Lilliam0216

49 Questions
6 Answers

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Math

Let $n$ be a positive integer.
(a) There are $n^2$ ordered pairs $(a,b)$ of positive integers, where $1 < a,$ $b < n.$ Using a counting argument, show that this number is also equal to \[n + 2 \binom{n}{2}.\]
(b) There are $n^3$ read more ..

Lilliam0216 May 23, 2024

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Binomial's

For nonnnegative integers a and b, where a >= 2 and b >= 2, simplify
binom{a + b}{2} + binom{2a + b}{2} + binom{a + 2b}{2} - binom{a - b}{2}

Lilliam0216 May 21, 2024

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Expected value

The grid below is made up of line segments, like the line segment in red.
[asy] unitsize(1 cm); int i; for (i = 0; i <= 3; ++i) { draw((i,0)--(i,2)); } for (i = 0; i <= 2; ++i) { draw((0,i)--(3,i)); } draw((3,1)--(3,2), linewidth(2*bp) + red);read more ..

Lilliam0216 May 18, 2024

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6 and 5

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 5 units?

Lilliam0216 May 18, 2024

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Stick and probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 5 units?

Lilliam0216 May 17, 2024

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Area and probability

Right triangle XYZ has legs of length XY=12 and YZ=6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 24?

Lilliam0216 May 16, 2024

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super lottery probability help

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 1 to read more ..

Lilliam0216 May 10, 2024

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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 10, 2024

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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 (1-7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck read more ..

Lilliam0216 May 10, 2024

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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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+190

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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+190

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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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

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Pls help

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. The read more ..

Lilliam0216 May 5, 2024

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1-315, how many 2's

Sam writes down the numbers 1-315
Sam chooses one of the digits written down at random. What is the probability that Sam chooses a 2?

Lilliam0216 Apr 27, 2024

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Cubes and probability

The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?

Lilliam0216 Apr 27, 2024

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HELP

The roots of the quadratic equation are and . What is ?

Lilliam0216 Apr 25, 2024

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pls help

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

Lilliam0216 Apr 25, 2024

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IDK WHAT TO DO

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

Lilliam0216 Apr 25, 2024

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Let's assume there are 100 games :

.75 * 100 * .35 = games won so far

.25 (100) x games remaining times the percentage needed to get to .5(100) <==== wins = losses

.75 (100) .35 + .25 (100) (x) = .5 (100)

26.25 + 25 x = 50

25 x = 23.75

x = .95 You need to win 95% of the remaining games

Lilliam0216May 18, 2024

+190

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The problem says round trip, from Penthaven to Jackson and back. Then the problem says that the wind is blowing from Penthaven to Jackson during our round trip.

Lilliam0216Mar 2, 2024