1.
One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?
Correct Answer
B. 24 horses and 50 humans
Explanation
Let's use a system of equations to solve this problem. Let H represent the number of humans and T represent the number of horses. We know that each human has 1 head and 2 legs, and each horse has 1 head and 4 legs. The person counted 74 heads and 196 legs, so we can write the following equations:
H + T = 74 (total number of heads)
2H + 4T = 196 (total number of legs)
Now, we can solve this system of equations:
From equation 1, we can express H in terms of T: H = 74 - T.
Substitute this into equation 2:
2(74 - T) + 4T = 196 148 - 2T + 4T = 196 2T = 196 - 148 2T = 48 T = 48 / 2 T = 24
Now that we know the number of horses (T = 24), we can find the number of humans using equation 1:
H = 74 - 24 H = 50
So, there were 50 humans and 24 horses.
2.
Y=log x
If y=10, then what is x?
Correct Answer
A. 10
3.
What is 10*9*8*7*6*5*4*3*2*1?
Correct Answer
A. 10! or 3628800
Explanation
The given question is asking for the product of all the numbers from 1 to 10. This is represented by the factorial notation, which is denoted by an exclamation mark (!). Therefore, 10! means multiplying all the numbers from 1 to 10 together. In this case, 10! equals 3628800.
4.
If 1/2x+1/2(1/2x+1/2(1/2x+1/2(1/2x+1/2...=y
What does x equal?
Correct Answer
D. 1
Explanation
The given equation represents an infinite geometric series with a common ratio of 1/2. To find the value of y, we can use the formula for the sum of an infinite geometric series: S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. In this case, a = 1/2x and r = 1/2. Plugging these values into the formula, we get y = (1/2x) / (1 - 1/2) = (1/2x) / (1/2) = (1/2x) * (2/1) = 1/x. Therefore, y = 1/x. Since the answer is given as 1, we can conclude that x must equal 1.
5.
What's the only place in this world who's Fahrenheit and Celsius degrees can be equal?
Correct Answer
B. Antarctica at -40 degrees
Explanation
Antarctica at -40 degrees is the only place in the world where Fahrenheit and Celsius degrees can be equal. This is because -40 degrees Fahrenheit is equal to -40 degrees Celsius. In all other options, the Fahrenheit and Celsius degrees are not equal.
6.
If x*x-2x-35=0
then x=?
Correct Answer(s)
C. -5
D. 7
7.
What is the square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power?
Correct Answer
C. 1
Explanation
The given expression can be simplified as follows: square root of 3 to the square root of 2 power is equal to 3^(sqrt(2)). Similarly, square root of 3 to the negative square root of 2 power is equal to 3^(-sqrt(2)). Therefore, the given expression becomes 3^(sqrt(2)) * 3^(-sqrt(2)), which is equal to 3^(sqrt(2) - sqrt(2)). Since the exponent is zero, any number raised to the power of zero is equal to 1. Hence, the answer is 1.
8.
What is the square root of 2 to the square root of 2 power to the square root of 2 power?
Correct Answer
A. 2
Explanation
The square root of 2 to the square root of 2 power can be simplified as 2^(âˆš2). Then, raising 2 to the power of âˆš2 is equivalent to taking the square root of 2. Therefore, the square root of 2 to the square root of 2 power is equal to 2.
9.
What is the square root of 2 to the negative 9 plus 3 power?
Correct Answer
B. 1/8
Explanation
To simplify the expression, we need to evaluate the square root of 2 to the negative 9 plus 3 power. First, we simplify the exponent by adding -9 and 3, which gives us -6. Then, we take the square root of 2 to the power of -6. The square root of 2 is approximately 1.414, and raising it to the power of -6 gives us a very small number. Therefore, the answer is 1/8, as it is the only option that represents a small fraction.
10.
Draw 2 supplementary angles. One angle is x-15 degrees and one is 2x degrees. What is the value of x in degrees?
Correct Answer
A. 65 degrees
Explanation
Two angles are called supplementary if the sum of their measures is equal to 180 degrees. In this question, we are given two angles: one is x-15 degrees and the other is 2x degrees. To find the value of x, we need to set up an equation. The sum of the measures of the two angles is (x-15) + (2x) = 180. Simplifying this equation, we get 3x - 15 = 180. Adding 15 to both sides, we have 3x = 195. Dividing both sides by 3, we find x = 65 degrees. Therefore, the value of x is 65 degrees.