All Questions ⁺⁰237784 Questions

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Algebra

Prove that if a, b, and c are positive real numbers, then
sqrt(a^2 + ab + b^2) + sqrt(a^2 + ac + c^2) + sqrt(b^2 + bc + c^2) >= sqrt(3) (sqrt(ab) + sqrt(ac) + sqrt(bc))
When does equality occur?

Guest Mar 19, 2023

Mar 18, 2023

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156

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precalc

In triangle PQT, R is on side PT such that QR = QP. Also, QS is an altitude, and QT = 10. The values of tan PQT, tan RQT, tan SQT form an arithmetic progression, and the values of cot SQT, cot RQT, cot SQR form a geometic progression. read more ..

Guest Mar 18, 2023

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143

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probability

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

Guest Mar 18, 2023

+1

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+5

Geometry Question

Consider any right triangle. Construct a square off of each side and then connect the corners
of the squares to form a convex hexagon as in the figure below. What is the area of the hexagon in terms of a and b?
how would you solve read more ..

sdkflhgsdkjgsh Mar 18, 2023

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137

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+4

need further explanation with problem answer

For this problem: A regular hexagon has side length $6$. If the perimeter and area of the hexagon are $p$ and $A$, respectively, what is the value of (p^4)/(a^2) why is the answer 192 and not 207.36? i thought for the area of an equilateral triangle(to read more ..

DarkShark Mar 18, 2023

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141

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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 Mar 18, 2023

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158

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Algebra

Plz help prove this inequality
(a) Show that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) >= 32abcdef.
(b) Show that if a, b, c, d, e, f are nonnegative real numbers, read more ..

Guest Mar 18, 2023

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138

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Algebra

Help this is hard
Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
(a) Is the number 1/7 in the set S? read more ..

Guest Mar 18, 2023

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138

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counting

A baking club wants to form an executive committee. There are people in the baking club, including mark. In how many ways can the baking club form an executive committee with people?

Guest Mar 18, 2023

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165

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geometry

Help with parallelogram
In the diagram below, PQRS is a parallelogram with a perimeter of 26 and an area of 28. What is the perimeter of rectangle OSTQ? Include an explanation of how you solved the problem.

Guest Mar 18, 2023

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163

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counting

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?
(c) What is the sum read more ..

Guest Mar 18, 2023

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146

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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.
(b) Find the number of ways read more ..

Guest Mar 18, 2023

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150

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+23

geometry help

1. Let O be the center of a circle with diameter AB. Let C be a point on the circle such that angle COA = 90. Point P lies on line segment OA, and when line segment CP is extended past P, it intersects the circle at Q. If PQ = 7 and PO = 20, then find read more ..

uwuoniichan Mar 18, 2023

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154

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Probability

How this work
We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilatera is shown below. distinct points are chosen on a circle. We draw all read more ..

Guest Mar 18, 2023

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160

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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 Mar 18, 2023

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141

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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, 2, read more ..

Guest Mar 18, 2023

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164

1

Circle $O$ is tangent to $\overline{AB}$ at $A$, and $\angle ABD = 90^\circ$. If $AB = 12$ and $CD = 18$, find the radius of the circle.

Circle $O$ is tangent to $\overline{AB}$ at $A$, and $\angle ABD = 90^\circ$. If $AB = 12$ and $CD = 18$, find the radius of the circle.

Guest Mar 18, 2023

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141

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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? read more ..

Guest Mar 18, 2023

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153

1

PLEASE HELP

If abc = 13, and
find a+b+c

Guest Mar 18, 2023

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147

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counting

Find the number of positive integers that satisfy the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 5

Guest Mar 18, 2023

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