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In the equation f(t) = 4t + 9, which of the following is the independent variable?
- A. f
- B. t
- C. 4
- D. 9
Correct Answer: B
Rationale: The independent variable is 't' in the equation f(t) = 4t + 9. In a mathematical equation, the independent variable is the one that can be changed or controlled. In this case, 't' is the variable that determines the value of the function f(t). The function f is dependent on the value of 't,' making 't' the independent variable.
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A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cups of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?
- A. 2 2/5 cups
- B. 7 1/5 cups
- C. 6 cups
- D. 3 8/15 cups
Correct Answer: B
Rationale: To determine the amount of milk needed for the bigger batch, we first establish the ratio of flour to milk, which is 1/3 : 1 1/5. Converting 1 1/5 to an improper fraction gives us 6/5. Therefore, the ratio becomes 1:6/5 = 1:1.2. If the chef uses 2 cups of flour, the calculation would be 2 x 1.2 = 2.4 cups of milk needed. This is equivalent to 2 2/5 cups. Hence, the correct answer is 7 1/5 cups.
Which term best describes the data set below: 1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9?
- A. Uniform
- B. Bimodal
- C. Right-skewed
- D. Left-skewed
Correct Answer: B
Rationale: A bimodal distribution is characterized by two peaks or distinct values that occur most frequently in the data set. In this specific data set, the values '2' and '8' appear more frequently than other values, indicating two modes, making it a bimodal distribution. The presence of two prominent peaks or modes distinguishes it from a uniform, right-skewed, or left-skewed distribution. In a uniform distribution, all values have similar frequencies, which is not the case here. Right-skewed and left-skewed distributions have a single peak but differ in the tail direction; however, this data set does not exhibit such characteristics.
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.
What is the mean of the test scores listed below? 100, 78, 47, 84, 93, 78
- A. 80
- B. 78
- C. 81
- D. 96
Correct Answer: A
Rationale: To find the mean of a set of numbers, you need to sum all the numbers together and then divide by the total count of numbers. In this case, the sum of the test scores is 100 + 78 + 47 + 84 + 93 + 78 = 480. Since there are 6 test scores in total, you divide the sum by 6 to get the mean. Therefore, the mean = 480 · 6 = 80. Hence, the correct answer is A, which is 80. It represents the average test score among the provided values.
A person weighed themselves at 180 lb. Three months later they weighed themselves at 160 lb. Which of the following is the percent of weight the person lost over 3 months? (Round to the nearest percent.)
- A. 13%
- B. 20%
- C. 10%
- D. 5%
Correct Answer: B
Rationale: The percent lost is calculated as 180?160180×100?11.1%\frac{180 - 160}{180} \times 100 \approx 11.1\%180180?160?×100?11.1%, which rounds to 11%.