Question 1

Cowling's rule is a method for calculating pediatric drug dosages. If a denotes the adult dosage (in milligrams) and if t is the child's age (in years), then the child's dosage is given by  If the adult dose of a drug is 500 mg, how much should a 4 year-old child receive?
A) 100.77 milligrams
B) 99.07 milligrams
C) 102.47 milligrams
D) 104.17 milligrams
E) 105.87 milligrams

Accepted Answer

The answer of Cowling's rule is a method for calculating...

Question 2

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . 
A) 
B) 
C) 
D) y is not a linear function of x

Accepted Answer

The given equation contains the product of y and x, which makes it a non-linear equation. Therefore, y is not a linear function of x.

Question 3

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b .
X = 4y - 8
A) 
B) 
C) 
D)

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 4

The quantity demanded for a certain brand of portable CD players is 400 units when the unit price is set at $80. The quantity demanded is 1,400 units when the unit price is $30. Find the demand equation.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The quantity demanded for a certain brand...

Question 5

The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded is 1,200 units when the unit price is $40. Find the demand equation.
A) p = - 0.05x + 90
B) p = - 0.04x + 100
C) p = - 0.04x + 90
D) p = - 0.05x + 100

Accepted Answer

The demand equation is found using the slope formula (change in price/change in quantity) and the point-slope form of a line. The slope is (40-90)/(1200-200) = -0.05. Using point (200, 90), the equation is p = -0.05x + 100.

Question 6

Consider the supply equation  , where x is the quantity supplied in units of 1,000 and p is the unit price in dollars. Determine the number of units of the commodity the supplier will make available in the market at the given unit price  .
A) 2,400
B) 2,700
C) 3,000
D) 3,300
E) 3,600

Accepted Answer

The answer of Consider the supply equation  , where...

Question 7

The relationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is  and  , and the boiling point is  and  , respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of The relationship between temperature measured in the...

Question 8

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is  , the crickets chirp at the rate of  , and when the temperature is  , they chirp at the rate of  . Find N as a function of T and use this formula to determine the rate at which the crickets chirp when the temperature is  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Entomologists have discovered that a linear relationship...

Question 9

Find the constants m and b in the linear function  so that  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the constants m and b in...

Question 10

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 5. 5x + 4p - 40 = 0
A) 3,000
B) 4,500
C) 4,000
D) 5,500

Accepted Answer

To find the quantity demanded at a unit price of $5 (p = 5), we need to solve for x in the equation:

5x + 4(5) - 40 = 0

Simplifying, we get:

5x + 20 - 40 = 0

5x = 20

x = 4

However, the problem states that x represents the quantity demanded in units of 1,000. Therefore, we need to multiply x by 1,000 to get the actual quantity demanded:

x = 4 * 1,000 = 4,000

So the quantity demanded at a unit price of $5 is 4,000 units. Therefore, the best choice is C.

Question 11

A server purchased at a cost of $108,000 in 2002 has a scrap value of $18,000 at the end of 5 years. Find the linear equation expressing the server's book value at the end of t years.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A server purchased at a cost of...

Question 12

An office building worth $1 million when completed in 2000 is being depreciated linearly over 80 years. What will be the book value of the building in 2048? (Assume the scrap value is $0.)
A) The book value of the building in 2048 will be $400,000.
B) The book value of the building in 2048 will be $600,000.
C) The book value of the building in 2048 will be $200,000.
D) The book value of the building in 2048 will be $300,000.

Accepted Answer

The building is being depreciated linearly over 80 years, so the annual depreciation is $1,000,000 / 80 = $12,500. In 2048, the building will have been depreciated for 48 years, so the book value will be $1,000,000 - $12,500 * 48 = $400,000.

Question 13

A manufacturer has a monthly fixed cost of $35,000 and production cost of $4 for each unit produced. The product sells for $10/unit. Compute the profit (loss) corresponding to production level of 8,000 units.
A) The profit is $14,000.
B) The profit is $14,500.
C) The profit is $11,000.
D) The profit is $13,000.

Accepted Answer

The answer of A manufacturer has a monthly fixed cost...

Question 14

Assume that a certain commodity's demand equation has the form p = ax + b, where x is the quantity demanded and p is the unit price in dollars. Suppose the quantity demanded is 3,000 units when the unit price is $17.00 and 7,000 when the unit price is $13.00. What is the quantity demanded when the unit price is $15.50?
__________ units

Accepted Answer

The answer of Assume that a certain commodity's demand equation...

Question 15

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 
A) 
B) 
C) 
D) y is not a linear function of x

Accepted Answer

The equation cannot be written in the form y = mx + b, which means it does not define y as a linear function of x.

Question 16

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b .
6x  12y  3 = 0
A) y =  x + 
B) 
C) 
D) 
E)

Accepted Answer

To determine if the equation defines y as a linear function of x, we need to see if we can write it in the form y = mx + b.
Starting with the given equation: 6x + 12y + 3 = 0
We can isolate y by subtracting 6x and dividing by 12:
12y = -6x - 3
y = (-1/2)x - 1/4
Now the equation is in slope-intercept form with m = -1/2 and b = -1/4, so we can write:
y = (-1/2)x - 1/4
This is a linear function of x, so choice A is the best answer.

Question 17

Assume that a certain commodity's demand equation has the form p = ax + b, where x is the quantity demanded and p is the unit price in dollars. Suppose the quantity demanded is 1,000 units when the unit price is $19.00 and 7,000 when the unit price is $13.00. What is the quantity demanded when the unit price is $18.50?
A) 6,000 units
B) 1,500 units
C) 6,500 units
D) 8,000 units

Accepted Answer

To find the demand equation, use the two points (1000, 19) and (7000, 13) to find the slope (a) and intercept (b). The slope a = (13 - 19) / (7000 - 1000) = -1/1000. Using point (1000, 19), solve for b: 19 = (-1/1000)(1000) + b, so b = 20. The equation is p = -1/1000 * x + 20. For p = 18.50, solve 18.50 = -1/1000 * x + 20, giving x = 1500.

Question 18

For the supply equation, where x represents the quantity supplied in units of 1,000 and p is the unit price in dollars, determine the number of units of the commodity the supplier will make available in the market at the given unit price. Please round your answer to the nearest unit. 3x - 4p + 24 = 0; p = 8
A) 2,967
B) 2,667
C) 2,567
D) 3,167

Accepted Answer

Substitute p=8 into the equation, we get: 
3x - 4(8) + 24 = 0 
3x = 8 
x = 2.667 
Rounding to the nearest unit, the answer is 2667.

Question 19

A certain economy's consumption function is given by the equation  where  is the personal consumption expenditure in billions of dollars and x is the disposable personal income in billions of dollars. Find  ,  , and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A certain economy's consumption function is given...

Question 20

Find the constants m and b in the linear function f(x) = mx + b so that f(2) = 6 and the straight line represented by f has slope - 1.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the constants m and b in...

Quiz 1: Straight Lines and Linear Functions

Cowling's rule is a method for calculating pediatric drug dosages. If a denotes the adult dosage (in milligrams) and if t is the child's age (in years) , then the child's dosage is given by If the adult dose of a drug is 500 mg, how much should a 4 year-old child receive?

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b .

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . X = 4y - 8

The quantity demanded for a certain brand of portable CD players is 400 units when the unit price is set at $80. The quantity demanded is 1,400 units when the unit price is $30. Find the demand equation.

The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded is 1,200 units when the unit price is $40. Find the demand equation.

Consider the supply equation , where x is the quantity supplied in units of 1,000 and p is the unit price in dollars. Determine the number of units of the commodity the supplier will make available in the market at the given unit price .

The relationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is and , and the boiling point is and , respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of .

Find the constants m and b in the linear function so that and .

For the demand equation, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, determine the quantity demanded corresponding to the unit price p = 5. 5x + 4p - 40 = 0

A server purchased at a cost of $108,000 in 2002 has a scrap value of $18,000 at the end of 5 years. Find the linear equation expressing the server's book value at the end of t years.

An office building worth $1 million when completed in 2000 is being depreciated linearly over 80 years. What will be the book value of the building in 2048? (Assume the scrap value is $0.)

A manufacturer has a monthly fixed cost of $35,000 and production cost of $4 for each unit produced. The product sells for $10/unit. Compute the profit (loss) corresponding to production level of 8,000 units.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . 6x 12y 3 = 0

A certain economy's consumption function is given by the equation where is the personal consumption expenditure in billions of dollars and x is the disposable personal income in billions of dollars. Find , , and .

Find the constants m and b in the linear function f(x) = mx + b so that f(2) = 6 and the straight line represented by f has slope - 1.