Question

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Explanation:

Problem 1

Step1: Define the unknown number

Let the number be $x$.

Step2: Translate to equation

$2x + (-7) + 8 = -x + 16$

Step3: Simplify left side

$2x + 1 = -x + 16$

Step4: Isolate $x$ terms

$2x + x = 16 - 1$

Step5: Solve for $x$

$3x = 15$
$x = \frac{15}{3} = 5$

Step1: Sort the test scores

Sorted scores: $64, 72, 78, 83, 89, 92, 94, 94, 98$

Step2: Calculate range

Range = Max - Min
$98 - 64 = 34$

Step3: Find median (middle value)

9 values, 5th value: $89$

Step4: Find mode (most frequent)

$94$ (appears twice)

Step5: Calculate mean

Mean = $\frac{\text{Sum of scores}}{\text{Number of scores}}$
$\frac{64+72+78+83+89+92+94+94+98}{9} = \frac{764}{9} \approx 84.89$

Step1: List unit conversion factors

1 foot = 12 inches, 1 mile = 5280 feet
Unit multipliers: $\frac{1\ \text{ft}}{12\ \text{in}}$, $\frac{1\ \text{ft}}{12\ \text{in}}$, $\frac{1\ \text{mi}}{5280\ \text{ft}}$, $\frac{1\ \text{mi}}{5280\ \text{ft}}$

Step2: Set up conversion

$42000\ \text{in}^2 \times \frac{1\ \text{ft}}{12\ \text{in}} \times \frac{1\ \text{ft}}{12\ \text{in}} \times \frac{1\ \text{mi}}{5280\ \text{ft}} \times \frac{1\ \text{mi}}{5280\ \text{ft}}$

Step3: Calculate denominator

$12^2 \times 5280^2 = 144 \times 27878400 = 4014489600$

Step4: Compute final value

$\frac{42000}{4014489600} \approx 1.046 \times 10^{-5}$

Answer:

$5$

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Problem 2