All Questions ⁺⁰237827 Questions

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197

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Sequence

Help how to do this

Cai writes down the list of positive integers, excluding squares and cubes and all perfect powers. His sequence starts
2, 3, 5, 6, 7, 10, 11, ...
What is the 100th term in Cai's list?

Guest Feb 19, 2023

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193

2

PLS help due in 1 hr

Circle O and circle P, with radii 3 and 5, respectively, are both tangent to line l at H. Enter all possible lengths of OP, separated by commas.

Guest Feb 19, 2023

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151

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Algebra

Factor (ab + ac + bc)^3 - a^3*b^3.

Guest Feb 19, 2023

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160

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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 19, 2023

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164

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Counting

Help plz with this

There are 97 students in South High School. South High School offers only Chinese and Spanish. There are more students in Chinese than in Spanish, and every student takes at least one language. If students read more ..

Guest Feb 19, 2023

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154

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Counting

How to solve this

Catherine rolls a 6-sided die five times, and the product of her roll is . How many different sequences of rolls could there have been? (The order of the rolls matters.)

Guest Feb 19, 2023

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150

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Counting

Help plz with counting

Find the number of ways of arranging the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in a row so that the product of any two adjacent numbers is even or a mutliple of 3

Guest Feb 19, 2023

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210

1

math

It takes
67
pounds of seed to completely plant a
9 read more ..

Guest Feb 19, 2023

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159

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Precalc

Plz help with parametric equations

The position of a particle is given by the parametric equations
x = 1 + sin pi*t - cos pi*t read more ..

Guest Feb 19, 2023

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160

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Algebra

How do you solve this equation

Find all values of c such that 3*(2c + 1) = 28*(3*c) - 9. If you find more than one value of c, then list your values in increasing order, separated by commas.

Guest Feb 19, 2023

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161

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Counting

Plz help

A standard six-sided die is rolled 7 times. You are told that among the rolls, there was one 1, two 2's, and three 4's. How many possible sequences of rolls could there have been? (For example, 5, 1, 2, read more ..

Guest Feb 19, 2023

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192

1

Algebra

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 180 meters per hour when walking across flat ground, and 250 meters per hour when walking downhill. One day, Carissa walks read more ..

Guest Feb 19, 2023

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166

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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 19, 2023

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207

1

Counting question

Sam writes down the numbers 1, 2, 3, ..., 99

(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down, at random. What is the probability that Sam chooses a 0? read more ..

Guest Feb 19, 2023

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156

0

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 19, 2023

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169

0

Counting

My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between read more ..

Guest Feb 19, 2023

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205

1

Counting

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least two children? read more ..

Guest Feb 19, 2023

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175

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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 19, 2023

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171

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counting question

When it rains, every student in Margo's school brings a raincoat, an umbrella, or both. And of the students bring both. The total number of umbrellas brought is equal to twice the number of raincoats.

What percent of the read more ..

Guest Feb 19, 2023

0

1

148

1

Polynomials

Find a polynomial f(x) of degree 5 such that both of these properties hold:
* f(x) is divisible by x^3
* f(x) + 1 is divisible by (x+ 1)(x + 2)(x + 3)
read more ..

Guest Feb 19, 2023

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156

0

Inequality

Let a, b, and c be nonnegative real numbers. Prove that for all x >= 0,
(x + abc)^3 >= abc(x + a)(x + b)(x + c) >= (x + a + b + c)^3.

Guest Feb 19, 2023

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159

0

Algebra

Let r be a root of x^3 - 2x + 5 = x^3 - x^2 + 9. Show that none of r, r^2, or r^3 is irrational.

Guest Feb 19, 2023

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170

0

Stats

A list of ten distinct, positive integers has a median of 5.5. What is the smallest possible average of the ten positive integers? Explain your ansswer in complete sentences.

Guest Feb 19, 2023

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187

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Counting

You are given the 4 x 4 grid below.

(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
read more ..

Guest Feb 19, 2023

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201

1

HELP

1. Find all -intercepts of the graph of . 2^2 - 10x + y^2 -10y + 25 =0
Write your answer as a list of ordered pairs, separated by commas. If there are no -intercepts, write "none".

2. Find all -intercepts read more ..

Guest Feb 19, 2023

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