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题目内容

Seventy-five boxes of light bulbs were examined during a quality control check. The number of defective light bulbs per box and the corresponding frequency are given in the table.

Quantity A

The average (arithmetic mean) number of defective light bulbs per box for the 75 boxes

Quantity B

The median number of defective light bulbs per box for the 75 boxes
$$b_1, b_2, b_3,$$………$$b_n,$$……..
In the sequence shown, $$b_1=1$$ and for all integers $$n \geq 2$$.
$$b_n=2b_{n-1} + r$$.
where $$r$$ is a positive integer. The sum of $$b_1, b_2,$$ and $$b_3$$ is 35.

Quantity A

$$r$$

Quantity B

$$7$$
$$0 \lt a \lt b \lt c \lt d \lt e$$

Quantity A

The median of $$a, b, c, d$$, and $$e$$

Quantity B

$$\frac{a+b+c+d+e}{5}$$
In the 65-74 age-group, the ratio of the number of males to the number of females is 2 to 3. What is the average number of prescriptions per person in that age-group?
$$n \neq 0$$ and $$n \neq -1$$

Quantity A

$$\frac{n+n^2}{n^3+n^4}$$

Quantity B

$$\frac{1}{n^2}$$
A rectangular solid has length $$l$$, width $$w$$, and height $$h$$, where $$l + w + h = 24$$.
Which of the following statements individually provide(s) sufficient additional information to determine the surface area of the solid?
Indicate all such statements.
Line $$l$$ passes through the center of circle $$R$$ and intersects circle $$R$$ at points $$P$$ and $$Q$$. Line $$k$$ is perpendicular to line $$l$$ and intersects circle $$R$$ at points $$M$$ and $$N$$.

Quantity A

The length of arc $$MPN$$

Quantity B

The length of arc $$MQN$$

A plot of land is to be divided into three smaller lots, as shown in the figure above. If the total length of the sides of the three lots along Main Street is 360 feet, what is the length, in feet, of the side of lot $$A$$ that is along Main Street?
If $$y=x^2-2x+3$$, for what values of $$x$$ is the value of $$y$$ positive?
$$x^2+x-6=0$$

Quantity A

\frac{1}{1+3^x}

Quantity B

\frac{1}{1+5^x}
In a certain board game a player must throw two dice for a sum of 8 to end the game. If there is an equal likelihood of getting any one of the numbers 1 through 6 on each of the dice thrown, what is the probability that the player will end the game on the next throw?
The probability that event $$A$$ will occur is 0.40 and the probability that event $$B$$ will occur is 0.30. If the two events are independent, what is the probability that at least one of the events will occur?
A science book, a philosophy book, a geometry book, and a trigonometry book are to be arranged next to each other on a shelf. There are $$n$$ possible arrangements of the 4 books such that the geometry book and the trigonometry book are next to each other.

Quantity A

$$n$$

Quantity B

$$10$$
$$P=23^{25}$$-23

In the equation above, what is the units digit of $$P$$?

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