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3 years ago

Simplify: (3y)^4 (times) y^-2 A) 1/2y^2 B) 3y^2 C) 1/81 y^2 D) 81 y^2

Mathematics

2 answers:

Gennadij [26K]3 years ago

8 0

$(3y)^{4} * y^{-2}$

$((3y)(3y)(3y)(3y)) * \frac{1}{y^{2}}$

$81y^{4} * \frac{1}{y^{2}}$

$81y^{2}$

D. 81y²

yulyashka [42]3 years ago

6 0

$(3y)^4\cdot y^{-2}=81y^4\cdot y^{-2}=81y^{2}$

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6 high school seniors choose from among 20 quotes for their yearbook. What is the probability that at least 2 of them choose the

shusha [124]

Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem, we have that:

There are 6 students, hence n = 6.

There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.

The probability of one quote being chosen at least two times is given by:

$P(X \geq 2) = 1 - P(X < 2)$

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351$

$P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321$

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328$

0.0328 = 3.28% probability that at least 2 of them choose the same quote.

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago

Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= he

alexgriva [62]

Answer:

$p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }$

g(t) = 0

And

The differential equation $9ty + e^{t}y' = \frac{y}{t^{2} + 81 }$ is linear and homogeneous

Step-by-step explanation:

Given that,

The differential equation is -

$9ty + e^{t}y' = \frac{y}{t^{2} + 81 }$

$e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0$

By comparing with y′+p(t)y=g(t), we get

$p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }$

g(t) = 0

And

The differential equation $9ty + e^{t}y' = \frac{y}{t^{2} + 81 }$ is linear and homogeneous.

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3 years ago

Simplify the polynomial. Then find its value for the given value of the variable.

vekshin1

Answer:

Step-by-step explanation:

Simplified expression:

$3x^3 -x^3 +5x^3-9x^3$

$2x^3 +5x^3-9x^3$

$7x^3 -9x^3$

$-2x^3$

If x = -1, the value of the expression is:

$-2x^3$

$-2(-1^3)$

$-2(-1)$

$2$

Hope this helps!

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3 years ago

Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

VARVARA [1.3K]

27/3 = 9 cm3
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Gelneren [198K]

Answer:

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have a good day and be safe

-Hops

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