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What is the area of the largest circle that can fit entirely inside a rectangle measuring 8 centimeters by 10 centimeters?
- A. 18Ï€ cm^2
- B. 16Ï€ cm^2
- C. 8Ï€ cm^2
- D. 10Ï€ cm^2
Correct Answer: B
Rationale: To find the largest circle that fits inside the given rectangle, the circle's diameter should match the shorter side of the rectangle, which is 8 cm. The radius of the circle is half the diameter, making it 4 cm. The area of a circle is determined using the formula A = πr^2, where r is the radius. Substituting r = 4 cm, we get A = π*(4)^2 = 16π cm^2. Therefore, the correct answer is 16π cm^2, as this is the maximum area circle that can fit entirely inside the given rectangle.
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An athlete runs 4 miles in 28 minutes and then changes pace to run the next 4 miles in 32 minutes. Overall, what is the average time in minutes it takes the athlete to run 1 mile?
- A. 7.5 minutes
- B. 7 minutes
- C. 8.5 minutes
- D. 8 minutes
Correct Answer: A
Rationale: To calculate the average time per mile, we add the total time taken for both parts (28 minutes + 32 minutes = 60 minutes) and divide it by the total distance covered (8 miles). This gives us 60 minutes / 8 miles = 7.5 minutes per mile. Therefore, the correct answer is 7.5 minutes, representing the average time it takes the athlete to run 1 mile.
Which of the following expressions represents the sum of three times a number and eight times another number?
- A. 3x + 8x
- B. 3x + 8y
- C. 8x - 3y
- D. 3x - 8y
Correct Answer: B
Rationale: To find the sum of three times a number and eight times another number, you need to multiply each number by its respective factor. Three times a number is represented by 3x, and eight times another number is represented by 8y. When adding these two terms together, the correct expression is 3x + 8y. Therefore, choice B is the correct answer as it accurately represents the sum of three times a number and eight times another number.
When the weights of newborn babies are graphed, the distribution of weights is symmetric with the majority of weights centered around a single peak. Which of the following describes the shape of this distribution?
- A. Skewed right
- B. Bimodal
- C. Uniform
- D. Bell-shaped
Correct Answer: D
Rationale: The described distribution, where the majority of weights are centered around a single peak and symmetric, is referred to as bell-shaped. In a bell-shaped distribution, the data is symmetric around the mean, with most values clustering near the peak and tapering off towards the extremes. This pattern is commonly seen in normal distributions, such as the distribution of birth weights in newborns. The bell-shaped curve represents a typical symmetric distribution, indicating that most newborn weights fall close to the average weight with fewer extreme values. Therefore, the correct answer is 'Bell-shaped'.
Of the numbers listed above, which number is the greatest? The numbers are 2/3, -0.7, -1.3, and -4/3.
- A. 2/3 (0.67)
- B. -0.7 (-0.7)
- C. -1.3 (-1.3)
- D. -4/3 (-1.33)
Correct Answer: A
Rationale: To compare these numbers, convert them to a common form. 2/3 is equivalent to approximately 0.67. -0.7, -1.3, and -4/3 are negative numbers. Among these choices, 2/3 (0.67) is the only positive number, making it greater than all the negative numbers (-0.7, -1.3, -4/3). Therefore, 2/3 is the greatest number among the options provided.
A consumer makes a $400 down payment on a television that costs $1,570. How many months will it take to pay off the television with monthly payments of $100? (Assume no interest)
- A. 16
- B. 12
- C. 11
- D. 15
Correct Answer: B
Rationale: To determine the number of months needed to pay off the television, subtract the down payment from the total cost: $1,570 - $400 = $1,170. Next, divide the remaining amount ($1,170) by the monthly payment of $100 to find the number of months: $1,170 · $100 = 11.7 months. Since you cannot make a fraction of a monthly payment, the consumer will need to make 12 monthly payments to fully pay off the television.