Math Test 1 Explanations

11. 2(2x-6)=10x-6 Solve for x above. Which of the following is correct? a. 5 b.-7 c.-9 d. 10

11. C: Multiplying the equation results in the following: 8x-24=10x-6 -18=2x x=-18/2 or -9

15. 4 2/3 divided by 1 1/6 Simplify the expression above. Which of the following is correct? a. 2 b. 3 1/3 c. 4 d. 4 1/2

15. C: Turn both expressions into fractions, and then multiply the first by the reverse of the second: 14/3 divided by 7/6 is 14/3 times 6/7 equals 4

19. If Stella's current weight is 56 kilograms, which of the following is her approximate weight in pounds? (Note: 1 kilogram is approximately equal to 2.2 pounds.) a. 123 pounds b. 110 pounds c. 156 pounds d. 137 pounds

19. A: To find the correct answer, simply multiply 56 by 2.2. The result is 123.2, or approximately 123. This is Stella's weight in pounds.

22. Between the years 2000 and 2010, the number of births in the town of Daneville increased from 1432 to 2219. Which of the following is the approximate percent of increase in the number of births during those ten years? a. 55% b. 36% c. 64% d. 42%

22. A: Begin by subtracting 1432 from 2219. The result is 787. Then, divide 787 by 1432 to find the percent of increase: 0.549, or 54.9%. Rounded up, this is approximately a 55% increase in births between 2000 and 2010.

23. 1/4 times 3/5 divided by 1 1/8 Simplify the expression above. Which of the following is correct? a. 8/15 b. 27/160 c. 2/15 d. 27/40

23. C: Solve the equation in the order of operations: 1/4 times 3/5, or 3/20. Follow this up with division, which requires a reversal of the fraction: 3/20 divided by 9/8, or 3/20 times 8/9. The result is 2/15

24. While at the local ice skating rink, Cora went around the rink 27 times total. She slipped and fell 20 of the 27 times she skated around the rink. What approximate percentage of the times around the rink did Cora not slip and fall? a. 37% b. 74% c. 26% d. 15%

24. C: Cora did not fall 7 out of 27 times. To find the solution, simply divide 7 by 27 to arrive at 0.259, or 25.9%. Rounded up, this is approximately 26%.

25. For her science project, Justine wants to develop a chart that shows the average monthly rainfall in her town. Which type of chart or graph is most appropriate? a. Circle graph b. Bar graph c. Pie chart d. Line graph

25. D: Justine's graph will be charting the amount of rainfall for each month. Line graph indicate change that occurs over a specified period of time, so this is the best type of graph for Justine to use.

26. 3 1/6 - 1 5/6 Simplify the expression above. Which of the following is correct? a. 2 1/3 b. 1 1/3 c. 2 1/9 d. 5/6

26. B: Since the denominator is the same for both fractions, this is simple subtraction. Start by turning each expression into a fraction: 19/6 - 11/6. The result is 8/6, or 1 1/3.

28. 2xy(sq) + 16x (sq) y - 20xy + 8 Which of the following expressions is equivalent to the one listed above? a. b. c. d.

28. C: To solve the equation, start by separating each element:

4. It is 18 degrees Celsius at Essie's hotel in London. What is the approximate temperature in degrees Fahrenheit? a. 25 b. 48 c. 55 d. 64

4. D: To convert from Celsius to Fahrenheit, start by multiplying by 9 and then dividing by 5. Add 32 to the quotient, and the conversion is complete. For question 4: 18(9) = 162 162/5 = 32.4 32.4 + 32 = 64.4, or approximately 64

9. 0.0178 x 2.401 Simplify the expression above. Which of the following is correct? a. 2.0358414 b. 0.0427378 c. 0.2341695 d. 0.3483240

9. B: Question 9 is a simple matter of multiplication. The product is 0.0427378

3. Which of the following is the Roman numeral representation for the year 1768? a. MDCCLXVIII b. MMCXLVIII c. MDCCCXLV d. MDCCXLIII

A: In Roman numerals, M is 1000, D is 500, C is 100, L is 50, X is 10, V is 5, and I is 1. For the year 1768, the Roman numeral MDCCLXVIII is correct - representing 1000 + 500 + 200 + 50 + 10 + 5 + 3. MMCXLVIII is 2148 (still yet to be achieved) MDCCCXLV is 1845, and MDCCXLIII is 1743.

How to calculate kilometers into miles

One kilometer is about 0.62 miles, so 45(0.62) is 27.9, or approximately 28 miles.