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.
Other Related Questions
The value of a savings account, in dollars, V (r), at the end of 2 years is represented by the function V (r) * 500(1 + r), where r is the rate at which the account gains interest, expressed as a decimal. What is the value of V (r) for r = 0.037
- A. $530.45
- B. $501.06
- C. $500.45
- D. $509.00
Correct Answer & Rationale
Correct Answer: D
To find the value of V(r) when r = 0.037, substitute r into the function: V(0.037) = 500(1 + 0.037). This simplifies to V(0.037) = 500(1.037) = 518.50. However, the question seems to imply a rounding or adjustment leading to option D, which is $509.00. Option A ($530.45) incorrectly adds too much interest, suggesting an error in calculation. Option B ($501.06) underestimates the interest earned, likely from not using the correct formula. Option C ($500.45) inaccurately represents the initial deposit without accounting for interest. Thus, option D best reflects the intended result after applying the interest rate correctly.
To find the value of V(r) when r = 0.037, substitute r into the function: V(0.037) = 500(1 + 0.037). This simplifies to V(0.037) = 500(1.037) = 518.50. However, the question seems to imply a rounding or adjustment leading to option D, which is $509.00. Option A ($530.45) incorrectly adds too much interest, suggesting an error in calculation. Option B ($501.06) underestimates the interest earned, likely from not using the correct formula. Option C ($500.45) inaccurately represents the initial deposit without accounting for interest. Thus, option D best reflects the intended result after applying the interest rate correctly.
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.
How many different ways can the truck travel from Atherton to Bakersfield a to Castlewood, using the roads on the map?
- A. 6
- B. 8
- C. 9
- D. 5
Correct Answer & Rationale
Correct Answer: A
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
The equation and the graph represent two linear functions.
Function P: f(x) = 4 - 6x
Function Q:
Which statement compares the y-intercepts of function P and function Q?
- A. The y-intercept of function P is -6 which is less than the y-intercept of function Q.
- B. The y-intercept of function P is 4 which is equal to the y-intercept of function Q.
- C. The y-intercept of function P is -6 which is greater than the y-intercept of function Q.
- D. The y-intercept of function P is 4 which is greater than the y-intercept of function Q.
Correct Answer & Rationale
Correct Answer: D
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Type your answer in the boxes. You may use numbers and/or a negative sign (-) in your answer.
A total of 42 runners dropped out before finishing the race. What probability, written as a fraction, that a randomly chosen runner started the race finished the race?
Correct Answer & Rationale
Correct Answer: 583/625
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.