All Questions ⁺⁰236092 Questions

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help with counting

Help how do I count
Let n be a positive integer. Let k be a positive integer.
(a) Using a counting argument, show that C(n - 1, k - 1) + C(n - 1, k) = C(n,k).
(b) Using a counting read more ..

sandwich Oct 6, 2023

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61

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+1348

fill in blanks

Fill in the blanks to make the equation true. (Each blank should contain an integer.)
n/k = ? *(n - 2)/(k - 2) + ?*(n - 2)/(k - 1) + ?*(n - 2)/k

sandwich Oct 6, 2023

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41

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need to simplify

For a positive integer n, the rational number r satisfies
2n/n + 2n/(n + 1) = r*2n/n - n/(n - 1)
Express r in terms of n. (Your expression should be as simplified as possible.)

sandwich Oct 6, 2023

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53

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+1348

Binomial coefficients

Write the following expression as a single combination $\binom{n}{k}$ so that $k \neq 1$ and $n-k \neq 1.$
\binom{3}{1} + \binom{3}{2} = ?

sandwich Oct 6, 2023

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63

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+1348

Simplify

For non-negative integers $a$ and $b,$ where $a \ge 2$ and $b \ge 2,$ simplify
(a + b)/2 - a/2 - b/2

sandwich Oct 6, 2023

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57

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counting paths

Find the number of paths from $A$ to $I,$ if each step must be in a right-ward direction. (For example, one possible path is $A \to B \to C \to E \to F \to H \to I.$) read more ..

sandwich Oct 6, 2023

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45

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+1348

pascal's triangle

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

sandwich Oct 6, 2023

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53

2

+28

Help problem please

1. Find the ordered pair (s, t) that satisfies the system (s/2)+5t=3 3t-6s=9
If anyone can help me with this problem, thank you. The answer is in fractions for both

Icebulb2 Oct 6, 2023

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53

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+816

help hard inequality

Find all $x$ such that neither $2x-5$ nor $-20x+13x-7$ is in the interval $(8,12)$.

maximum Oct 6, 2023

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37

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+816

help inequalities

Find all $x$ so that neither $-2(6+2x)\le -16-x+8-5x$ nor $-3x\ge 18-7x+25$.

maximum Oct 6, 2023

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38

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+816

inequality question

Find all $x$ such that neither $2+x+5x$ nor $2-x-8-3x$ is in the interval $(-2,11]$. Express your answer as an interval or as a union of intervals.

maximum Oct 6, 2023

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43

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+4

Please help me please

For the triangle below, let x be the area of the circumcircle, and let y be the area of the incircle. Compute x - y.
read more ..

bobrobert Oct 6, 2023

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59

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+16

Pls give answer by ASAP. Thank you.

Xavier sold some pairs of sneakers and sandals for $21 692. The total cost of a pair of sneakers and a pair of sandals is $374. Each pair of sandals cost 4/11 as much as the total cost of a pair of sneakers and a pair of sandals. 2/5 read more ..

kendrickotiswalker10 Oct 6, 2023

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41

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help plz

Help I'm stuck
Find all values of $x$ which do not satisfy $$1 \le 4-3x+5x < 10-8x.$$ Express your answer in interval notation.

sandwich Oct 6, 2023

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32

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+816

probability question

Two points on a circle of radius $1$ are chosen at random. Find the probability that the distance between the two points is at most $3/2.$

maximum Oct 6, 2023

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50

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+816

help plz

In a series of coin flips, a run is a series of one or more consecutive coin flips that all have the same result. For example, in the sequence
\[TT \textcolor{red}{HHH} TTHHHTH,\]
the red letters form a run.
If a fair coin is flipped read more ..

maximum Oct 6, 2023

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73

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+816

expected value

Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $5$ on them and the other two have an $12$ on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What read more ..

maximum Oct 6, 2023

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64

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+1911

distance

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

tomtom Oct 6, 2023

+1

41

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+1911

line intercept

A line has a slope of $m,$ and its $y$-intercept is $(0,b)$. If $m = 2$ and $b = 2,$ then what is the $x$-intercept of the line?

tomtom Oct 6, 2023

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69

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+1911

equation of line

A line passes through the points $A,$ $B,$ and $C.$ If $A = (-2,5),$ $B = (-3,1),$ and $C = (4,y),$ then find $y.$

tomtom Oct 6, 2023

Oct 5, 2023

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30

1

+82

Probability and counting

Three adults and three children are to be seated at a circular table. In how many different ways can they be seated if each child must be next to two adults? (Two seatings are considered the same if one can be rotated to form the other.)

xxyoohoo Oct 5, 2023

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28

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+15

Physics Amoeba Math

Scientists wanted to know how many individual amoeba cells go into a slug. To figure this out, they estimated the volume of an individual amoeba and the volume of a slug, then did arithmetic to find the number of amoeba in a slug.
In 1953, read more ..

LachrymoseMath Oct 5, 2023

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39

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+1911

help help

Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 2x - 4y$.

tomtom Oct 5, 2023

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50

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+1911

linear equation

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (1,7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive. read more ..

tomtom Oct 5, 2023

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38

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+1911

lines

How do you solve lines
Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common read more ..

tomtom Oct 5, 2023

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