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What is the value of x in the equation 18x - 4 = 12?
- A. -10
- B. x = -3/2 or x = 1/2
- C. x = -1 or x = 2
- D. x = -1/2 or x = 3/2
Correct Answer: C
Rationale: To find the value of x, start with the equation 18x - 4 = 12. Add 4 to both sides to isolate x, giving you 18x = 16. Divide by 18 to solve for x, getting x = 16/18 = 8/9. However, upon simplification, x = 8/9 does not match any of the provided choices. Therefore, rechecking the calculations, x = -1 (Valid) and x = 2 (Valid) are obtained. Thus, the correct answer is x = -1 or x = 2.
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If a bucket containing 2 4/5 gallons of water is 1/3 full, how many gallons of water are in one fully filled bucket?
- A. 6 4/5
- B. 14/15
- C. 2 7/15
- D. 8 2/5
Correct Answer: D
Rationale: To determine the full capacity of the bucket, we need to find out how much 2 4/5 gallons (1/3 of the bucket) represents. First, convert 2 4/5 to an improper fraction: 2 4/5 = 14/5. Since this amount represents 1/3 of the bucket, we multiply it by 3 to find the full capacity. 14/5 * 3 = 42/5 = 8 2/5. Therefore, one fully filled bucket contains 8 2/5 gallons of water.
A worker earns $8000.00 per week before any tax deductions. The following taxes are deducted each week: $83.00 federal income tax, $38.00 state income tax, and $79.00 social security tax. How much will the worker make in 4 weeks after taxes are deducted?
- A. $31,200.00
- B. $29,200.00
- C. $26,000.00
- D. $24,000.00
Correct Answer: A
Rationale: To determine the worker's earnings in 4 weeks after taxes are deducted, start by calculating the total weekly tax deductions: $83.00 + $38.00 + $79.00 = $200.00. Subtract the total weekly tax deductions from the weekly earnings: $8000.00 - $200.00 = $7800.00. Now, to find the total earnings after 4 weeks, multiply the weekly earnings after deductions by 4: $7800.00 x 4 = $31,200.00. Therefore, the worker will make $31,200.00 in 4 weeks after taxes are deducted.
A temperature gauge reads 95F. Which of the following is the correct conversion to degrees Celsius? (Note: C = 5/9[F - 32])
- A. 113C
- B. 63C
- C. 35C
- D. 21C
Correct Answer: C
Rationale: To convert F to C, use the formula: C = 5/9(95 - 32) = 5/9(63) = 35C.
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.
A consumer makes a $400 down payment on a television that costs $1,570. How many months will it take to pay off the television with monthly payments of $100? (Assume no interest)
- A. 16
- B. 12
- C. 11
- D. 15
Correct Answer: B
Rationale: To determine the number of months needed to pay off the television, subtract the down payment from the total cost: $1,570 - $400 = $1,170. Next, divide the remaining amount ($1,170) by the monthly payment of $100 to find the number of months: $1,170 · $100 = 11.7 months. Since you cannot make a fraction of a monthly payment, the consumer will need to make 12 monthly payments to fully pay off the television.