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A circle has an area of 49Ï€ square inches. What is the circumference of the circle in terms of pi?
- A. 7Ï€ inches
- B. 28Ï€ inches
- C. 14Ï€ inches
- D. 3.5Ï€ inches
Correct Answer: C
Rationale: To find the circumference of a circle with an area of 49π square inches, you first need to find the radius using the area formula A = πr^2. Given the area is 49π, then 49π = πr^2, which simplifies to r^2 = 49, resulting in r = 7. The circumference formula is C = 2πr. Substituting r = 7 gives C = 2π(7) = 14π. Therefore, the correct circumference of the circle in terms of pi is 14π inches.
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Elevation above sea level and temperature are negatively correlated variables. Which of the following statements describes the relationship between the variables?
- A. As elevation decreases, temperature decreases
- B. As elevation decreases, temperature remains the same
- C. As elevation increases, temperature increases
- D. As elevation increases, temperature decreases
Correct Answer: D
Rationale: When two variables are negatively correlated, as one variable increases, the other decreases. In this case, as elevation above sea level increases, the temperature decreases. This relationship is often observed due to changes in atmospheric pressure and temperature with altitude. As altitude rises, the air becomes less dense, leading to lower temperatures. Therefore, the correct statement is 'As elevation increases, temperature decreases.' This relationship is crucial in understanding climate patterns, especially in mountainous regions where temperature changes significantly with elevation.
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.
What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)
- A. 40 feet
- B. 4 feet
- C. 14.4 feet
- D. 8.9 feet
Correct Answer: D
Rationale: To find the length of the unknown leg of a right triangle, you can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse (12 feet) is equal to the sum of the squares of the other two sides. Let x be the length of the unknown leg. So, 12^2 = 8^2 + x^2. Solving for x gives x = √(12^2 - 8^2) = √(144 - 64) = √80 ≈ 8.9 feet. Therefore, the length of the unknown leg is approximately 8.9 feet.
As the number of credit hours a student takes in a semester increases, the amount of tuition, access fees, and the number of student loans available also increase. Which of the following is the independent variable?
- A. Amount of tuition
- B. Number of credit hours
- C. Number of student loans available
- D. Amount of access fees
Correct Answer: B
Rationale: The independent variable in this scenario is the number of credit hours taken by the student. The independent variable is the one that is manipulated or controlled in an experiment to observe its effect on the dependent variables. In this case, the dependent variables are the amount of tuition, access fees, and the number of student loans available. By changing the number of credit hours, it influences the other variables, making it the independent variable.
A farmer grows apple, orange, lemon, banana, and pear trees. The number of trees planted this year is shown in the table above. Which of the following would best display the data?
- A. Bar graph
- B. Scatter plot
- C. Stem-and-leaf plot
- D. Line graph
Correct Answer: A
Rationale: A bar graph is the most appropriate way to display categorical data like the number of each type of tree planted by the farmer. In a bar graph, each type of tree can be represented by a separate bar, allowing for easy visual comparison of the quantities. Scatter plots are used to illustrate relationships between two sets of data, which is not the case here. Stem-and-leaf plots are more suitable for displaying numerical data in a grouped format, not categorical data like types of trees. Line graphs are typically used to portray trends or changes over time, making them less suitable for this scenario.