Question

1. the village was polyglot. if the ratio of bilingual denizens to trilingual denizens was 14 to 3 and the denizens totaled 3400, how many were trilingual?
2. the scores on the test were 74, 89, 62, 74, 94, 97, 74, 78, 67, and 85. find the range, median, mode, and mean of the test scores.
3. use four unit multipliers to convert 10,000 feet to kilometers. (go from feet to inches to centimeters to meters to kilometers.)
4. the diameter of a circle is 22 in.

(a) find the circumference of the circle.
(b) find the area of the circle.

1. twenty - five percent of 200 is what number? work the problem and then draw a diagram of the problem.

Explanation:

Problem 1

Step1: Define variable for groups

Let the number of bilingual denizens be $14x$, trilingual be $3x$.

Step2: Set total population equation

$14x + 3x = 3400$

Step3: Solve for $x$

$17x = 3400 \implies x = \frac{3400}{17} = 200$

Step4: Calculate trilingual count

$3x = 3 \times 200 = 600$

Step1: Sort the test scores

Sorted scores: $62, 67, 71, 71, 74, 74, 78, 85, 89, 97$

Step2: Calculate range

Range = Max - Min = $97 - 62 = 15$

Step3: Find median

Middle values: 74, 74. Median = $\frac{74+74}{2} = 74$

Step4: Identify mode

Most frequent values: 71, 74

Step5: Calculate mean

Mean = $\frac{62+67+71+71+74+74+78+85+89+97}{10} = \frac{768}{10} = 76.8$

Step1: Feet to inches

$10000 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 120000 \text{ in}$

Step2: Inches to centimeters

$120000 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 304800 \text{ cm}$

Step3: Centimeters to meters

$304800 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 3048 \text{ m}$

Step4: Meters to kilometers

$3048 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 3.048 \text{ km}$

Answer:

600

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Problem 2