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Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0, π] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)

Answers

Answer 1

Answer:

The average value of the function is $-(2)/(\pi)$ .

Average value :

The average value of the function is given as,

$Average=(1)/(\pi) \int\limits^\pi_0 {f(x)} \, dx$

Given function is, $f(x)=-sinx$

Substitute values in above relation.

$Average=(1)/(\pi) \int\limits^\pi_0 {-sinx} \, dx\n\nAverage=(1)/(\pi) (cosx)^(\pi) _(0)\n\nAverage=(1)/(\pi)(cos\pi - cos 0)\n\nAverage=(1)/(\pi)(-1-1)\n\nAverage=-(2)/(\pi)$

The values of x in the interval for which the function equals its average value is,

$-sinx=-(2)/(\pi)\n \nx=sin^(-1) ((2)/(\pi) )=39.56$

Learn more about the average value of function here:

brainly.com/question/20118982

Answer 2

Answer:

Answer with Step-by-step explanation:

We are given that

$f(x)=-sin x$

$[0,\infty]$ ]

Average value of the function is given gy

$f_(avg)=(1)/(b-a)\int_(a)^(b)f(x)dx=(1)/(\pi-0)\int_(0)^(\pi)-sinx dx$

$f_(avg)=(1)/(\pi)[cosx]^(\pi)_(0)$

Using the formula

$\int sin xdx=-cos x$

$f_(avg)=(1)/(\pi)(cos\pi-cos0)$

$f_(avg)=(1)/(\pi)(-1-1)=-(2)/(\pi)$

$f(x)=f_(avg)$

$-sinx=-(2)/(\pi)$

$sinx=(2)/(\pi)$

$x=sin^(-1)((2)/(\pi))=0.69radian$

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How do you calculate the approximate mean monthly salary of 100 graduatesmonthly salary number of graduate

1001-1400 1
1401-1800 11
1801-2200 14
2201-2600 38
2601 3000 36.

Answers

Answer:

The mean monthly salary of these 100 graduates is $2388.5

Step-by-step explanation:

First, lets make all of the salaries a set, so:

S = {S1,S2,S3,S4,S5}

where

S1 = {1001-1400}

S2 = {1401-1800}

S3 = {1801-2200}

S4 = {2201-2600}

S5 = {2601-3000}

Each element S1,S2,..,S5 will have it's own mean, that will be the upper range + lower range divided by 2.

M(S1) = (1400+1001)/2 = 2401/2 = 1200.5

M(S2) = (1401+1800)/2 = 3201/2 = 1600.5

M(S3) = (1801+2200)/2 = 4001/2 = 2000.5

M(S4) = (2201+2600)/2 = 4801/2 = 2400.5

M(S5) = (2601+3000)/2 = 5601/2 = 2800.5

To find the approximate mean, now we calculate a weigthed mean between M(S1),M(S2),...,M(S5)

So the mean will be

M = (M(S1)+11*M(S2)+14*M(S3)+38*M(S4)+36*M(S5))/100

M = 238850/100

M = 2388.5

So the mean monthly salary of these 100 graduates is $2388.5

The area of the square is 36 cm. 2 what is the formula that shows the length or side b

Answers

Answer:

36=b^2 or b=the square root of 36

Step-by-step explanation:

The sides of a square are all equal in length. To find the area of a square you can multiply the two sides together. Considering that they are the same length, you can just square one of the side lengths to get your answer. To find a side length you can take the square root of the area.

Answer:

Step-by-step explanation:

b · b = 36

Suppose that the US plans to send a shipment of "rovers" to Mars. These are mobile robots, programmed to collect rock and soil samples, and then return to the landing site. The rovers operate independently of each other. The mean weight a rover is programmed to collect is 50 pounds, and the standard deviation of weights is 5 pounds. Weights collected by rovers are approximately normally distributed. If the US sends 10 rovers, what is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds? What sampling distribution should we use to compute this probability?

Answers

Answer:

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 50, \sigma = 5, n = 10, s = (5)/(√(10)) = 1.58$

What is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds?

This is the pvalue of Z when X = 52 subtracted by the pvalue of Z when X = 48. So

X = 52

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (52 - 50)/(1.58)$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962

X = 48

$Z = (X - \mu)/(s)$

$Z = (48 - 50)/(1.58)$

$Z = -1.26$

$Z = -1.26$ has a pvalue of 0.1038

0.8962 - 0.1038 = 0.7924

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

What sampling distribution should we use to compute this probability?

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Y<-2/3 x-1 graphing the inequality

Answers

Answer:

y < − 2/3x − 1

Step-by-step explanation:

The table on the left is that of a linear function, and the one on the right is that of an exponential function. Can you tell which function has the higher rate of growth? How?

Answers

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

$\begin{array}{c|c|c}\text{x value}&\text{linear}&\text{exponential}\n4&28&8\n5&35&16\n6&42&32\n7&49&64\n8&56&128\n9&63&256\end{array}$

and you can see how the exponential growth is much faster than the linear one.

What is 19% of 103?

Answers

Answer:

19.57

Step-by-step explanation:

When you do 19% of 103

you get 19.57

Hope this helps! <3

Answer: 19% of 103 is 19.57

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