1.
If you take the digits 1, 2, 3, 4, and 5, how many different 5-digit numbers can be formed without repeating any digits?
Correct Answer
B. 120
Explanation
To find the number of different 5-digit numbers that can be formed without repeating any digits, we can use the concept of permutations. Since there are 5 digits available (1, 2, 3, 4, and 5), we need to find the number of permutations of 5 digits taken at a time without repetition. This can be calculated using the formula for permutations: nPr = n! / (n-r)!, where n is the total number of items and r is the number of items taken at a time. In this case, n = 5 and r = 5, so the number of different 5-digit numbers that can be formed is 5! / (5-5)! = 5! / 0! = 5! = 5 x 4 x 3 x 2 x 1 = 120.
2.
What is the Roman numeral for 100?
Correct Answer
B. C
Explanation
The Roman numeral for 100 is C. In the Roman numeral system, C represents the number 100. It is derived from the Latin word "centum," which means 100. The letter C is often used to represent this value in various contexts, including dates, centuries, and numerical calculations.
3.
What is the mean length of a track on a music CD with tracks that are 3.05, 4.23, and 4.03 minutes long?
Correct Answer
D. 3.77 Minutes
Explanation
The mean length of a track on a music CD is calculated by summing up the lengths of all the tracks and dividing it by the total number of tracks. In this case, the sum of the track lengths is 3.05 + 4.23 + 4.03 = 11.31 minutes. Since there are 3 tracks, the mean length would be 11.31 / 3 = 3.77 minutes.
4.
What is the population of a set that contains North and South Carolina, Vermont, Maine and Alaska?
Correct Answer
B. 5
Explanation
The population of the set that contains North and South Carolina, Vermont, Maine, and Alaska is 5. This is because the set includes 5 states, and the question is asking for the population of the set, not the population of each individual state.
5.
How would you give someone 96 cents in change using the least number of coins?
Correct Answer
C. 3 Quarters, 2 Dimes, 1 Penny
Explanation
To give someone 96 cents in change using the least number of coins, we need to find combinations that add up to 96 cents. The first option of 3 quarters, 2 nickels, and 11 pennies totals 96 cents, but we can reduce the number of coins by using dimes instead of nickels. The second option of 3 quarters, 4 nickels, and 1 penny totals 96 cents and is a valid combination. However, the third option of 3 quarters, 2 dimes, and 1 penny also totals 96 cents and uses the least number of coins. Therefore, the correct answer is 3 Quarters, 2 Dimes, 1 Penny.
6.
What is the surface area of a rectangular box which is 100 mm long, 70 mm wide and 50 mm high?
Correct Answer
C. 31,000 Square Millimeters
Explanation
The surface area of a rectangular box can be calculated by finding the area of each face and then summing them up. In this case, the box has six faces: the top and bottom faces are both 100 mm long and 70 mm wide, so each has an area of 100 mm * 70 mm = 7000 square mm. The front and back faces are both 100 mm long and 50 mm high, so each has an area of 100 mm * 50 mm = 5000 square mm. The left and right faces are both 70 mm wide and 50 mm high, so each has an area of 70 mm * 50 mm = 3500 square mm. Adding up all the areas gives a total surface area of 7000 + 7000 + 5000 + 5000 + 3500 + 3500 = 31,000 square mm.
7.
What is the volume of a box that has a length of 100 mm, a height of 50 mm, and a width of 70 mm?
Correct Answer
C. 350,000 Cubic Millimeters
Explanation
The volume of a box is calculated by multiplying its length, height, and width. In this case, the length is 100 mm, the height is 50 mm, and the width is 70 mm. Multiplying these values together, we get 100 mm * 50 mm * 70 mm = 350,000 cubic millimeters. Therefore, the correct answer is 350,000 Cubic Millimeters.
8.
Which property is demonstrated by "a(b + c) = ab + ac"?
Correct Answer
A. Distributive Property
Explanation
The given equation "a(b + c) = ab + ac" demonstrates the Distributive Property. This property states that when multiplying a number by the sum of two other numbers, the result is equal to the sum of the products of the number multiplied by each of the other two numbers separately. In this case, "a" is being multiplied by the sum of "b" and "c", and the result is equal to the sum of "a" multiplied by "b" and "a" multiplied by "c".
9.
If two of the interior angles in a triangle are 45 degrees and 90 degrees, how much is 3rd angle?
Correct Answer
A. 45 Degrees
Explanation
In a triangle, the sum of all interior angles is always 180 degrees. Given that two of the interior angles are 45 degrees and 90 degrees, we can find the third angle by subtracting the sum of these two angles from 180 degrees. 45 + 90 = 135, so the third angle must be 180 - 135 = 45 degrees.
10.
If property taxes in 2006 were $4126 and in 2007 they went up to $4400, what is the percent increase in taxes?
Correct Answer
C. 6.64%
Explanation
The percent increase in taxes can be calculated by finding the difference between the two amounts ($4400 - $4126 = $274), dividing that difference by the original amount ($274 / $4126 = 0.0664), and then converting the decimal to a percentage (0.0664 * 100 = 6.64%). Therefore, the correct answer is 6.64%.
11.
The volume of a 4 inches wide and 3 inches high box is 36 cubic inches, what is its length?
Correct Answer
A. 3 Inches
Explanation
To find the length of the box, we can use the formula for volume, which is length × width × height. Given that the width is 4 inches and the height is 3 inches, and the volume is 36 cubic inches, we can set up the equation 4 × 3 × length = 36. Solving for length, we divide both sides by 12 to get length = 36 ÷ (4 × 3) = 3 inches. Therefore, the length of the box is 3 inches.
12.
You start at (0,2) on a rectangular coordinate system and move 3 down and 7 right, where are you now?
Correct Answer
C. (7, -1)
Explanation
Starting at (0,2), moving 3 down means subtracting 3 from the y-coordinate, giving us (0, -1). Moving 7 right means adding 7 to the x-coordinate, giving us (7, -1). Therefore, the correct answer is (7, -1).
13.
The congruent sides of an isosceles triangle are 4" each; if the perimeter is 14", how long is the 3rd side?
Correct Answer
C. 6"
Explanation
In an isosceles triangle, two sides are congruent. In this case, the congruent sides are each 4". The perimeter of the triangle is given as 14". To find the length of the third side, we subtract the sum of the congruent sides from the perimeter. So, 14" - (4" + 4") = 6". Therefore, the length of the third side is 6".
14.
If we start at (0,0) on a rectangular coordinate system and move 5 right and 6 down, where are we?
Correct Answer
A. (5, -6)
Explanation
Starting at (0,0) and moving 5 units to the right means we move along the positive x-axis to the point (5,0). Then, moving 6 units down means we move along the negative y-axis to the point (5,-6). Therefore, we end up at the coordinates (5, -6).
15.
If we start at (0,0) on a rectangular coordinate system, and move right 2 and up 9 , where are we?
Correct Answer
B. (2, 9)
Explanation
Starting at (0,0) and moving right 2 and up 9 means we move 2 units to the right along the x-axis and 9 units up along the y-axis. Therefore, we end up at the point (2, 9) on the coordinate system.