Question

set 45 1. the ratio of those who stayed awake to those who dozed was 5 to 18. if 125 stayed awake, how many dozed? 2. every discipline has key words that many neophytes find difficult to remember. three key words in statistics are median, mode, and mean. mnemonics are often helpful. we suggest the “median in the middle,” the “fashionable mode,” and the “mean old average.” find the range, median, mode, and mean of the following numbers: 5, 6, 9, 6, 12, 8, 7 3. use three unit multipliers to convert 80,500 centimeters to miles. 4. the area of a circle is 36 cm². (a) find the radius of the circle. (b) find the circumference of the circle. 5. draw a number line and graph the solution of x < 3. 6. draw a number line and graph the solution of x ≥ -2.

Explanation:

Problem 1

Step1: Set up ratio equation

Let $x$ = number who dozed.
$\frac{5}{18} = \frac{125}{x}$

Step2: Cross-multiply to solve for $x$

$5x = 125 \times 18$
$x = \frac{125 \times 18}{5}$
$x = 25 \times 18$

Step1: Sort the data set

Sorted numbers: $5, 6, 6, 7, 8, 9, 12$

Step2: Calculate range

Range = Max - Min
$12 - 5$

Step3: Find median (middle value)

7th term, 4th value = 7

Step4: Find mode (most frequent)

6 appears twice, others once

Step5: Calculate mean (average)

$\frac{5+6+6+7+8+9+12}{7} = \frac{53}{7}$

Step1: Convert cm to inches

Use $\frac{1\ \text{inch}}{2.54\ \text{cm}}$
$80500\ \text{cm} \times \frac{1\ \text{inch}}{2.54\ \text{cm}}$

Step2: Convert inches to feet

Use $\frac{1\ \text{foot}}{12\ \text{inches}}$
$\frac{80500}{2.54}\ \text{inches} \times \frac{1\ \text{foot}}{12\ \text{inches}}$

Step3: Convert feet to miles

Use $\frac{1\ \text{mile}}{5280\ \text{feet}}$
$\frac{80500}{2.54 \times 12}\ \text{feet} \times \frac{1\ \text{mile}}{5280\ \text{feet}}$

Step4: Compute final value

$\frac{80500}{2.54 \times 12 \times 5280} ≈ 0.5002$

Answer:

450

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Problem 2