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A jar contains only red marbles and black marbles. The jar contains more than one red marble and 5 times as many black marbles as red marbles. Five marbles are to be selected from the jar without replacement.

Quantity A

Of the marbles selected, the number that will be red

Quantity B

Of the marbles selected, the number that will be black


There are 5 gifts in a bag, of which 3 are cash and 2 are movie tickets, one person selects 2 of them without replacement. What is the probability that at least one cash bag could be selected?

Give your answer as a fraction.
A certain spacecraft has 2 separate computer systems, X and Y, each of which functions independently of the other. The probabilities that systems X and Y will function correctly at liftoff are 0.90 and 0.99, respectively. What is the probability that at least one system will function correctly at liftoff?
Event A and event B are independent. The probability that event A occurs is 0.6 and B occurs is 0.5. What is the probability that neither A nor B occurs?

Give your answer as a decimal.
The possibility of Event A occurs is 0.75, while the possibility of Event B occurs is 0.58. What is the maximum possibility that both events will occur?
a and b are distinct odd prime numbers.

Quantity A

The number of positive factors of $$2ab^{2}$$

Quantity B

The number of positive factors of $$a^{2}$$ $$b^{3}$$


How many of the multiples of 3 between 100 and 200 are odd integers?
Let $$n$$ be a nonnegative integer such that when $$6n$$ is divided by $$75$$, the remainder is $$30$$. Which of the following is a list of all possible remainders when $$7n$$ is divided by $$75$$?
The units digit of $$7^{n}$$ is r, and the units digit of $$9^{n}$$ is t, where n, r, and t are positive integers. Which of the following could be the value of r+t?

Indicate all such values.
What is the reminder when $$ (345,606)^{2}$$ is divided by 20?
Let $$q$$ be a prime number less than $$100$$. When $$q$$ is divided by $$5$$, the remainder is $$2$$. When $$q$$ is divided by $$7$$, the remainder is $$6$$, what is the remainder when $$q$$ is divided by $$8$$?
For all positive even integers $$n$$, $$n」$$ represents the product of all even integers from 2 to $$n$$, inclusive. For example, $$12」=12\times10\times8\times6\times4\times2$$. What is the greatest prime factor of $$20」+22」$$?
How many positive integers less than or equal to 603 are multiples of 2 or multiples of 3 or both?
How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?
How many integers between 100 and 1,000 are multiples of 7?
If the sum of two numbers is 10, what is the greatest possible value of the product of the two numbers?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
Z=$$123^{4}$$-$$123^{3}$$+$$123^{2}$$-123

What is the remainder when Z is divided by 122?
Which of the following numbers satisfy their sum of reciprocals is either less than $$\frac{1}{3}$$ or greater than $$\frac{1}{2}$$ ?

Indicate all such numbers.
x≠0, y≠0

|x|+|y|=|x+y|

Which of the following statements must be true?

Indicate all such statements.

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