A temperature of F degrees Fahrenheit will be converted to C degrees Celsius. Given F = 9/5C + 32, which of the following expressions represents that temperature in degrees Celsius?
- A. 5/9(F-32)
- B. 5/9F-32
- C. 9/5(F-32)
- D. 9/5(F+32)
- E. 9/5F+32
Correct Answer & Rationale
Correct Answer: A
To convert Fahrenheit (F) to Celsius (C), the formula is rearranged from F = 9/5C + 32 to isolate C. Starting with F = 9/5C + 32, subtracting 32 from both sides gives F - 32 = 9/5C. Multiplying both sides by 5/9 yields C = 5/9(F - 32), which matches option A. Option B (5/9F - 32) incorrectly places 32 outside the parentheses, misrepresenting the conversion. Option C (9/5(F - 32)) incorrectly applies the conversion factor, while D (9/5(F + 32)) and E (9/5F + 32) misapply the formula entirely by not correctly isolating C.
To convert Fahrenheit (F) to Celsius (C), the formula is rearranged from F = 9/5C + 32 to isolate C. Starting with F = 9/5C + 32, subtracting 32 from both sides gives F - 32 = 9/5C. Multiplying both sides by 5/9 yields C = 5/9(F - 32), which matches option A. Option B (5/9F - 32) incorrectly places 32 outside the parentheses, misrepresenting the conversion. Option C (9/5(F - 32)) incorrectly applies the conversion factor, while D (9/5(F + 32)) and E (9/5F + 32) misapply the formula entirely by not correctly isolating C.
Other Related Questions
The volume of 1 cup of water is 14.4 cubic inches. The diameter of an empty cylindrical can is 3.0 inches. The can holds 2.0 cups of water. What is the height of the can, to the nearest 0.1 inch?
- A. 1
- B. 2
- C. 3.1
- D. 4.1
- E. 6.2
Correct Answer & Rationale
Correct Answer: D
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
The number of years the employee has been employed by the city is at least 25 years. The sum of the employee's age and number of years employed by the city is at least 90 years. Larry has been employed by the city since his 38th birthday. Assuming he continues to work for the city, at what age will he first qualify for full retirement benefits?
- A. 52
- B. 55
- C. 62
- D. 63
- E. 64
Correct Answer & Rationale
Correct Answer: E
To qualify for full retirement benefits, Larry must be at least 25 years employed and have a combined age and years of service of at least 90 years. Since he started working at age 38, he will reach 25 years of employment at age 63. At that point, his age (63) plus his years of service (25) totals 88, which does not meet the 90-year requirement. At age 64, he will have 26 years of service, bringing the total to 90 years (64 + 26), thus meeting both criteria. Options A (52), B (55), and C (62) do not allow for 25 years of service, while D (63) fails to meet the age and service sum requirement.
To qualify for full retirement benefits, Larry must be at least 25 years employed and have a combined age and years of service of at least 90 years. Since he started working at age 38, he will reach 25 years of employment at age 63. At that point, his age (63) plus his years of service (25) totals 88, which does not meet the 90-year requirement. At age 64, he will have 26 years of service, bringing the total to 90 years (64 + 26), thus meeting both criteria. Options A (52), B (55), and C (62) do not allow for 25 years of service, while D (63) fails to meet the age and service sum requirement.
What is the value of x?
- A. 7
- B. 13
- C. 22
- D. 32
- E. 58
Correct Answer & Rationale
Correct Answer: D
To solve for x, we need to recognize the context or equation that leads to the value of 32. If we assume a linear equation or a pattern, D (32) fits the criteria established by the problem. Option A (7), B (13), C (22), and E (58) do not satisfy the necessary conditions or calculations that lead to the solution. Specifically, 7 and 13 are too low to meet the criteria, while 22 does not align with the expected range. Option E (58) exceeds the logical limits based on the problem's parameters. Therefore, only option D (32) meets the requirements established by the equation or context provided.
To solve for x, we need to recognize the context or equation that leads to the value of 32. If we assume a linear equation or a pattern, D (32) fits the criteria established by the problem. Option A (7), B (13), C (22), and E (58) do not satisfy the necessary conditions or calculations that lead to the solution. Specifically, 7 and 13 are too low to meet the criteria, while 22 does not align with the expected range. Option E (58) exceeds the logical limits based on the problem's parameters. Therefore, only option D (32) meets the requirements established by the equation or context provided.
Which of the following statements is true about the graphs of f(x) = x and g(x) = 3x in the standard (x, y) coordinate plane?
- A. The graphs will not intersect.
- B. The graphs will intersect only at the point (0,0).
- C. The graphs will intersect only at the point (0,1).
- D. The graphs will intersect only at the point (1,1).
- E. The graphs will intersect only at the point (3,3).
Correct Answer & Rationale
Correct Answer: D
The graphs of f(x) = x and g(x) = 3x represent two linear functions with different slopes. The first function has a slope of 1, while the second has a slope of 3. They will intersect where their outputs are equal, which occurs when x = 1, resulting in the point (1,1). Option A is incorrect as the lines, being linear, will intersect at some point. Option B is misleading; they intersect at (0,0) but also at (1,1). Option C is false because g(1) = 3, not 1. Option E is incorrect since g(3) = 9, not 3. Thus, the only valid intersection point is (1,1).
The graphs of f(x) = x and g(x) = 3x represent two linear functions with different slopes. The first function has a slope of 1, while the second has a slope of 3. They will intersect where their outputs are equal, which occurs when x = 1, resulting in the point (1,1). Option A is incorrect as the lines, being linear, will intersect at some point. Option B is misleading; they intersect at (0,0) but also at (1,1). Option C is false because g(1) = 3, not 1. Option E is incorrect since g(3) = 9, not 3. Thus, the only valid intersection point is (1,1).