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Explanation When multiplying variables with exponents, you add the exponents together. In this case, x^32 * x^4 * x^-4 * x^12 can be simplified by adding the exponents: 32 + 4 - 4 + 12 = 44. Therefore, the answer is x^44.
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2.
Simplify
A.
4x^3/y
B.
4x/y
C.
X^3y/4
D.
4y/x^3
Correct Answer A. 4x^3/y
Explanation The given expression can be simplified by dividing the numerator and denominator by 4. This gives us 4x^3/y. Therefore, the correct answer is 4x^3/y.
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3.
Simplify
A.
-9x^6y^3
B.
9x^5y^2
C.
9x^6y^2
D.
-9x^5y^2
Correct Answer C. 9x^6y^2
Explanation To simplify the given expression, we need to combine like terms. The negative sign in front of -9x^6y^3 indicates that the term is negative. When we divide -9x^6y^3 by 9x^5y^2, we get -x. Since the exponents of x and y are the same in both terms, we can subtract the exponents and keep the base. Therefore, the simplified expression is -x. However, the given answer is 9x^6y^2, which is incorrect.
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4.
Consider the graph of the function , how will affect the graph?
A.
Shift 3 left and 2 up
B.
Shift 3 right and 2 up
C.
Shift 3 up and 2 right
D.
Shift 3 down and 2 right
Correct Answer B. Shift 3 right and 2 up
Explanation When we shift the graph 3 units to the right, all the x-coordinates of the points on the graph will increase by 3. This means that the entire graph will move horizontally to the right. Additionally, when we shift the graph 2 units up, all the y-coordinates of the points on the graph will increase by 2. This means that the entire graph will move vertically upwards. Therefore, the correct answer is to shift the graph 3 units to the right and 2 units up.
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5.
Sales of IPads The iPad has become the most quickly adopted nonphone consumer electronics product in history, topping the DVD player. Apple sole over 300,000 ipads in its first day and took just 28 days to reach 1 million units sold. Sales of the iPad can be modeled by , where x is the number of months after April 1, 2010 and y is the number of millions of iPads sold. According to this model, how many iPads would be sold by August 2011?
A.
324 million
B.
473 million
C.
13 million
D.
14.5 million
Correct Answer A. 324 million
6.
Rewrite as a single logarithm.
Answer Choices:
A.
B.
C.
D.
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
7.
Solve for x:
A.
3
B.
1.442
C.
0.815
D.
2
Correct Answer D. 2
8.
Solve for x:
A.
20
B.
100
C.
1000
D.
26.853
Correct Answer B. 100
9.
Solve for x:
A.
1/3
B.
3
C.
1/9
D.
27
Correct Answer A. 1/3
Explanation The given answer, 1/3, is the correct solution for the equation. By dividing 1 by 3, we get the value of x as 1/3.
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10.
Life Span Based on data from 1920 and projected to 2020, the expected life span of people in the United States can be described by the function , where x is the number of years from 1900 to the person's birth year. Estimate the life span for someone born in 2008.
A.
120 years
B.
6 years
C.
78 years
D.
80 years
Correct Answer C. 78 years
Explanation Based on the given function, the life span of people in the United States is described by the equation. Since the question asks for an estimate of the life span for someone born in 2008, we need to find the value of the function when x is equal to 108 (2008 - 1900). Therefore, the estimated life span for someone born in 2008 is 78 years.