Mathematics College

8. Tara pays a base rate for her long distance phone service plus a per-minute charge.
The graph below shows what she would pay for her long distance phone service for the
first 60 minutes. What does the y-intercept of this graph represent?
9. Rich is a number of a gym. He pays a monthly fee plus a per-visit fee. The equation

Answers

Answer 1

The y-intercept of the graph, of b = 5, represents that Tara pays a base fee of $5.

How to define a linear function?

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

m is the slope.b is the intercept.

The intercept on the graph is the value of y at which the graph touches or crosses the y-axis, hence it is given as follows:

b = 5.

At the y-intercept, we have that x = 0, hence it represents the base fee of Tara's plan.

Missing Information

Question 9 is incomplete, hence it cannot be answered.

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8. Tara Pays A Base Rate For Her Long Distance Phone Service Plus A Per-minute Charge. The Graph Below

Related Questions

A physical therapist is working with a 57-year-old cardiac patient who is recovering from surgery.
The patient’s exercise goal for this week is moderate intensity with a target heart rate of 50% to
70% percent. The target heart rate is based on the patient’s maximum heart rate, which is calculated
by subtracting the patient’s age from 220.
What is the range for the patient’s target heart rate? Round to the nearest whole number.

Answers

The range for the patient's target heart rate, based on a moderate exercise goal and a maximum heart rate calculated by subtracting the patient's age from 220, is approximately 82 to 114 beats per minute.

To calculate the range for the patient's target heart rate, we need to determine the minimum and maximum target heart rates based on the patient's age.

The patient's maximum heart rate can be calculated by subtracting the patient's age from 220. In this case, the patient is 57 years old.

Maximum Heart Rate = 220 - Age

Maximum Heart Rate = 220 - 57

Maximum Heart Rate = 163

The target heart rate range is typically expressed as a percentage of the maximum heart rate. In this case, the patient's target heart rate range is 50% to 70% of the maximum heart rate.

Minimum Target Heart Rate = 50% of Maximum Heart Rate

Minimum Target Heart Rate = 0.50 * 163

Minimum Target Heart Rate ≈ 81.5

Maximum Target Heart Rate = 70% of Maximum Heart Rate

Maximum Target Heart Rate = 0.70 * 163

Maximum Target Heart Rate ≈ 114.1

Rounding these values to the nearest whole number, the range for the patient's target heart rate is approximately 82 to 114 beats per minute.

Therefore, the range for the patient's target heart rate is 82 to 114 beats per minute.

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The product of sin 30° and sin 60°

Answers

The multiplication of sin 30° and sin 60° results in √3/2, representing the value of their product without any alteration.

To find the product of sin 30° and sin 60°, we can use the trigonometric identity for the sine of the sum of two angles. The identity states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

Let's consider sin 30° and sin 60°:

sin 30° = 1/2

sin 60° = √3/2

Using the identity, we have:

sin (30° + 60°) = sin 30°cos 60° + cos 30°sin 60°

Now, we can substitute the values:

sin (30° + 60°) = (1/2)(√3/2) + (√3/2)(1/2)

Simplifying, we get:

sin (30° + 60°) = √3/4 + √3/4

Combining like terms, we have:

sin (30° + 60°) = 2√3/4

Now, let's simplify the expression:

sin (30° + 60°) = √3/2

Therefore, the product of sin 30° and sin 60° is √3/2

In summary, the product of sin 30° and sin 60° is equal to √3/2, which can be derived by using the trigonometric identity for the sine of the sum of two angles.

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Debt (Kd) 8.5 % 20 % 1.70 %
Preferred stock (Kp) 7.2 10 0.72
Common equity (Ke) (retained earnings) 7.5 70 5.25
Weighted average cost of capital (Ka) 7.67 %
A) If the firm has $42 million in retained earnings, at what size capital structure will the firm run out of retained earnings? (Enter your answer in millions of dollars (e.g., $10 million should be entered as "10").)
B) The 8.5 percent cost of debt referred to earlier applies only to the first $14 million of debt. After that the cost of debt will go up. At what size capital structure will there be a change in the cost of debt? (Enter your answer in millions of dollars (e.g., $10 million should be entered as "10").)

Answers

A) , the firm will run out of retained earnings at a capital structure size of $560 million for the first capital structure, $60 million for the second capital structure, and $800 million for the third capital structure.

B)  there will be a change in the cost of debt at a capital structure size of approximately $19.95 million.

A) To determine the size of the capital structure at which the firm will run out of retained earnings, we need to calculate the retained earnings limit. Retained earnings are expressed as a percentage of the common equity (Ke). From the given information, the retained earnings are 7.5%, 70, and 5.25 for the three different capital structures. Let's assume the size of the capital structure as "x" million dollars.

For the first capital structure (7.5% Ke), the retained earnings limit is given by:

0.075x = 42

x = 42 / 0.075

x ≈ 560

For the second capital structure (70 Ke), the retained earnings limit is given by:

0.70x = 42

x = 42 / 0.70

x ≈ 60

For the third capital structure (5.25 Ke), the retained earnings limit is given by:

0.0525x = 42

x = 42 / 0.0525

x ≈ 800

Therefore, the firm will run out of retained earnings at a capital structure size of $560 million for the first capital structure, $60 million for the second capital structure, and $800 million for the third capital structure.

B) The 8.5% cost of debt applies only to the first $14 million of debt. After that, the cost of debt will go up. To find the capital structure size at which the cost of debt changes, we need to consider the different debt levels and their associated costs.

Assuming the capital structure size as "y" million dollars, we can calculate the change in cost of debt:

For the first $14 million of debt, the cost of debt is 8.5%. Therefore, we have:

0.085(14) = 1.19

Once the debt exceeds $14 million, the cost of debt will change. From the given information, the cost of debt increases to 20% after $14 million. So, we have:

0.20(y - 14) = 0.20y - 2.8

To find the size of the capital structure at which the cost of debt changes, we need to equate the two expressions:

1.19 = 0.20y - 2.8

0.20y = 1.19 + 2.8

0.20y = 3.99

y = 3.99 / 0.20

y ≈ 19.95

Therefore, there will be a change in the cost of debt at a capital structure size of approximately $19.95 million.

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drag tiles to the boxes to form correct pairs. match the cube roots and square roots with their values.​

Answers

The square root of 9 is 3
the cubed root of 729 is 9
the square root of 100 is 10
the cubed root of 216 is 6
the square root of 64 is 8
and the cubed root of 343 is 7


This should be right

8. Tara pays a base rate for her long distance phone service plus a per-minute charge.
The graph below shows what she would pay for her long distance phone service for the
first 60 minutes. What does the y-intercept of this graph represent?

Answers

The y-intercept of this graph represent 5 and it means the base rate for the long distance phone service is $5.

What is y-intercept?

In Mathematics and Geometry, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the graph and the function y = 1/20(x) + 5 shown in the image attached below, we can reasonably infer and logically deduce the following y-intercept:

y-intercept of y = (0, 5).

In conclusion, we can reasonably infer and logically deduce that the base rate for the long distance phone service is equal to $5.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Work out the length of x. Give your answer rounded to 3 significant figures. 13.3 mm 5.5 mm The diagram is not drawn accurately. X = 0 mm x​

Answers

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Which graph represents the linear equation y = −4x − 3?
a graph of a line that passes through the points negative 2 comma 2 and 0 comma negative 4 a graph of a line that passes through the points negative 4 comma negative 2 and 0 comma negative 3 a graph of a line that passes through the points negative 1 comma 1 and negative 3 comma 0 a graph of a line that passes through the points negative 4 comma 0 and negative 3 comma negative 4

Answers

The correct graph representing the linear equation y = -4x - 3 is the graph that passes through the points (-4, 0) and (-3, -4).

To determine which graph represents the linear equation y = -4x - 3, let's examine the given options:

A graph of a line that passes through the points (-2, 2) and (0, -4)

A graph of a line that passes through the points (-4, -2) and (0, -3)

A graph of a line that passes through the points (-1, 1) and (-3, 0)

A graph of a line that passes through the points (-4, 0) and (-3, -4)

To identify the correct graph, we need to find the slope-intercept form of the equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

In the given equation y = -4x - 3, we can see that the slope is -4 and the y-intercept is -3.

Now, let's examine the options one by one:

The slope of the line passing through (-2, 2) and (0, -4) can be calculated as (change in y)/(change in x) = (2 - (-4))/(-2 - 0) = -6/-2 = 3. Since the slope is not -4, this graph does not represent the given equation.

The slope of the line passing through (-4, -2) and (0, -3) can be calculated as (change in y)/(change in x) = (-2 - (-3))/(-4 - 0) = 1/-4 = -1/4. Since the slope is not -4, this graph does not represent the given equation.

The slope of the line passing through (-1, 1) and (-3, 0) can be calculated as (change in y)/(change in x) = (1 - 0)/(-1 - (-3)) = 1/2. Since the slope is not -4, this graph does not represent the given equation.

The slope of the line passing through (-4, 0) and (-3, -4) can be calculated as (change in y)/(change in x) = (0 - (-4))/(-4 - (-3)) = 4/-1 = -4. Since the slope is -4, this graph represents the given equation.

Therefore, the correct graph representing the linear equation y = -4x - 3 is the graph that passes through the points (-4, 0) and (-3, -4).

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