What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)
A: 40 feet
B: 4 feet
C: 14.4 feet
D: 8.9 feet
Correct Answer: D
Rationale: To find the length of the unknown leg of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (12 feet) is equal to the sum of the squares of the other two sides. Let x be the length of the unknown leg. So, 12^2 = 8^2 + x^2. Solving for x, we get x = √(12^2 - 8^2) = √(144 - 64) = √80 ≈ 8.9 feet. Therefore, the length of the unknown leg is approximately 8.9 feet.
Question 2:
Translate the phrase 'Five less than twice the number' into a mathematical expression.
A: 5x-2
B: 2x-5
C: 2-5x
D: 5-2x
Correct Answer: B
Rationale: The phrase 'Five less than twice the number' means 2 times a number minus 5. In mathematical terms, this translates to 2x-5. Therefore, choice B is the correct expression that represents 'Five less than twice the number.'
Question 3:
A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. Which of the following is the estimated gratuity?
A: $6.00
B: $5.00
C: $4.00
D: $7.00
Correct Answer: A
Rationale: To calculate the 15% gratuity on a $38.40 bill, you multiply the bill amount by 0.15 (15%). $38.40 x 0.15 = $5.76. Rounding up, the estimated gratuity would be $6.00, which is closest to the correct answer A.
Question 4:
Lana has $60. She spends 80% of the money. She then invests the remaining amount and earns a profit of 80%. How much does she have now?
A: $21.60
B: $9.60
C: $86.40
D: $60.00
Correct Answer: A
Rationale: If Lana spends 80% of $60, she spends $48. She is left with $12. When she invests this remaining amount, and earns an 80% profit on $12, it amounts to $21.60 ($12 + 80% of $12). Therefore, Lana now has $21.60.
Question 5:
Which of the following percentages is equivalent to the fraction 5/8?
A: 160%
B: 65.25%
C: 62.50%
D: 1.60%
Correct Answer: C
Rationale: To convert a fraction to a percentage, you divide the numerator by the denominator, then multiply by 100. In this case, 5/8 = 0.625 * 100 = 62.50%. Therefore, choice C, 62.50%, is the correct percentage equivalent to the fraction 5/8.
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