All Questions ⁺⁰237827 Questions

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152

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Counting

How to count the possibles

A coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of heads was at least ?

Guest Feb 12, 2023

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221

1

+24

Counting plz help asap

Let n be a positive integer.
(a) There are ordered pairs of positive integers, where Using a counting argument, show that this number is also equal to
(b) There are ordered read more ..

TheOneXWZ Feb 12, 2023

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156

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Binomials

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

Guest Feb 12, 2023

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160

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Probability

Four points W, X, Y, and Z are chosen at random on a circle. Find the probabiity that WX > YZ.

Guest Feb 12, 2023

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162

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Counting

(a) In how many ways can you distribute 4 distinguishable balls among 6 indistinguishable boxes?

(b) In how many ways can you distribute 4 indistinguishable balls among 5 distinguishable boxes?

Guest Feb 12, 2023

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177

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tính hợp lí 38/45-(8/25-8/51-3/11)

tính hợp lí 38/45-(8/25-8/51-3/11)

Guest Feb 12, 2023

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213

4

PLEASE HELP i may fail school if i dont get my homework right!

Find the equation of the axis of symmetry of the parabola. Each box in the grid represents unit.

Enter the answer as an equation. read more ..

Guest Feb 12, 2023

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170

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Geometry

In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown. If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.

Guest Feb 12, 2023

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172

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Geometry

In tetrahedron ABCO, angle AOB = angle AOC = angle BOC = 90^\circ. A cube is inscribed in the tetrahedron so that one of its vertices is at O, and the opposite vertex lies on face ABC. Let OA = 1, OB = 1, OC = 1. Show that the read more ..

Guest Feb 12, 2023

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167

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Counting

When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.

Find all possible ways of numbering two 6-sided dice read more ..

Guest Feb 12, 2023

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154

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Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color, and at lest three of the squares are red. How many ways are there to color the five squares?

Guest Feb 12, 2023

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172

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Counting

Help how to solve using combination

I run a book club with n people, not including myself. Every day, for 100 days, I invite members in the club to review a book. What is the smallest positive integer n so that I can avoid ever having read more ..

Guest Feb 12, 2023

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159

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Function

The function f(n) satisfies
binom(2n)n - binom(2n + 1)(2n) = f(n) *binom(2n + 1)(n + 1)
for all positive integers n. Find f(n).

Guest Feb 12, 2023

Feb 11, 2023

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163

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Counting

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and read more ..

Guest Feb 11, 2023

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172

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system

For a certain value of k, the system
x + y + 3z = 10
-4x + 8y + 5z = 7
kx + z = 3 read more ..

Guest Feb 11, 2023

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189

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Functions

The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).

Explain why the functions f and h are not the same function. read more ..

Guest Feb 11, 2023

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175

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coordinate

A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.

Note that the three medians appear to intersect at the same point! Let's read more ..

Guest Feb 11, 2023

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200

2

PLease help

For what positive integers c, with c<100, does the following quadratic have rational roots?

3x^2+20x+c read more ..

Guest Feb 11, 2023

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168

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Expected value

I need help with these

Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) read more ..

Guest Feb 11, 2023

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166

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Counting

Can anyone help plz?

A debate team consists of 5 freshmen and 4 sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so at least two of the sophomores are standing next to each other, and read more ..

Guest Feb 11, 2023

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165

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Probability

I need the answer to this

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 20?

Guest Feb 11, 2023

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172

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counting

In how many ways can you distribute 10 indistinguishable balls among 8 distinguishable boxes, if at least one of the boxes must be empty?

Guest Feb 11, 2023

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165

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Counting

Find the number of six-digit numbers, where the sum of the digits is divisible by 8.

Guest Feb 11, 2023

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