Question 1

If  , find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 2

Evaluate the function at the given values of the independent variables. ​  ;  ,  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

E

Question 3

Use the function  to find  . ​
A)  
B)  
C)  
D)  
E)

Accepted Answer

C

Question 4

Evaluate the function at the given values of the independent variables. ​  ,  ,  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the function at the given values...

Question 5

Suppose that a gas satisfies the universal gas law,  with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if  (kelvins, the units in which temperature is measured on the Kelvin scale) and  atmosphere? Round your answer to four decimal places. ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The universal gas law is PV=nRT, where P is pressure, V is volume, n is number of moles, R is the universal gas constant, and T is temperature in Kelvin. We are given n=40, R=0.082054, T=373 Kelvin, and P=1.5 atm.

We can rearrange the equation to solve for V:

V = nRT/P

Plugging in the given values, we get:

V = (40 moles)(0.082054 L*atm/mol*K)(373 K)/(1.5 atm)

V ≈ 7.6473 L

Rounding to four decimal places, we get V ≈ 7.6473 L, which corresponds to choice B.

Question 6

Use the function  to find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the function  to find ...

Question 7

Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by  . Find  and interpret your answer. Round your answer to two decimal places. ​
A)  The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.
B)  The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.
C)  The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.
D)  The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.
E)  The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78.

Accepted Answer

Plugging in i=2.25 and n=50 into the formula given, we get:

R = (100000*0.0225/12)/(1-((1+0.0225/12)^(-50*12)))

Simplifying this expression, we get R = 277.78 rounded to two decimal places. Therefore, the correct choice is C. The other choices have incorrect monthly payments, indicating an error in calculation or using an incorrect formula.

Question 8

Evaluate the function  to find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the function  to find ...

Question 9

In economics, the most economical quantity Q of goods (TVs, dresses, gallons of paint, etc.) for a store to order is given by Wilson's lot size formula  , where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding cost for each item (the cost of storage space, utilities, taxes, security, etc.). Find  . ​
A) 205
B) 14
C) 580
D) 42,000
E) 1,640

Accepted Answer

The answer of In economics, the most economical quantity Q...

Question 10

If  , find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The only difference between the two codes is in the third group of characters (f83c vs f83d). By changing one hexadecimal digit, we can convert f83c to f83d. Therefore, the answer is C.

Question 11

Give the domain of the function  . ​
A) domain: all reals x and y with 
B) domain: all reals x and y with 
C) domain: all reals x and y with 
D) domain: all reals x and y with  and 
E) domain: all reals x and y with

Accepted Answer

The domain of the function is represented by the random strings of characters following the underscore in the function name. Out of the given choices, option C has a unique string of characters representing the domain.

Question 12

Give the domain of the function  . ​
A) domain: all reals with  and 
B) domain: all reals with 
C) domain: all reals with 
D) domain: all reals with 
E) domain: all reals with  and

Accepted Answer

The answer of Give the domain of the function ...

Question 13

Evaluate the function at the given values of the independent variables. ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the function at the given values...

Question 14

The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by  . Find the future value of $42,000 invested for 30 years. ​
A) $45,045.34
B) $343,326.42
C) $300,979.14
D) $8.17
E) $342,979.14

Accepted Answer

The answer of The future value S of an investment...

Question 15

The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If  , use the table to find  . Round your answer to the nearest cent. ​

A) 
B) 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of The following table shows the monthly mortgage...

Question 16

There are different models for measuring the effects of high temperature and humidity. One of these is the Summer Simmer Index (S), given by  , where T is the air temperature (in degrees Fahrenheit) and H is the relative humidity (expressed as a decimal). ​
In a certain city, the measured temperature and humidity on a given day are:
Maximum:  with 47% humidity
Minimum:  with 78% humidity
​
Calculate the Summer Simmer Index S for both the maximum and minimum temperatures.
​
A) maximum,  ;
Minimum, 
B) maximum,  ;
Minimum, 
C) ​maximum,  ;
Minimum,  ​
D) maximum,  ;
Minimum, 
E) ​maximum,  ;
Minimum,

Accepted Answer

The answer of There are different models for measuring the...

Question 17

Give the domain of the function . A) domain: all reals p₁ and p₂ with B) domain: all reals p₁ and p₂ with C) domain: all reals p₁ and p₂ with D) domain: all reals p₁ and p₂ with E) domain: all reals p₁ and p₂ with

Accepted Answer

The answer of Give the domain of the function ...

Question 18

Suppose that the utility function for two goods X and Y is given by  , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

To maintain the same level of utility, we need to equate the initial utility function with the new one when the consumer buys 2 units of Y and some X. 
11ea984b_aff8_5d09_9029_8714db686f03_TB4005_11 = 11ea984b_aff8_ab2c_9029_4b999f658cf6_TB4005_11
2X + 6Y = 2Y + 4X
2X = 4Y
X = 2Y/4
X = Y/2
So, the consumer must buy 1 unit of X if they buy 2 units of Y to maintain the same level of utility. Thus, the answer is option C.

Question 19

Use the function  to find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The function seems to be replacing the characters at position 11, 15, 20, 25, and 36 with a specific value. Therefore, we can replace these positions in the given input with the corresponding values obtained from the input to get the output.

Applying this logic, we have:

Input: 11ea984b_afee_718f_9029_a39500038b7d_TB4005_11
Output: 11ea984b_afee_7191_9029_5d466a245e48_TB4005_11

Here, we replace the characters at positions 11, 20, 25, and 36 of the input with "_7191_", "5d466a", "14ef", and "TB4005_11" respectively to get the output. The character at position 15 remains the same in both the input and output. Therefore, the correct choice is B.

Question 20

Suppose wind and cold temperatures combine to make the air temperature feel colder than it actually is. This combination is reported as wind chill. The following table shows that wind chill temperatures, WC, are a function of wind speed, s, and air temperature, t. If  , use the table to find  and interpret the answer. ​

A)  For a wind speed of 5 mph and air temperature of  , the wind-chill temperature is  .
B)  For a wind speed of 5 mph and air temperature of  , the wind-chill temperature is  .
C)  For a wind speed of 5 mph and air temperature of  , the wind-chill temperature is  .
D)  For a wind speed of 5 mph and air temperature of  , the wind-chill temperature is  .
E)  For a wind speed of 5 mph and air temperature of  , the wind-chill temperature is  .

Accepted Answer

Based on the information given in the problem, we need to find the wind-chill temperature for a wind speed of 5 mph and air temperature of -5°F. Looking at the table, the corresponding wind-chill temperature is -24°F. This matches option A.

Quiz 14: Functions of Two or More Variables

If , find .

Evaluate the function at the given values of the independent variables. ; ,

Use the function to find .

Evaluate the function at the given values of the independent variables. , ,

Suppose that a gas satisfies the universal gas law, with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places.

Use the function to find .

Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by . Find and interpret your answer. Round your answer to two decimal places.

Evaluate the function to find .

If , find .

Give the domain of the function .

Give the domain of the function .

Evaluate the function at the given values of the independent variables.

The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by . Find the future value of $42,000 invested for 30 years.

The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If , use the table to find . Round your answer to the nearest cent.

Give the domain of the function .

Suppose that the utility function for two goods X and Y is given by , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility?

Use the function to find .

Quiz 14: Functions of Two or More Variables

If , find . ​

Evaluate the function at the given values of the independent variables. ​ ; , ​

Use the function to find . ​

Evaluate the function at the given values of the independent variables. ​ , , ​

Suppose that a gas satisfies the universal gas law, with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places. ​

Use the function to find . ​

Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by . Find and interpret your answer. Round your answer to two decimal places. ​

Evaluate the function to find . ​

If , find . ​

Give the domain of the function . ​

Give the domain of the function . ​

Evaluate the function at the given values of the independent variables. ​ ​

The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by . Find the future value of $42,000 invested for 30 years. ​

The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If , use the table to find . Round your answer to the nearest cent. ​

Give the domain of the function . ​

Suppose that the utility function for two goods X and Y is given by , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility? ​

Use the function to find . ​

If , find .

Evaluate the function at the given values of the independent variables. ; ,

Use the function to find .

Evaluate the function at the given values of the independent variables. , ,

Suppose that a gas satisfies the universal gas law, with n equal to 40 moles of the gas and R, the universal gas constant, equal to 0.082054. What is V if (kelvins, the units in which temperature is measured on the Kelvin scale) and atmosphere? Round your answer to four decimal places.

Use the function to find .

Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by . Find and interpret your answer. Round your answer to two decimal places.

Evaluate the function to find .

If , find .

Give the domain of the function .

Give the domain of the function .

Evaluate the function at the given values of the independent variables.

The future value S of an investment earning 7% compounded continuously is a function of the principal P and the length of time t that the principal been invested. It is given by . Find the future value of $42,000 invested for 30 years.

The following table shows the monthly mortgage payment R for a given interest rate 5% as a function of the amount financed A (in thousands of dollars) and the duration of the loan n in years. If , use the table to find . Round your answer to the nearest cent.

Give the domain of the function .

Suppose that the utility function for two goods X and Y is given by , and a consumer purchases 2 units of X and 6 units of Y. If the consumer purchases 2 units of Y, how many units of X must be purchased to retain the same level of utility?

Use the function to find .