1.
What is the answer of the following equation?
(2/3+4/6)0=?
Correct Answer
A. 0
Explanation
The given equation is (2/3 + 4/6) * 0. To solve this equation, we first simplify the expression inside the parentheses by finding a common denominator, which is 6. So, (2/3 + 4/6) becomes (4/6 + 4/6), which equals 8/6. Multiplying 8/6 by 0 gives us 0. Therefore, the answer to the equation is 0.
2.
What is the answer of the following equation?
8+8=?
Correct Answer
B. 16
Explanation
The answer to the equation 8+8 is 16.
3.
Inverse
a + (-a) = 0
(-a) + a = 0
0 is the additive inverse
or opposite of a
Correct Answer
A. True
Explanation
The explanation for the given correct answer is that the additive inverse of a number is the number that, when added to the original number, results in zero. In this case, the additive inverse of 'a' is '-a'. Therefore, when 'a' is added to its additive inverse '-a', the result is zero. Similarly, when '-a' is added to 'a', the result is also zero. Therefore, the statement 'a + (-a) = 0' and '(-a) + a = 0' is true.
4.
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?
Correct Answer
C. $400
5.
If y(x-1)=z then x=
Correct Answer
B. Z/y + 1
Explanation
The given equation is y(x-1) = z. To find the value of x, we need to isolate it on one side of the equation. Dividing both sides of the equation by y gives us (x-1) = z/y. Adding 1 to both sides of the equation gives us x = z/y + 1. Therefore, the correct answer is z/y + 1.
6.
Which of the following would be an appropriate unit to measure sugar for a cookie recipe?
Correct Answer
B. Cups
Explanation
Cups would be an appropriate unit to measure sugar for a cookie recipe because it is a commonly used unit for measuring dry ingredients in baking. Liters and quarts are units of volume and would be more suitable for measuring liquids. Kilograms is a unit of weight and would not be appropriate for measuring the volume of sugar in a recipe.
7.
Which of the following values is NOT equal to 34(58+9)?
Correct Answer
B. 58(34+9)
Explanation
The given expression is 34(58+9). To find the value that is not equal to this expression, we can evaluate each option. Evaluating 34 x 67 gives us a different value. Evaluating 58(34+9) gives us the same value as the given expression. Evaluating 34 x 58 + 34 x 9 gives us the same value as the given expression. Evaluating 1,972 + 306 gives us a different value. Therefore, the value that is NOT equal to 34(58+9) is 1,972 + 306.
8.
Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?
Correct Answer
D. 80Â°
Explanation
The sum of the angles in a triangle is always 180Â°. Therefore, to find the measure of the third angle, we subtract the sum of the given angles (15Â° + 85Â° = 100Â°) from 180Â°. This gives us the measure of the third angle as 80Â°.
9.
If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?
Correct Answer
C. 896
Explanation
If 5 ounces is equal to 140 grams, then we can use this ratio to find out how many grams are in 2 pounds of ground meat. Since there are 16 ounces in 1 pound, we can calculate that 2 pounds is equal to 32 ounces. Using the given ratio, we can set up a proportion: 5 ounces/140 grams = 32 ounces/x grams. Cross multiplying and solving for x, we find that x is equal to 896 grams. Therefore, 2 pounds of ground meat is equal to 896 grams.
10.
What is 5 multiplied by the result of subtracting 3 from 7?
Correct Answer
B. 20
Explanation
First, subtract 3 from 7 to get 4.
Then, multiply 4 by 5.
The final answer is 20.
11.
Which year did the most children take swimming lessons?
Correct Answer
D. 1995
12.
Between which year did the largest decrease in children taking swimming lessons occur?
Correct Answer
C. 1992-1993
Explanation
The largest decrease in children taking swimming lessons occurred between the years 1992-1993.
13.
What was the average number of children taking swim lessons from 1990 to 1995?
Correct Answer
B. 308
Explanation
The average number of children taking swim lessons from 1990 to 1995 is 308. This means that if we add up the number of children taking swim lessons each year from 1990 to 1995 and divide it by 6 (since there are 6 years in that time period), we will get an average of 308.
14.
Which of the following is equal to 5.93 x 10^{-2}?
Correct Answer
A. 0.0593
Explanation
The given expression, 5.93 x 10-2, represents a decimal number in scientific notation. In scientific notation, the number is written as a decimal multiplied by a power of 10. In this case, the decimal number is 5.93 and it is multiplied by 10 raised to the power of -2. When we multiply 5.93 by 10 raised to the power of -2, we move the decimal point two places to the left, resulting in the decimal number 0.0593. Therefore, the correct answer is 0.0593.
15.
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?
Correct Answer
C. 124 miles
Explanation
If 1 inch represents 20 miles on the map, and the distance between the two towns is 6 1/5 inches, then we can calculate the actual distance by multiplying 20 miles by 6.2 inches. This gives us a total of 124 miles between the two towns.
16.
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 8 inches high with the lid still being able to be closed?
Correct Answer
B. 24
Explanation
The volume of the Christmas tin is calculated by multiplying its dimensions: 9 inches (depth) x 12 inches (width) x 8 inches (height) = 864 cubic inches. The volume of each cubed piece of fudge is calculated by cubing the length of its edge: 3 inches x 3 inches x 3 inches = 27 cubic inches. To determine how many cubed pieces of fudge can be packed into the tin, divide the volume of the tin by the volume of each piece of fudge: 864 cubic inches / 27 cubic inches = 32 pieces. However, since the lid still needs to be able to close, it is necessary to subtract the height of the lid from the total height of the tin. In this case, the height of the lid is not given, so it is assumed to be 1 inch. Therefore, the total height available for packing the fudge is 8 inches - 1 inch = 7 inches. Dividing the adjusted volume of the tin (9 inches x 12 inches x 7 inches = 756 cubic inches) by the volume of each piece of fudge (27 cubic inches) gives us 756 cubic inches / 27 cubic inches = 28 pieces. Thus, the correct answer is 24 pieces, which is the closest option available.
17.
Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
Correct Answer
B. 15
Explanation
Sarah's age is twice that of her youngest brother, so if we let the youngest brother's age be x, then Sarah's age would be 2x. The difference between their ages is given as 15 years, so we can set up the equation 2x - x = 15. Simplifying this equation gives x = 15, which represents the age of Sarah's youngest brother. Therefore, the correct answer is 15.
18.
Which of the following fractions is equal to 5/6?
Correct Answer
C. 25/30
Explanation
The fraction 25/30 is equal to 5/6 because both fractions can be simplified to 5/6 by dividing the numerator and denominator by their greatest common divisor, which is 5.
19.
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?
Correct Answer
B. $237.60
Explanation
To find the cost of tiling the kitchen floor, we first need to calculate the area of the floor. The area of the floor is given by multiplying the width (12 feet) by the length (20 feet), which gives us 240 square feet. Since the cost of the tile is given per square yard, we need to convert the area from square feet to square yards. Since 1 yard is equal to 3 feet, 1 square yard is equal to 9 square feet. Therefore, the area in square yards is 240 square feet divided by 9, which is approximately 26.67 square yards. Finally, we can find the cost by multiplying the area (26.67 square yards) by the cost per square yard ($8.91), which gives us $237.60.
20.
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?
Correct Answer
C. $12,000
Explanation
The first place winner receives half of the prize money, which means they receive $6,000. The second runner up receives a quarter of what the winner won, which is $6,000/4 = $1,500. To find the total amount of prize money distributed, we add the amount received by the winner and the second runner up: $6,000 + $1,500 = $7,500. However, this is only half of the total prize money, so we need to double it to find the total amount: $7,500 x 2 = $15,000. Therefore, the correct answer is $12,000.
21.
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?
Correct Answer
C. 8.6
Explanation
The average rate for the round trip can be calculated by taking the total distance traveled and dividing it by the total time taken. Since the distance traveled in both directions is the same, the total distance is 2x. The time taken for the first leg of the trip is x/10 and the time taken for the return leg is x/8. Adding these two times gives us (x/10) + (x/8). Dividing the total distance by the total time, we get 2x / ((x/10) + (x/8)). Simplifying this expression gives us 8.6.
22.
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?
Correct Answer
D. 130 feet
Explanation
When you are lying 120 ft away from a tree that is 50 ft tall, you can form a right triangle with the tree as the height and the distance from you to the tree as the base. The straight line distance from your head to the top of the tree is the hypotenuse of this triangle. By using the Pythagorean theorem, we can calculate the length of the hypotenuse. The square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, it is equal to (120^2 + 50^2) = 14400 + 2500 = 16900. Taking the square root of 16900 gives us the length of the hypotenuse, which is approximately 130 feet.
23.
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?
Correct Answer
D. $194.88
Explanation
To find the cost of edging the flower bed, we need to calculate the perimeter of the flower bed and then multiply it by the cost per stone.
The flower bed is 6 yards by 1 yard, so the perimeter is (6+6+1+1) yards = 14 yards.
Since each stone is 12 inches long, we need (14 yards * 36 inches/yard) / 12 inches = 42 stones.
Therefore, the cost of edging the flower bed is (42 stones * $2.32 per stone) = $97.44.
However, since we want a double layer of edging, we need to multiply this by 2, resulting in a total cost of $194.88.
24.
If 3x=6x-15 then x + 8=
Correct Answer
D. 13
Explanation
If 3x = 6x - 15, we can solve for x by subtracting 3x from both sides of the equation, resulting in -3x = -15. Dividing both sides by -3 gives x = 5. Therefore, substituting this value of x into the expression x + 8 gives us 5 + 8 = 13.