MATHEMATICS MIDDLE SCHOOL

Arm Span(x) Height(y) (58, 60)
(49, 47)
(51, 55)
(19, 25)
(37, 39)
(44, 45)
(47, 49)
(36, 35)
(41, 40)
(46, 50)
(58, 61)
(67, 63)

1. Representation of Data with Plots Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph. Copy and paste your scatter plot into a word processing document.

2. The Line of Best Fit Include your scatter plot and the answers to the following questions in your word processing document:

Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.

Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.

What does the slope of the line represent within the context of your graph? What does the y-intercept represent?

Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation.

Using the line of best fit that you found in 2, approximate how tall is a person whose arm span is 66 inches?

According to your line of best fit, what is the arm span of a 74-inch-tall person?

Answers

Answer 1

Answer:

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

$a = (\sum y \sum x^(2) - \sum x \sumxy)/(n\sum x^(2)- \left (\sum x\right )^(2))\n\nb = (n\sumx y - \sum x \sumxy)/(n\sum x^(2)- \left (\sum x\right )^(2))$

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

$\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\n\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\n25 & 19 & 22.3 & -3.3\n40 & 41 & 38.2 & 2.8\n55 & 51 & 54.1 & -3.1\n65 & 67 & 62.6 & 4.4\n \end{array}$

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\n66 & = & 1.0595x - 4.1524\n70.1524 & = & 1.0595x\nx & = & (70.1524)/(1.0595)\n\n& = & \textbf{66 in}\n\end{array}\n\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\n& = & 1.0595*74 - 4.1524\n& = & 78.4030 - 4.1524\n& = & \textbf{74 in}\n\end{array}\n\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}$

Related Questions

I need help with this!!! Which has a greater area, a triangle with a base of 100 feet and a height of 100 feet or a circle with diameter of 100 feet, please justify your selection.
What fraction of Emmas garden is planted with vegetables
Helps please ~(-_-)~What is the slope-intercept form of the function described by this table?x 1 2 3 4y −2 −6 −10 −14y =____ x +____Fill in the blanks (Again ^_^)
W -7 7/12 equals 5 + 5/12 what is w show work
-Help?-Simplify.Assume x and y are nonnegative.A: B: C: D:

(BRAINLIEST) (05.01)A scale drawing of a kitchen is shown below. The scale is 1 : 20.

A rectangle is shown. The length of the rectangle is labeled 4 inches. The width of the rectangle is labeled 5 inches.

Show your work to determine the area of the room in square feet.

Answers

The area of the given room is 166 2/3 ft².

What is a scale drawing?

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension.

The area of the room can be calculated as;

The length of the room = 20 x 4 = 80 inches

The width of the room = 20 x 5 = 100 inches.

Now, 1 inch = 1/12 foot

80 inches / 12 = 6 2/3 ft

100 / 12 = 8 1/3 ft

The Area = 6 2/3 x 8 1/3

The Area = 25/3 x 20/3

The Area = 500 / 3

The Area = 166 2/3 ft²

Therefore, The area of the given room is 166 2/3 ft².

To learn more about calculate the area of a rectangle, please check: brainly.com/question/16595449

#SPJ2

Answer:

the room will be 80 inches by 100 inches

( 1 inch ----> 20 inches

so 4 inches ----> 80 inches )

6 2/3 ft by 8 1/3 ft

A snake is 2 ft 4" long how long is the snake?

Answers

The snake is 2-ft 4-inches long.
I learned that from reading the question carefully,
including all of the given information..

In my opinion I would think it would make more sense if it was 4ft 2in.

The quotient is 71 2/3 what is the divisor

Answers

since quotient =divisor ×dividend +remainder.
here, quotient =71 2/3=215/3
therefore dividend is 3

the answer to your question is 215

(question is included in the image) answer in a simple way and on point to be marked brainilest

Answers

Answer:

a) Missing y-values
x = - 2 ==> y = 5

x = - 1 ==> y = 2

x = 1 ==> y = 2

x = 3 ==> y = 10

b) Values of x for y = 4:
x = 1.7 and x = -1.7

Step-by-step explanation:

Given the quadratic function,
y = x² + 1

part a)

to find the y-value for a specific x, just plug in that value of x into the right side and simplify

There are four missing values for

The x values and the corresponding y values are
x = - 2 ==> y = (-2)² + 1 = 4 + 1 = 5

x = - 1 ==> y = (-1)² + 1 = 1 + 1 = 2

x = 1 ==> y = (1)² + 1 = 1 + 1 = 2

x = 3 ==> y = (3)² + 1 = 9 + 1 = 10

part b)

The graph has each unit on the grid for the x-axis = 0.5
and
each unit on the grid for the y-axis = 2

I got this by seeing that between x = 0 and x = 1 there are two units

the value of y at x = -1 or x = 1 is only one vertical unit on the grid and since y = 2 for these values of x, each vertical unit must be 2

Therefore look at the value of y = 4 (which should be two vertical units) on the graph. You can also draw a horizontal line parallel to the x axis at 2 units from the x-axis

It appears that on the positive x-axis for y = 4, x is about halfway between 1.5 and 2 so I would estimate it at 1.75

On the negative x-axis, at y = 4, x is about halfway between -1.5 and -2 so it would be -1.75

One thing to note about quadratic functions is that you get the same value of y for x and -x

So at y = 4, the two possible values of x are
x = 1.75 and x = -1.75

which when using one decimal place will round to 1.7 and 1;75

I am rounding down rather than rounding up since the x value appears be less than 1.75

Mathematically we can solve for x at y = 4 by plugging in values
y = 4 = x² + 1

x² + 1 = 4

x² = 4 - 1 = 3

x =±√3 = ±1.732

which when rounded to 1 decimal place becomes
x = 1.7 and x = -1.7

Answer:

Step-by-step explanation:

a) y = (-2)² + 1 = 5

y = (-1)² + 1 = 2

y = (1)² + 1 = 2

y = (3)² + 1 = 10

b) 4 = x² + 1

x² = 4 - 1 = 3

x = ±√3 = ±1.7

A manufacturer wants to make a box with a volume of 24 cubic feet.a. Sketch two possible designs for the box.

b. If the box is to be made out of wood that costs $4 per square foot, which of your designs would be less expensive to produce? Explain.

Answers

First: You should know the formulas for volume and surface area of a rectangular prism.
$V=whl$
$SA=2wl+2wh+2hl$

Now, if our volume is 24 ft³, then the 3 dimensions of the box must multiply to make 24. We want to make two designs, so let's think of some possible dimensions.
Let's say...2 × 2 × 6 and 2 × 3 × 4.
You should be able to sketch boxes and label the sides. Just draw two rectangles and draw lines between all of the points. (see attached for reference)

Now all we have to do is find the surface area. Plug in our width, length, and height and solve.
First box
SA = 2wl + 2wh + 2hl
SA = 2×2×2 + 2×2×6 + 2×2×6
SA = 8 + 24 + 24
SA = 56
Second box
SA = 2wl + 2wh + 2hl
SA = 2×2×3 + 2×2×4 + 2×3×4
SA = 12 + 16 + 24
SA = 52

At $4 / ft²...
56 ft² = $224
52 ft² = $208

The second box is less expensive to produce because it has less surface area and therefore less wood needed to build the sides of the box.

Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor. Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour. If it takes 25 hours to paint Paul’s house, the most cost effective company will be

Answers

Answer:

The most cost effective company will be Painting USA that charge $700 to paint Paul house .

Step-by-step explanation:

As given

Paul is going to have the exterior of his home painted.

Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor.

If it takes 25 hours to paint Paul’s house.

Total amount charge by Painting USA = Painting USA charges for come out and evaluate the house + Cost of per hour of labor × Total hours take to paint Paul house .

Total amount charge by Painting USA = 75 + 25 × 25

= 75 + 625

= $ 700

As given

Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.

Total amount charge by Upscale Home Painting = Cost of per hour of labor × Total hours take to paint Paul house

= 40 × 25

= $ 1000

Therefore the most cost effective company will be Painting USA that charge $700 to paint Paul house .

Given:$75
25 hours

Painting USA : Fixed cost: $75 ; Variable Cost: $25x
Total Cost = 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting: No Fixed Cost ; Variable Cost : $40x
Total Cost = 40(25) = 1,000

The most cost effective company will be Painting USA whose charge will amount to $700.