All Questions ⁺⁰237673 Questions

-1

96

0

+1808

distributions

There is a group of five children, where two of the children are twins. In how many ways can I distribute 18 identical pieces of candy to the children, if the twins must get 7 pieces of candy?

blackpanther Oct 31, 2023

-1

88

0

+1808

solutions

How many solutions are there to the equation
u + v + w + x + y + z = 18,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $8?$

blackpanther Oct 31, 2023

-1

114

0

+1808

probability

Miyu is giving out 8 identical chocolates to her 8 friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly 1 chocolate?

blackpanther Oct 31, 2023

-1

106

0

+1808

sum

Compute
\binom{5}{3} - \binom{6}{3} + \binom{7}{3} - \dots - \binom{22}{3} + \binom{23}{3} - \binom{24}{3}

blackpanther Oct 31, 2023

0

58

1

+1808

Algebra

Fill in the blanks to make the equation true. (Each blank should contain a 2-digit number.)
18*18 + 19*18 + 20*18 + ... + 45*18 = ___ * ___

blackpanther Oct 31, 2023

-1

101

0

+1808

counting questions

Find the number of ways that Magnus can give out 12 identical stickers to 8 of his friends. (Not everyone has to get a sticker.)
Find the number of ways that Magnus can give out 12 identical stickers to 8 of his friends, if every friend read more ..

blackpanther Oct 31, 2023

Oct 30, 2023

0

114

0

+1932

help with distance

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

tomtom Oct 30, 2023

0

93

1

+1932

numbers

Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2*1/2*4*1/6
B = 12*128
C = 1*8*1/5^2 read more ..

tomtom Oct 30, 2023

0

98

0

+1932

help with inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

tomtom Oct 30, 2023

+1

74

1

+9

Rational Functions

9. THere are values A and B such that ((Bx-11)/(x^2-7x+10))=((A)/(x-2))+((3)/(x-5)). Find A + B.
PLEASE HELPP

adssdds Oct 30, 2023

0

107

0

+1348

help hard geo

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

sandwich Oct 30, 2023

0

97

0

+1348

help plz

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 ..

sandwich Oct 30, 2023

0

89

0

+1348

need help

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

sandwich Oct 30, 2023

0

71

1

+1348

geometry question

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

sandwich Oct 30, 2023

0

40

1

+1348

Expected value

A standard deck of cards contains 52 cards. These 52 cards are arranged in a circle, at random. Find the expected number of pairs of adjacents cards that are both Aces or Kings

sandwich Oct 30, 2023

+9

64

2

+180

im not sure how to do this...

A and B are two points on a unit sphere. We know the space distance between A and B is sqrt3 What is distance from A to B along the (minor) arc of a great circle?

itsash Oct 30, 2023

-1

95

1

+1808

geometry

Point D is the midpoint of median \overline{AM} of triangle ABC. Point E is the midpoint of \overline{AB}, and point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle AMC if [ABC] =180.

blackpanther Oct 30, 2023

-1

99

0

+1808

help me

Points M, N, and O are the midpoints of sides \overline{KL}, \overline{LJ}, and \overline{JK}, respectively, of triangle JKL. Points P, Q, and R are the midpoints of \overline{NO}, \overline{OM}, and \overline{MN}, respectively. If the area of triangle read more ..

blackpanther Oct 30, 2023

Oct 29, 2023

-1

103

0

+1808

triangles

Let M, N, and P be the midpoints of sides \overline{TU}, \overline{US}, and \overline{ST} of triangle STU, respectively. Let \overline{UZ} be an altitude of the triangle. If \angle TSU = 70^\circ, \angle STU = 30^\circ, and \angle TUS = 70^\circ, then what read more ..

blackpanther Oct 29, 2023

-1

116

0

+1808

angles

Triangle ABC is a right triangle with \angle BAC = 90^\circ and \angle B > \angle C. Suppose \overline{AP} is an altitude of the triangle, \overline{AQ} is an angle bisector of the triangle, and \overline{AR} is a median of the triangle, and \angle PAQ read more ..

blackpanther Oct 29, 2023

0

110

0

+1662

binomial theorem

(a) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a, b, c that satisfy a:b:c = 1:2:3. What must n be?
(b) If a:b:c = 1:8:40 and a + b + c = 100, then what is a?

wiseowl Oct 29, 2023

0

118

0

+1662

Binomial Theorem

For some real number $a$ and some positive integer $n,$ the first few terms in the expansion of $(1 + ax)^n$ are
\[1 - 6x + 12x^2 + cx^3 + \dotsb.\]
Find $c.$

wiseowl Oct 29, 2023

0

100

0

+1662

Binomial Theorem

Find the positive integers n such that the expansion of (4x^2 - 7y^3)^n contains a term of the form cx^2*y^3.

wiseowl Oct 29, 2023

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