Two car services charge different rates. A charges .60 per mile plus 3.00initial charge B charges .75 per mile mile traveled . the situation is modeled bu this system where x is the number of miles traveled and y is the charge for that distance ,in cents. How many miles must each car travel for the charges to be equal and ehat is the charge for that distance

Answers

Answer 1

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Related Questions

Which choice is a solution to this system of equations? -x=y-4 y=4x+9

Answers

The solution to the system of equations is  x = 5.4 and y = -1.4

How to determine the solution to the system of equations?

From the question, we have the following parameters that can be used in our computation:

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

[a] 12 units

Step-by-step explanation:

Answer:

The answer is (D) 44 units

Step-by-step explanation:

1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]

2. Fill in the information we know:

A = 264d1 = 12

3. Now work backward:

If A= [tex]\frac{d_{1} d_{2}}{2}[/tex] then that means 264 =  [tex]\frac{12_ {} d_{2}}{2}[/tex] So 12 multiplied by a number divided by 2 is equal to 264That means that 264 multiplied by two and divided by 12 will give you the mystery number.

4. Solve it:

264 multiplied by 2 is equal to 528 528 divided by 12 is equal to 44

Hence 44 units (D) is your answer

You are asked to use the grouping method to factor x^2 - 12x + 13
How should the term -12x be rewritten?

A) 1x +35x
B)-5x -7x
C) 5x+7x
D) -1x-35x

Answers

The zeros of this expression are irrational, so it cannot be factored using integers.

When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.

In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.

In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)

= 144 - 52

= 92.

Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.

This means that the expression cannot be factored into two binomial factors with integer coefficients.

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100 Points! Multiple choice Geometry question. Photo attached. Thank you!

Answers

Answer:

2. C. 50.3 ft²

3. A. 75.4 ft²

Step-by-step explanation:

The lateral surface area of a cylinder is the area of the curved surface of the cylinder. It is calculated by multiplying the circumference of the base by the height of the cylinder. The formula for the lateral surface area of a cylinder is:

Lateral Surface Area = 2πrh

Where:

r is the radius of the baseh is the height of the cylinder

The total surface area of a cylinder is the area of the lateral surface plus the area of the two circular bases. The formula for the total surface area of a cylinder is:

Total Surface Area = 2πrh + 2πr^2

Where:

r is the radius of the baseh is the height of the cylinder

2.

r=2 ft

h=4 ft

Lateral Surface Area = 2πrh=2*22/7*2*4=50.3 ft²

3.

Total Surface Area = 2πrh + 2πr^2=2*22/7*2*4+2*22/7*2

=50.3+25.1=75.4 ft²

4. The ratio of the length of the corresponding side of two
regular polygons is 3:4. The area of the larger polygon is
320 m². What is the area of the smaller polygon?


A-240 m²
B-427 m²
C-569 m²
D-180 m²

Answers

Let's assume that the smaller polygon has a length of 3x, where x is a positive number representing the common ratio. Similarly, the length of the larger polygon would be 4x.

The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths. Therefore, the ratio of the areas of the smaller and larger polygons would be (3x)^2 : (4x)^2, which simplifies to 9x^2 : 16x^2.

Given that the area of the larger polygon is 320 m², we can set up the following equation:

9x^2 : 16x^2 = Area of smaller polygon : 320

Cross-multiplying, we get:

9x^2 * 320 = 16x^2 * Area of smaller polygon

2880x^2 = 16x^2 * Area of smaller polygon

Cancelling out x^2, we have:

2880 = 16 * Area of smaller polygon

Dividing both sides by 16, we find:

Area of smaller polygon = 2880 / 16 = 180 m²

Therefore, the area of the smaller polygon is 180 m² (option D).
If the ratio of the length of the corresponding side of two regular polygons is 3:4, then the ratio of their areas is (3/4)² = 9/16.

Let A be the area of the smaller polygon. Then we have:

A x (9/16) = 320 m²

Multiplying both sides by (16/9), we get:

A = (320 m²) x (16/9) = 568.89 m²

Rounding to the nearest whole number, we get:

A ≈ 569 m²

Therefore, the area of the smaller polygon is approximately 569 m².

The answer is (C) 569 m².

What is the solution to this system?
3x+2y=6
-4x+ 5y = 15
4-3-2-1
1 2 3 4 5
-
S

Answers

Answer:

solution:  (0,3)

Step-by-step explanation:

You can find the solution when the two lines intersect.

Use the function f(x) to answer the questions:

f(x) = 2x2 − 5x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

Answers

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Two hundred eighty-two people attended a recent performance of Cinderella. Adult tickets sold for $5 and children’s tickets sold for $3 each. Find the number of adults and the number of children that attended the play if the total revenue was $1046.

Part A: Write a system of equations in standard form (Ax + By = C) that can be solved to find the number of adults and children who attended the performance. Define the variables used in the equations. (4 points)

Part B: How many adults attended the performance? How many children attended the performance? Show your work and steps of how you found your answer using elimination.

Answers

A. A system of equations in standard form that can be solved to find the number of adults and children who attended the performance is:

x + y = 282

3x + 5y = 1046

B. The number of adults who attended the performance is 182 adults.

The number of children who attended the performance is 100 children.

How to determine the number of each type of tickets sold?

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of children tickets sold, and then translate the word problem into an algebraic equation as follows:

Let the variable x represent the number of adult tickets sold.Let the variable y represent the number of children tickets sold.

Since 282 people attended the recent performance by Cinderella, a linear equation that models the situation is given by:

x + y = 282     ....equation 1.

Additionally, adult tickets sold for $5 while children tickets sold for $3 each with a total revenue was $1046, a linear equation that models the situation is given by:

3x + 5y = 1046   .......equation 2.

Part B.

By multiplying equation 1 by 3, we have:

3x + 3y = 846     .......equation 3.

By subtracting equation 3 from equation 2, we have:

2y = 200

y = 100 children.

For the x-value, we have:

x = 282 - y

x = 282 - 100

x = 182 adults.

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What is the value of x?
NO SPAM OR I WILL REPORT YOU AND BAN YOU IMMEDIATELY

Answers

Using a trigonometric relation, we can see that the value of x is 10.39

How to find the value of x?

Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.

Then to get the value of x, we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get.

sin(60°) = x/12

solve that for x:

12*sin(60°) = x

10.39 = x

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I need help with this.

Answers

Answer:

Step-by-step explanation:

Area of parallelograph = bh

b=20  h =42

A=(20)(42) = 840 mm²

Show your work show me how you got the answer HELP DUE TOMORROW!!

Answers

Your least common denominator amongst these three mixed fractions is 10. Once you determine this, the rest should fall into place!

What is the meaning of "[tex] Y^{X}\subset P(X \times Y) [/tex]"?

Answers

It implies that the collection of all ordered pairs (x, y) formed by taking an element from the set x and an element from the set y is a subset of the set containing all possible subsets of the Cartesian product of sets X and Y.

The expression "y^x ⊂ p(X x Y)" represents a subset relationship between two sets.

Let's break it down:

"y^x" represents the set of all possible ordered pairs (x, y) where x is an element of the set x and y is an element of the set y. This set represents the Cartesian product of the sets x and y.

"⊂" denotes a subset relationship. If we have two sets A and B, A ⊂ B means that every element in A is also an element of B. In other words, A is a subset of B.

"p(X x Y)" represents the power set of the Cartesian product of sets X and Y. The power set of a set is the set of all possible subsets of that set.

Therefore, "y^x ⊂ p(X x Y)" means that the set of all possible ordered pairs (x, y) where x is an element of the set x and y is an element of the set y is a subset of the power set of the Cartesian product of sets X and Y.

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How do -3.8 and -4 1/2 compare

Answers

Answer:

-3.8 > -4.5

Step-by-step explanation:

Convert the fraction to decimal and then compare.

[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]

          = -4.5

Now compare (-3.8) & (-4.5)

-3.8 > -4.5

Pls help me in math!!!!!!!!!!

Answers

In the given triangle value of b is,

⇒ b = 16

We have to given that,

A triangle with three angles (b + 20), (b + 32) and 6b.

Now, WE know that;

Sum of all interior angles of triangle is 180 degree.

Hence., We can formulate;

⇒ (b + 20) + (b + 32) + 6b = 180

Solve for b,

⇒ 8b + 52 = 180

⇒ 8b = 180 - 52

⇒ 8b = 128

⇒ b = 128/8

⇒ b = 16

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Which two points could be removed to make this relation a function?
A. Points R and S
B. Points Q and T
C. Points P and Q
D. Points Q and R

Answers

Option (D) D. Points Q and R is used to removed to make this relation a function.

To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.

Let's analyze the given options:

A. Points R and S: (R, 3), (S, 5)

B. Points Q and T: (Q, 2), (T, 5)

C. Points P and Q: (P, 1), (Q, 2)

D. Points Q and R: (Q, 2), (R, 3)

In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:

D. Points Q and R.

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This number pattern -1:5 ;x; 35 ; ...
Is a quadratic number pattern.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.

This sequence 4;9; x; 37; .... is a quadratic sequence.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.

Answers

Answer:

x = 17; an = 3n² -3n -1x = 20; an = 3n² -4n +5

Step-by-step explanation:

Given the following quadratic sequences, you want the value of x and the expression for the n-th term.

-1, 5, x, 354, 9, x, 37

Differences

One way to determine x is to look at the differences between terms. The "second difference" is constant for a quadratic sequence, and the third difference is zero.

N-th term

The quadratic equation for the n-th term can be found by solving for its coefficients. The three known values of the sequence can give rise to three linear equations in the three unknown coefficients. These can be solved by your favorite method. We use this approach in the following.

1. -1, 5, x, 35

First differences are the differences between each term and the one before:

  {6, x-5, 35-x}

Second differences are the differences of these:

  {x -11, 40 -2x}

Third differences are zero:

  51 -3x = 0   ⇒   x = 17

The value of x is 17.

The expression for the n-th term of the sequence can be written as ...

  an = a·n² +b·n +c

We are given values of a1, a2, and a4. This lets us write 3 equations for a, b, and c. The solution of those is shown on the first line of the first attachment. (The second line shows the evaluation of this quadratic equation for n=3. It gives 17, which we already knew.)

  an = 3n² -3n -1

2. 4, 9, x, 37

The last line of the first attachment shows us the expression for the third differences. The value of that is zero, so ...

  -3x +60 = 0   ⇒   x = 20

The value of x is 20.

As in the above problem, the matrix of equations for the quadratic coefficients can be reduced to give the coefficient values. That tells us the n-th term of this sequence is ...

  an = 3n² -4n +5

The last line in the second attachment tells us this expression for the n-th term properly computes the 3rd term (x), as above.

__

Additional comments

You can also use quadratic regression to find the coefficients of the formula for the quadratic sequence. This is shown in the 3rd attachment.

If you're trying to avoid using a calculator, you can write the equations out and solve them in an ad hoc way. In case you cannot tell, the equations for the coefficients of an = a·n² +b·n +c for the first problem are ...

1·a +1·b +1·c = -14·a +2·b +1·c = 516·a +4·b +c = 35

You can also use the first values of the sequence (p), first difference (q), second difference (r) to write the quadratic:

  an = p +(n -1)(q +(n -2)/2(r))

For (p, q, r) = (-1, 6, 6), this is an = -1 +(n -1)(3n) . . . . . . for the first sequence.

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Find the degrees of freedom, alpha or significance level, and the t-critical value using the t-table n = 27 ;CL=98\%

Answers

The degrees of freedom for a sample size of 27 is 26, the alpha or significance level for a 98% confidence level is 0.02, and the t-critical value can be found using the t-table corresponding to a 98% confidence level and 26 degrees of freedom.

To find the degrees of freedom, alpha (significance level), and the t-critical value using the t-table, we need to consider the given information:

n = 27: This represents the sample size, which is 27 in this case.

CL = 98%: CL stands for the confidence level.

It indicates the level of confidence we want to have in our interval estimate.

In this case, the confidence level is 98%.

Degrees of Freedom (df): For a t-distribution, the degrees of freedom depend on the sample size.

Since we have a sample size of 27, the degrees of freedom would be n - 1.

Therefore, the degrees of freedom would be 27 - 1 = 26.

Alpha (α): Alpha, or the significance level, represents the probability of making a Type I error, which is rejecting a true null hypothesis.

The alpha level is determined by subtracting the confidence level from 1. In this case, the alpha level would be 1 - 0.98 = 0.02.

T-Critical Value: To find the t-critical value corresponding to a specific confidence level and degrees of freedom, we can consult the t-table. Since we have a confidence level of 98% and degrees of freedom of 26, we need to find the value that corresponds to the area of 0.01 (half of 1 - 0.98) in the t-distribution table.

The t-critical value would be the value from the table that matches these criteria.

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Find the equation of the axis of symmetry of the following parabola algebraically. y=−3x^2−42x−159

Answers

The equation of the axis of symmetry is x = -7.

Given is an equation of a parabola, y = -3x² - 42x - 159, we need to find the equation of the axis of the symmetry.

To find the equation of the axis of symmetry of a parabola in the form of y = ax² + bx + c, you can use the formula x = -b / (2a).

In this case, the given equation is y = -3x² - 42x - 159.

Comparing it to the general form, we have a = -3 and b = -42.

Applying the formula, we can calculate the x-coordinate of the vertex (the axis of symmetry):

x = -b / (2a)

x = -(-42) / (2(-3))

x = 42 / (-6)

x = -7

Therefore, the x-coordinate of the vertex is -7.

To find the equation of the axis of symmetry, we use the value of x in the form x = h, where (h, k) is the vertex.

Hence, the equation of the axis of symmetry is x = -7.

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What is the solution to the proportion 2/3 m/9

Answers

= 8/3

m = 40

yep no problem

Write in exponential form. ln54.60=4

Answers

Step-by-step explanation:

ln 54.60 = 4         e^x both sides

e ^ (ln 54.60) = e^4

         54.60 = e^4                 Done.

NEED HELP ASAP WILL GIVE BRAINLIEST HELP!

Answers

The relationship between angles 8 and 7 is that they are supplementary. option B is correct.

Given that a quadrilateral, with three parallel lines, we need to find the relation between angles 8 and 7,

We know that the adjacent angles between the parallel lines are supplementary,

We know that,

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures will always be 180 degrees.

So,

The relation between the angles is that they are Supplementary angles.

Hence the option B is correct.

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There are 840 learners and 17 teachers at Orefile Primary school.what is the learner to teacher ratio?

Answers

Answer: 49.4 thats the answer i devided it

!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)

A) Inside the Square
B) Outside the Triangle

Answers

Answer:

A. 16.7%

B. 89.5%

Step-by-step explanation:

A) Inside the Square

length:4

The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:

(area of square)/(area of rectangle)

= 16/96

= 0.16666666666666666

This is equal to 16.7%.

B) Outside the right angles Triangle

base:4 height 5

The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:

(area of rectangle - area of triangle)/(area of rectangle)

= (96 - 10)/96

= 0.8958333333

This is equal to 89.5%.

Please help I have to get 100 in order to graduate to my next grade level please if you can help me do it I will give big points and there is more than 1 answer.

Answers

The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

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What is the slope of the line that is perpendicular to the line of y=3x -8

Answers

The slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

The given line has an equation in slope-intercept form, which is y = 3x - 8. In this form, the coefficient of x represents the slope of the line.

Therefore, the slope of the given line is 3.

To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope.

The negative reciprocal of 3 is -1/3.

Therefore, the slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

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pleaseseee help


Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable

pls help 100 points

Answers

Answer:

Step-by-step explanation:

PLEASE HELP AND SHOW WORK

Answers

The amount of fabric required is 400.551 ft².

We have,

CB= 8 feet

CF= 13 feet

AM = 8 feet

Using Pythagoras

AC² = AM² + CM²

AC = √64+16 = √80 = 4√5 feet

Now, the formula for Triangular prism is

= (Sum of three sides of triangle face)l + base area

= (4√5 + 4√5 + 8)13 + 8 x 8

= 104√5 + 104 + 64

= 104√5 + 168

= 232.551 + 168

= 400.551 ft²

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find the volume of cylinder 8in r 2in h

Answers

Answer:

402.12 or just 402

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer:

C. 50 cm²

Step-by-step explanation:

The volume of a triangular pyramid is calculated using the following formula:

Volume = (1/3) * Area of the base * Height

Area of the base is the area of the triangular base of the pyramid.Height is the distance from the apex of the pyramid to the plane of the base.

For Question:

length: 5cm

Breadth:5cm

Height : 6 cm

Now,

Volume = ⅓* Area of the base * Height

Volume = ⅓*length*breadth*height

Volume= ⅓*5*5*6=50 cm³

HELP !!! URGENTTTTT PLS ANSWER!!!

Answers

Answer: z=3

Step-by-step explanation:

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This principle describes how someone who knows how to perform a back squat will more easily learn an overhead squat because the basic framework for the movement has already been learned and it only needs to be adapted to the new skill.a. Motor program theoryb. Generalized motor programc. Homunculusd. Movement patterne. Short-term retention on long duration projects, it is often better to capture lessons frequently because people may not remember clearly what happened a few weeks or months earlier. trueor false assume the university sells 107,500 season tickets to six home games before the season begins, and the athletic department collects $64.50 million in ticket sales. What is the average price per season ticket and average price per individual game ticket sold? Unreasonable Results What is wrong with the claim that a cyclical heat engine does 4.00 kJ of work on an input of 24.0 kJ of heat transfer while 16.0 kJ of heat transfers to the environment? _________ theories view development as an incremental and cumulative process.A.StageB.BiologicalC.ContinuousD.Outdated The common stock of Kansas City Power and Light has a beta of 0.80. The Treasury bill rate is 4 percent and the market risk premium is 8 percent. What is their cost of equity capital?Multiple Choice12.0 percent10.4 percent7.20 percent6.4 percent (PLEASE HELP 30 POINTS ROMEO AND JULIET) write text messages or other social media posts the characters from romeo and juliet might have written Find f. USN Top Defensive Sto... UC f(t) = 91Vt, f(4) = 27, f'(4) = 16 - f(t) = Business Calculus Spring 2022 MW 5.30-7:35 pm FC Jocelyn Gomes 05/15/2262 Homework: 9.2 Question 7,9.2.41 Part 1 of 4 HW SCOON. O ponta O Point 0011 Find t. y.x). WXYyx), and Gy.x) for Consider the differential equation y' + p(x)y = g(x) and assume that this equation has the following two particular solutions y() = 621 cos(2x) + sin(2x), y(x) = 2 cos(2x) + sin(2x) 2e24. Which of the following is the general solution to the same differential equation: COS (a) y(x) = C1[e22 - cos(2x) + sin(2.c)] + c2[2 cos(2x) + sin(2x) - 2e2 (b) y(x) = C1621 cos(2x) + sin(2x) (c) y(x) = Ci [e2x cos(2x)] + sin(2x) (d) y(1) = e21 cos(2x) + C2 sin(2x), where C1 and C2 are arbitrary constants. A bearing with an inside diameter of 1/14 inches is found to be 0. 008 inch oversize for the armature shaft. What should the diameter of the bearing be to fit the shaft? Allow 0. 002-inch clearance for lubrication. ________________ Consider the vector v=(2 -1 -3) in Rz. v belongs to Sp n{( 2 -10), (1 2 -3)}. - Select one: True False One of the sales managers has approached the development team to ask for some changes to one of the web applications that his team uses. He made some great suggestions, but the development team manager told him they can't just make those changes without going through the formalized process. Which of the following should the development manager ask the sales manager for?a. Business justificationb. ROIc. Change requestd. CAB winnie corporation is expected to pay the following dividends over the next four years: $9, $10, $11, and $12. afterward, the company pledges to maintain a constant 3.5 percent growth rate in dividends forever. if the required return on the stock is 9 percent, what is the current share price? Under which of the following conditions will an overcurrentcondition develop in the inverter section of an AC drive?A. The inertia of the load is excessively small.B. Overvoltage occurs at the inverter's output terminals.C. The incoming line voltage falls below a certain level.D. A component inside the inverter section shorts. The wrongdoers cannot escape from the __________________ on the Day of Judgment which sentence is preferable?select an answer:solvent use will not exceed 5,000 gallons per month.solvents should be limited in use to 5,000 gallons per month.solvent usage should be optimized at 5,000 gallons per month.solvent usage will be restricted if 5,000 gallons are needed in any given month. Use the divergence theorem to find the outward flux of xa F(x, y, z) = x^2i - 2xy +3 xz the closed surface enclosing the portion of the sphere x + y + z = 4 (in first octant) The Cold War saw three major conflicts in Asia the Korean War [early 1950s], the Vietnam War [1960s and 1970s] and a Soviet war in Afghanistan [1979-1989] Before her death in 2009, Lucy entered into the following transactions:a. In 2000, Lucy borrowed $600,000 from her brother, Irwin, so that Lucy could start a business. The loan was on open account, and no interest or due date was provided for. Under applicable state law, collection on the loan was barred by the statute of limitations before Lucy died. Because the family thought that Irwin should recover his funds, the executor of Lucy's estate paid him $600,000.b. In 2007, she borrowed $300,000 from a bank and promptly loaned that sum to her controlled corporation. The executor of Lucy's estate prepaid the bank loan, but never attempted to collect the amount due Lucy from the corporation.c. In 2008, Lucy promised her sister, Ida, a bequest of $500,000 if Ida would move in with her and care for her during an illness (which eventually proved to be terminal). Lucy never kept her promise, as her will was silent on any bequest to Ida. After Lucy's death, Ida sued the estate and eventually recovered $600,000 for breach of contract.d. One of the assets in Lucy's estate was a palatial residence that passed to George under a specific provision of the will. George did not want the residence, preferring cash instead. Per George's instructions, the residence was sold. Expenses incurred in connection with the sale were claimed as section 2053 expenses on Form 706 filed by Lucy's estate.e. Before her death, Lucy incurred and paid certain medical expenses but did not have the opportunity to file a claim for partial reimbursement from her insurance company. After her death, the claim was filed by Lucy's executor, and the reimbursement was paid to the estate.Disucss the estate and income tax ramifications of each of these transactions.