Question 1

Solve the problem.
-The temperature of water in a certain lake on a day in October can be determined by using the model y = 15.2 - 0.537x where x is the number of feet down from the surface of the lake and y is the Celsius
Temperature of the water at that depth. Based on this model, how deep in the lake is the water 8 degrees?
(Round to the nearest foot.)

Accepted Answer

The answer of Solve the problem.
-The temperature of water in...

Question 2

Solve the formula for the specified variable.
- for n

Accepted Answer

The answer of Solve the formula for the specified variable.
-...

Question 3

Solve the equation.
-

Accepted Answer

The answer of Solve the equation.
-
...

Question 4

Solve the equation.
-

Accepted Answer

The answer of Solve the equation.
-
...

Question 5

Solve the problem.
-Median family income in Country X between 1990 and 1999 can be modeled by f(x) = 1174.6(x - 1990) + 35,265, where x is the year. Determine symbolically when the median income was $42,092.

Accepted Answer

The answer of Solve the problem.
-Median family income in Country...

Question 6

Solve the problem.
-A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many
Minutes would it take for the cost of repair to reach $120? (Round to the nearest minute.)

Accepted Answer

The answer of Solve the problem.
-A repair company's charge for...

Question 7

Solve the formula for the specified variable.
-F =  C + 32 for C

Accepted Answer

The answer of Solve the formula for the specified variable.
-F...

Question 8

Solve the formula for the specified variable.
-V =  Bh for B

Accepted Answer

The answer of Solve the formula for the specified variable.
-V...

Question 9

Solve the problem.
-In the following formula, y is the minimum number of hours of studying required to attain a test score of x: y =  . How many hours of study are needed to score 87? Round to the nearest hundredth of an hour.

Accepted Answer

The answer of Solve the problem.
-In the following formula, y...

Question 10

Solve the problem.
-The temperature, t, in degrees Fahrenheit, of water being heated is  where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Accepted Answer

The answer of Solve the problem.
-The temperature, t, in degrees...

Question 11

Solve the problem.
-Mark has $75 to spend on salmon at $5.00 per pound and/or chicken at $3.00 per pound. If he buys s pounds of salmon and c pounds of chicken, the equation 5s + 3c = 75 must be satisfied. How much salmon did Mark buy if
He bought 5 pounds of chicken?

Accepted Answer

Substituting c = 5 into the equation 5s + 3c = 75 gives 5s + 3(5) = 75. Simplifying, 5s + 15 = 75. Subtracting 15 from both sides gives 5s = 60. Dividing both sides by 5 gives s = 12.

Question 12

Solve the formula for the specified variable.
-A =  bh for b

Accepted Answer

The answer of Solve the formula for the specified variable.
-A...

Question 13

Solve the formula for the specified variable.
-S =  for h

Accepted Answer

The answer of Solve the formula for the specified variable.
-S...

Question 14

Solve the formula for the specified variable.
-P = s

Accepted Answer

The answer of Solve the formula for the specified variable.
-P...

Question 15

Solve the problem.
-When going more than 38 miles per hour, the gas mileage of a certain car fits the model y = 43.81 - 0.395x where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what
Speed will the car average 15 miles per gallon? (Round to nearest whole number.)

Accepted Answer

To find the speed at which the car averages 15 miles per gallon, we set y = 15 in the equation and solve for x: 15 = 43.81 - 0.395x. Rearranging the equation gives 0.395x = 43.81 - 15, which simplifies to 0.395x = 28.81. Dividing both sides by 0.395 gives x ≈ 72.94, which rounds to the nearest whole number as 73 mph.

Question 16

Solve the equation.
-

Accepted Answer

The answer of Solve the equation.
-
...

Question 17

Solve the problem.
-Yearly sales at a certain department store follow the model y = 85 - 13.254x where y is the total sales in thousands of dollars and x is the number of years after 1992. In what year will the sales first be less than
$35,000?

Accepted Answer

To find the year when sales first drop below $35,000, we need to solve for x in the equation $y = 85 - 13.254x < 35$. Converting $35,000 to thousands gives us 35. So, we solve $85 - 13.254x < 35$. Subtracting 85 from both sides gives $-13.254x < -50$. Dividing by -13.254 (and remembering to flip the inequality because we're dividing by a negative number) gives $x > 3.77$. Since x represents years after 1992, and we're looking for the first year sales drop below $35,000, we take the next whole number after 3.77, which is 4. Adding this to 1992 gives 1996. However, since we're looking for the first year it drops below $35,000, and the calculation shows it happens sometime during the fourth year after 1992, the first full year it would be below $35,000 is 1996.

Question 18

Solve the equation.
-

Accepted Answer

The answer of Solve the equation.
-
...

Question 19

Solve the equation.
-

Accepted Answer

The answer of Solve the equation.
-
...

Question 20

Solve the problem.
-Suppose a cost-benefit model is given by  , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 40% to the nearest dollar.

Accepted Answer

The answer of Solve the problem.
-Suppose a cost-benefit model is...

Quiz 1: Equations, Inequalities, and Modeling

Solve the formula for the specified variable. - for n

Solve the equation. -

Solve the equation. -

Solve the problem. -Median family income in Country X between 1990 and 1999 can be modeled by f(x) = 1174.6(x - 1990) + 35,265, where x is the year. Determine symbolically when the median income was $42,092.

Solve the formula for the specified variable. -F = C + 32 for C

Solve the formula for the specified variable. -V = Bh for B

Solve the problem. -In the following formula, y is the minimum number of hours of studying required to attain a test score of x: y = . How many hours of study are needed to score 87? Round to the nearest hundredth of an hour.

Solve the problem. -The temperature, t, in degrees Fahrenheit, of water being heated is where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Solve the problem. -Mark has $75 to spend on salmon at $5.00 per pound and/or chicken at $3.00 per pound. If he buys s pounds of salmon and c pounds of chicken, the equation 5s + 3c = 75 must be satisfied. How much salmon did Mark buy if He bought 5 pounds of chicken?

Solve the formula for the specified variable. -A = bh for b

Solve the formula for the specified variable. -S = for h

Solve the formula for the specified variable. -P = s

Solve the equation. -

Solve the problem. -Yearly sales at a certain department store follow the model y = 85 - 13.254x where y is the total sales in thousands of dollars and x is the number of years after 1992. In what year will the sales first be less than $35,000?

Solve the equation. -

Solve the equation. -

Solve the problem. -Suppose a cost-benefit model is given by , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 40% to the nearest dollar.