Mallory loaded 200 digital pictures into a digital picture frame. 78 are pictures of family members, 26 are pictures of pets, the rest are pictures of friends. The frame displays one picture every 10 seconds. Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?
- A. 0.33
- B. 0.43
- C. 0.48
- D. 0.52
- E. 0.96
Correct Answer & Rationale
Correct Answer: C
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
Other Related Questions
What is the sum of the two polynomials? 4x² + 3x + 5 + x² + 6x - 3?
- A. 4x² + 9x + 2
- B. 5x² + 9x + 2
- C. 5x² + 9x + 8
- D. 4x² + 9x² + 2
- E. 5x² + 9x² + 8
Correct Answer & Rationale
Correct Answer: B
To find the sum of the polynomials \(4x^2 + 3x + 5\) and \(x^2 + 6x - 3\), we combine like terms. 1. For \(x^2\) terms: \(4x^2 + x^2 = 5x^2\). 2. For \(x\) terms: \(3x + 6x = 9x\). 3. For constant terms: \(5 - 3 = 2\). Thus, the resulting polynomial is \(5x^2 + 9x + 2\), which corresponds to option B. Option A incorrectly adds the \(x^2\) terms, leading to an incorrect polynomial. Option C miscalculates the constant term. Option D mistakenly adds the \(x^2\) terms incorrectly and does not follow proper polynomial addition. Option E also miscalculates by incorrectly summing the \(x^2\) terms and the constants.
To find the sum of the polynomials \(4x^2 + 3x + 5\) and \(x^2 + 6x - 3\), we combine like terms. 1. For \(x^2\) terms: \(4x^2 + x^2 = 5x^2\). 2. For \(x\) terms: \(3x + 6x = 9x\). 3. For constant terms: \(5 - 3 = 2\). Thus, the resulting polynomial is \(5x^2 + 9x + 2\), which corresponds to option B. Option A incorrectly adds the \(x^2\) terms, leading to an incorrect polynomial. Option C miscalculates the constant term. Option D mistakenly adds the \(x^2\) terms incorrectly and does not follow proper polynomial addition. Option E also miscalculates by incorrectly summing the \(x^2\) terms and the constants.
Square PQRS, with a side length of 5 units, will be translated 2 units to the right and 2 units up in the standard (x, y) coordinate plane. What is the area, in square units, of the image of PQRS?
- A. 20
- B. 25
- C. 40
- D. 50
- E. 100
Correct Answer & Rationale
Correct Answer: B
The area of a square is calculated by squaring the length of its sides. For square PQRS, with a side length of 5 units, the area is \(5 \times 5 = 25\) square units. Translating the square 2 units to the right and 2 units up does not alter its dimensions or area; it simply changes its position on the coordinate plane. Options A (20), C (40), D (50), and E (100) suggest changes in area due to incorrect assumptions about the effects of translation or miscalculations. The area remains constant at 25 square units, confirming option B as the only accurate choice.
The area of a square is calculated by squaring the length of its sides. For square PQRS, with a side length of 5 units, the area is \(5 \times 5 = 25\) square units. Translating the square 2 units to the right and 2 units up does not alter its dimensions or area; it simply changes its position on the coordinate plane. Options A (20), C (40), D (50), and E (100) suggest changes in area due to incorrect assumptions about the effects of translation or miscalculations. The area remains constant at 25 square units, confirming option B as the only accurate choice.
The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
- A. The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
- B. The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases
- C. The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases
- D. The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
- E. The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
Correct Answer & Rationale
Correct Answer: B
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
Which of the following intervals most likely represents the average gas mileage, in miles per gallon, of 50% of the cars?
- A. 20 to 32
- B. 24 to 32
- C. 29 to 32
- D. 30 to 44
- E. 32 to 44
Correct Answer & Rationale
Correct Answer: B
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.