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Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and $$\overline{PR}$$ is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities $$-4 \le x \le 5$$ and $$6 \le y \le 16$$. How many different triangles with these properties could be constructed?
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OG12
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 The table above shows the number of employees at each of four salary levels at Company X. What is the average (arithmetic mean) salary for the 20 employees?
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$$0.1+{0.1}^{2}+{0.1}^{3}=$$
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If n is a prime number greater than 3, what is the remainder when $${n}^{2}$$ is divided by 12 ?
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$$\frac{1}{(0.75-1)}=$$
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OG12
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if |a c b d|= ad-bc for all numbers a, b, c, and d, then |3 -2 5 4|
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How many integers n are there such that 1 < 5n + 5 < 25 ?
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$$\sqrt{80}+\sqrt{125}=$$
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y=kx+3In the equation above, k is a constant. If y = 17 when x = 2, what is the value of y when x = 4 ?
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At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formulaN=$$20L\frac{d}{(600+s^2)}$$where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a $$\frac{1}{2}$$ mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)
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$$\frac{(0.0036)(2.8)}{(0.04)(0.1)(0.003)}=$$
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The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is
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If s is the product of the integers from 100 to 200, inclusive, and t is the product of the integers from 100 to 201, inclusive, what is $$\frac{1}{s}+\frac{1}{t}$$ in terms of t?
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A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
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For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the median
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OG12
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If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x =$${2}^{i}{3}^{k}{5}^{m}{7}^{p}$$, then i + k + m + p =
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In a certain sequence, the term $${x}_{n}$$, is given by the formula $${x}_{n}={2}{x}_{n-1}-\frac{1}{2}({x}_{n-2})$$ for all $${n}\geq{2}$$. If $${x}_{0}=3$$ and $${x}_{1}=2$$, what is the value of $${x}_{3}$$
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If the operation * is defined by $$x*y=\sqrt{xy}$$ for all positive numbers x and y, then (5 * 45) * 60 =
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A club collected exactly $599 from its members. If each member contributed at least $12, what is the greatest number of members the club could have?
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Of the 3,600 employees of Company X, $$\frac{1}{3}$$ are clerical. If the clerical staff were to be reduced by $$\frac{1}{3}$$, what percent of the total number of the remaining employees would then be clerical?
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