A bag contains $8$ blue marbles, $4$ red marbles and $3$ green marbles. In a single draw, what is the probability of not drawing a green marble?
The arithmetic mean of 11 numbers is 78. If 1 is subtracted from the first, 2 is subtracted from the second, 3 is subtracted from the third, and so forth, until 11 is subtracted from the eleventh, what is the arithmetic mean of the 11 resulting numbers?
An optometrist has this logo on his storefront. The center circle has area 36\u03c0 $in^2$, and it is tangent to each crescent at its widest point (A and B). The shortest distance from A to the outer circle is $\frac{1}{3}$ the diameter of the smaller circle. What is the area of the larger circle? Express your answer in terms of \u03c0.
Excluding sales tax, how much will Doris save when she buys a DVD originally priced at \$12.00 and now on sale for 20% off?
What is the value of $\frac{444^2-111^2}{444-111}$ ?
The product of the digits of positive integer $n$ is $20$, and the sum of the digits is $13$. What is the smallest possible value of $n$?
Quadrilateral ABCD is a square with BC = 12 cm. $\overset{\frown} {BOC}$ and $\overset{\frown} {DOC}$ are semicircles. what is the area of the shaded region?
Real numbers a and b satisfy the equation $\frac{2a-4}{5}+\frac{3a+1}{5}=b$. What is the value of $a - b$? Express your answer as a common fraction.
If the point $(x, x)$ is equidistant from (-2, 5) and (3, -2), what is the value of $x$?
In a bag of marbles, $\frac{2}{5}$ of the marbles are red, $\frac{3}{10}$ of the marbles are white and $\frac{1}{10}$ of the marbles are blue. If the remaining 10 marbles are green, how many marbles are in the bag?
If $t$ is 40% greater than $p$, and $p$ is 40% less than 600, what is the value of $t \u2013 p$?
How many ways can all six numbers in the set $\{4, 3, 2, 12, 1, 6\}$ be ordered so that $a$ comes before $b$ whenever $a$ is a divisor of $b$?
What is the units digit of the product $7^{23} \times 8^{105} \times 3^{18}$?
If $4(a - 3) - 2(b + 5) = 14$ and $5b -a = 0$, what is the value of $a + b$?
The two cones shown have parallel bases and common apex $T$. $TW = 32$ m, $WV = 8$ m and $ZY = 5$ m. What is the volume of the frustum with circle $W$ and circle $Z$ as its bases? Express your answer in terms of $\pi$.
A coin is flipped until it has either landed heads two times or tails two times, not necessarily in a row. If the first flip lands heads, what is the probability that a second head occurs before two tails? Express your answer as a common fraction.
The product of two consecutive integers is five more than their sum. What is the smallest possible sum of two such consecutive integers?
Four nickels, one penny and one dime were divided among three piggy banks so that each bank received two coins. Labels indicating the amount in each bank were made (6 cents, 10 cents and 15 cents), but when the labels were put on the banks, no bank had the correct label attached. Soraya shook the piggy bank labeled as 15 cents, and out fell a penny. What was the actual combined value of the two coins contained in the piggy bank that was labeled 6 cents?
Suppose the 9 \u00d7 9 multiplication grid, shown here, were filled in completely. What would be the sum of the 81 products?
In some languages, every consonant must be followed by a vowel. How many seven-letter "words" can be made from the Hawaiian word MAKAALA if each consonant must be followed by a vowel?
If $f(x) = 3x^2$, what is the x-coordinate of the point of intersection of the graphs of $y = f(x)$ and $y = f(x \u2212 4)$?
In isosceles trapezoid $ABCD$, shown here, $AB = 4$ units and $CD = 10$ units. Points $E$ and $F$ are on $\overline{CD}$ with $\overline{BE}$ parallel to $\overline{AD}$ and $\overline{AF}$ parallel to $\overline{BC}$. $\overline{AF}$ and $\overline{BE}$ intersect at point $G$. What is the ratio of the area of triangle $EFG$ to the area of trapezoid $ABCD$? Express your answer as a common fraction.
The sum of five consecutive, positive even integers is a perfect square. What is the smallest possible integer that could be the least of these five integers?
If $12_3$ + $12_5$ + $12_7$ + $12_9$ + $12_x$ = $101110_2$ , what is the value of $x$, the base of the fifth term?
A box contains $r$ red balls and $g$ green balls. When $r$ more red balls are added to the box, the probability of drawing a red ball at random from the box increases by $25\%$. What was the probability of randomly drawing a red ball from the box originally? Express your answer as a common fraction.