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.
Other Related Questions
Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.
- A. (b-d)/(a-c)
- B. (d-b)/(c-a)
- C. (b-d)/(c-a)
- D. (d-b)/(a-c)
Correct Answer & Rationale
Correct Answer: B
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.
The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
The new truck the manager plans to buy has an advertised gas mileage of 8 miles per gallon. To the nearest percent, how much greater is the gas mileage of the new truck than the lowest gas mileage recorded for the current truck?
- A. 14
- B. 25
- C. 23
- D. 33
Correct Answer & Rationale
Correct Answer: D
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
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.
((5^3 * 2^4)^2)(5^(-2) * 2^5)
- A. 5^3 * 2^11
- B. 5^(-12) * 2^40
- C. 5^4 * 2^13
- D. (-5)^8 * 2^13
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \(((5^3 * 2^4)^2)(5^{-2} * 2^5)\), first apply the power of a product rule. This gives \(5^{6} * 2^{8}\) from the first part. Next, combine this with the second part, \(5^{-2} * 2^{5}\). Adding the exponents for the base 5: \(6 + (-2) = 4\). For base 2: \(8 + 5 = 13\). Thus, the final expression simplifies to \(5^4 * 2^{13}\). Option A is incorrect as it miscalculates the exponents. Option B has incorrect exponents and signs. Option D introduces an unnecessary negative sign and does not match the simplified expression.
To simplify the expression \(((5^3 * 2^4)^2)(5^{-2} * 2^5)\), first apply the power of a product rule. This gives \(5^{6} * 2^{8}\) from the first part. Next, combine this with the second part, \(5^{-2} * 2^{5}\). Adding the exponents for the base 5: \(6 + (-2) = 4\). For base 2: \(8 + 5 = 13\). Thus, the final expression simplifies to \(5^4 * 2^{13}\). Option A is incorrect as it miscalculates the exponents. Option B has incorrect exponents and signs. Option D introduces an unnecessary negative sign and does not match the simplified expression.