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2 years ago

Help please I will mark brainliest

Mathematics

1 answer:

SSSSS [86.1K]2 years ago

8 0

$a) \: 4 \times 3 \times 2 \times 1 = 24 \: ways$

$b) \: this \: one \: is \: a \: little \: more \: \\ complex \: so \: bear \: with \: me \\ poss \: 1 = all \: \: tie \: for \: first \\ poss \: 2 = 3 \: tie \: for \: second \\ poss \: 3 = 2 \: tie \: for \: third \\ poss \: 4 = no \: one \: ties$

They can all tie for first place in one way,

which is, that they all arrive first with no order.

<h3>Possibility 1 = 1 way</h3>

If one person arrives in first place, this leaves 3 to tie for second, All 4 players can arrive first and the other 3 would have to tie in second so,

<h3>Possibility 2 = 4 ways</h3>

If two people take the first two spots, this leaves two people to tie for third place, All four players can occupy the first position and the other 3 can switch in second leaving two to tie at last. and this can happen in 4 ways.

<h3>Possibility 3 = 4(3) = 12 ways</h3>

<h3>Possibility 4 = 24 ways (solved)</h3>

<h3>Total ways = 1 + 4 + 12 + 24 = 41 ways</h3>

<h2>Answer = 41 ways</h2>

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A battery has a lifetime that is approximately normally distributed with a mean of 600 hours and a standard deviation of 50 hour

miss Akunina [59]

Answer:

A. Your battery is likely defective since such poor performance is extremely unlikely.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is more than two standard deviations from the mean, it is considered an unlikely outcome.

In this question, we have that:

$\mu = 600, \sigma = 50$

Which of the following conclusions is the most appropriate given this information?

Lasted 400 hours, so X = 400.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{400 - 600}{50}$

$Z = -4$

4 standard deviations from the mean, so unlikely.

So the correct answer is:

A. Your battery is likely defective since such poor performance is extremely unlikely.

3 0

3 years ago

Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

4 years ago

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KengaRu [80]

Answer: 0.0062

Step-by-step explanation:

Given : Mean : $\mu=\ 31$

Standard deviation : $\sigma= 4$

Sample size : $n=100$

Assume that age of people in the country is normally distributed.

The formula to calculate the z-score :-

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x = 32

$z=\dfrac{32-31}{\dfrac{4}{\sqrt{100}}}=5$

The p-value = $P(x\geq32)=P(z\geq5)$

$=1-P(z$

Hence, the the probability that the average age of our sample is at least =0.0062

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4 years ago

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Answer:

$xe^{x} - e^{x} +C$

Step-by-step explanation:

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∫ $xe^{x}$

u=x ,

du= 1

dv = $e^{x}$

v=∫dv= $e^{x}$

Substituting into equ 1

∫udv = $xe^{x}$ - ∫ $e^{x}dx$

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4 years ago

Using first principal find the gradient of the curve whose equation is y=x^5. show working pleas

Keith_Richards [23]

Answer:

The gradient of $y = x^{5}$ is $\frac{dy}{dx} = 5\cdot x^{4}$ .

Step-by-step explanation:

Geometrically speaking, the gradient of a curve is the slope of the tangent line at a given point of the curve. From perspective of Differential Calculus, the gradient is the first derivative of the curve. Let $y = x^{5}$ , then the gradient of the curve is:

$\frac{dy}{dx} = 5\cdot x^{4}$ (1)

The gradient of $y = x^{5}$ is $\frac{dy}{dx} = 5\cdot x^{4}$ .

6 0

3 years ago