The figure shows the graphs, in the xy-plane, of the equations y=ax+b and y=cx+k, where a, b, c, and k are constants. Which of the following statements must be true?
Indicate all such statements.
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A list of 42 numbers has an average (arithmetic mean) of 110.0. A second list of 58 numbers has an average of 150.0. What is the average of the 100 numbers in the two lists combined?
_____
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The volume of a large cube is twice the volume of a small cube. If the length of an edge of the small cube is 2, what is the length of an edge of the large cube?
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The average (arithmetic mean) of x,x+2 ,x+4, and x+6 is 6.
What is the average of $$x^{2}$$,$$(x+2)^{2}$$ ,$$(x+4)^{2}$$ , and $$(x+6)^{2}$$ ?
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y≥0
Quantity A:$$(\sqrt{y+5}-\sqrt{y})(\sqrt{y+5}+\sqrt{y})$$
Quantity B:5
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In the xy-plane, the graph of $$y=g_{(x)}$$ intersects the x-axis at 3 points.
Quantity A:The number of points at which the graph of $$y=g_{(x-5)}$$ intersects the x-axis
Quantity B:3
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m and n are positive integers.
n and n+2 are factors of m.
Quantity A:$$\frac{m}{n}$$
Quantity B:n+2
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x>7,999
Quantity A:The digit in the thousands place of x
Quantity B:6
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n is a negative integer, and p is a positive integer.
Quantity A:The product of the integers from n to p, inclusive
Quantity B:0
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x percent of y is $$\frac{3}{4}$$ of z, where xyz≠0 .
Quantity A:$$\frac{xy}{z}$$
Quantity B:75
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Quantity A:x
Quantity B:85
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In the figure above, the circles centered at $$O_{1}$$ and $$O_{2}$$ have radii of equal length. If $$O_{1}O_{2}=9$$ and AB=3, what is the circumference of the circle centered at $$O_{1}$$ ?
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If n is an integer, what is the least value of n for which $$4^{-n}<\frac{1}{512}$$ ?
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On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is $$\frac{1}{4}$$ inch thick, which of the following is closest to the volume inside the box, in cubic inches?
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In the xy-plane above, what is the area of quadrilateral OABC ?
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The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?
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How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?
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What is the range of the average costs for the eight home remodeling projects listed?
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