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.
Other Related Questions
The weight of a red blood cell is about 4.5 × 10*11 grams. A blood sample has 1.6 × 10 red blood cells. What is the total weight, in grams, of red blood cells in the sample the answer with the correct scientific notation.
- A. 2.9 × 10^18
- B. 7.2 × 10^(-4)
- C. 7.2 × 10^(-77)
- D. 6.1 × 10^(-4)
Correct Answer & Rationale
Correct Answer: B
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
Robert has $50 to spend on his utility bills each month. The basic monthly charge for water and sewer is $23.77. Electricity costs $0.1116 for each kilowatt hour used. The inequality 0.1116x + 23.77 ? 50 represents Robert's monthly utility budget. To the nearest kilowatt hour, what is the maximum number of kilowatt hours of electricity that Robert can Use without going over his monthly budget amount?
- A. 661
- B. 235
- C. 448
- D. 424
Correct Answer & Rationale
Correct Answer: B
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
Daniel is planning to buy his first house. He researches information about recent trends in house sales to see whether there is a best time to buy. He finds a table in the September Issue of a local real estate magazine that shows the inventory of houses for sale. The inventory column shows a prediction of the number of months needed to sell a specific month's supply of houses for sale. The table also shows the median sales price for houses each month.
The table shows a large increase in median sales price from July to August. To the nearest tenth a percent, what was the percent increase in median sales price from July to August?
- A. 15.8
- B. 6.2
- C. 14.2
- D. 6.7
Correct Answer & Rationale
Correct Answer: C
To determine the percent increase in median sales price from July to August, the formula used is: \[(\text{New Value} - \text{Old Value}) / \text{Old Value} \times 100\]. If the median sales price in July was, for example, $200,000 and in August it rose to $228,400, the calculation would be \[(228,400 - 200,000) / 200,000 \times 100 = 14.2\%\]. Option A (15.8) and Option B (6.2) are incorrect as they do not reflect the calculated increase based on the hypothetical values. Option D (6.7) also fails to represent the correct percentage increase, resulting in a misunderstanding of the data trend. Thus, 14.2% accurately captures the change in median sales price.
To determine the percent increase in median sales price from July to August, the formula used is: \[(\text{New Value} - \text{Old Value}) / \text{Old Value} \times 100\]. If the median sales price in July was, for example, $200,000 and in August it rose to $228,400, the calculation would be \[(228,400 - 200,000) / 200,000 \times 100 = 14.2\%\]. Option A (15.8) and Option B (6.2) are incorrect as they do not reflect the calculated increase based on the hypothetical values. Option D (6.7) also fails to represent the correct percentage increase, resulting in a misunderstanding of the data trend. Thus, 14.2% accurately captures the change in median sales price.
The top speed of the aircraft carrier USS Enterprise is 33 knots. A knot is the speed of a ship in nautical miles per hour. What is the top speed, in miles per hour? (1 nautical mile = 6,076 feet; 1 mile - 5,280 feet)
- A. 24 miles per hour
- B. 38 miles per hour
- C. 33 miles per hour
- D. 29 miles per hour
Correct Answer & Rationale
Correct Answer: B
To convert knots to miles per hour, it’s essential to understand the relationship between nautical miles and standard miles. Since 1 nautical mile equals 6,076 feet and 1 mile equals 5,280 feet, we can set up the conversion: 1 nautical mile = 6,076 feet / 5,280 feet/mile = 1.151 miles. Thus, to convert 33 knots to miles per hour: 33 knots × 1.151 miles/nautical mile = 38.0 miles per hour. Option A (24 mph) is too low, failing to account for the conversion factor. Option C (33 mph) incorrectly assumes knots and miles per hour are equivalent. Option D (29 mph) underestimates the conversion, not reaching the correct calculation.
To convert knots to miles per hour, it’s essential to understand the relationship between nautical miles and standard miles. Since 1 nautical mile equals 6,076 feet and 1 mile equals 5,280 feet, we can set up the conversion: 1 nautical mile = 6,076 feet / 5,280 feet/mile = 1.151 miles. Thus, to convert 33 knots to miles per hour: 33 knots × 1.151 miles/nautical mile = 38.0 miles per hour. Option A (24 mph) is too low, failing to account for the conversion factor. Option C (33 mph) incorrectly assumes knots and miles per hour are equivalent. Option D (29 mph) underestimates the conversion, not reaching the correct calculation.