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Miguel drove a distance of 150 miles nonstop from his house to his brother's house. Miguel drove the first half of the distance at an average speed of 30 miles per hour, and he drove the second half of the distance at an average speed of 50 miles per hour. Which of the following statements must be true?

Indicate all such statements.
Last year, the price of commodity X was 23 percent less at the end of September than at the beginning of the year, and the price of commodity X was 23 percent greater at the end of the year than at the end of September.

Quantity A

The price of commodity X at the beginning of last year

Quantity B

The price of commodity X at the end of last year






In the figure, the coordinates of point P are (a, b) and ab ≠ 0.

Quantity A

|a+b|

Quantity B

|a-b|


In a distribution of data, x and y are data values with frequencies n and p, respectively, where n and p are positive nonzero integers, and n = p.

Quantity A

$$\frac{nx+py}{n+p}$$

Quantity B

$$\frac{x+y}{2}$$




Quantity A

RS

Quantity B

ST


Integer n is a multiple of 6.

Quantity A

The remainder when 26n is divided by 4

Quantity B

2




Quantity A

$$x^{2}$$+1

Quantity B

x+ $$\frac{7}{8}$$




A homeowner wants to pour concrete for a new patio and walkway according to the layout shown above. If the concrete is to be $$\frac{1}{3}$$ foot thick, how many cubic feet of concrete will be needed to form the patio and walkway?
For a class of more than 100 students, a teacher has calculated the grades of 100 students, and 22 of those grades were A's. If all of the students whose grades remain to be calculated will receive A's and a total of 25 percent of the entire class will receive A's, then how many students' grades remain to be calculated?
In the xy-plane, the graph of which of the following equations does NOT intersect the y-axis?
If a triangle and a square have exactly n points in common, which of the following CANNOT be the value of n?
m is an integer and 4 is a factor of 5m - 9. Which of the following must be an odd integer?
7, 9, 10, 12, 14, 15, 17, 18, 19, 21, 23

A car dealership sold a total of 165 cars for the first 11 months of a certain year, and the list shows the monthly numbers of cars sold, which are ordered from least to greatest. The dealership sold x cars for the last month of the year. If the average (arithmetic mean) of the 12 monthly numbers of cars sold is equal to the median of the 12 monthly numbers of cars sold, what is the greatest possible value of x?
The graph shows the numbers of all immigrants admitted to the United States in year Y who intended to reside in nine selected areas.



For year Y, approximately what was the median of the numbers of immigrants admitted to the United States who intended to reside in the nine areas shown?
The graph shows the numbers of all immigrants admitted to the United States in year Y who intended to reside in nine selected areas.



One immigrant is to be randomly chosen from the immigrants admitted to the United States in year Y who intended to reside in one of three areas: Chicago, Los Angeles, and New York. Approximately what is the probability that the immigrant chosen will be one who intended to reside in Chicago?
The graph shows the numbers of all immigrants admitted to the United States in year Y who intended to reside in nine selected areas.



Based on the information given, which of the following statements about the numbers of immigrants who intended to reside in the 9 areas shown are true?

Indicate all such statements.


AD=$$\frac{1}{3}$$AB

AF=$$\frac{1}{3}$$AC

BE=$$\frac{1}{3}$$BC

The sum of the areas of the shaded regions is what fraction of the area of triangle ABC above?

Give your answer as a fraction.
$$1,575$$ = ($$3^{2}$$) ($$5^{2}$$) ($$7$$)

How many positive factors does the integer $$1,575$$ have, including the factors $$1$$ and $$1,575$$?
Six identical marbles are to be distributed among 4 cups numbered 1 through 4 so that in the resulting distribution there will be at least one marble in each cup. How many different distributions are possible?

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