Nokea
What is the domain for the function f(x)=2x+5?
- A. All real numbers
- B. x ≥ 0
- C. x > 0
- D. x ≤ 0
Correct Answer: A
Rationale: The domain of a function represents all possible input values that the function can accept. In this case, the function f(x)=2x+5 is a linear function, and linear functions have a domain of all real numbers. This means that any real number can be substituted for x in the function f(x)=2x+5, making choice A, 'All real numbers,' the correct domain for this function. Choices B, C, and D, restrict the domain unnecessarily by limiting the values of x to specific subsets of real numbers, which does not accurately reflect the nature of the given function.
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Divide 4/3 by 9/13 and reduce the fraction.
- A. 52/27
- B. 51/27
- C. 52/29
- D. 51/29
Correct Answer: A
Rationale: To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, (4/3) · (9/13) = (4/3) * (13/9) = 52/27. This fraction is already in its reduced form, making choice A the correct answer. Choices B, C, and D are incorrect as they do not represent the correct result of dividing the fractions 4/3 by 9/13.
The phone bill is calculated each month using the equation y = 50x. The cost of the phone bill per month is represented by y and x represents the gigabytes of data used that month. What is the value and interpretation of the slope of this equation?
- A. 75 dollars per day
- B. 75 gigabytes per day
- C. 50 dollars per day
- D. 50 dollars per gigabyte
Correct Answer: D
Rationale: The slope of the equation y = 50x is 50, which means that for each additional gigabyte of data used, the cost increases by 50 dollars. Therefore, the interpretation of the slope is that it represents the cost per gigabyte, making '50 dollars per gigabyte' the correct answer. Choices A, B, and C are incorrect because they do not reflect the relationship between the cost and the amount of data used in the given equation.
Mom's car drove 72 miles in 90 minutes. How fast did she drive in feet per second?
- A. 0.8 feet per second
- B. 48.9 feet per second
- C. 0.009 feet per second
- D. 70.4 feet per second
Correct Answer: B
Rationale: To convert miles per hour to feet per second, you need to convert miles to feet and minutes to seconds. First, convert 72 miles to feet using the conversion factor 1 mile = 5280 feet: 72 miles * 5280 feet/mile = 380160 feet. Then, convert 90 minutes to seconds: 90 minutes * 60 seconds/minute = 5400 seconds. Now, to find the speed in feet per second, divide the distance traveled in feet by the time in seconds: 380160 feet / 5400 seconds = 70.4 feet per second. Therefore, the correct answer is 70.4 feet per second. Choice A, 0.8 feet per second, is incorrect as it is a much lower speed. Choice C, 0.009 feet per second, is also incorrect as it is too low. Choice D, 70.4 feet per second, would be correct if the conversion calculations were accurate, but in this case, it's not the correct answer.
What is the product of two irrational numbers?
- A. Irrational
- B. Rational
- C. Irrational or rational
- D. Complex and imaginary
Correct Answer: C
Rationale: The correct answer is C: 'Irrational or rational.' When you multiply two irrational numbers, the result can be either irrational or rational. For example, multiplying the square root of 2 (√2) by itself results in the rational number 2. This shows that the product of two irrational numbers can lead to a rational result. Choices A, B, and D are incorrect because the product of two irrational numbers is not limited to being irrational; it can also be rational.
A closet is filled with red, blue, and green shirts. If 2/5 of the shirts are green and 1/3 are red, what fraction of the shirts are blue?
- A. 4/15
- B. 1/5
- C. 7/15
- D. 1/2
Correct Answer: C
Rationale: To find the fraction of blue shirts, subtract the fractions of green and red shirts from 1. Green shirts are 2/5 and red shirts are 1/3, which sum up to 11/15. Therefore, blue shirts would be 1 - 11/15 = 4/15. So, the correct answer is 4/15. Choice A (4/15) is incorrect as it represents the overall fraction of green shirts. Choice B (1/5) is incorrect as it does not account for the fractions of green and red shirts. Choice D (1/2) is incorrect as it does not consider the given fractions of green and red shirts.