All Questions ⁺⁰237826 Questions

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Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

LiIIiam0216 May 7, 2024

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74

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+2730

Counting

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

LiIIiam0216 May 7, 2024

0

81

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+2730

Probability

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

LiIIiam0216 May 7, 2024

0

54

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+2730

Counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ 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 $14$ members read more ..

LiIIiam0216 May 7, 2024

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53

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+363

PROBABILITY

In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12 and one SuperBall is drawn (at random) from red balls numbered from 13 to 20 When you buy a ticket, you choose three numbers from read more ..

Lilliam0216 May 7, 2024

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35

2

+363

probability

In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12 and one SuperBall is drawn (at random) from red balls numbered from 13 to 20 When you buy a ticket, you choose three numbers from read more ..

Lilliam0216 May 7, 2024

0

54

1

+363

probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ( 1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

Lilliam0216 May 7, 2024

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76

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+2730

help probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probablility that all three pieces are shorter than 2 units?

LiIIiam0216 May 7, 2024

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44

2

+363

help

A bag has 4 red marbles, 5 white marbles, and 6 blue marbles. Three marbles are drawn from the bag (without replacement). What is the probability that they are all the same color?

Lilliam0216 May 7, 2024

+1

18

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+1955

Pythagorean Theorem!

I'm studying for this test about the Pythagorean Theorem when I came across this question, and ummm, yeah my small brain can't figure it out... :)
In a right triangle ABC, length of the medians to the sides AB and BC are and respectively. read more ..

NotThatSmart May 7, 2024

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59

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+305

help geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

rtsdylifdts May 7, 2024

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57

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+305

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.

rtsdylifdts May 7, 2024

0

62

1

+305

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

rtsdylifdts May 7, 2024

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74

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+305

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 $BXA$.

rtsdylifdts May 7, 2024

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61

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+305

Geometry

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 1 and QC = 4. Find sin angle PAQ.

rtsdylifdts May 7, 2024

0

49

3

+68

Precalc

Let a and b be two vectors such that neither of a-b and a+b is the zero vector.
(a) Prove that if the vectors a and b are of equal length, then a-b and a+b are perpendicular.
(b) Prove that if a-b and a+b are perpendicular, then a and b are read more ..

LearningCat May 7, 2024

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51

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+2730

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D. If angle BAC=60 degrees, angle ABC=60 degrees and AD=24 then find the area of triangle ABC.

LiIIiam0216 May 7, 2024

0

84

1

+2730

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 $BXA$.

LiIIiam0216 May 7, 2024

0

70

1

+2730

Geometry

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

LiIIiam0216 May 7, 2024

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76

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+2730

Geometry

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

LiIIiam0216 May 7, 2024

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79

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+2730

Geometry

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect PX (AX incorrect) at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR</ read more ..

LiIIiam0216 May 7, 2024

0

70

1

+157

Help

Father's Day was coming up. Adam and Joe decided to share the cost of a Father's Day present for their father. The ratio of Adam's share to Joe's share was 4:6. When they checked the price of the present again, the cost increased by 20%. As a result, Adam read more ..

sugabreaddoughman May 7, 2024

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61

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+157

Help

Jackson had some red, blue and green t-shirts. For every 5 red t-shirts, there were 6 blue t-shirts. For every 2 blue t-shirts, there were 3 green t-shirts. He gave away 12 red t-shits and the red shirts that he had left were 1/10 the original number read more ..

sugabreaddoughman May 7, 2024

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48

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+157

Help

James had a rectangular piece of art paper. He painted 2/5 of it yellow, 1/3 of it purple and 1/2 of the remaining space pink. He had 240 cm² of the paper left to be painted. If the length of the whole art paper was twice its breadth, what was its read more ..

sugabreaddoughman May 7, 2024

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67

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+157

Hi pls help thanks

Stuart and Dave each had some money. If Stuart spends 3 times the amount Dave spends each day, Stuart would have left $280 by the time Dave spends all his money. If Stuart spends 1/3 the amount that Dave spends each day, Stuart would have $568 by read more ..

sugabreaddoughman May 7, 2024

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