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3 years ago

A pianist plans to play 7 pieces at a recital. In how many ways can she arrange these pieces in the program?

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

3 0

Answer:

5040

Step-by-step explanation:

7 x 6 x 5 x 4 x 3 x 2 = 5040 different ways. Look at it this way: The first place can be taken by any of the 7 objects, which leaves any of 6 objects available for second place, which leaves any of 5 objects that then leaves 4 then 3 then 2 then 1

HOPE THIS HELPS

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12.50x = 15 What is the value of x? What is the percent increase?

kolezko [41]

Answer:

x = 1.2

Step-by-step explanation:

12.50x = 15

12.50/12.50 x = 15/12.50

x = 1.2

(Sorry i dont understand what you mean by percent increase)

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3 years ago

90 POINTS PLEASE HELP

11111nata11111 [884]

$sin\alpha = - 0.8$

<u>Step-by-step explanation:</u>

We have , $cos\alpha = \frac{3}{5}$ , where $\alpha$ is located in IV quadrant! Let's find out value of $sin\alpha$ :

$sin\alpha = \sqrt{1-(cos\alpha )^2$

⇒ $sin\alpha = \sqrt{1-(cos\alpha )^2$

⇒ $sin\alpha = \sqrt{1-(\frac{3}{5} )^2$

⇒ $sin\alpha = \sqrt{1-(\frac{9}{25} )$

⇒ $sin\alpha = \sqrt{(\frac{25-9}{25} )$

⇒ $sin\alpha = \sqrt{(\frac{16}{25} )$

⇒ $sin\alpha = \pm {(\frac{4}{5} )$

Value of $sin\alpha$ is dependent on which quadrant it is . Since, in question it's given that $\alpha$ is located in IV quadrant , So $sin\alpha$ is negative i.e.

⇒ $sin\alpha = - {(\frac{4}{5} )$

⇒ $sin\alpha = - 0.8$

Therefore, $sin\alpha = - 0.8$ .

4 0

3 years ago

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USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eight people at random off

Law Incorporation [45]

Answer:

a) Figure and code attached

b) $E(X)=\mu = np = 8*0.2= 1.6$

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

c) $P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=8, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

We can use the following R code to generate the histogram for this case:

> x <- seq(0,8,by = 1)

> y <- dbinom(x,8,0.2)

> plot(x,y,type = "h",main="Histogram")

And as we can see we got the result on the figure attached. And the distribution seems to be skewed to the right.

Part b

For this case the expected value is given by:

$E(X)=\mu = np = 8*0.2= 1.6$

The variance is given by:

$Var(X) =\sigma^2= np(1-p) = 8*0.2*(1-0.2) = 1.28$

And the standard deviation would be:

$Sd(X)=\sigma= \sqrt{1.28}= 1.131$

Part c

For this case we have the following inequality:

$P(X\geq 7) =0.97$

And we can calculate this with the complement rule.

$P(X \geq 7) = 1-P(X$

So then we have:

$P(X \leq 6) = 0.03$

And we are interested on the valueof n who satisfy this expression.

And for this we can verify this with the following code:

"=BINOM.DIST(6,E54,0.2,TRUE)"

And as we can see on the second figure attached the value who satisfy the condition would be n = 60.

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zlopas [31]

Answer:

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Step-by-step explanation:

pen pinapple apple pen

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2 years ago

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padilas [110]

I think second must b the answee

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3 years ago

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