Question 1

Solve the problem.
-The formula $C = \frac { 5 } { 9 } ( F - 32 )$ expresses the relationship between Fahrenheit temperature, $F$, and Celsius temperature, C. Use the formula to convert $86 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

Accepted Answer

To convert $86 ^ { \circ } \mathrm { F }$ to Celsius, substitute $F = 86$ into the formula $C = \frac { 5 } { 9 } ( F - 32 )$. This gives $C = \frac { 5 } { 9 } ( 86 - 32 ) = \frac { 5 } { 9 } \times 54 = 30$, so $86 ^ { \circ } \mathrm { F }$ is equivalent to $30 ^ { \circ } \mathrm { C }$.

Question 2

Solve the problem.
-During a certain football game, a player gained 94 yards rushing and -2 yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories?
Why or why not?

Accepted Answer

The total yardage is calculated by adding the yards gained rushing (94 yards) and the yards lost returning fumbles (-2 yards), which equals 92 yards. However, the sum of the absolute values is 94 + 2 = 96 yards, which is not the same as the total yardage.

Question 3

Simplify the expression. Assume all variables represent nonzero real numbers.
-$4 ^ { 8 } \cdot 4 ^ { 6 }$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $4^8 \cdot 4^6 = 4^{8+6} = 4^{14}$.

Question 4

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$- \frac { x } { y } > 0$$

Accepted Answer

For the fraction $- \frac{x}{y}$ to be greater than 0, the fraction $\frac{x}{y}$ must be negative, which occurs when x and y have different signs.

Question 5

Solve the problem.
-The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the expression
number of $\mathrm { oz } \times \%$ alcohol $\times .075 \div$ body weight in $\mathrm { lb }$ - hours of drinking $\times .015$.
Find the BAC to the nearest thousandth for a $170 - \mathrm { lb }$ woman, who, in 5 hours, has drunk $410 - \mathrm { oz }$ beers ( $40 \mathrm { oz } )$, each having a $3.2 \%$ alcohol content.

Accepted Answer

The correct BAC is calculated by substituting the given values into the formula: $BAC = \frac{410 \times 3.2\% \times 0.075}{170} - 5 \times 0.015$. This simplifies to $BAC = \frac{410 \times 0.032 \times 0.075}{170} - 0.075$, which when calculated gives a BAC close to $-0.019$, rounding to the nearest thousandth.

Question 6

Solve the problem.
-The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss).

The absolute value of the profit or loss was smallest in

Accepted Answer

The answer of Solve the problem.
-The NSC Corporation has just...

Question 7

Solve the problem.
-A stone is dropped from a tower that is 730 feet high. The formula $h = 730 - 16 t ^ { 2 }$ describes the stone's height above the ground, $h$, in feet, $t$ seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Accepted Answer

The answer of Solve the problem.
-A stone is dropped from...

Question 8

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 3 } } { y } > 0$$

Accepted Answer

Since $x^3$ preserves the sign of $x$ (a negative number cubed is negative, and a positive number cubed is positive), for the fraction to be greater than 0, $y$ must have the same sign as $x^3$ (and thus the same sign as $x$). This means $x$ and $y$ must either both be positive or both be negative.

Question 9

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$x ^ { 2 } y < 0$$

Accepted Answer

The answer of Determine what signs on values of x...

Question 10

Solve the problem.
-The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss).

The loss was greatest in

Accepted Answer

The answer of Solve the problem.
-The NSC (Not So Consistent)...

Question 11

Solve the problem.
-It is recommended that a woman who is pregnant should exercise such that her heart rate does not exceed 140 beats per minute. Use absolute value notation to write an expression that describes the
Difference between the heart rate achieved by each of the following pregnant women and the
Recommended maximum heart rate. Then evaluate that expression. (i) Abigail: 122 beats per minute
(ii) Mathilda: 144 beats per minute

Accepted Answer

Absolute value notation is used to express the magnitude of the difference between two numbers, regardless of their order, and always yields a non-negative result. For Abigail, $| 122 - 140 | = 18$ and for Mathilda, $| 144 - 140 | = 4$, indicating the difference in heart rates from the recommended maximum.

Question 12

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 2 a ^ { 7 } \right) \cdot \left( 5 a ^ { 2 } \right)$

Accepted Answer

When multiplying two powers that have the same base, you add the exponents. Thus, $2a^7 \cdot 5a^2 = 10a^{7+2} = 10a^9$.

Question 13

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x } { y } > 0$$

Accepted Answer

For the fraction $\frac{x}{y}$ to be greater than 0, x and y must either both be positive or both be negative, meaning they have the same sign.

Question 14

Solve the problem.
-As the relative humidity increases, the temperature seems higher than it is. The formula $\mathrm { T } = 0.113 \mathrm { x }$ + $82.57$ approximates the apparent temperature for an actual temperature of $90 ^ { \circ } \mathrm { F }$, where $\mathrm { x }$ is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of $50 \%$ ?

Accepted Answer

To find the apparent temperature, substitute $x = 50$ into the formula: $T = 0.113 \times 50 + 82.57 = 5.65 + 82.57 = 88.22$. Rounded to the nearest degree, the apparent temperature is $88 ^{\circ} F$.

Question 15

Solve the problem.
-Find the magnitude of the difference between a windchill factor of -43 and a windchill factor of -13.

Accepted Answer

The magnitude of the difference between two numbers is the absolute value of their difference, which is |-43 - (-13)| = |-43 + 13| = |-30| = 30.

Question 16

Solve the problem.
-Use the formula
Passing Rating $= 85.68 \left( \frac { \mathrm { C } } { \mathrm { A } } \right) + 4.31 \left( \frac { \mathrm { Y } } { \mathrm { A } } \right) + 326.42 \left( \frac { \mathrm { T } } { \mathrm { A } } \right) - 419.0 \% \left( \frac { \mathrm { I } } { \mathrm { A } } \right)$, where $\mathrm { A } =$ number of passes attempted, $\mathrm { C } =$ number of passes completed, $\mathrm { Y } =$ total number of yards gained passing, $\mathrm { T } =$ number of touchdown passes, and $\mathrm { I }$ = number of interceptions, to approximate the passing rating for $\mathrm { C }$. Felix. Round to the nearest tenth.

Accepted Answer

The answer of Solve the problem.
-Use the formula
Passing Rating \(=...

Question 17

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 4 n ^ { 2 } \right) \cdot \left( 6 n ^ { 7 } \right)$

Accepted Answer

When multiplying powers with the same base, you add the exponents. Thus, $4n^2 \cdot 6n^7 = 24n^{2+7} = 24n^9$.

Question 18

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 2 } } { y } < 0$$

Accepted Answer

The answer of Determine what signs on values of x...

Question 19

Solve the problem.
-If a rock falls from a height of 100 meters above the ground, the height $\mathrm { H }$ (in meters) after $\mathrm { x }$ seconds can be approximated using the formula $\mathrm { H } = 100 - 4.9 \mathrm { x } ^ { 2 }$. What is the height of the rock after 2 seconds?

Accepted Answer

To find the height of the rock after 2 seconds, substitute $x = 2$ into the formula: $H = 100 - 4.9(2)^2 = 100 - 4.9(4) = 100 - 19.6 = 80.4$ meters.

Question 20

Solve the problem.
-Find the magnitude of the difference between a windchill factor of 88 and a windchill factor of -77.

Accepted Answer

The magnitude of the difference between two numbers is the absolute value of their difference. Here, |88 - (-77)| = |88 + 77| = 165.

Quiz 12: Review of Basic Concepts

Solve the problem. -The formula $C = \frac { 5 } { 9 } ( F - 32 )$ expresses the relationship between Fahrenheit temperature, $F$ , and Celsius temperature, C. Use the formula to convert $86 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

Solve the problem. -During a certain football game, a player gained 94 yards rushing and -2 yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories? Why or why not?

Simplify the expression. Assume all variables represent nonzero real numbers. - $4 ^ { 8 } \cdot 4 ^ { 6 }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $- \frac { x } { y } > 0$

Solve the problem. -The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss) . The absolute value of the profit or loss was smallest in

Solve the problem. -A stone is dropped from a tower that is 730 feet high. The formula $h = 730 - 16 t ^ { 2 }$ describes the stone's height above the ground, $h$ , in feet, $t$ seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 3 } } { y } > 0$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x ^ { 2 } y < 0$

Solve the problem. -The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss) . The loss was greatest in

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 2 a ^ { 7 } \right) \cdot \left( 5 a ^ { 2 } \right)$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x } { y } > 0$

Solve the problem. -Find the magnitude of the difference between a windchill factor of -43 and a windchill factor of -13.

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 4 n ^ { 2 } \right) \cdot \left( 6 n ^ { 7 } \right)$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 2 } } { y } < 0$

Solve the problem. -If a rock falls from a height of 100 meters above the ground, the height $\mathrm { H }$ (in meters) after $\mathrm { x }$ seconds can be approximated using the formula $\mathrm { H } = 100 - 4.9 \mathrm { x } ^ { 2 }$ . What is the height of the rock after 2 seconds?

Solve the problem. -Find the magnitude of the difference between a windchill factor of 88 and a windchill factor of -77.

Quiz 12: Review of Basic Concepts

Solve the problem. -During a certain football game, a player gained 94 yards rushing and -2 yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories? Why or why not?

Simplify the expression. Assume all variables represent nonzero real numbers. - 48⋅464 ^ { 8 } \cdot 4 ^ { 6 }48⋅46

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - −xy>0- \frac { x } { y } > 0−yx​>0

Solve the problem. -The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss) . The absolute value of the profit or loss was smallest in

Solve the problem. -A stone is dropped from a tower that is 730 feet high. The formula h=730−16t2h = 730 - 16 t ^ { 2 }h=730−16t2 describes the stone's height above the ground, hhh , in feet, ttt seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x3y>0\frac { x ^ { 3 } } { y } > 0yx3​>0

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x2y<0x ^ { 2 } y < 0x2y<0