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MAT-136-T2129 20EW2 Intro to Quantitative Analysis, 5-2 Problem Set: Module Five
Angie Mann, 11/29/20 at 7:58:49 PM EST
Question1: Score 4/4
A clothing business finds there is a linear relationship between the number of shirts, n, it can sel
and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be
sold at a price of $30, while 3,000 shirts can be sold at a price of $14. Find a linear equation in the
form p(n) = mn + b that gives the price p they can charge for n shirts.
p(n) =
Your response Correct response
-.008*n+38 -1/125*n+38
Auto graded Grade: 1/1.0
Total grade: 1.0×1/1 = 100%
Feedback:
We can use the given information to calculate the slope.
m = p 2−p 1n 2−n 1
= 14−303,000−1,000
= − 162,000
= − 1125
Substitute the slope and the coordinates of one of the points into the slope-intercept form.
, p = mn + b
(30) = − 1125(1,000) + b
30 + 8 = b
b = 38
The linear equation that gives the price p they can charge for n shirts is p(n) = − 1125n + 38.
Question2: Score 4/4
A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and
the yield, y, each plant produces. When she plants 30 stalks, each plant yields 28 oz of beans
When she plants 34 stalks, each plant produces 26 oz of beans. Find a linear relationship in the
form y = mn + b that gives the yield when n stalks are planted.
y=
Your response Correct response
-1/2n+43 -1/2*n+43
Auto graded Grade: 1/1.0
Total grade: 1.0×1/1 = 100%
Feedback:
The given information gives us two input-output pairs: (30, 28) and (34, 26). We start by finding
the rate of change.
, m = y 2−y 1n 2−n 1
= 26−2834−30
= -24
= − 12 oz of beans per stalk
We substitute the slope and a given point into the slope-intercept form to find the equation of the
line.
y = mn + b
28 = − 12(30) + b
28 + 15 = b
b = 43
The linear relationship that gives the yield when n stalks are planted is y = − 12n + 43.
Question3: Score 3/3
Determine if the points (3, 1), (0, 4), and (-2, 8) are solution points to the inequality below.
If the point is a solution, enter yes, otherwise, enter no.
y>5−x
a. Is (3, 1) a solution?
Your response Correct response
no no
Auto graded Grade: 1/1.0
MAT-136-T2129 20EW2 Intro to Quantitative Analysis, 5-2 Problem Set: Module Five
Angie Mann, 11/29/20 at 7:58:49 PM EST
Question1: Score 4/4
A clothing business finds there is a linear relationship between the number of shirts, n, it can sel
and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be
sold at a price of $30, while 3,000 shirts can be sold at a price of $14. Find a linear equation in the
form p(n) = mn + b that gives the price p they can charge for n shirts.
p(n) =
Your response Correct response
-.008*n+38 -1/125*n+38
Auto graded Grade: 1/1.0
Total grade: 1.0×1/1 = 100%
Feedback:
We can use the given information to calculate the slope.
m = p 2−p 1n 2−n 1
= 14−303,000−1,000
= − 162,000
= − 1125
Substitute the slope and the coordinates of one of the points into the slope-intercept form.
, p = mn + b
(30) = − 1125(1,000) + b
30 + 8 = b
b = 38
The linear equation that gives the price p they can charge for n shirts is p(n) = − 1125n + 38.
Question2: Score 4/4
A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and
the yield, y, each plant produces. When she plants 30 stalks, each plant yields 28 oz of beans
When she plants 34 stalks, each plant produces 26 oz of beans. Find a linear relationship in the
form y = mn + b that gives the yield when n stalks are planted.
y=
Your response Correct response
-1/2n+43 -1/2*n+43
Auto graded Grade: 1/1.0
Total grade: 1.0×1/1 = 100%
Feedback:
The given information gives us two input-output pairs: (30, 28) and (34, 26). We start by finding
the rate of change.
, m = y 2−y 1n 2−n 1
= 26−2834−30
= -24
= − 12 oz of beans per stalk
We substitute the slope and a given point into the slope-intercept form to find the equation of the
line.
y = mn + b
28 = − 12(30) + b
28 + 15 = b
b = 43
The linear relationship that gives the yield when n stalks are planted is y = − 12n + 43.
Question3: Score 3/3
Determine if the points (3, 1), (0, 4), and (-2, 8) are solution points to the inequality below.
If the point is a solution, enter yes, otherwise, enter no.
y>5−x
a. Is (3, 1) a solution?
Your response Correct response
no no
Auto graded Grade: 1/1.0
