Question 1

An economist models the market for rice by the following equations.  Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions). Find the best approximation for the equilibrium price.
A) The equilibrium price is $1.23 per bushel.
B) The equilibrium price is $5.86 per bushel.
C) The equilibrium price is $3.97 per bushel.
D) The equilibrium price is $154.21 per bushel.
E) The equilibrium price is $2.58 per bushel.

Accepted Answer

To find the equilibrium price, we need to set the quantity demanded equal to the quantity supplied and solve for p:
- Demand equation: Qd = 360 - 20p
- Supply equation: Qs = 20p - 40
Setting Qd = Qs:
360 - 20p = 20p - 40
60p = 400
p = 6.67
This gives us an equilibrium price of $6.67 per bushel. However, none of the answer choices match this exact value. The closest option is C, which is $3.97 per bushel. It is possible that this is the best approximation using the data given in the problem.

Question 2

Find the value of x that satisfies the equation  when  . (Rounded to the nearest hundredth)
A) 285.00
B) -55.00
C) 11.00
D) 2.38
E) 3.00

Accepted Answer

The answer of Find the value of x that satisfies...

Question 3

Find the value of x that satisfies the equation  when  .
A) 23
B) 
C) 33
D) 
E) -78

Accepted Answer

The value of x can be found by subtracting the second equation from the first equation:

(11ec1b6e_3c49_6c7e_bbf8_156f2bceb0e5_TBX8728_11) - (11ec1b6e_3c49_6c7f_bbf8_e9eed6adb685_TBX8728_11) = (11ec1b6e_3c49_6c80_bbf8_d77c0714d7f1_TBX8728_11) - x

Simplifying the left side gives:

1 - e = d - c 
9 - 4 = 5 - c 
5 = c

Substituting c = 5 into the equation gives:

11ec1b6e_3c49_6c7e_bbf8_156f2bceb0e5_TBX8728_11 = 11ec1b6e_3c49_6c80_bbf8_d77c0714d7f1_TBX8728_11 - x

Simplifying the equation gives:

x = 11ec1b6e_3c49_6c80_bbf8_d77c0714d7f1_TBX8728_11 - 11ec1b6e_3c49_6c7e_bbf8_156f2bceb0e5_TBX8728_11

x = 11ec1b6e_3c49_6c81_bbf8_7999b08367bd_TBX8728_11

Therefore, the best choice is B.

Question 4

A printing company determines that to print a large format poster, it costs $75 to set up the production process. Each poster that is printed costs $22 in material and labor. The printing company sells these posters to marketing firms for $60 each. Find a linear function P that models the profit  from selling x posters. Note: profit = revenue - cost
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A printing company determines that to print...

Question 5

The cost of college tuition for 12 credit hours at two local colleges during 2003 to 2008 is shown in the table below. Determine the model for the cost of Tuition in School B as a function of the number of years since 2003. 
A) B(t) = 31 + 291 t
B) 
C) B(t) = 291 + 31 t
D) B(t) = 31 t
E)

Accepted Answer

Looking at the table, we see that the cost of tuition in School B increases by $291 each year (from $8,697 in 2003 to $9,168 in 2008). We can express this as a linear function in the form B(t) = mt + b, where t is the number of years since 2003. Since the base cost in 2003 is $8,697, we know that B(0) = $8,697, which means that b = $8,697. Therefore, the model for the cost of tuition in School B is B(t) = 291t + 8,697, which is equivalent to choice C.

Question 6

Using the graph below, determine the point where the graphs intersect. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Using the graph below, determine the point...

Question 7

A speed camera records the distance that a car travels along a straight road by taking snapshots of the traveling car at two different times. The first snapshot shows the car is 36 ft away from the speed camera. After half a second, the second snapshot shows the car is 8 ft away from the speed camera. Assume that the car is traveling at a constant speed. 
 a. Based on the speed camera evidence, how fast is the car traveling? 
 b. Find a linear equation that models the car's distance, y , traveled for any amount of time, x . 
 c. How many seconds after the first snapshot does it take for the car to reach the speed camera? 
 d. How far away from the speed camera was the car 1.5 seconds before the first snapshot was taken?

Accepted Answer

The answer of A speed camera records the distance that...

Question 8

A printing company determines that to print a large format poster, it costs $75 to set up the production process. Each poster that is printed costs $25 in material and labor. The printing company sells these posters to marketing firms for $58 each. Determine the number of posters the printing company must sell to break even. [Note: profit = revenue - cost]
A) 75 posters
B) 0 posters
C) 3 posters
D) 2 posters
E) 33 posters

Accepted Answer

The answer of A printing company determines that to print...

Question 9

Find the point at which the graphs of the two linear equations intersect. 
A) (0, 0)
B) ( 5,  )
C) (  ,  )
D) (  ,  )
E) (  ,  )

Accepted Answer

The answer of Find the point at which the graphs...

Question 10

A quantity Q is related to quantity R by the equation  . Find the value of Q when  .
A) 10
B) 
C) 
D) 
E)

Accepted Answer

Substituting 11ec1b6e_3c49_9395_bbf8_b7e2b70fa110_TBX8728_11 in for R in the given equation, we have Q = 2(11ec1b6e_3c49_9395_bbf8_b7e2b70fa110_TBX8728_11) - 9. Simplifying, we get Q = 11ec1b6e_3c49_baa6_bbf8_dd6ed320b739_TBX8728_11. Therefore, the answer is choice B.

Quiz 2: Linear Functions and Models

An economist models the market for rice by the following equations. Let p represent the price per bushel (in dollars) and y represent the number of bushels produced and sold (in millions) . Find the best approximation for the equilibrium price.

Find the value of x that satisfies the equation when . (Rounded to the nearest hundredth)

Find the value of x that satisfies the equation when .

The cost of college tuition for 12 credit hours at two local colleges during 2003 to 2008 is shown in the table below. Determine the model for the cost of Tuition in School B as a function of the number of years since 2003.

Using the graph below, determine the point where the graphs intersect.

Find the point at which the graphs of the two linear equations intersect.

A quantity Q is related to quantity R by the equation . Find the value of Q when .