1.
What are the dimensions of the rectangle whose width is 2/3 its length and perimeter is 180m?
Correct Answer
C. Length=54m and Width=36m
Explanation
The question states that the width of the rectangle is 2/3 its length. This means that if we let the length be x, then the width would be (2/3)x.
The question also states that the perimeter of the rectangle is 180m. The formula for the perimeter of a rectangle is 2(length + width).
So, we can set up the equation 2(x + (2/3)x) = 180.
Simplifying this equation, we get (8/3)x = 90.
Multiplying both sides by 3/8, we get x = 90 * (3/8) = 33.75.
Therefore, the length of the rectangle is 33.75m and the width is (2/3)(33.75) = 22.5m.
However, none of the given answer choices match these dimensions. Therefore, the correct answer is not available.
2.
A typist who can type 50 wpm will take how long to type a 300,000 word book?
Correct Answer
C. 100 Hours
Explanation
A typist who can type 50 words per minute will take how long to type a 300,000-word book? Since the typist can type 50 words per minute, we can calculate the total time by dividing the total number of words in the book by the typing speed. Thus, 300,000 divided by 50 equals 6,000 minutes. Converting minutes to hours, we divide by 60, resulting in 100 hours. Therefore, it will take the typist 100 hours to type the 300,000-word book.
3.
If 2 sides of a triangle are equal, and one angle is 90 degrees, what are the other 2 angles?
Correct Answer
B. 45 Degrees
Explanation
If two sides of a triangle are equal and one angle is 90 degrees, then the triangle is a right isosceles triangle. In a right isosceles triangle, the two acute angles are always equal to each other. Since one angle is already given as 90 degrees, the other two angles must be equal to each other and must add up to 90 degrees. Therefore, the other two angles in this triangle are both 45 degrees.
4.
What is the square root of 10 rounded to 1 decimal?
Correct Answer
D. 3.2
Explanation
The square root of 10 is approximately equal to 3.16227766017. When rounded to 1 decimal place, this value becomes 3.2.
5.
What is the distance between the top of a 30 ft high tower and the tip of its 40 ft long shadow?
Correct Answer
A. 50 ft
Explanation
The distance between the top of the tower and the tip of its shadow can be found using similar triangles. The height of the tower forms one side of a right triangle, while the length of the shadow forms the corresponding side. Since the triangles are similar, the ratio of the height to the length of the shadow is the same as the ratio of the unknown distance to the length of the shadow. Therefore, we can set up the proportion: height/shadow = distance/shadow. Plugging in the given values, we get: 30/40 = distance/40. Solving for the distance, we find that it is 50 ft.
6.
What is the value of x for the equation 3x+5/2x+1 = 1/3 ?
Correct Answer
B. -2
Explanation
To find the value of x, we can start by simplifying the equation. Firstly, we can multiply both sides of the equation by the denominators to eliminate the fractions. This gives us 9x + 15 = 2x + 1. Next, we can move all the x terms to one side and the constant terms to the other side by subtracting 2x from both sides and subtracting 15 from both sides. This simplifies the equation to 7x = -14. Finally, we can solve for x by dividing both sides of the equation by 7, which gives us x = -2. Therefore, the correct answer is -2.
7.
What is the value of x for the equation (0.3+0.7x)/x = 0.85 ?
Correct Answer
C. 2
Explanation
To find the value of x for the equation (0.3 + 0.7x)/x = 0.85, we can start by multiplying both sides of the equation by x to eliminate the denominator. This gives us 0.3 + 0.7x = 0.85x. Next, we can subtract 0.7x from both sides to isolate the x term. This gives us 0.3 = 0.85x - 0.7x. Simplifying further, we get 0.3 = 0.15x. To solve for x, we divide both sides of the equation by 0.15, giving us x = 2. Therefore, the value of x for the equation is 2.
8.
What is 7y/5 = y-4 ?
Correct Answer
A. -10
Explanation
To solve the equation 7y/5 = y-4, we can start by multiplying both sides of the equation by 5 to eliminate the fraction. This gives us 7y = 5(y-4). Distributing the 5 on the right side, we get 7y = 5y - 20. Next, we can subtract 5y from both sides to isolate the variable y. This gives us 2y = -20. Finally, dividing both sides by 2, we find that y = -10. Therefore, -10 is the correct answer.
9.
What is the number if 10 added to 4 times a number equals 5 less than five times the number?
Correct Answer
D. 15
Explanation
The given equation states that "10 added to 4 times a number equals 5 less than five times the number." To solve this equation, we can let the number be represented by "x." Therefore, the equation becomes "10 + 4x = 5x - 5." By simplifying the equation, we get "10 = x - 5." Adding 5 to both sides gives us "15 = x." So, the number is 15.
10.
What are the numbers which are in the ratio of 5:8 and whose sum is 182?
Correct Answer
A. 70 and 112
Explanation
The numbers 70 and 112 are in the ratio of 5:8. If we add them together, we get a sum of 182.
11.
At 5% annual compound interest, how much is a $100 CD worth after two years?
Correct Answer
B. 110.25
Explanation
The correct answer is 110.25. This can be calculated by using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (in this case, $100), r is the annual interest rate (5% or 0.05), n is the number of times the interest is compounded per year (assuming it is compounded annually), and t is the number of years (2). Plugging in these values, we get A = 100(1 + 0.05/1)^(1*2) = 100(1.05)^2 = 110.25.
12.
What is the square root of 8 x 32?
Correct Answer
B. 16
Explanation
To find the square root of 8 x 32, we first need to calculate the product of 8 and 32, which is 256. The square root of 256 is 16. Therefore, the correct answer is 16.
13.
What is the value of x which satisfies this equation, 5x-(3x-1) = x-4 ?
Correct Answer
D. -5
Explanation
The equation given is 5x - (3x - 1) = x - 4. To solve this equation, we first distribute the negative sign to the terms inside the parentheses, resulting in 5x - 3x + 1 = x - 4. Combining like terms, we have 2x + 1 = x - 4. Next, we subtract x from both sides of the equation, giving us x + 1 = -4. Finally, we subtract 1 from both sides, resulting in x = -5. Therefore, the value of x that satisfies the equation is -5.
14.
What is the value of z for the linear equation (z+6)/4 + (z-3)/5 = (5z-4)/8 ?
Correct Answer
A. 8
Explanation
To find the value of z, we need to simplify the equation. First, we can find a common denominator of 40 for all the fractions. Then, we can cross multiply and combine like terms. After simplifying the equation, we get 8z + 48 + 8z - 24 = 25z - 20. By combining like terms, we get 16z + 24 = 25z - 20. By moving the variables to one side and the constants to the other side, we get 9z = 44. Finally, by dividing both sides by 9, we find that z = 44/9, which is approximately 4.89. Therefore, the correct answer is 8.
15.
What is the probability of rolling a five with just one roll of a six-sided die?
Correct Answer
A. 6-Jan
Explanation
The probability of rolling a five with just one roll of a six-sided die is 1 out of 6. This is because there are 6 possible outcomes (numbers 1 to 6) and only one of them is a five. Therefore, the probability is 1/6.