David's mother flew on a plane for a business trip. The plane averaged 500 miles per hour for the entire 1,250-mile flight. The plane was 45 minutes on the runway. How many hours did David's mother spend on the plane?

The measure of the side J of the triangle ΔIJK will be 43 units.

The law of sines defines the ratio of triangle sides, and their respective sine angles are equivalent. The law of sines is also known as the sine law, sine rule, and sine formula.

Given that in the triangle i = 100 inches,  m∠I=115° and m∠J=23°. The measure of the length J will be calculated as:-

100 / sin115 = J / sin23

J = (100) x sin23 / sin115

J = 100 x 0.43

J = 43 units

The length of side J will be 43 units.

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Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]

[tex].142 \times 59.5 = 8.449[/tex]

So 8.449 square centimeters of this figure is green.

Answer:

Step-by-step explanation:

The credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

First, let's calculate the monthly interest rate by dividing the APR by 12:

11.99% / 12 = 0.99917%

Next, let's calculate the interest paid on the monthly balance for each of the 11 months before the final payment:

Month 1:

Interest = $7,568.19 x 0.99917% = $75.59

Month 2:

Balance = $7,568.19 - $350 - $75.59 = $7,142.60

Interest = $7,142.60 x 0.99917% = $71.38

Month 3:

Balance = $7,142.60 - $350 - $71.38 = $6,721.82

Interest = $6,721.82 x 0.99917% = $67.11

Month 4-11: (follow the same process as above)

Interest for Month 4: $63.82

Interest for Month 5: $60.51

Interest for Month 6: $57.17

Interest for Month 7: $53.80

Interest for Month 8: $50.41

Interest for Month 9: $47.00

Interest for Month 10: $43.56

Interest for Month 11: $40.11

Now, at the end of month 11, the cardholder has a balance of:

$7,568.19 - ($350 x 11) - $75.59 - $71.38 - $67.11 - $63.82 - $60.51 - $57.17 - $53.80 - $50.41 - $47.00 - $43.56 - $40.11 = $1,225.74

Finally, the cardholder pays off the remaining balance of $1,225.74 at the end of month 12. The interest charged for this month would be:

Interest = $1,225.74 x 0.99917% = $12.25

So the total interest paid by the cardholder over the 12 months is:

$75.59 + $71.38 + $67.11 + $63.82 + $60.51 + $57.17 + $53.80 + $50.41 + $47.00 + $43.56 + $40.11 + $12.25 = $720.27

Therefore, the credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.

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The value of angle m<4 is 66 degrees

The angles on a straight line are supplementary, this means that the angles sum up to 180 degrees.

From the information given, we have that;

Equate the angles to 180 degrees

We have;

m<4 + m<5 = 180

Substitute the expression for each of the angles , we have;

x + 9 + 2x = 180

collect the like terms

3x = 180 - 9

subtract the values

3x = 171

Divide by the coefficient

x = 57

But m<4 = 57 + 9 = 66 degrees

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Answer: 19 tickets

Step-by-step explanation:  $45 - $7 = 38      38 divided by $2 = 19 tickets

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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Answer:

Based on the information in the table, the statement that best describes the customers' preferences on shirt colors is:

A. At both stores, more customers prefer white shirts than shirts in either of the other two colors.

Looking at the table, we can see that at store 1, 30 customers prefer white shirts, while only 20 prefer blue and 10 prefer black. Similarly, at store 2, 25 customers prefer white shirts, while only 15 prefer blue and 10 prefer black. Therefore, we can conclude that at both stores, more customers prefer white shirts than shirts in either of the other two colors.

Option B is incorrect because the table shows that at store 2, 20 customers prefer blue shirts while 10 prefer black shirts. Therefore, a different number of customers prefer blue and black shirts.

Option C is also incorrect because at both stores, more customers prefer white shirts than blue shirts, and the same number of customers prefer black and blue shirts.

Option D is incorrect because at store 1, only 10 customers prefer black shirts, while 20 prefer blue and 30 prefer white. Therefore, more customers prefer white or blue shirts than black shirts.

The length of OM, given that the triangles are similar to each other, is calculated as: 14.4.

Similar triangles are triangles that have the same shape but may have different sizes. They have the same angles, but the lengths of their sides are proportional. This means that corresponding sides of similar triangles are in proportion, and the ratio of their corresponding sides is constant.

Since triangle JKL is similar to triangle MNO, therefore:

JK/MN = JL/MO

Substitute:

5/24 = 3/x

Cross multiply:

5x = 72

5x/5 = 72/5

x = 14.4

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Answer:

1. -2/7

2. 7/6

3. 53/8

4. do u mean sum? if yes then the answer is 1

5. 5/12

6. 2/5

7. -2/3

8.

9.90

10.240

11.60

12. 4/15

13.4/7

14.8/5

15.24/7

16.15/16

17.4/9

18.8/7

19.-2/5

20.-1/12

Answer: 12/5

Step-by-step explanation:

Answer: $194.79

Step-by-step explanation:

It is easiest to approach this question in two parts.

First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50

Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -

($12.50) | (60 min)  -    (x dollars) | (35 min)

then cross multiply and divide -  (12.5 * 35) / 60 = 7.291

This means you make $7.29 for 35 minutes of work.

$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.

(this is based on a per minute/hour scale)

Answer:

See below.

Step-by-step explanation:

a)

Since Y1, ..., Yn are independent and identically distributed, we have Y¯Bar ~ Exp(θ/n) and Y(1) ~ Exp(nθ).

b)

We want to find c1 and c2 such that E[T1] = θ and E[T2] = θ. We have E[Y(1)] = 1/θ and E[Y¯Bar] = θ/n, so setting T1 = c1Y(1) gives E[T1] = c1/θ = θ, and setting T2 = c2Y¯Bar gives E[T2] = c2θ/n = θ. Thus, c1 = θ^2 and c2 = n. To compare the MSE of T1 and T2, we compute,

MSE(T1) = V(T1) + [E(T1) - θ]^2

= V(θY(1)) + [θ - θ]^2

= θ^2V(Y(1))

= θ^2/θ^2

= 1

MSE(T2) = V(T2) + [E(T2) - θ]^2

= V(nY¯Bar) + [θ - θ]^2

= n^2V(Y¯Bar)/n^2

= V(Y¯Bar)/n

= (θ^2/n^2)(n/θ)

= θ^2/n

Since MSE(T2) < MSE(T1) for n > 1, T2 is the preferred estimator.

c)

Let Q(Y1, ..., Yn; θ) = 2nY(1)/θ. We have E[Q] = 2n/θ and V(Q) = 4n^2V(Y(1))/θ^2 = 4n^2/θ^2. To show that Q ~ Chi-squared(2), we need to show that Q has a gamma distribution with parameters k = 2 and θ = 1/2. We have,

fQ(q) = (1/θ^k)(q^(k-1) exp(-q/θ))/Γ(k) = (1/2^2)(q/2)exp(-q/2) = (1/4)q/2 exp(-q/2)

which is the pdf of a gamma distribution with k = 2 and θ = 1/2.

d)

To construct a two-sided 1 - α confidence interval for θ, we use the fact that 2nY(1)/Q(Y1, ..., Yn; θ) ~ F(2, 2n). Let Fα/2 be the (1 - α/2) quantile of the F distribution with 2 and 2n degrees of freedom. Then we have,

P(2nY(1)/(Fα/2) < θ < 2nY(1)/(F1-α/2)) = 1 - α

So the confidence interval is [2nY(1)/(Fα/2), 2nY(1)/(F1-α/2)].

The zeros and vertex of each quadratic equation are:

Case 1: y = 4 · (x + 2) · (x - 2), Roots: - 2, 2, Vertex: (0, - 16)

Case 2: y = (1 / 2) · (x + 5) · (x - 3), Roots: - 5, 3, Vertex: (- 1, - 8)

Case 3: y = - 2 · (x + 4) · (x + 2), Roots: - 4, - 2, Vertex: (- 3, 2)

Case 4: y = - 2 · (x + 6) · (x + 2), Roots: - 6, - 2

Vertex: (- 4, 8)

Graphically speaking, quadratic functions have the form of the parabola. The zeros are the points of parabola that are on the horizontal axis (x-axis) and the vertex is the only point of the parabola. The factor form of the parabola is:

y = C · (x - r₁) · (x - r₂)

Where:

Now we proceed to determine all the features of the quadratic function:

Case 1

Roots: r₁ = - 2, r₂ = 2

Vertex: (h, k) = (0, - 16)

C = y / [(x - r₁) · (x - r₂)]

C = - 16 / [2 · (- 2)]

C = - 16 / (- 4)

C = 4

Factor form: y = 4 · (x + 2) · (x - 2)

Case 2

Roots: r₁ = - 5, r₂ = 3

Vertex: (h, k) = (- 1, - 8)

C = y / [(x - r₁) · (x - r₂)]

C = - 8 / [(- 1 + 5) · (- 1 - 3)]

C = - 8 / [4 · (- 4)]

C = - 8 / (- 16)

C = 1 / 2

Factor form: y = (1 / 2) · (x + 5) · (x - 3)

Case 3

Roots: r₁ = - 4, r₂ = - 2

Vertex: (h, k) = (- 3, 2)

C = y / [(x - r₁) · (x - r₂)]

C = 2 / [(- 3 + 4) · (- 3 + 2)]

C = 2 / [1 · (- 1)]

C = - 2

Factor form: y = - 2 · (x + 4) · (x + 2)

Case 4

Roots: r₁ = - 6, r₂ = - 2

Vertex: (h, k) = (- 4, 8)

C = y / [(x - r₁) · (x - r₂)]

C = 8 / [(- 4 + 6) · (- 4 + 2)]

C = 8 / [2 · (- 2)]

C = 8 / (- 4)

C = - 2

Factor form: y = - 2 · (x + 6) · (x + 2)

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Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.

Here,

1. The z-score for a sample mean of $75 is calculated as:

z = (75 - 76) / (6 / √(40)) = -2.36

Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).

2. The z-score for a sample mean of $75 is calculated as:

z1 = (75 - 76) / (6 / √(40))

= -2.36

The z-score for a sample mean of $77 is calculated as:

z2 = (77 - 76) / (6 / √(40))

= 0.79

Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).

3. The z-score for a sample mean of $77 is calculated as:

z1 = (77 - 76) / (6 / √(40))

= 0.79

The z-score for a sample mean of $78 is calculated as:

z2 = (78 - 76) / (6 / √(40))

= 1.57

Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).

4. The standard error of the mean (SEM) is calculated as:

SEM = standard deviation / sqrt(sample size)

SEM = 6 / √(40) = 0.9487

The z-score for a sampling error of $1.50 is calculated as:

z = 1.50 / 0.9487 = 1.58

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

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The intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

What are the intercepts?

To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.

Therefore, the x-intercept is (3, 0).

To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):

Slope of the line = (y2 - y1) / (x2 - x1)

= (0 - y) / (3 - 0)

= -y / 3

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:

y - 0 = (-y/3)(x - 3)

Simplifying this equation, we get:

y = (-y/3)x + 1

Multiplying both sides by 3, we get:

3y = -yx + 3

Adding yx to both sides, we get:

yx + 3y = 3

This is the equation of the line in standard form. To find the y-intercept, we set x = 0:

0 + 3y = 3

Solving for y, we get:

y = 1

Therefore, the y-intercept is (0, 1).

Hence, the intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

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Answer: 47

Step-by-step explanation:

28+19=47

47-19=28

In response to the stated question, we may state that Hence the slope equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.

Slope is just the curvature of a bend or line in mathematics. It is a measure of the manner in which the y-value of something like a function varies because when x-value changes. The slope of a line is commonly symbolized by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 options on the line. A bridge's slope might be negative, negative, zero, or unknown. A positive slope indicates that the line ascends to left to right, whereas a slope indicates that the line drops from left to right.

We must use the point-slope form of the equation of a line to obtain the equation of a line of the form Ax+By=C that goes through two points:

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is the location of one of the points and m is the line's slope.

Then, we must determine the slope of the line.

[tex]m = (y2 - y1) / (x2 - x1) (x2 - x1)\\where (4, 5) = (x1, y1) and (x2, y2) = (-1, -1)m = (-1 - 5) / (-1 - 4) = -6 / (-5) = 6/5\\y - y1 = m(x - x1) (x - x1)\\y - 5 = (6/5)(x - 4) (x - 4)\\5y - 25 = 6x - 24\\6x - 5y = -1\\[/tex]

Hence the equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.

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Answer:

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

Step-by-step explanation:

To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.

The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:

(7/9) x 84 = 66.67

Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

"Triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.

Multiplication is a fundamental arithmetic operation that involves combining two or more numbers to find their product. It is represented by the symbol "x" or "•" or sometimes simply by placing two numbers next to each other.

"Triple the sum of K and 2" can be expressed mathematically as:

3(K + 2)

This expression represents the value we get by adding K and 2, and then multiplying the sum by 3.

To evaluate this expression, we first add K and 2 together, giving us a sum of (K + 2). Then, we multiply that sum by 3, giving us a final result of 3(K + 2).

As a result, "triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.

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The full question is How do you write "triple the sum of K and 2" as an expression?

Answer:

To find the width of the clubhouse on the plans, we need to use the given scale of 1 inch on the plans being equivalent to 8 inches on the actual clubhouse. Let's assume that "x" inches on the plan correspond to the actual width of 126 inches of the clubhouse.

Using the proportionality of the scale, we can set up the following equation:

1 inch / 8 inches = x inches / 126 inches

Simplifying the equation, we can cross-multiply to get:

8 inches * x inches = 1 inch * 126 inches

8x = 126

x = 15.75

Therefore, the width of the clubhouse on the plans is 15.75 inches.

Answer:

Answer:  6/25

======================================================

Explanation:

The table shows the spinner lands on "4" exactly 12 times out of the 50 total.

12/50 = (2*6)/(2*25) = 6/25

In decimal form that is 6/25 = 0.24 which converts to 24%

Answer: True

Step-by-step explanation:

They have four sides

Answer:true.

Step-by-step explanation: All Rectangles are indeed quadrilaterals because all rectangles have 4 sides and quadrilaterals are known as a four sided shape,

Answer:

mm eh its too hard im onwy one!

Step-by-step explanation:

Answer:

p= -3-1/2

p= -7/2

Step-by-step explanation:

(you transpose the fraction /take the liketerms)

( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .

Answer: x=2 is the answer

Answer:

Step-by-step explanation

Rearrange terms

-16=(- 4)- 6 x

-16=-6x - 4

Add 4 to both sides

-16= - 6x - 4

-16 + 4=  -6x  - 4 + 4

Simplify the expression

-16+4=6x - 4+4

-12=6x

Divide both sides by the same factor

-12=6x

-12/-6= -6x/-6

so

x=2

Answer:

(x - 2)(4x + 1)

Answer: $24.5

Step-by-step explanation:

8 Books = $19.60

1 Book = $19.60/8 = $2.45

10 Books = $2.45 X 10 = $24.5                                            

Answer:

E  none of the above

Step-by-step explanation:

a correct equation would be:

8/19.60 = 10/x

or

19.60/8 = x/10

Answer:

Let's call the number of boxes delivered by the truck x. We know that the warehouse initially contains 55 boxes, and the truck delivers x boxes, so the total number of boxes in the warehouse after the delivery is 55 + x.

We also know that the workers unload the boxes at a constant rate, which we can express as a number of boxes per hour. Let's call this rate r. Since the workers unload boxes for 3.5 hours (from 12:00 p.m. to 3:30 p.m.), we can express the number of boxes unloaded as:

Number of boxes unloaded = r * 3.5

Therefore, the total number of boxes in the warehouse at 3:30 p.m. is:

55 + x - r * 3.5

We're told that this number is 90, so we can write the equation:

55 + x - r * 3.5 = 90

Simplifying this equation, we get:

x - r * 3.5 = 35

We're also told that the truck is empty at 8:30 p.m., which means that all the boxes it delivered have been unloaded by then. So the total number of boxes in the warehouse at 8:30 p.m. is:

55 + (x - r * 8)

where 8 is the number of hours between 12:00 p.m. and 8:00 p.m.

We can use the equation x - r * 3.5 = 35 to solve for x in terms of r:

x = 35 + r * 3.5

Substituting this into the equation for the total number of boxes at 8:30 p.m., we get:

55 + (35 + r * 3.5 - r * 8)

Simplifying this expression, we get:

55 - 35 + 28r

= 20 + 28r

Therefore, the warehouse contains 20 + 28r boxes at 8:30 p.m.