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The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

c,c,c,2c,4c,4c,5c,6c

In the list of 8 numbers shown, c > 0. Which of the following is closest to the standard deviation of the 8 numbers?
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

Data sets K and T have the same number of values.Each value in K is either 0 or 2, and both 0 and 2 occur in K at least once. Each value in T is either 0 or 1,and both 0 and 1 occur in T at least once.

Quantity A

The standard deviation of the values in K

Quantity B

The standard deviation of the values in T


The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

The mean and standard deviation of the 17 values in a list are 0 and 40, respectively. If one more value is included in the list, the mean of the 18 values will be 0. The standard deviation of the 18 values will be closest to which of the following?
When the positive integer $$n$$ is divided by $$7$$, the remainder is $$2$$.

Quantity A

The remainder when $$2n+1$$ is divided by $$7$$

Quantity B

$$5$$
Of the 30 college students taking a certain course, 10 are less than 21 years old and 4 received a score higher than 85 percent on the last test.

Quantity A

The number of students who are less than 21 years old and who received a score higher than 85 percent on the last test

Quantity B

3
If the product of integers a, b, c, and d is an even integer, which of the following statements about a, b, c, and d must be true?
What is the units digit of the sum $$13^{10}+17^{10}$$ ?
For how many of the possible orderings of the 5 letters of the word "merit" is the first letter m or r ot t?
A package contains between 75 and 100 marbles. When the marbles are divided into as many groups of 6 marbles as possible, the same number of marbles are left over as when the marble are divided into as many groups of 7 marbles as possible.

Quantity A

The number of marbles in the package

Quantity B

80
$$n$$ is a positive integer

$$x=n^{2}+7n+10$$

Quantity A

The remainder when $$x$$ is divided by $$2$$

Quantity B

$$1$$
n is a four-digit positive integer such that its four digits are all different and each digit is either 4, 7, 8, or 9.

Quantity A

The remainder when n is divided by 5

Quantity B

The remainder when n is divided by 9

Quantity A

The digit in the hundredths place in the the number 0.083

Quantity B

The digit in the hundreds place in number 1600


If the function $$f$$ is defined by $$f(x)=1-2^{x}$$ for all integers $$x$$, then $$-f(10)$$ is closest to which of the following?

Quantity A

(1.98)(81)(99)(1,249)

Quantity B

25,000,000
How many noncongruent triangles are there such that the length of each side of each triangle is an integer and the perimeter of each triangle is 15?


In the figure above, what is the perimeter of the shaded region?


Quantity A

$$y$$

Quantity B

$$1$$
List A consists of the 5 numbers x, x+ 1, x+ 1, x+ 1, and x+ 2, where x is a positive integer. List B is formed by adding 3 times the range of the numbers in list A to each number in list A. How much greater is the average (arithmetic mean) of the numbers in list B than the average of the numbers in list A?
One piece of candy is to be selected at random from each of 4 different boxes of assorted candies. For each of the boxes, the probability that the candy selected will be a chocolate candy is 1/10, and the 4 selections are to be made independently of each other.

Quantity A

The probability that none of the 4 pieces of candy selected will be a chocolate candy

Quantity B

$$\frac{4}{5}$$
To wake up in the morning, Doug sets two alarm clocks that operate independently of each other, in case one alarm clock fails to ring. If the probability that the first clock will ring is 0.95 and the probability that the second clock will ring is 0.90, what is the probability that neither alarm clock will ring?

Give your answer as a decimal.

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