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
The equation d/f = g represents gallons of gasoline used, g, in terms of distance traveled in miles, d, and fuel efficiency, / miles per gallon of gasoline. Which combination of distance traveled and fuel efficiency uses 3 gallons of gasoline?
- A. 7 miles and 21 miles per gallon
- B. 57 miles and 19 miles per gallon
- C. 23 miles and 20 miles per gallon
- D. 32 miles and 35 miles per gallon
Correct Answer & Rationale
Correct Answer: B
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
How many more tickets did Larry buy than Jim?
- A. 3
- B. 12
- C. 6
- D. 1
Correct Answer & Rationale
Correct Answer: C
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
Which list shows the numbers arranged from least to greatest?
- A. -(2/9), -0.21, -0.2, -(2/11), -1
- B. -1, -(2/9), -0.21, -0.2, -(2/11)
- C. -1, -(2/11), -0.21, -0.2, -(2/9)
- D. -(2/11), -0.2, -0.21, -(2/9), -1
Correct Answer & Rationale
Correct Answer: C
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.