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Which of the following expressions represents the sum of three times a number and eight times a different number?
- A. 3x + 8y
- B. 8x + 3x
- C. 3x - 8y
- D. 8x - 3y
Correct Answer: A
Rationale: The correct expression for the sum of three times a number and eight times a different number is given by 3x + 8y. This represents adding three times the variable x (3x) to eight times the variable y (8y). Choice B (8x + 3x) is incorrect as it represents adding eight times x to three times x, which is redundant. Choice C (3x - 8y) is incorrect because it represents subtracting eight times y from three times x, not their sum. Choice D (8x - 3y) is also incorrect as it represents subtracting three times y from eight times x, not their sum.
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Solve for x in the equation above: (x/y) - z = rw
- A. X = y(z + rw)
- B. X = rw(y - z)
- C. X = rwy + z
- D. X = rwy - z
Correct Answer: A
Rationale: To solve for x, first, isolate x by moving the term involving x to one side of the equation. Begin by adding z to both sides of the equation to get (x/y) = rw + z. Then, multiply both sides by y to get x = y(rw + z), which simplifies to x = y(z + rw). Therefore, choice A is correct. Choices B, C, and D are incorrect because they do not correctly rearrange the terms in the equation to solve for x.
Three friends are sharing a burger. One friend eats a quarter of the burger. The other two friends equally divide the rest among themselves. What portion of the burger did each of the other two friends receive?
- A. 6-Jan
- B. 4-Jan
- C. 4-Mar
- D. 8-Mar
Correct Answer: D
Rationale: After one friend eats a quarter of the burger, 3/4 of the burger remains. Dividing this equally between the other two friends means each receives 3/8 of the whole burger. Therefore, the correct answer is 8-Mar. Choice A (6-Jan), Choice B (4-Jan), and Choice C (4-Mar) are incorrect as they do not accurately represent the portion each of the other two friends receives after one friend consumes a quarter of the burger.
The force applied is directly proportional to the stretch of a coil. If a force of 132 Newtons stretches a coil 0.07 meters, what force would be needed to stretch a coil 0.1 meter? Round your answer to the nearest tenth.
- A. 92.4 Newtons
- B. 1885.7 Newtons
- C. 188.6 Newtons
- D. 136.0 Newtons
Correct Answer: C
Rationale: To find the force needed to stretch the coil 0.1 meters, we can set up a proportion based on the given information. The initial force and stretch are in direct proportion, so we can use this relationship to determine the unknown force. (132 N / 0.07 m) = X / 0.1 m. Cross-multiplying, we get 132 N * 0.1 m / 0.07 m = 188.57 N, which rounds to 188.6 N. Therefore, the correct answer is 188.6 Newtons. Choice A is incorrect as it does not match the calculated answer. Choice B is significantly higher and does not align with the proportional relationship. Choice D is close but does not account for the correct rounding as specified in the question.
A teacher earns $730.00 per week before any tax deductions. The following taxes are deducted each week: $72.00 federal income tax, $35.00 state income tax, and $65.00 Social Security tax. How much will the teacher make in 4 weeks after taxes are deducted?
- A. $2,250.00
- B. $2,550.00
- C. $2,400.00
- D. $2,232.00
Correct Answer: D
Rationale: After deducting $172 weekly for taxes ($72 + $35 + $65), the teacher's net weekly income is $558. Over 4 weeks, the total income is $2,232.00. Choice A is incorrect as it does not account for the taxes deducted. Choice B is incorrect as it overestimates the income by not deducting the taxes. Choice C is incorrect as it also does not consider the tax deductions.
Solve the equation 3(2x+5)=11x+5 for x. Which of the following is correct?
- A. 1
- B. 2
- C. -1
- D. -2
Correct Answer: B
Rationale: To solve the equation, distribute 3 to both terms inside the parentheses: 6x + 15 = 11x + 5. Then, move 11x to the left side by subtracting it from both sides: 6x - 11x = 5 - 15. Simplify to get -5x = -10. Divide by -5 to isolate x: x = 2. Therefore, the correct answer is x = 2. Choices A, C, and D are incorrect because they do not match the correct solution obtained by solving the equation step by step.