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^{+0}
232433 Questions
0
21
1
+1347
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
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sandwich
Oct 6, 2023
0
30
0
+1347
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
0
25
0
+1347
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
0
22
0
+1347
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
0
35
0
+1347
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
0
31
1
+1347
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 $A \to B \to C \to E \to F \to H \to I.$)
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sandwich
Oct 6, 2023
0
26
1
+1347
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 $n$.
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sandwich
Oct 6, 2023
0
19
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
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Icebulb2
Oct 6, 2023
0
33
0
+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
0
22
1
+816
help inequalities
Find all $x$ so that neither $-2(6+2x)\le -16-x+8-5x$ nor $-3x\ge 18-7x+25$.
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maximum
Oct 6, 2023
0
18
1
+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.
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maximum
Oct 6, 2023
0
26
1
+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.
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bobrobert
Oct 6, 2023
0
28
0
+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
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kendrickotiswalker10
Oct 6, 2023
0
30
1
+1347
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.
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sandwich
Oct 6, 2023
0
11
1
+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 $3/2.$
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maximum
Oct 6, 2023
0
22
0
+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
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maximum
Oct 6, 2023
0
39
1
+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
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maximum
Oct 6, 2023
0
30
0
+1847
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
18
1
+1847
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?
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tomtom
Oct 6, 2023
0
39
0
+1847
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
0
19
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.)
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xxyoohoo
Oct 5, 2023
+1
19
2
+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,
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LachrymoseMath
Oct 5, 2023
0
16
1
+1847
help help
Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 2x - 4y$.
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tomtom
Oct 5, 2023
0
21
1
+1847
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.
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tomtom
Oct 5, 2023
0
17
1
+1847
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
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tomtom
Oct 5, 2023
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