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 graph shows data for a 5-hour glucose tolerance test for four patients.
Symptoms of a patient with diabetes during a 5-hour glucose tolerance test include a high blood-glucose level that increases quickly and then decreases only minimally over the 5-hour period. Which patient displays symptoms of diabetes?
- A. patient 2
- B. patient 1
- C. patient 4
- D. patient 3
Correct Answer & Rationale
Correct Answer: C
Patient 4 exhibits a rapid increase in blood glucose levels followed by a minimal decrease over the 5-hour test, indicating poor glucose regulation typical of diabetes. This pattern reflects the body's inability to effectively utilize insulin. In contrast, Patient 1 shows a quick rise followed by a significant decline, suggesting normal glucose metabolism. Patient 2 may demonstrate a slight increase but returns to baseline, indicating no diabetes. Patient 3's levels remain stable, which is also indicative of normal glucose tolerance. Thus, only Patient 4 aligns with the expected symptoms of diabetes during the test.
Patient 4 exhibits a rapid increase in blood glucose levels followed by a minimal decrease over the 5-hour test, indicating poor glucose regulation typical of diabetes. This pattern reflects the body's inability to effectively utilize insulin. In contrast, Patient 1 shows a quick rise followed by a significant decline, suggesting normal glucose metabolism. Patient 2 may demonstrate a slight increase but returns to baseline, indicating no diabetes. Patient 3's levels remain stable, which is also indicative of normal glucose tolerance. Thus, only Patient 4 aligns with the expected symptoms of diabetes during the test.
Which graph shows 3y - 2x = 6?
-
A.
-
B.
Correct Answer & Rationale
Correct Answer: B
To determine the graph of the equation \(3y - 2x = 6\), we can rearrange it into slope-intercept form \(y = mx + b\). This gives us \(y = \frac{2}{3}x + 2\), indicating a slope of \(\frac{2}{3}\) and a y-intercept of 2. Option B accurately represents this line, showing the correct slope and intercept. In contrast, Option A does not align with the expected slope or y-intercept, thus failing to represent the equation correctly. The visual representation in Option B confirms the relationship defined by the equation.
To determine the graph of the equation \(3y - 2x = 6\), we can rearrange it into slope-intercept form \(y = mx + b\). This gives us \(y = \frac{2}{3}x + 2\), indicating a slope of \(\frac{2}{3}\) and a y-intercept of 2. Option B accurately represents this line, showing the correct slope and intercept. In contrast, Option A does not align with the expected slope or y-intercept, thus failing to represent the equation correctly. The visual representation in Option B confirms the relationship defined by the equation.
What is the value of 0.6 - (0.7)(1.4)?
- A. -0.38
- B. -0.14
- C. -0.42
- D. -1.5
Correct Answer & Rationale
Correct Answer: A
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
Kelly has a home business making jewellery. It takes 2 hours for her to make each bracelet and 3.5 hours to make each necklace. Next month she plans to spend 140 hours to make jewellery. If she fills a special order for 22 bracelets at the beginning of the mouth and spends the rest of the month making necklaces, how many necklaces can Kelly make in the month
- A. 52
- B. 27
- C. 40
- D. 31
Correct Answer & Rationale
Correct Answer: B
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.