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A family paid 12 percent of its annual after-tax income on food last year. This amount was equal to 10 percent of its annual before-tax income last year. Which of the following is closest to the percent of the family's annual before-tax income that was paid for taxes last year?
Vladimir invested $10,000 for one year.He invested some of the amount at 4 percent simple annual interest and the rest of the amount at 6 percent simple annual interest. If the total interest earned for the year was between $450 and $550, which of the following statements must be true?. Indicate all such statements.
$$x \geq 0$$ Quantity A $$2^{x}$$+$$2^{x}$$+$$2^{x}$$+$$2^{x}$$ Quantity B $$4^{x}$$+$$4^{x}$$
List D: $$(-\frac{1}{2})^{2}$$, $$(-\frac{1}{2})^{-2}$$, $$(-\frac{1}{3})^{2}$$, $$(-\frac{1}{3})^{-2}$$ What is the range of the numbers in list D?
In the figure, a regular 8-side polygon is inscribed in the circle with Center O. What is the value of x?
In △ABC, point D lies between A and C, and BD is an altitude. The degree measure of which of the angles of △ABC, if any, could be greater than 90?
Eugene and Penny started a job in sales on the same day. Eugene's sales for the first month were r dollars and each month after the first his sales for that month were twice his sales for the preceding month. Penny's sales for the first month were 10r dollars, and each month after the first her sales for that month were 10r dollars more than her sales for the preceding month. Which of the following statements are true? Indicate all such statements.
The figure above shows a rectangle inscribed in a large circle. Inside the rectangle is a small circle of radius 2 that is tangent to two sides of the rectangle. If the length of the rectangle is twice its width, what is the area of the large circle?
The boxplot above summarizes a list of 240 numbers. Which of the following statements must be true? Indicate all such expressions.
In the distribution of measurements of the variable x, the mean is 56 and the measurement r lies between the 65th and 70th percentiles. In the distribution of measurements of the variable y, the mean is 56 and the measurement t lies between the 75th and 80th percentiles. Quantity A r Quantity B t
In 1998, how many of the imported towels were not imported from China?
If the average (arithmetic mean) number of towels imported from China per month was the same for the last 3 months of 2000 as it was for the first 9 months of 2000, approximately how many million dozen towels were imported from China during the 12 months of 2000?
In 1999, the ratio of the number of towels imported from China to the total number of towels imported from countries other than China was closest to which of the following?
For each value $$x$$ in a list of values with mean $$m$$, the absolute deviation of $$x$$ from the mean is defined as $$\|x-m\|$$. A certain online course is offered once a month at a university. The number of people who register for the course each month is at least $$5$$ and at most $$30$$. For the past $$6$$ months, the mean number of people who registered for the course per month was $$20$$. For the numbers of people who registered for the course monthly for the past $$6$$ months, which of the following values could be the sum of the absolute deviations from the mean? Indicate all such values.
Which of the following could be a factor of $$\frac{9!}{(6!)(3!)}$$? Indicate all such numbers.
x and y are prime numbers x+y is odd x < y Quantity A x Quantity B 3
If $$y=1-\frac{1}{x}$$, where $$x$$ is a nonzero integer, which of the following could be the value of $$y$$? Indicate all such values.
\|x\| ≤ 6 and \|y\| ≤ 4 x and y are integers, where x≠0. M is the greatest possible value of \|$$\frac{y}{x}$$\|. Quantity A M Quantity B 1
In the four quarters of 2013, denoted by $$Q_1$$, $$Q_2$$, $$Q_3$$ and $$Q_4$$, Company C hired the same number of employees in $$Q_2$$ as in $$Q_1$$ and twice as many employees in $$Q_3$$ as in $$Q_2$$. The number of employees hired by the company in $$Q_4$$ was greater than the number of hired in $$Q_3$$; however, the number hired in $$Q_4$$ was also less than 3 times the number hired in $$Q_3$$. All of the employees were hired only once. If an employee is to be selected at random from all the employees hired during the four quarters, which of the following values could be the probability that the employee will be one who was hired in $$Q_4$$? Indicate all such values.
A tank initially contains $$g$$ gallons of water. Beginning at 1 o'clock in the afternoon, water flows into the top of the tank at a constant rate of $$x$$ gallons per minute and out of the bottom of the tank at a constant rate of $$y$$ gallons per minute. If $$ x \lt y$$, in how many minutes after 1 o'clock in the afternoon is the volume of water in the tank equal to $$\frac{1}{2}g$$, in terms of $$g$$, $$x$$, and $$y$$?

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