Question 1

Find the linear equation that is the straight line through (3, 4)and (9, 40).
A) 
B) 
C) 
D) 
E)

Accepted Answer

We want to find the equation of the line passing through the points (3,4) and (9,40). We can use the point-slope form of the equation of a line: y − y1 = m(x − x1), where m is the slope of the line and (x1,y1) is one of the points on the line. 
First, we can find the slope of the line using the two points:

m = (y2 − y1)/(x2 − x1) 
m = (40 − 4)/(9 − 3) 
m = 36/6 
m = 6

Now we can plug in one of the points and the slope into the point-slope form:

y − 4 = 6(x − 3)

To get the equation into slope-intercept form (y = mx + b), we can simplify:

y − 4 = 6x − 18 
y = 6x − 14

So the linear equation that describes the straight line passing through (3,4) and (9,40) is y = 6x − 14.

Question 2

In 1950 the number of retirees was approximately 150 per thousand people aged 20-64. In 1990 this number rose to approximately 200, and it is projected to rise to 275 in 2020. Model  as a piecewise linear function of the time  in years since 1950, and use your model to project the number of retires per thousand people aged 20-64 in 1955. (Round you answer to the nearest integer.)
A)  people per thousand
B)  people per thousand
C)  people per thousand
D)  people per thousand
E)  people per thousand

Accepted Answer

The answer of In 1950 the number of retirees was...

Question 3

A car that was being pursued by the police was at Jones Beach at exactly 9:57 p.m. ( t = 0), and passed Oak Beach (13 miles from Jones Beach)at exactly 10:05 p.m.,where it was overtaken by the police. How fast, in miles per minute, was the car traveling? (Round your answer to the nearest tenth.)
A)  miles/min.
B)  miles/min.
C)  miles/min.
D)  miles/min.
E)  miles/min.

Accepted Answer

The answer of A car that was being pursued by...

Question 4

The demand for your college newspaper is 1200 copies per week if the paper is given a way free of charge, and the demand drops to 600 if the charge is $0.10 per copy. However, the university is prepared to supply only 500 copies per week free of charge but will supply 2500 per week at $0.50 per copy. At what price should the college newspapers be sold so that there is neither a surplus nor a shortage of papers?
A) 
B) 
C) 
D) 
E)

Accepted Answer

Let x be the price per copy in dollars. At $0.50 per copy, the total demand is: 2500 - 5x At $0.10 per copy, the total demand is: 1200 - 10x Since the university can supply a maximum of 2500 copies, we have: 2500 - 5x = 2500, if 2500 - 5x > 0 or 2500 - 5x = 500, if 2500 - 5x < 0 Solving, we get: x = 1, if 2500 - 5x > 0 or x = 5, if 2500 - 5x < 0 Now, we need to find the price that will make the total demand equal to the total supply: 1200 - 10x = 2500 - 5x Solving, we get: x = 8/5 = 1.6 Therefore, the price per copy should be $1.60 to neither have a surplus nor a shortage of papers.

Question 5

In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature  and the Celsius temperature  are related by a linear equation, find the Fahrenheit temperature that correspond to 31 C, to the nearest degree.
A)  F
B)  F
C)  F
D)  F
E)  F

Accepted Answer

The answer of In the Fahrenheit temperature scale, water freezes...

Question 6

In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature  and the Celsius temperature  are related by a linear equation, find the Fahrenheit temperature that corresponds to 71 C, to the nearest degree. __________ F

Accepted Answer

The answer of In the Fahrenheit temperature scale, water freezes...

Question 7

The position of a model train, in feet along the railroad track, is given by  after  seconds. Where is the train after 10 seconds?
A)  feet
B)  feet
C)  feet
D)  feet
E)  feet

Accepted Answer

The answer of The position of a model train, in...

Question 8

You can sell 95 pet chias per week if they are marked as $5 each,but only 45 per week if they are marked $6 per chia. Your chia supplier is prepared to sell you 20 chias per week if they are marked $5 per chia, and 70 per week if they are marked $6 per chia. At what price should the chias be marked so that there is neither surplus nor a shortage of chias?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of You can sell 95 pet chias per...

Question 9

The Snowtree cricket behaves in a rather interesting way: The rate at which it chirps depends linearly on the temperature. One summer evening you hear a cricket chirping at a rate of 140 chirps per minute, and you notice that the temperature is 80°F. Later in the evening, the cricket has slowed down to 120 chirps per minute, and you notice that the temperature has dropped to 75°F. What is the temperature if the cricket is chirping at a rate of 108 chirps per minute?
A)  F
B)  F
C)  F
D)  F
E)  F

Accepted Answer

The answer of The Snowtree cricket behaves in a rather...

Question 10

Find the linear equation that is the straight line through (9, 5)and parallel to the line  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the linear equation that is the...

Question 11

The position of a model train, in feet along the railroad track, is given by  after  seconds. When will the train have moved a distance of 30 feet?
A)after  seconds
B)after  seconds
C)after  seconds
D)after  seconds
E)after  seconds

Accepted Answer

The answer of The position of a model train, in...

Question 12

The linear function is given. Find  .

Accepted Answer

The answer of The linear function is given. Find ...

Question 13

Calculate the slope of the straight line through the points (4, 1)and (6, -5). Try to do the calculations mentally.

Accepted Answer

The answer of Calculate the slope of the straight line...

Question 14

U.S. imports of pasta increased from 290 million pounds in 1990 ( t = 0), by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds)in the year 2010, assuming the import trend continued.
A)1,382 million pounds
B)342 million pounds
C)1,040 million pounds
D)2,300 million pounds
E)1,330 million pounds

Accepted Answer

The answer of U.S. imports of pasta increased from 290...

Question 15

In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature  and the Celsius temperature  are related by a linear equation, find the Celsius temperature that correspond to 68 F, to the nearest degree.
A)  C
B)  C
C)  C
D)  C
E)  C

Accepted Answer

We can use the formula $C = \frac{5}{9}(F-32)$ to convert Fahrenheit to Celsius. Substituting $F=68$, we get $C = \frac{5}{9}(68-32) = \frac{5}{9}(36) \approx 20$. To the nearest degree, $20$ Celsius corresponds to $\boxed{	extbf{(C) }20}$ Celsius.

Question 16

You can sell 80 pet chias per week if they are marked as $4 each, but only 30 per week if they are marked $5 per chia. Your chia supplier is prepared to sell you 20 chias per week if they are marked $4 per chia, and 70 per week if they are marked $5 per chia. Write the associated linear demand and supply functions.
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of You can sell 80 pet chias per...

Question 17

The height of the falling sheet of paper, in feet from the ground, is given by  after  seconds. When will the sheet of paper reach the ground?
A)after  seconds
B)after  seconds
C)after  seconds
D)after  seconds
E)after  seconds

Accepted Answer

The sheet of paper will reach the ground when h(t) = 0. Therefore, we need to solve the equation 11ebfe6a_2ca8_f1cb_96cc_614028b21f2c_TBX8650_11 = 0 for t. This gives us t = 11ebfe6a_2ca8_f1cf_96cc_5b14414eec51_TBX8650_11 seconds.

Question 18

A police car was traveling down Ocean Parkway in a high-speed chase from Jones Beach. The car was at Jones Beach at exactly 7:00 p.m. ( t = 0), and was at Oak Beach, 13 miles from Jones Beach, at exactly 7:04 p.m. How fast was the police car traveling? (Round your answer to the nearest tenth.)
A)  miles/min.
B)  miles/min.
C)  miles/min.
D)  miles/min.
E)  miles/min.

Accepted Answer

The answer of A police car was traveling down Ocean...

Question 19

Calculate the slope of the straight line through the points (4.1, 1)and (9.1, -14). Try to do the calculations mentally.

Accepted Answer

The answer of Calculate the slope of the straight line...

Question 20

In the Fahrenheit temperature scale, water freezes at 32 F and boils at 212 F. In the Celsius (or centigrade)scale, water freezes at 0 C and boils at 100 C. Assuming that the Fahrenheit temperature  and the Celsius temperature  are related by a linear equation, find the Celsius temperature that correspond to 175 F, to the nearest degree. __________ C

Accepted Answer

The answer of In the Fahrenheit temperature scale, water freezes...

Quiz 1: Functions and Linear Models

Find the linear equation that is the straight line through (3, 4) and (9, 40) .

A car that was being pursued by the police was at Jones Beach at exactly 9:57 p.m. ( t = 0) , and passed Oak Beach (13 miles from Jones Beach) at exactly 10:05 p.m.,where it was overtaken by the police. How fast, in miles per minute, was the car traveling? (Round your answer to the nearest tenth.)

The position of a model train, in feet along the railroad track, is given by after seconds. Where is the train after 10 seconds?

Find the linear equation that is the straight line through (9, 5) and parallel to the line .

The position of a model train, in feet along the railroad track, is given by after seconds. When will the train have moved a distance of 30 feet?

The linear function is given. Find .

Calculate the slope of the straight line through the points (4, 1)and (6, -5). Try to do the calculations mentally.

U.S. imports of pasta increased from 290 million pounds in 1990 ( t = 0) , by an average of 52 million pounds per year. Estimate U.S. pasta import (in million pounds) in the year 2010, assuming the import trend continued.

The height of the falling sheet of paper, in feet from the ground, is given by after seconds. When will the sheet of paper reach the ground?

A police car was traveling down Ocean Parkway in a high-speed chase from Jones Beach. The car was at Jones Beach at exactly 7:00 p.m. ( t = 0) , and was at Oak Beach, 13 miles from Jones Beach, at exactly 7:04 p.m. How fast was the police car traveling? (Round your answer to the nearest tenth.)

Calculate the slope of the straight line through the points (4.1, 1)and (9.1, -14). Try to do the calculations mentally.