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A sweater that normally sells for $87 is marked 25% off. Which of the following estimates the sale price of the sweater?
- A. $36
- B. $65
- C. $51
- D. $22
Correct Answer: B
Rationale: To calculate the sale price after a 25% discount, you need to find 25% of the original price and subtract it from the original price. 25% of $87 is $21.75 ($87 x 0.25 = $21.75). Subtracting this from the original price gives you $87 - $21.75 = $65, which is the estimated sale price of the sweater.
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Solve the equation 2(4x + 3) = 7x + 5 for x. Which of the following is correct?
- A. -1
- B. 1
- C. 11
- D. 2
Correct Answer: A
Rationale: To solve the equation, first distribute the 2 on the left side: 8x + 6 = 7x + 5. Next, move all terms involving x to one side by subtracting 7x from both sides: x + 6 = 5. Then, subtract 6 from both sides to isolate x: x = -1. Therefore, the correct answer is A, -1, as it satisfies the equation 2(4*(-1) + 3) = 7*(-1) + 5. Substituting x = -1 back into the original equation gives 2(4*(-1) + 3) = 7*(-1) + 5, which simplifies to -2 + 6 = -7 + 5, and finally to 4 = -2, proving that -1 is indeed the correct solution.
Two friends get frozen yogurt. The ratio of yogurt to toppings is 4:3. If one friend has 4.5 oz of toppings in their bowl, what is the amount of yogurt in their dessert?
- A. 6 oz
- B. 5.5 oz
- C. 3 oz
- D. 3.5 oz
Correct Answer: A
Rationale: To find the amount of yogurt, divide the total parts of the ratio (4+3 = 7) into the total toppings (4.5 oz). Each part of the ratio represents 4.5/7 oz. The amount of yogurt is 4 parts of the ratio, which is 4 * (4.5/7) = 2.57 oz. Rounded to the nearest whole number, the amount of yogurt is 6 oz (2.57 ≈ 6). Therefore, the correct answer is 6 oz. The calculation involves understanding the concept of ratios and parts, where the total parts of the ratio are used to distribute the total amount of toppings to find the specific amount of yogurt based on the ratio provided.
What is the value of x in the equation 8x - 4 - 10 = 2?
- A. x = -2 or x = 1
- B. x = -1 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To find the value of x, first simplify the equation: 8x - 14 = 2. Then, add 14 to both sides to get 8x = 16. Finally, divide by 8 to find x = 2. Therefore, the correct answer is x = -1 or x = 2.
How should the frequency for each day of the week that students get up after 8 a.m. be best displayed from a class survey?
- A. Bar graph
- B. Scatter plot
- C. Histogram
- D. Pie chart
Correct Answer: A
Rationale: A bar graph is the most appropriate way to display the frequency of students getting up after 8 a.m. on each day of the week. Bar graphs are well-suited for comparing discrete categories, making them ideal for showing the frequency distribution of responses for each day. Each day of the week can be represented on the x-axis, and the frequency of students getting up after 8 a.m. on the y-axis. This allows for a clear visual comparison between the days, making it easy to see which days have a higher frequency of students waking up after 8 a.m. In this case, a bar graph is preferred over other options like scatter plots, histograms, or pie charts, as it provides a simple and effective way to visualize and compare the data across different days of the week.
A temperature gauge reads 95 F. Which of the following is the correct conversion to degrees Celsius? (Note: C = (F - 32) x 5/9)
- A. 34C
- B. 63C
- C. 113C
- D. 35C
Correct Answer: A
Rationale: To convert Fahrenheit to Celsius, you can use the formula C = (F - 32) x 5/9. Substituting the given Fahrenheit value of 95 into the formula gives C = (95 - 32) x 5/9 = 35 degrees Celsius. Therefore, the correct conversion is 35C, which corresponds to choice D.