5733 Core Academic Skills For Educators Mathematics Version 2 Questions
5 questions
Review Mode
Exam Mode
1. Which of the following pairs of numbers, when placed from left to right in the boxes above in the order given, make the equation true? 15 = (9 x []) / 5 + []
A. 15, 1
B. 10, 2
C. 10, 3
D. 5, 4
E. 5, 6 Correct
Explanation
Step 1: Let the pair be (a, b) in the equation 15 = (9 x a) / 5 + b. Step 2: Test pair (5, 6): (9 x 5) / 5 = 45 / 5 = 9, then 9 + 6 = 15, which is true. Step 3: Other pairs fail (e.g., (10, 3): (9 x 10) / 5 = 18, 18 + 3 = 21, not 15). Thus, (5, 6) is correct.
2. Based on the scatterplot above, which of the following is true?
A. As price increases, the number of pairs of earrings sold tends to remain constant.
B. As price increases, the number of pairs of earrings sold tends to decrease. Correct
C. As price increases, the number of pairs of earrings sold tends to increase.
D. As price decreases, the number of pairs of earrings sold tends to remain constant.
E. As price decreases, the number of pairs of earrings sold tends to decrease.
Explanation
Step 1: Observe the scatterplot, which plots the number of pairs of earrings sold (y-axis) against price (x-axis), showing points starting high around 8 thousand at low prices and declining toward 0 as price rises to 12 dollars. Step 2: Identify the trend as negative correlation, where higher prices are associated with fewer sales, consistent with the economic principle of demand decreasing as price increases. Step 3: Evaluate the options—A suggests constant sales with increasing price (false), B suggests decreasing sales with increasing price (true), C suggests increasing sales with increasing price (false), D suggests constant sales with decreasing price (irrelevant to the trend), E suggests decreasing sales with decreasing price (opposite of observed). Thus, the correct answer is B.
3. If (2x - 4) / 7 = 6, what is the value of x?
A. 5
B. 8
C. 19 Correct
D. 23
E. 35
Explanation
Step 1: Multiply both sides by 7: 2x - 4 = 42. Step 2: Add 4: 2x = 46. Step 3: Divide by 2: x = 23. Step 4: Verify: (2 x 23 - 4) / 7 = (46 - 4) / 7 = 42 / 7 = 6.
4. Which of the following is a factor of both 36 and 64?
A. 4
B. 6
C. 8 Correct
D. 12
E. 18
Explanation
Step 1: Find factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36; and 64: 1, 2, 4, 8, 16, 32, 64. Step 2: Common factors: 1, 2, 4, 8. Step 3: Among choices, 8 is the largest common factor.
5. How many mugs with a capacity of 8 fluid ounces are needed to hold 68 fluid ounces of water?
A. 5
B. 6
C. 7
D. 8
E. 9 Correct