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The operations $$\oplus$$ and $$\bigotimes$$ are defined for all numbers $$x$$ and $$y$$ by
$$x \oplus y = 2x-y$$ and
$$x \bigotimes y= x+3y$$.
If $$3 \oplus (2z)=z \bigotimes 6$$, what is the value of $$z$$?

For a certain high school, the bar graph above shows the frequency distribution of all the students by grade, and the circle graph above shows the distribution of all the students who study Spanish, also by grade. If the total number of students studying Spanish is equal to the total number of students in grade 10, approximately how many of the students in grade 9 do not study Spanish?
If $$-7 \leq x \leq 5$$ and $$-5 \leq y \leq 3$$, then the maximum value of $$x^2-y^2$$ is
The solutions of the equation $$2y^2+5y=3$$ are $$\frac{1}{2}$$ and $$-3$$. What are the solutions of the equation $$2(x-2)^2+5(x-2)=3$$?
The numbers in a certain list are $$a_1, a_2, a_3, a_4$$ and $$a_5$$, where $$a_n= n((-1)^n-1)$$. What is the difference between the greatest number in the list and the least number in the list?
For each car sold at a certain dealership, the salesperson receives a commission of $$$30$$ plus 20 percent of the amount of profit in excess of $$$300$$ from the sale. If the profit from the sale of a certain car was $$$2,000$$, how much money did the salesperson receive for commission on the sale of this car?
In a distribution of the heights of 50,000 people, the 40th percentile is 63 inches and the 64th percentile is 69 inches.

Quantity A

The 52nd percentile in the distribution

Quantity B

66 inches


$$1+2x \gt -3$$

Quantity A

$$x$$

Quantity B

$$-1.999$$


A 3-foot by 3-foot-square closet floor is to be covered completely using a combination of 1-foot by 1-foot square tiles and 1-foot by 2-foot rectangular tiles.

Quantity A

The number of 1-foot by 1-foot square tiles used

Quantity B

The number of 1-foot by 2-foot rectangular tiles used



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

$$\frac{a+b+c+d+e}{5}$$


For which of the nine age-groups is the ratio of the average number of prescriptions per female to the average number of prescriptions per male greatest?
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?

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