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All Questions
^{+0}
235031 Questions
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2
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+614
Algebra
A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 3p + 12 problems per hour. In fact,
read more ..
gnistory
Sep 14, 2024
0
3
2
+13
Probability Question
A fair coin is flipped until either three heads in a row or four tails in a row occur. What is the expected number of times the coin is flipped? Express your answer as a common fraction.
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Halplz
Sep 14, 2024
-1
3
0
+280
Algebra
The graphs of x = y^4 and x + y^2 = 1 + x^2 - y^3 intersect at two points. The distance between these points is of the form sqrt(u + v*sqrt(5)), where u and v are integers. Find the ordered pair (u,v).
Stanry
Sep 14, 2024
-1
3
2
+280
Algebra
A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to five times the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right
read more ..
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Stanry
Sep 14, 2024
-1
2
0
+280
Algebra
Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.
Stanry
Sep 14, 2024
0
4
1
+32
Geometry help
The two circles below are externally tangent. A common external tangent intersects line PQ at R. Find QR
Circle radius-> 12 (p)and 8(q)
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surfz
Sep 14, 2024
Sep 13, 2024
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3
0
+398
Geometry
In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.
cooIcooIcooI17
Sep 13, 2024
0
3
1
+702
Geometry
All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co
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AnswerscorrectIy
Sep 13, 2024
0
4
1
+702
Geometry
There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$
read more ..
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AnswerscorrectIy
Sep 13, 2024
0
3
0
+702
Geometry
Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$
AnswerscorrectIy
Sep 13, 2024
0
2
1
+128
Counting
Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c
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jaekg
Sep 13, 2024
0
2
1
+157
Confusing Probability Question...
Ryan has 3 red lava lamps and 3 blue lava lamps. He arranges them in a row on a shelf randomly, then turns 3 random lamps on. What is the probability that the leftmost lamp on the shelf is red, and the leftmost lamp which is turned on is also red?
Thanks
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BlackjackEd
Sep 13, 2024
0
4
1
+77
Please Help! - Probability Question
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.
Any
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NotLatePY
Sep 13, 2024
Sep 12, 2024
0
4
0
+1095
Algebra
Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.
learnmgcat
Sep 12, 2024
0
3
0
+1095
Algebra
Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.
learnmgcat
Sep 12, 2024
0
4
0
+1095
Algebra
Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.
learnmgcat
Sep 12, 2024
0
6
0
+1095
Algebra
Solve the inequality
\frac{3-z}{z+1} \ge 2(z + 4).
Write your answer in interval notation.
learnmgcat
Sep 12, 2024
0
4
0
+802
Geometry
The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.
RedDragonl
Sep 12, 2024
0
2
0
+1352
Algebra
Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
\[f(p) = f(q) = f(r) = f(s) = 1\]
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$
blackpanther
Sep 12, 2024
0
5
0
+1352
Algebra
Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.
blackpanther
Sep 12, 2024
0
2
1
+479
Counting
Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)
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Pythagorearn
Sep 12, 2024
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