The Celsius-to-Fahrenheit conversion formula is:

\(\displaystyle F = \frac{9}{5} C + 32\)

Substitute 45 for \(\displaystyle C\):

\(\displaystyle F = \frac{9}{5} \cdot 45+ 32 = 81 +32 = 113\)

The answer is \(\displaystyle 113 ^{\circ } \textrm{ F}\).

If \(\displaystyle F\) is the Fahrenheit temperature, then the equivalent Celsius temperature is 

\(\displaystyle C = \frac{5}{9} (F - 32)\).

Substitute \(\displaystyle F = 80\) into the equation.

\(\displaystyle C = \frac{5}{9} (80 - 32)\)

\(\displaystyle C = \frac{5}{9} \cdot 48 = \frac{5}{9} \cdot \frac{48}{1} = \frac{5}{3} \cdot \frac{16}{1} = \frac{80}{3} =26 \frac{2}{3}\)

This rounds up to \(\displaystyle 27 ^{\circ }C\).

1 inch = 2.54 centimeters, so 1 square inch = \(\displaystyle 2.54 ^{2} = 6.4516\) square centimeters.

100 square inches are equal to \(\displaystyle 6.4516 \times 100 = 645.16\) square centimeters, which rounds to 645.2 square centimeters.

We need to translate the words into a mathematical equation.  Since we need to solve for the distance the rock travels on the first bounce, let's use a variable to represent that distance.

Let "\(\displaystyle x\)" = distance traveled on the first bounce.

Notice that we can describe the distances traveled on the 2nd and 3rd bounces in terms of \(\displaystyle x\):

Distance traveled on the 2nd bounce is half the distance of the 1st bounce, so 2nd bounce = \(\displaystyle \frac{1}{2}x\)

Distance traveled on the 3rd bounce is 1/4 of the 2nd bounce, so, 3rd bounce = \(\displaystyle \frac{1}{4}*\frac{1}{2}x=\frac{1}{8}x\)

The total distance, then, is:

\(\displaystyle x+\frac{1}{2}x+\frac{1}{8}x=65\)

\(\displaystyle \frac{13}{8}x=65\)

\(\displaystyle x=65\bigg(\frac{8}{13}\bigg)\)

\(\displaystyle x=40\)

First, we set up the variables and the equations. Let:

\(\displaystyle A\)= Anna's age three years ago

\(\displaystyle J\) = Jeff's age three years ago. So:

\(\displaystyle A+3\) = Anna's age today

\(\displaystyle J+3\) = Jeff's age today

Therefore: \(\displaystyle A = 4J\) and \(\displaystyle (A+3) = 3 (J+3)\). Then we solve for the system of equations:

\(\displaystyle A - 4J = 0\)

\(\displaystyle (A+3) - 3 (J+3) = 0\) or \(\displaystyle A - 3J = 6\)

When we solve for J first we get \(\displaystyle J = 6\).

Then we solve for A using the first equation of the system:

\(\displaystyle A = 4J = 4 (6) = 24\)

Therefore Anna was 24 years old three years ago.

Since

\(\displaystyle 1 \text{ km}=3.9\times10^4 \text{ inches}\),

\(\displaystyle 1 \text{ inch}= \frac{1}{(3.9\times10^4)} \text{ km}\)

Therefore we multiply 1,170,000 by 1/(3.9*10⁴) to obtain the number of kilometers in 1,170,000 inches.

\(\displaystyle \frac{1170000}{3.9\times 10^{4}}=\frac{1170}{39}=30\)

One gallon of gasoline is about \(\displaystyle 3.8\) liters of gasoline. The number of liters in eighteen gallons is:

\(\displaystyle 18\times 3.8=68.4\)

One liter costs \(\displaystyle \$1.50\). Therefore, eighteen gallons (\(\displaystyle 68.4\) liters) will cost:

\(\displaystyle 68.4\times 1.50=68.4\times 1 +\frac{68.4}{2}=68.4+34.2=102.6=\$102.60\)

If an object travels at 10 feet per second, then in half an hour it will travel 10 feet for every second there is in 30 minutes. We can set this multiplication up as follows:

\(\displaystyle 10\frac{feet}{sec}\cdot60\frac{sec}{min}\cdot30\:min=18,000\:ft\)

Here we can see that the units of seconds are cancelled after the first operation, and the units of minutes are cancelled after the second operation, leaving us with the unit of feet for our answer.

One pound is equal to 16 ounces. 

Multiply: 

\(\displaystyle 3 \frac{1}{4} \times 16 = 52\)

52 ounces is the correct choice.

One yard is equal to 36 inches; one square yard is equal to \(\displaystyle 36^{2} = 1,296\).

Multiply this conversion factor by 13:

\(\displaystyle 13 \times 1,296 = 16,848\), the correct choice.