A scientist uses the expression 5/9(F - 32) to convert temperatures from degrees Fahrenheit (°F), F, to degrees Celsius (°C). To the nearest degree, what is the temperature, in °F, of a substance at -25°C?
- A. 13
- B. -32
- C. -13
- D. 18
Correct Answer & Rationale
Correct Answer: C
To find the Fahrenheit equivalent of -25°C, use the formula \( F = \frac{9}{5}C + 32 \). Substituting -25 for C gives \( F = \frac{9}{5}(-25) + 32 = -45 + 32 = -13 \). Thus, the temperature in Fahrenheit is -13°F. Option A (13°F) is incorrect as it does not reflect the negative temperature conversion. Option B (-32°F) is too low and does not correspond to the calculated value. Option D (18°F) is also incorrect as it is significantly higher than the expected result for -25°C.
To find the Fahrenheit equivalent of -25°C, use the formula \( F = \frac{9}{5}C + 32 \). Substituting -25 for C gives \( F = \frac{9}{5}(-25) + 32 = -45 + 32 = -13 \). Thus, the temperature in Fahrenheit is -13°F. Option A (13°F) is incorrect as it does not reflect the negative temperature conversion. Option B (-32°F) is too low and does not correspond to the calculated value. Option D (18°F) is also incorrect as it is significantly higher than the expected result for -25°C.
Other Related Questions
Which expression is equivalent to (3a + 4ab - 7b) - (a + 2ab - 4b)?
- A. 2a + 2ab - 11b
- B. 2a + 6ab - 11b
- C. 2a + 2ab - 3b
- D. 2a + 6ab - 35
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \((3a + 4ab - 7b) - (a + 2ab - 4b)\), start by distributing the negative sign across the second set of parentheses: \[ 3a + 4ab - 7b - a - 2ab + 4b \] Next, combine like terms: - For \(a\): \(3a - a = 2a\) - For \(ab\): \(4ab - 2ab = 2ab\) - For \(b\): \(-7b + 4b = -3b\) This results in the expression \(2a + 2ab - 3b\), matching option C. Option A introduces an incorrect coefficient for \(b\), while option B miscalculates the \(ab\) term. Option D incorrectly combines terms, leading to an erroneous constant. Thus, option C is the only accurate simplification.
To simplify the expression \((3a + 4ab - 7b) - (a + 2ab - 4b)\), start by distributing the negative sign across the second set of parentheses: \[ 3a + 4ab - 7b - a - 2ab + 4b \] Next, combine like terms: - For \(a\): \(3a - a = 2a\) - For \(ab\): \(4ab - 2ab = 2ab\) - For \(b\): \(-7b + 4b = -3b\) This results in the expression \(2a + 2ab - 3b\), matching option C. Option A introduces an incorrect coefficient for \(b\), while option B miscalculates the \(ab\) term. Option D incorrectly combines terms, leading to an erroneous constant. Thus, option C is the only accurate simplification.
John and Mike are participating in a long-distance bicycling event. Mike bicycled 24 miles in the first 2 hours. The distance John has bicycled over the first 11 minutes is shown in the chart. If John and Mike continue at the same rates, which statement will be true about their distances 4 hours into the event?
- A. John will be 6 miles ahead of Mike.
- B. John will be 12 miles ahead of Mike.
- C. Mike will be 6 miles ahead of John.
- D. Mike will be 12 miles ahead of John.
Correct Answer & Rationale
Correct Answer: D
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles ÷ 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles ÷ 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.
What is the area, in square inches, of a circle with diameter 2 inches?
- A. 6.28
- B. 3.14
- C. 1
- D. 12.56
Correct Answer & Rationale
Correct Answer: B
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. Given a diameter of 2 inches, the radius is 1 inch. Substituting this into the formula yields \( A = \pi (1)^2 = \pi \), which approximates to 3.14. Option A (6.28) incorrectly doubles the area, possibly confusing it with the circumference. Option C (1) neglects the use of \(\pi\), leading to an inaccurate calculation. Option D (12.56) mistakenly uses the formula for circumference, multiplying the diameter by \(\pi\) instead of squaring the radius. Thus, 3.14 accurately represents the area of the circle.
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. Given a diameter of 2 inches, the radius is 1 inch. Substituting this into the formula yields \( A = \pi (1)^2 = \pi \), which approximates to 3.14. Option A (6.28) incorrectly doubles the area, possibly confusing it with the circumference. Option C (1) neglects the use of \(\pi\), leading to an inaccurate calculation. Option D (12.56) mistakenly uses the formula for circumference, multiplying the diameter by \(\pi\) instead of squaring the radius. Thus, 3.14 accurately represents the area of the circle.
2^3 * 27^(1/3) * 1^3
- A. 54
- B. 24
- C. 72
- D. 18
Correct Answer & Rationale
Correct Answer: B
To solve the expression \(2^3 \times 27^{(1/3)} \times 1^3\), we first simplify each component. Calculating \(2^3\) gives \(8\). Next, \(27^{(1/3)}\) equals \(3\) since the cube root of \(27\) is \(3\). Finally, \(1^3\) remains \(1\). Now, multiplying these values together: \(8 \times 3 \times 1 = 24\). Option A (54) results from incorrect multiplication. Option C (72) miscalculates the values, and Option D (18) stems from misunderstanding the cube root. Thus, \(24\) is the correct outcome.
To solve the expression \(2^3 \times 27^{(1/3)} \times 1^3\), we first simplify each component. Calculating \(2^3\) gives \(8\). Next, \(27^{(1/3)}\) equals \(3\) since the cube root of \(27\) is \(3\). Finally, \(1^3\) remains \(1\). Now, multiplying these values together: \(8 \times 3 \times 1 = 24\). Option A (54) results from incorrect multiplication. Option C (72) miscalculates the values, and Option D (18) stems from misunderstanding the cube root. Thus, \(24\) is the correct outcome.