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Darina [25.2K]
3 years ago
7

An on-demand movie company charges $2.95 per movie plus a monthly fee of $39.95. Which expression represents the yearly cost for

movie rentals?
Mathematics
1 answer:
natulia [17]3 years ago
8 0

Answer:

y=$2.95x+$479.4

Step-by-step explanation:

Let

x----> the number of movie rentals

y ----> the cost for movie rentals

we know that

The expression that represent the monthly cost is equal to

y=$2.95x+$39.95

1 year has 12 months

so

The expression that represent the yearly cost is equal to

y=$2.95x+$39.95*(12)

y=$2.95x+$479.4

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Arm Span(x) Height(y)
natita [175]

Answer:

Here's what I get.

Step-by-step explanation:

1. Representation of data

I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.

2. Line of best fit

(a) Variables

I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).

It seems to me that arm span depends on your height rather than the other way around.

(b) Regression equation

The calculation is easy but tedious, so I asked Excel to do it.

For the equation y = ax + b, the formulas are

a = \dfrac{\sum y \sum x^{2} - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\b = \dfrac{n\sumx y  - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}

This gave the regression equation:

y = 1.0595x - 4.1524

(c) Interpretation

The line shows how arm span depends on height.

The slope of the line says that arm span increases about 6 % faster than height.

The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).

(d) Residuals

\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\\\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\\25 & 19 & 22.3 & -3.3\\40 & 41 & 38.2 & 2.8\\55 & 51 & 54.1 & -3.1\\65 & 67 & 62.6 & 4.4\\ \end{array}

The residuals appear to be evenly distributed above and below the predicted values.

A graph of all the residuals confirms this observation.  

The equation usually predicts arm span to within 4 in.

(e) Predictions

(i) Height of person with 66 in arm span

\begin{array}{rcl}y& = & 1.0595x - 4.1524\\66 & = & 1.0595x - 4.1524\\70.1524 & = & 1.0595x\\x & = & \dfrac{70.1524}{1.0595}\\\\& = & \textbf{66 in}\\\end{array}\\\text{A person with an arm span of 66 in  should have a height of about $\large \boxed{\textbf{66 in}}$}

(ii) Arm span of 74 in tall person

\begin{array}{rcl}y& = & 1.0595x - 4.1524\\& = & 1.0595\times74 - 4.1524\\& = & 78.4030 - 4.1524\\& = & \textbf{74 in}\\\end{array}\\\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}

6 0
3 years ago
What is the y-intercept of the line whose equation is:
salantis [7]

Answer:

2

Step-by-step explanation:

Use the intercept method.  Where is y when x = 0?

3 0
3 years ago
Ken receives $521 for maintenance on his grandmother's house and $347 for yard work. Which is the best estimate for how much mon
VikaD [51]

Answer:

521

+347

868

870

Step-by-step explanation:

8 0
3 years ago
What is the square root of r64?
IceJOKER [234]

Answer:8

Step-by-step explanation:

Simplify the radical.

4 0
3 years ago
Read 2 more answers
If m ABC = 118°, solve for x.
ziro4ka [17]

Given:

m∠ABC = 118°

m∠DAC = (9x - 33)°

m∠CAB = (2x + 7)°

To find:

The value of x.

Solution:

Sum of the adjacent angles in a parallelogram = 180°

m∠ABC + m∠CAB + m∠DAC = 180°

118° + 9x° - 33° + 2x° + 7° = 180°

92° + 11x° = 180°

Subtract 92° from both sides.

92° + 11x° - 92° = 180° - 92°

11x° = 88°

Divide by 11° on both sides.

x = 8

The value of x is 8.

6 0
3 years ago
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