All Questions ⁺⁰236027 Questions

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help

With each stroke, a pump removes 2/5 of the air in a container. After 3 strokes, what is the fraction of the original amount of air in the container that is left.

Souleater Oct 17, 2024

0

8

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+862

Counting

I run a book club with $n$ people, not including myself. Every day, for $400$ days, I invite $2$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $2$ read more ..

magenta Oct 17, 2024

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4

1

+862

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

magenta Oct 17, 2024

Oct 16, 2024

0

6

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+862

Counting

Joanna has seven beads that she wants to assemble into a bracelet. Three of the beads have the same color, and the other four all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

magenta Oct 16, 2024

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3

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+1521

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

blackpanther Oct 16, 2024

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8

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+1521

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

blackpanther Oct 16, 2024

0

9

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+1521

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

blackpanther Oct 16, 2024

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5

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+1521

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

blackpanther Oct 16, 2024

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7

2

+281

Counting

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?

jaekg Oct 16, 2024

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5

5

+281

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

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jaekg Oct 16, 2024

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10

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+281

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

jaekg Oct 16, 2024

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7

0

+281

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

jaekg Oct 16, 2024

Oct 15, 2024

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5

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+893

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

AnswerscorrectIy Oct 15, 2024

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6

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+893

Geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

AnswerscorrectIy Oct 15, 2024

0

7

1

+862

Counting

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

magenta Oct 15, 2024

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+35

Calculus help...

Approximate the area under the curve:
f(x) = x^2 + 2, -2 ≤ x ≤1
with a Riemann sum, using six sub-intervals and right endpoints.

server Oct 15, 2024

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6

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+785

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

gnistory Oct 15, 2024

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+1839

Algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

ABJeIIy Oct 15, 2024

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4

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+1839

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

ABJeIIy Oct 15, 2024

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4

1

+1839

Algebra

The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).

ABJeIIy Oct 15, 2024

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