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Television screen sizes are measured by the diagonal length of the rectangular screen. Assuming proportionality, if a vehicle on a 32-inch screen appears 9 inches long, how long will it appear on a 50-inch screen? (Round to the nearest inch.)
- A. 27 in
- B. 18 in
- C. 15 in
- D. 11 in
Correct Answer: C
Rationale: Using the proportion: 9 in / 32 in = x in / 50 in. Cross multiplying gives 32*x = 9*50. Solving for x gives x = 14.06 in, rounding to 14 in. Therefore, the vehicle will appear approximately 15 inches long on a 50-inch screen.
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After spending 80% of her $60, Lana is left with how much money when she invests the remaining amount and earns an 80% profit?
- A. $21.60
- B. $9.60
- C. $86.40
- D. $60.00
Correct Answer: A
Rationale: After spending 80% of $60, Lana spends $48, leaving her with $12. When she invests this remaining amount and earns an 80% profit on $12, it amounts to $21.60 ($12 + 80% of $12 = $12 + $9.60 = $21.60). Therefore, Lana now has $21.60 in total.
If a box of 35 syringes costs $560.00, what is the cost for two syringes?
- A. $8.00
- B. $16.00
- C. $15.00
- D. $32.00
Correct Answer: D
Rationale: To determine the cost for two syringes, you first need to calculate the cost per syringe by dividing the total cost of the box by the total number of syringes in the box: $560.00 · 35 syringes = $16.00 per syringe. Therefore, each syringe costs $16.00. To find the cost of two syringes, you multiply the cost per syringe by 2: $16.00 x 2 = $32.00. Hence, the correct answer is option D, which is $32.00 for two syringes.
What is the median of the following set of data: 5, -3, 10, -2, 0?
- A. 10
- B. 5
- C. -2
Correct Answer: D
Rationale: To find the median, we first need to arrange the data in ascending order: -3, -2, 0, 5, 10. Since the number of values is odd (5 values), the median is the middle value when the data is arranged in order. In this case, the middle value is 0. Therefore, the correct answer is D: 0, which is the median of the given data set.
What is the mean of the test scores listed below? 100, 78, 47, 84, 93, 78
- A. 80
- B. 78
- C. 81
- D. 96
Correct Answer: A
Rationale: To find the mean of a set of numbers, you need to sum all the numbers together and then divide by the total count of numbers. In this case, the sum of the test scores is 100 + 78 + 47 + 84 + 93 + 78 = 480. Since there are 6 test scores in total, you divide the sum by 6 to get the mean. Therefore, the mean = 480 · 6 = 80. Hence, the correct answer is A, which is 80. It represents the average test score among the provided values.
Which of the following expressions represents the sum of three times a number and eight times another number?
- A. 3x + 8x
- B. 3x + 8y
- C. 8x - 3y
- D. 3x - 8y
Correct Answer: B
Rationale: To find the sum of three times a number and eight times another number, you need to multiply each number by its respective factor. Three times a number is represented by 3x, and eight times another number is represented by 8y. When adding these two terms together, the correct expression is 3x + 8y. Therefore, choice B is the correct answer as it accurately represents the sum of three times a number and eight times another number.