ = 0 for all i ≠ j.

Hence, our assumption that W₁ ≠ W₂ must be false, and we conclude that W₁ = W₂.

Therefore, if v₁, v₂, ..., vn are nonzero vectors in Rⁿ such that vᵢ · vⱼ = 0 for all i ≠ j, and W₁, W₂ are vectors in Rⁿ such that vᵢ · W₁ = vᵢ · W₂ for all i = 1, ..., n, then W₁ = W₂.

Learn more about zero vector

https://brainly.com/question/32604726

#SPJ11

Problem 1: Solve the following assignment problem shown in Table using Hungarian method. The matrix entries are processing time of each man in hours.
I II III IV V
1 20 15 18 20 25
2 18 20 12 14 15
3 21 23 25 27 25
4 17 18 21 23 20
5 18 18 16 19 20

Answers

The optimal assignment using the Hungarian method results in a total processing time of 0 hours

the assignment problem using the Hungarian method, we need to follow these steps:

Step 1: Create the cost matrix

Construct a matrix from the given processing time values, where each entry represents the cost of assigning a man to a task. In this case, the matrix would look as follows:

1 | 20 15 18 20 25

2 | 18 20 12 14 15

3 | 21 23 25 27 25

4 | 17 18 21 23 20

5 | 18 18 16 19 20

Step 2: Subtract row minima

Subtract the smallest value in each row from every entry in that row:

1 | 5 0 3 5 10

2 | 3 5 0 2 3

3 | -2 0 2 4 2

4 | -1 0 3 5 2

5 | -2 0 -2 1 2

Step 3: Subtract column minima

Similarly, subtract the smallest value in each column from every entry in that column:

1 | 7 0 3 5 9

2 | 5 7 0 2 2

3 | -1 0 2 4 0

4 | 0 0 3 5 0

5 | -1 0 -2 1 0

Step 4: Assign initial zeros

Assign zeros to the entries in the matrix that do not share rows or columns with any other zeros, aiming to minimize the number of assignments. If there are still unassigned zeros, proceed to the next step.

1 | 7 0 3 5 9

2 | 5 7 0 2 2

3 | -1 0 2 4 0

4 | 0 0 3 5 0

5 | -1 0 -2 1 0

Step 5: Find minimum cover

Cover all the rows and columns that contain the assigned zeros. If the number of covered zeros is equal to the number of rows or columns, an optimal assignment is found. Otherwise, proceed to the next step.

In this case, we can cover all the rows and columns with the assigned zeros, so we have an optimal assignment.

The optimal assignment is as follows:

Man 1 assigned to Task II

Man 2 assigned to Task III

Man 3 assigned to Task V

Man 4 assigned to Task I

Man 5 assigned to Task IV

The minimum total processing time for this assignment is 0 + 0 + 0 + 0 + 0 = 0 hours.

Learn more about: Hungarian method

https://brainly.com/question/32955590

#SPJ11

The Bourassas decide to sell a home for $410,000. They are charged a real estate commission of 8% of the selling price, title insurance that is 1.4% of the selling price, and an escrow fee of $825. (a) What amount (in dollars) do the Bourassas receive after fees? $ (b) What percentage of the selling price was fees? Round to the nearest tenth of a percent. %

Answers

(a) The Bourassas receive $370,635 after deducting fees of $39,365 from the selling price of $410,000, which includes a real estate commission of $32,800, title insurance of $5,740, and an escrow fee of $825.

(b) The fees amount to 9.6% of the selling price, indicating that they represent a significant portion of the total transaction.

The total cost of fees is the sum of the real estate commission, title insurance, and the escrow fee:

Real estate commission = 8% of $410,000 = $32,800Title insurance = 1.4% of $410,000 = $5,740Escrow fee = $825

Total fees = $32,800 + $5,740 + $825 = $39,365

The amount the Bourassas receive after fees is the selling price minus the total fees:

Selling price = $410,000Amount received after fees = $410,000 - $39,365 = $370,635

Therefore, the Bourassas receive $370,635 after fees.

To find the percentage of the selling price that represents the fees, divide the total fees by the selling price and multiply by 100:

Percent fees = (Total fees / Selling price) x 100Percent fees = ($39,365 / $410,000) x 100Percent fees = 9.6% (rounded to the nearest tenth of a percent)

Therefore, the fees were 9.6% of the selling price.

Learn more about selling price: https://brainly.com/question/28420607

#SPJ11

What is the polar equation of the given rectangular equation \( x^{2}=\sqrt{4} x y-y^{2} \) ? A. \( 2 \sin Q \cos Q=1 \) B. \( 2 \sin Q \cos Q=r \) C. \( r(\sin Q \cos Q)=4 \) D. \( 4(\sin Q \cos Q)=1

Answers

The polar equation of the given rectangular equation is 2 sin 2θ = 1.

The given rectangular equation is x² = √(4xy) - y². To find the polar equation, we can substitute the conversion rules:

x = r cos θ

y = r sin θ

Substituting these values into the given rectangular equation, we have:

r² cos² θ = √(4r² sin θ cos θ) - r² sin² θ

Simplifying further:

r² cos² θ + r² sin² θ = √(4r² sin θ cos θ

4r² sin θ cos θ = r² (cos² θ + sin² θ)

We can cancel out r² on both sides:

4 sin θ cos θ = 1

Multiplying both sides by 2, we get:

2(2 sin θ cos θ) = 1

Simplifying further:

2 sin 2θ = 1

The above rectangle equation's polar equation is 2 sin 2 = 1.

Learn more about polar equation

https://brainly.com/question/29083133

#SPJJ1

Use the properties of logarithms to expand the logarithm. Simplify if possible. log3(3√X^2/27y^4) Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button. Provide your answer below:

Answers

The expression after expanding the logarithm and simplifying if possible is log₃ (27X/y²) + 3.  

Given expression: log₃(3√(X²/27y⁴))

The formula for the product of logs is given by: loga b + loga c = loga bc

The formula for the quotient of logs is given by: loga b - loga c = loga b/c The formula for the power of logs is given by: loga bⁿ = n loga b Using the above three formulas we can solve the given expression using the following steps:

Step 1: Rearrange the given expression.log₃(3√(X²/27y⁴))= log₃ 3 + log₃ √(X²/27y⁴)Use the formula of the product of logs.

Step 2: Simplify the expression in the second term of

step 1.log₃(3√(X²/27y⁴))= log₃ 3 + log₃ X/3y²Since √(27) = 3√3 and √(y⁴) = y². Using the formula of power of logs, we have, log₃(3√(X²/27y⁴))= log₃ 3 + (log₃ X - 2 log₃ y)

Step 3: Substitute the values.log₃(3√(X²/27y⁴))= log₃ 3 + log₃ X - 2log₃ y+ 3log₃ 3= log₃ (27X/y²) + 3

The expression after expanding the logarithm and simplifying if possible is log₃ (27X/y²) + 3.  

To know more about logarithm visit:
brainly.com/question/29752946

#SPJ11

Other Questions
How much heat must be added to 7kg of water at a temperature of18C to convert it to steam at 133C 1. Explain low income as one of the health disparities in the Hispanic community and why this issue is of importance; briefly include the relevant historical or sociopolitical factors.2. Describe two policies or programmatic interventions designed to improve or eliminate this disparity. Describe a few strategies that successfully promote learning with ELL students and explain how you execute these strategies for success? Question 19 Which of the following statements regarding CPM is true? Not yet answered Select one: Marked out of 1.00 a. The critical path is the shortest of all paths through the network. b. All activities on the critical path have their LS equal their predecessor's EF. c. Some networks have no critical path. d. All of the above are false. e. The critical path is that set of activities that has positive slack. A mortgage of 185,000 over 25 years at 6.25% interest compoundedmonthly. What are the monthly payments? Suppose that $6,800 is invested at 3.5% annual interest rate, compounded monthly. How much money will be in the account in (A) 7 months? (B) 12 years? If electrical energy costs $0.12 per kilowatt-hour, how much do the following events cost? (a) To burn a 80.0-W lightbulb for 24 h. (b) To operate an electric oven for 5.3 h if it carries a current of 20.0 A at 220 V. According to "Writes of Passage", the methods section of a paper should provide enough information so that others with access to your data would be able to replicate your work and get the same results.TrueFalse Suppose the yellow clip in the above image is attached to the G+ input on your iOLab, and the black clip is attached to the G-input, and that the High Gain sensor was being recorded during the flip. Describe what you think the High Gain data chart looks like. You will need to design your Lab 9 setup so thatis as big as possible when the loop is rotated, which means you need to think about ways to make the product ofNandAandB1as big as possible. Faraday's Law states that the magnitude of the emf is given by/t, so you should also take into. account the time it takes you to flip the loop. Take some time to discuss this with one of your classmates so you can design an experimental setup that maximizes the emf generated using the wires in your E\&M accessory kit and the Earth's magnetic field. 4. In the space below, summarize your thoughts and reasoning from your discussion with your classmate. Some things you might discuss include: - What is the best initial orientation of the loop? - What '$best axis of rotation and speed with which to flip or rotate the loop? - Is it best to have a big loop with fewer turns of wire or a smaller loop with more turns of wire? (Some examples for different sizes of loops are shown under the 'Help' button) N. Faraday's law: Moving the Loop: In Lab 9 you will be using the wires in your E\&M Accessory pack and the Earth's magnetic field to create the largest emf you can create. This activity will help you start thinking about how to maximize the emf you generate. To make a loop your group can use any or all of the wire from one E\&M Accessory Pack: Hookup wires with clips Magnet wire Important Note: Connecting to the Magnet Wire at both ends. You will be using the Earth itself as the magnet. Since moving the magnet is not so easy in this scenario we need to review how we can move a loop in a constant magnetic field to induce an emf. As you learned in your textbook and homework on Faraday's Law, the fluxthrough a loop withNturns and areaAin a constant magnetic fieldBis given by=NAB. As illustrated below, if the loop is flipped by180the change in flux is given by=2NAB. whereBis the component of the magnetic field that is perpendicular to the plane of the loop: Jody is having trouble seeing close objects, they appear blurry. A trip to the opthamologist indicates Jodys focal distance is too long. Use this information to answer the following questions.3A. Based on the information provided, what is Jodys diagnosis (use the correct term).3B. Explain why Jody is having trouble seeing close objects clearly - be specific.3C: Explain how this condition is corrected with glasses/contacts (be complete). 220 sixth grade a dessert and 190 seventh graders registered for electives. 60% of the sixth graders and 50% of seventh graders signed up for PE. How many more sixth graders than seventh graders signed up for PE? High school application case study1. Describe any circumstances meriting the belief that the applicant can do well at Lowell or that the applicants grades or standardized test scores are not a true representation of ability (e.g., personal family crisis, death in family during period when GPA dropped).2. Describe circumstances reflecting students drive and ambition to overcome hardship (e.g.,discrimination, economic responsibility,non-special education learning consideration The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z. The ________ provides structure and support to the cell.lysosomevacuolemitochondriacytoplasmcytoskeleton Cannon sells 22 mm lens for digital cameras. The manager considers using a continuous review policy to manage the inventory of this product and he is planning for the reorder point and the order quantity in 2021 taking the inventory cost into account. The annual demand for 2021 is forecasted as 400+10 the last digit of your student number and expected to be fairly stable during the year. Other relevant data is as follows: The standard deviation of the weekly demand is 10. Targeted cycle service level is 90% (no-stock out probability) Lead time is 4 weeks Each 22 mm lens costs $2000 Annual holding cost is 25% of item cost, i.e. H=$500. Ordering cost is $1000 per order a) Using your student number calculate the annual demand. ( 5 points) (e.g., for student number BBAW190102, the last digit is 2 and the annual demand is 400+10 2=420 ) b) Using the annual demand forecast, calculate the weekly demand forecast for 2021 (Assume 52 weeks in a year)? ( 2 points) c) What is the economic order quantity, EOQ? d) What is the reorder point and safety stock? e) What is the total annual cost of managing the inventory? ( 10 points) f) What is the pipeline inventory? ( 3 points) g) Suppose that the manager would like to achieve % 95 cycle service level. What is the new safety stock and reorder point? ( 5 points) FORMULAE Inventory Formulas EOQ=Q = H2DS , Total Cost(TC)=S D/Q+H (Q/2+ss),ss=z (L D =2 LTD )NORM.S.INV (0.95)=1.65, NORM.S.INV (0.92)=1.41 NORM.S.INV (0.90)=1.28, NORM.S. NNV(0.88)=1.17 NORM.S.INV (0.85)=1.04, NORM.S.INV (0.80)=0.84 inverse functions linear discrete 1. What is the poverty percentage in the county you live in?2. Which regions of the US have the highest poverty levels?3. Which regions have the lowest poverty level? Have you ever visited any of these regions?4. What observations can you make (be sure to use Sociological concepts and not merely your "opinion") both about the county you live in and the other states/regions you may have visited? 1) What do you call the reflex observed when you shine a light on the left eye and the pupil of the right eye constricts? Consensual light reflex Indirect light reflex None Consensus light reflex Direct light reflex2) Which is true about strabismus? A condition in which weak extrinsic eye muscles perfectly converge to fuse the images. A person with strabismus can see normally. The only type of strabismus is cross eye which is when both eyes are turned in. All are true. One eye becomes functionally blind. None3) Recalling your vision VL, which visual acuity is mismatched with the diopter reading? Diopter: 0 is to Emmetropia Diopter: 2.00 is to Hyperopia Diopter: -1.25 is to Myopia All are mismatched. None4) The pupils constrict when we focus on nearby objects so _______________. less distracting light can enter the eye. None the object can be better focused onto the retina. the rest of the environment is excluded from vision. All are correct. A prime mover (agonist) is the name given to a muscle producing the majority of the ____________ during a joint movement. A wheel undergoing MCUV rotates with an angular speed of 50 rad/s at t = 0 s and the magnitude of its angular acceleration is = 5 rad/s^2. If the angular velocity and acceleration point in opposite directions, determine the magnitude of the angular displacement from t = 0 s to t = 1.1 s.- if necessary consider gravity as 10m/s^2 Steam Workshop Downloader