The graph shows a handyman's fees, f(x), in terms of the hours worked, x. The fees include a fuel charge and an hourly rate. What is the handyman's hourly rate?
- A. $5
- B. $55
- C. $30
- D. $25
Correct Answer & Rationale
Correct Answer: D
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
Other Related Questions
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.
Daniel wonders whether housing prices are more likely to increase or decrease in any special month. If he randomly selects a month other than January from the table, what is the price as a fraction, that the median sales price in that month was an increase over the previous month?
Correct Answer & Rationale
Correct Answer: 4\7
To determine the fraction of months where the median sales price increased over the previous month, one must analyze the data presented in the table. The correct answer, 4/7, indicates that out of the seven months considered (excluding January), there were four months where prices rose compared to the month prior. Other options, such as 3/7 or 5/7, misrepresent the data by either underestimating or overestimating the actual increases. A fraction of 3/7 would imply that only three months saw an increase, which contradicts the evidence. Similarly, 5/7 would suggest an unrealistic majority of months experienced price hikes, not aligning with the data. Thus, 4/7 accurately reflects the observed trends in the provided data.
To determine the fraction of months where the median sales price increased over the previous month, one must analyze the data presented in the table. The correct answer, 4/7, indicates that out of the seven months considered (excluding January), there were four months where prices rose compared to the month prior. Other options, such as 3/7 or 5/7, misrepresent the data by either underestimating or overestimating the actual increases. A fraction of 3/7 would imply that only three months saw an increase, which contradicts the evidence. Similarly, 5/7 would suggest an unrealistic majority of months experienced price hikes, not aligning with the data. Thus, 4/7 accurately reflects the observed trends in the provided data.
What is the value of 2/5 multiplied by ¾ divide by 8/5
- A. 12\25
- B. 1\3
- C. 3\16
- D. 64/75
Correct Answer & Rationale
Correct Answer: C
To solve \( \frac{2}{5} \times \frac{3}{4} \div \frac{8}{5} \), first, convert the division into multiplication by flipping the second fraction: \[ \frac{2}{5} \times \frac{3}{4} \times \frac{5}{8} \] Next, multiply the fractions: \[ \frac{2 \times 3 \times 5}{5 \times 4 \times 8} = \frac{30}{160} \] Simplifying \( \frac{30}{160} \) gives \( \frac{3}{16} \), confirming option C. Option A (12/25) is incorrect as it does not simplify correctly from the original operation. Option B (1/3) results from an incorrect multiplication or division process. Option D (64/75) does not match the calculated result and suggests an error in fraction handling.
To solve \( \frac{2}{5} \times \frac{3}{4} \div \frac{8}{5} \), first, convert the division into multiplication by flipping the second fraction: \[ \frac{2}{5} \times \frac{3}{4} \times \frac{5}{8} \] Next, multiply the fractions: \[ \frac{2 \times 3 \times 5}{5 \times 4 \times 8} = \frac{30}{160} \] Simplifying \( \frac{30}{160} \) gives \( \frac{3}{16} \), confirming option C. Option A (12/25) is incorrect as it does not simplify correctly from the original operation. Option B (1/3) results from an incorrect multiplication or division process. Option D (64/75) does not match the calculated result and suggests an error in fraction handling.
Which equation represents the graphed line?
- A. y = -1/3x +3
- B. y = 3x - 7
- C. y = 3x + 7
- D. y = 1/3x + 1
Correct Answer & Rationale
Correct Answer: D
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
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 ÷ 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 ÷ 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.