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题目内容
At a certain candy store, the price of a box of taffy is $$ $6$$ and the price of a box of chocolates is $$ $9$$. The store sells $$x$$ boxes of taffy and $$y$$ boxes of chocolates for a total price of $$ $360$$. Which of the following statements must be true? Indicate all such statements.
$$5t$$ is a negative integer. Quantity A $$5t+4$$ Quantity B $$0$$
If $$-8 \leq h \leq 10$$ and $$h+m=-4$$, what is the least possible value of $$m-h$$？
When the positive integer $$x$$ is divided by $$42$$, the remainder is $$19$$. What is the remainder when x is divided by $$7$$?
$$m$$,$$n$$, $$q$$, and $$r$$ are positive integer such that $$m=nq+r$$ and $$r \lt n$$. Quantity A The greatest integer less than $$\frac{m}{n}$$ Quantity B $$q$$
$$y \gt 100,000$$ Quantity A $$\frac{100}{1+\frac{1}{y}}$$ Quantity B $$90$$
$$OA=OB=OC=OD$$ Quantity A $$x$$ Quantity B $$35$$
In the figure shown, $$3$$ squares intersect at points $$A$$, $$B$$, and $$C$$. If each of the squares has area $$16$$, and $$AB = BC$$, what is the perimeter of right triangle $$ABC$$?
Two sides of a right triangle have lengths $$5$$ and $$12$$. Quantity A The length of the third side of the triangle Quantity B $$11$$
$$PQ$$ is a diameter of the circle, line $$l$$ is tangent to the circle at $$P$$, line $$m$$ is tangent to the circle at $$Q$$, line $$n$$ is tangent to the circle, and $$x \lt 90$$. Quantity A $$RS$$ Quantity B $$PQ$$
A ball is dropped from a height of $$6$$ meters and bounces to no more than $$90$$ percent of its original height. It falls back down and then repeatedly bounces to no more than $$90$$ percent of its maximum height after the previous bounce. What is the maximum height, in meters, that the ball can reach after the $$5th$$ bounce?
A sequence of numbers $$P_1, P_2, P_3.......P_n........$$ is defined as follows: $$P_1=1, P_2=2, and P_n=4\frac{P_{n-1}}{P_{n-2}}$$ for each integer $$n$$ greater than $$2$$. What is the value of $$P_4$$?
The figure above shows the xy-coordinate system with its quadrants labeled. Line $$l$$ (not shown) has the equation $$y=ax+b$$, where $$a$$ and $$b$$ are constants $$a \lt 0$$, and $$b \lt 0$$. Which quadrant or quadrants cannot contain any part of line $$l$$?
Triangles $$ABC$$ has sides of lengths $$6, 7$$, and $$j$$, where $$j$$ is an integer. Triangle $$DEF$$ has sides of lengths $$2, 13$$, and $$j$$. What is the value of $$j$$?
In a certain high school graduating class,$$80$$ percent of the students applied to college and $$60$$ percent of those who applied have been accepted. Quantity A The percent of the students in the graduating class who applied to college and have not been accepted Quantity B $$20\%$$
A certain experiment consists of making $$25$$ observations of the variable $$x$$, which can have integer values between $$-3$$ and $$3$$, inclusive. The experiment was performed twice, and Tables I and II represent the results. Which of the three statistics—mean, median, and mode—were the same both times the experiment was performed?
The table summarizes the waiting times, in minutes, of $$500$$ patients at a certain doctor's office. Of the $$500$$ waiting times, a waiting time of $$15$$ minutes is at the $$25$$th percentile and a waiting time of $$25$$ minutes is at the $$k$$th percentile. Quantity A $$k$$ Quantity B $$50$$
If $$2^{3x} -64=0$$, what is the value of $$2^x$$?
$$n$$ and $$k$$ are integers greater than $$1$$ for which $$\sqrt{n^k}=(n^{13})\sqrt{n}$$ Quantity A $$k$$ Quantity B $$14$$
The right circular cylindrical tank above has inner dimensions of radius $$4$$ feet and height $$10$$ feet. What is the greatest possible distance, in feet, between $$2$$ points inside the tank?