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The number 64 is divisible by which of the following?
A.
3
B.
5
C.
6
D.
4
Correct Answer D. 4
Explanation The number 64 is divisible by 4 because it can be divided evenly by 4 without leaving a remainder.
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2.
In the expression (-4)^2 , -4 is called the ___________?
A.
Product
B.
Power
C.
Exponent
D.
Base
Correct Answer D. Base
Explanation In the expression (-4)^2, -4 is referred to as the base. The base is the number that is being raised to a power or exponent. In this case, -4 is being squared, which means it is being multiplied by itself. Therefore, -4 is the base of the expression.
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3.
List the factors of 42.
Correct Answer 1,2,3,6,7,14,21,42
Explanation The factors of a number are the numbers that divide evenly into it. In this case, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. These numbers can be multiplied together to give the original number, 42.
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4.
Find y for y=x^2 - 15 if x = 6.
A.
21
B.
49
C.
-3
D.
51
Correct Answer A. 21
Explanation When x is equal to 6, we can substitute this value into the equation y = x^2 - 15. Therefore, y = 6^2 - 15 = 36 - 15 = 21. Thus, the value of y is 21.
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5.
Factor 144 completely.
Correct Answer 2X2X2X2X2X3X3
Explanation The number 144 can be completely factored as 2 multiplied by itself 5 times (2^5) and multiplied by 3 squared (3^2). Therefore, the complete factorization of 144 is 2 multiplied by itself 5 times, multiplied by 3 squared.
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6.
What is a monomial?
Correct Answer A monomial is a number or variable or the product of a number and a variable
Explanation A monomial is a mathematical expression that consists of either a number, a variable, or the product of a number and a variable. It is a single term expression that can be simplified or evaluated. Monomials are important in algebraic expressions and equations as they help in simplifying and solving mathematical problems.
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7.
Write the ratio of 24 to 96 in simplest form.
A.
12/48
B.
1/4
C.
4/1
D.
3/12
Correct Answer B. 1/4
Explanation The ratio of 24 to 96 can be simplified by dividing both numbers by their greatest common factor, which is 24. Dividing 24 by 24 gives 1, and dividing 96 by 24 gives 4. Therefore, the simplified ratio is 1/4.
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8.
How would 9.3 X 10^-7 be written in standard form?
A.
93,000,000
B.
930,000,000
C.
.00000093
D.
.000000093
Correct Answer C. .00000093
Explanation The given number, 9.3 x 10^-7, is in scientific notation. To convert it to standard form, we move the decimal point 7 places to the left, resulting in .00000093.
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9.
Find the GCF of 3x^2y and 15xy.
A.
3xy^2
B.
3x^2y
C.
3xy
D.
3x^2y^2
Correct Answer C. 3xy
Explanation The GCF (Greatest Common Factor) is the largest number or term that divides evenly into two or more numbers or terms. In this case, the GCF of 3x^2y and 15xy is 3xy because it is the largest term that both 3x^2y and 15xy can be divided by without leaving a remainder.
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10.
Evaluate y^-5 if y = -2
A.
32
B.
-1/32
C.
1/32
D.
-32
Correct Answer B. -1/32
Explanation To evaluate y^-5, we need to substitute the value of y, which is -2, into the expression. So, (-2)^-5 = 1/(-2)^5 = 1/(-32) = -1/32. Therefore, the correct answer is -1/32.
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11.
Factor the expression 48s^3t^2 + 12st
A.
4st
B.
12st
C.
12s^3t^2
D.
4s^3t^2
Correct Answer B. 12st
Explanation The given expression can be factored by finding the greatest common factor (GCF) of the terms. In this case, the GCF of 48s^3t^2 and 12st is 12st. By factoring out the GCF, we get 12st multiplied by the expression (4s^2t + 1), which cannot be simplified further. Therefore, the correct answer is 12st.
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12.
What is a prime number?
Correct Answer A number with exactly 2 factors, 1 and itself.
Explanation A prime number is a number that can only be divided by 1 and itself. It does not have any other factors. This means that prime numbers cannot be divided evenly by any other number except for 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers because they can only be divided by 1 and themselves.
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13.
What is a composite number?
Correct Answer A number that has more than 2 factors.
Explanation A composite number is a number that has more than 2 factors. In other words, it is a number that can be divided evenly by at least one other number besides 1 and itself. For example, the number 6 is a composite number because it can be divided evenly by 1, 2, 3, and 6.
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14.
Write the prime factorization of 300.
Correct Answer 2^2 X 3 X 5^2
Explanation The prime factorization of 300 is 2^2 x 3 x 5^2. This means that 300 can be expressed as the product of its prime factors raised to their respective powers. In this case, 2 is raised to the power of 2, 3 is raised to the power of 1, and 5 is raised to the power of 2.
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15.
What is the quotient of (42/-6) (g^8/g^0)
A.
7g^7
B.
-7g^7
C.
7g^8
D.
-7g^8
Correct Answer D. -7g^8
Explanation The given expression can be simplified by dividing the coefficients and subtracting the exponents of the variables. When dividing 42 by -6, the quotient is -7. When dividing g^8 by g^0, the quotient is g^(8-0) which simplifies to g^8. Therefore, the quotient of (42/-6) (g^8/g^0) is -7g^8.
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16.
Write using scientific notation: .000546
Correct Answer 5.46 X 10^-4
Explanation The given number, .000546, can be written in scientific notation as 5.46 x 10^-4. In scientific notation, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, the decimal is 5.46, and the power of 10 is -4. This means that the decimal point is moved 4 places to the left to obtain the original number.
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17.
Use positive exponents .1
A.
10
B.
1/10
C.
1^0
D.
1
Correct Answer B. 1/10
Explanation The given list includes numbers raised to the power of positive exponents. The numbers are 10, 1/10, 1^0, and 1. The only number that is raised to a positive exponent is 10, which is equal to 10^1. Therefore, the correct answer is 10.
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18.
Write fraction in simplest form 42xyz^3/49xy
Correct Answer 6z^3/7
Explanation The given expression is a fraction with a numerator of 42xyz^3 and a denominator of 49xy. To simplify this fraction, we can cancel out the common factors in the numerator and denominator. Both the numerator and denominator have factors of xy, so we can cancel them out. This leaves us with 42z^3/49. The remaining fraction can be simplified further by dividing both the numerator and denominator by 7, resulting in the final answer of 6z^3/7.
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19.
Is 243 divisible by 2,3,4,5,6,9,10?
Correct Answer 3,9
Explanation To determine if 243 is divisible by 2, we check if the last digit is even, which it is not. Therefore, 243 is not divisible by 2. To determine if 243 is divisible by 3, we sum the digits (2+4+3=9) and check if the result is divisible by 3, which it is. Therefore, 243 is divisible by 3. Since 243 is divisible by 3, it is also divisible by 9, as 9 is a factor of 3. Therefore, the correct answer is 3,9.
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20.
Evaluate n^0 + 2n^3p^0 - 3m^1 when m = 3, n = 2, p = -4.
A.
8
B.
-9
C.
-73
D.
0
Correct Answer A. 8
Explanation To evaluate the expression, we substitute the given values for m, n, and p into the expression. Since any number raised to the power of 0 is 1, n^0 becomes 1. Similarly, p^0 is also 1. Therefore, the expression simplifies to 1 + 2(2^3)(1) - 3(3^1). Evaluating further, we get 1 + 2(8)(1) - 3(3) = 1 + 16 - 9 = 17 - 9 = 8. Therefore, the correct answer is 8.