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Which of the following is the correct Simplification of the expression below? 12 +3 × 4 -1+ 2^3
- A. 31
- B. 7
- C. 15
- D. 101
Correct Answer: A
Rationale: Following the order of operations (PEMDAS): 12 + (3 × 4) -1 + (2³) = 12 + 12 -1 + 8 = 31.
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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.
A pharmaceutical company's stock price was $50.33 on Monday. On Tuesday, the price increased by $2.35. On Wednesday, the price decreased by $1.07 from Tuesday's price. On Thursday, the price increased by $0.75 from Wednesday's price. What was the final price on Thursday?
- A. $53.43
- B. $54.50
- C. $52.36
- D. $50.85
Correct Answer: C
Rationale: To find the final price on Thursday, start with $50.33 (Monday's price) and apply the changes: +$2.35 (Tuesday's increase), -$1.07 (Wednesday's decrease), and +$0.75 (Thursday's increase). Calculate the total by adding and subtracting the price changes: $50.33 + $2.35 - $1.07 + $0.75 = $52.36. Therefore, the final price on Thursday was $52.36. The correct answer is $52.36, as calculated from the given price changes throughout the week.
What is 31% of 426?
- A. 425.69
- B. 0.07
- C. 13.7
- D. 132.06
Correct Answer: D
Rationale: To find 31% of 426, you multiply 426 by 0.31 (which represents 31% in decimal form). The calculation is 426 * 0.31 = 132.06. Therefore, the correct answer is D, 132.06.
Which of the following expressions has the greatest value?
- A. 34 + 96
- B. 0.372
- C. 03-Aug
- D. 37%
Correct Answer: A
Rationale: To determine the greatest value among the given expressions, we need to evaluate each one. When we calculate 34 + 96, the result is 130. Option B is a decimal less than 1, option C is in date format, and option D is a percentage. Comparing the values obtained, 130 (option A) is greater than 0.372, 03-Aug, and 37%. Therefore, the correct answer is A since it has the greatest value, which is 130.
Given x/y - 3x = rw, solve for x in the equation above.
- A. x = rw y + z
- B. x = rw y - z
- C. x = rw(y - z)
- D. None of the Above
Correct Answer: D
Rationale: To solve for x in the equation x/y - 3x = rw, you need to isolate x. This equation involves a term with x on both sides and a division by y, making it challenging to find a direct solution for x. By combining these complexities, there is no single correct expression for x. Therefore, 'None of the Above' is the correct answer as there is no straightforward solution for x in this particular equation.