Compare the zeros of function P and function Q. Which statement about the zeros of the functions is true?
- A. Function P has the greater zero, which is 9.
- B. Function P has the greater zero, which is 1.
- C. Function Q has the greater zero, which is 5.
- D. Function Q has the greater zero, which is 4.
Correct Answer & Rationale
Correct Answer: C
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.
Other Related Questions
Read the phrase below.
the quotient of three less than a number and six more than four times a number
Which expression is equivalent to this phrase?
- A. (3-x)/(4x + 6)
- B. (x - 3)(4x + 6)
- C. (x-3)/(4x + 6)
- D. 4x - 3 + 6
Correct Answer & Rationale
Correct Answer: C
The phrase describes a mathematical expression involving a number, denoted as \( x \). "Three less than a number" translates to \( x - 3 \), while "six more than four times a number" translates to \( 4x + 6 \). Therefore, the entire expression is the quotient of these two parts, resulting in \( \frac{x - 3}{4x + 6} \), which matches option C. Option A incorrectly suggests a subtraction in the numerator, altering the intended expression. Option B implies multiplication instead of division, misrepresenting the relationship. Option D presents a simplified expression rather than a quotient, which does not align with the original phrase.
The phrase describes a mathematical expression involving a number, denoted as \( x \). "Three less than a number" translates to \( x - 3 \), while "six more than four times a number" translates to \( 4x + 6 \). Therefore, the entire expression is the quotient of these two parts, resulting in \( \frac{x - 3}{4x + 6} \), which matches option C. Option A incorrectly suggests a subtraction in the numerator, altering the intended expression. Option B implies multiplication instead of division, misrepresenting the relationship. Option D presents a simplified expression rather than a quotient, which does not align with the original phrase.
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 Willis Canyon Dam releases an average of 1,733,400 cubic feet of water every day. Based on that average, how many cubic feet of water does the dam release every minute?
Correct Answer & Rationale
Correct Answer: 1200.4167
To find the water released per minute, divide the daily release by the number of minutes in a day. There are 1,440 minutes in a day (24 hours x 60 minutes). Dividing 1,733,400 cubic feet by 1,440 minutes gives approximately 1,200.4167 cubic feet per minute. Other options are incorrect because they either miscalculate the division or fail to account for the total number of minutes in a day, leading to significantly higher or lower values. Accurate conversion of daily figures to minute rates is crucial for proper understanding.
To find the water released per minute, divide the daily release by the number of minutes in a day. There are 1,440 minutes in a day (24 hours x 60 minutes). Dividing 1,733,400 cubic feet by 1,440 minutes gives approximately 1,200.4167 cubic feet per minute. Other options are incorrect because they either miscalculate the division or fail to account for the total number of minutes in a day, leading to significantly higher or lower values. Accurate conversion of daily figures to minute rates is crucial for proper understanding.
John and Mike are participating in a long-distance bicycling event. Mike bicycled 24 miles in the first 2 hours. The distance John has bicycled over the first 11 minutes is shown in the chart. If John and Mike continue at the same rates, which statement will be true about their distances 4 hours into the event?
- A. John will be 6 miles ahead of Mike.
- B. John will be 12 miles ahead of Mike.
- C. Mike will be 6 miles ahead of John.
- D. Mike will be 12 miles ahead of John.
Correct Answer & Rationale
Correct Answer: D
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles รท 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles รท 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.