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题目内容
The prizes for a certain contest are in 5 sealed envelopes: 2 containing cash and the other 3 containing gift certificates. If 2 envelopes are to be randomly selected from the 5 envelopes, one at a time without replacement, what is the probability that at least one of the envelopes selected will contain a cash prize?

Quantity A

The number of real roots of $$2x- \frac{4}{7}$$=0

Quantity B

The number of real roots of $$2x^2 + \frac{4}{7}$$=0


0 < $$x$$ < 90

Quantity A

$$y$$

Quantity B

5

Quantity A

The median of the 115 scores

Quantity B

76
If twice the sum of the positive integers x, y, and z is divided by 7, the remainder is 1. What is the remainder if the sum of x, y, and z is divided by 7?
Calvin drives east along a straight road from point A to point B. His speed is never more than 60 miles per hour. Which of the following graphs could represent Calvin's distance from point A as a function of time?

Indicate all such graphs.
Each copy of Magazine X is sold either at the cover price of $3.25 per copy or at the subscription price of $1.75 per copy. The average (arithmetic mean) price of the copies of Magazine X that were sold last month was $2.25 per copy.

Quantity A

The number of copies of Magazine X that were sold last month at the subscription price

Quantity B

Twice the number of copies of Magazine X that were sold last month at the cover price
Of the people surveyed about the effectiveness of various treatments for insomnia, 65 percent reported that prescription drugs were effective and 48 percent reported that exercise was effective. If 22 percent of those surveyed reported that prescription drugs were effective but did not report that exercise was effective,what percent of those surveyed reported that exercise was effective but did not report that prescription drugs were effective?
For all integers $$x$$ greater than $$1$$, the function $$p(x)$$ is defined as the number of different prime factors of $$x$$. What is the value of $$\frac{p(12)}{p(9)}$$?
In 1961, Julia Child published Mastering the Art of French Cooking, frequently described as revolutionary. According to legend, Child inspired Americans to exchange their bland cooking for French cuisine's rich flavors. Yet Child's book was hardly singular among cookbooks. One publishing catalog lists almost as many books about French cooking in the decade before Child's book as in the decade after. While Child's book influenced a particular American cohort, its effect on the American publishing industry was minimal, a fact at odds with popular assumptions both about publishers and about Child's importance. We might expect Child's success to foster many imitations. Instead American cookbooks pursued themes popular before Child's book was published, including a growing interest in the American cooking styles allegedly vanquished by Child.
The passage suggests that the "popular assumptions"
Which of the following. if true. could be most plausibly cited as evidence in support of the "legend"?
The passage implies that Du Bois attributed which of the following beliefs to Spencerian sociologists?



The figure shows part of a circle with two inscribed regular polygons—one with $$6$$ sides and one with $$12$$ sides. The two polygons have $$6$$ vertices in common. The radius of the circle is $$r$$, and the area of the $$6$$-sided polygon is $$x$$.

Quantity A

$$\pi r^2-x$$

Quantity B

$$24$$ times the area of the shaded region $$S$$
$$n$$ is the number of $$8$$-digit positive integers consisting only of the digits $$1$$ and $$2$$, where the digit $$1$$ appears three times and the digit $$2$$ appears five times.

$$r$$ is the number of combinations of $$8$$ different letters taken $$3$$ at a time.

Quantity A

$$n$$

Quantity B

$$r$$
On a bookshelf, Pat arranges 7 different books: 2 history books, 3 philosophy books, and 2 science books. If Pat arranges the books so that the history books are next to each other, the science books are next to each other, and the philosophy books are next to each other, how many different arrangements are possible?
If $$p$$ is an prime number greater than $$5$$, and if $$5$$ is a factor of $$p+p^{2}$$,which of the following might be the remainder when $$p$$ is divided by $$5$$?
The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip $$x$$ inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip $$x$$ inches wide is removed. For what value of $$x$$ will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)
The cost of producing 1 unit of a product at a certain manufacturing company is $0.75. According to a sales model, if each unit has a selling price of $1.00, the company expects to sell 1,000 units each month. For each $0.05 increase in the unit selling price, the company expects to see a decrease of 100 units sold each month. According to the model, which of the following could be a unit selling price at which the company would expect a profit of at least $250.00 each month? (Profit equals revenue minus cost.)

Indicate all such unit selling prices.

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