Mathematics Flashcards

1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?

Answer: $400

To find the original cost, we need to reverse the discounts. First, the $306 price represents 85% of the price after the initial 10% discount (100% - 15% = 85%). So, $306 / 0.85 = $360. This $360 then represents 90% of the original cost (100% - 10% = 90%). Therefore, $360 / 0.90 = $400, which is the original cost.

2. If y(x-1)=z then x=

Answer: z/y + 1

To solve for x, first divide both sides of the equation y(x-1)=z by y, which gives x-1 = z/y. Then, add 1 to both sides of the equation to isolate x. This results in x = z/y + 1.

3. Which of the following values is NOT equal to 34(58+9)?

Answer: 58(34+9)

The original expression 34(58+9) simplifies to 34 * 67, which equals 2278. Option B, 58(34+9), simplifies to 58 * 43, which equals 2494. This value is different from 2278, making it the expression that is NOT equal to the original. Options A, C, D, and E all correctly represent or simplify to 2278 due to the distributive and commutative properties.

4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?

Answer: 80°

The sum of the interior angles in any triangle is always 180 degrees. Given two angles of 15° and 85°, their sum is 100°. To find the third angle, subtract this sum from 180 degrees (180° - 100° = 80°).

5. If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?

Answer: 896

First, convert 2 pounds to ounces, knowing that 1 pound equals 16 ounces, so 2 pounds is 32 ounces. Next, use the given conversion rate: if 5 ounces equals 140 grams, then 1 ounce equals 140/5 = 28 grams. Finally, multiply 28 grams/ounce by 32 ounces to find the total grams: 28 * 32 = 896 grams.

6. Which year did the most children take swimming lessons?

Answer: 1995

To determine the year with the most children taking swimming lessons, one would examine the provided data (likely a bar graph or table). The year 1995 would show the highest number of participants compared to all other years listed.

7. Between which year did the largest decrease in children taking swimming lessons occur?

Answer: 1992-1993

To identify the largest decrease, you would calculate the difference in the number of children taking lessons between consecutive years. The period from 1992 to 1993 would show the greatest negative change, indicating the largest drop in participation.

8. What was the average number of children taking swim lessons from 1990 to 1995?

Answer: 308

To calculate the average, you need to sum the number of children who took swimming lessons for each year from 1990 to 1995. Then, divide this total sum by the number of years, which is six. The result of this calculation is 308.

9. Which of the following is equal to 5.93 x 10-2?

Answer: 0.0593

To convert a number from scientific notation with a negative exponent to standard form, move the decimal point to the left. The exponent of -2 indicates that the decimal point should be moved two places to the left. Starting with 5.93, moving the decimal two places left results in 0.0593.

10. On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5 inches. How many miles are actually between the two towns?

Answer: 124 miles

First, convert the mixed number 6 1/5 inches to a decimal, which is 6.2 inches. Since 1 inch on the map represents 20 miles in reality, multiply the map distance by the scale factor. Therefore, 6.2 inches * 20 miles/inch = 124 miles.

11. Which of the following is a correct graph of x>1, x<4 ?

Answer: Line A

The inequalities x > 1 and x < 4 describe all numbers greater than 1 but less than 4. On a number line, this is represented by an open interval between 1 and 4. This means there should be open circles (or parentheses) at 1 and 4, with the line segment between them shaded.

12. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 9 inches high with the lid still being able to be closed?

Answer: 36

To find how many cubes fit, calculate how many can fit along each dimension of the tin. For the 12-inch width, 12/3 = 4 cubes fit. For the 9-inch depth, 9/3 = 3 cubes fit. For the 9-inch height, 9/3 = 3 cubes fit. Multiply these numbers together (4 * 3 * 3) to get the total number of cubes that can be packed, which is 36.

13. Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?

Answer: 15

Let the youngest brother's age be 'B'. Sarah is twice as old, so her age is '2B'. The difference between their ages is 15 years, which can be written as 2B - B = 15. Solving this equation, we find that B = 15. Therefore, her youngest brother is 15 years old.

14. Which of the following fractions is equal to 5/6?

Answer: 25/30

To find a fraction equal to 5/6, you need to multiply both the numerator and the denominator by the same non-zero number. In this case, multiplying both by 5 gives (5 * 5) / (6 * 5) = 25/30. This process creates an equivalent fraction that represents the same value.

15. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?

Answer: $237.60

First, calculate the area of the kitchen floor: 12 feet * 20 feet = 240 square feet. Since the tile cost is given per square yard, convert the area to square yards by dividing by 9 (as 1 square yard = 3 feet * 3 feet = 9 square feet): 240 sq ft / 9 sq ft/sq yd = 26.666... square yards. Finally, multiply the area in square yards by the cost per square yard: 26.666... * $8.91 = $237.60.

16. In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000?

Answer: $12,000

The winner received $6,000, which is stated to be 1/2 of the total prize money. To find the total prize money, you simply multiply the winner's amount by 2. Therefore, $6,000 * 2 = $12,000 was the total amount of prize money distributed. The information about the second runner-up is extraneous for this calculation.

17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line?

Answer: 130 feet

This problem forms a right-angled triangle, where the distance from you to the tree (120 ft) and the height of the tree (50 ft) are the two legs. The straight-line distance from your head to the top of the tree is the hypotenuse. Using the Pythagorean theorem (a² + b² = c²), we calculate 50² + 120² = c², which simplifies to 2500 + 14400 = 16900. Taking the square root of 16900 gives c = 130 feet.

18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

Answer: 8.9

To find the average rate, divide the total distance by the total time. Let 'x' be the one-way distance, so the total distance for the round trip is 2x. The time going is x/10 hours, and the time returning is x/8 hours. The total time is x/10 + x/8 = (4x + 5x)/40 = 9x/40 hours. The average rate is (2x) / (9x/40) = 2x * (40/9x) = 80/9, which approximately equals 8.9 miles per hour.

19. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?

Answer: $194.88

First, calculate the perimeter of the flower bed in yards: 2 * (6 yards + 1 yard) = 14 yards. Convert this to inches: 14 yards * 3 feet/yard * 12 inches/foot = 504 inches. Since a double layer of edging is desired, the total length needed is 2 * 504 inches = 1008 inches. Each stone is 12 inches, so 1008 inches / 12 inches/stone = 84 stones are needed. Finally, multiply the number of stones by the cost per stone: 84 * $2.32 = $194.88.

20. If 3x=6x-15 then x + 8=

Answer: 13

First, solve the equation 3x = 6x - 15 for x. Subtract 6x from both sides to get -3x = -15, then divide by -3 to find x = 5. The question asks for the value of x + 8. Substitute x = 5 into the expression: 5 + 8 = 13.