Pls help!!!!!!!!!!!!

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

3 years ago

What are the roots of this equation? x2-4x+9=0

zysi [14]

Considering the definition of zeros of a function, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.

<h3>Zeros of a function</h3>

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

$x1,x2=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

The quadratic function is f(x) = x² + 4x +9

Being:

a= 1
b= 4
c= 9

the zeros or roots are calculated as:

$x1=\frac{-4+\sqrt{4^{2}-4x1x9 } }{2x1}$

$x1=\frac{-4+\sqrt{16-36 } }{2x1}$

$x1=\frac{-4+\sqrt{-20 } }{2x1}$

and

$x2=\frac{-4-\sqrt{4^{2}-4x1x9 } }{2x1}$

$x2=\frac{-4-\sqrt{16-36 } }{2x1}$

$x2=\frac{-4-\sqrt{-20} }{2x1}$

If the content of the root is negative, the root will have no solution within the set of real numbers. Then $\sqrt{-20}$ has no solution.

Finally, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.

Learn more about the zeros of a quadratic function:

brainly.com/question/842305

brainly.com/question/14477557

#SPJ1

6 0

1 year ago

Can somoene help me with this question please

Alex

Answer:

About 260 seconds

Step-by-step explanation:

Tha rate is:

A: 8L/1.66666m

b: 10L/1m (converted to litres)

Divide 2400 by those rates above which:

2400 / (8/1.66666) = 500

2400 / (10/1) = 240

500 - 240 = 260

7 0

2 years ago

Brandon has a jar of quarters and dimes with a total value of $7.05. The number of quarters is 3 less than twice the number of d

miv72 [106K]

Answer:

quarters: 23
dimes: 13

Step-by-step explanation:

Let d represent the number of dimes. Then the number of quarters is 2d-3 and the total value of the coins is ...

0.10d + 0.25(2d-3) = 7.05

0.60d -0.75 = 7.05 . . . . . . . simplify

d = (7.05 +0.75)/0.60 = 13 . . . . add 0.75, divide by 0.60

2d-3 = 2·13 -3 = 23

Brandon has 23 quarters and 13 dimes.

4 0

3 years ago

Which of the following is NOT true about unit rates?

OLEGan [10]

Answer:

Unit rates can be used to compare two rates.

Step-by-step explanation:

This is not true because unit rates CAN'T be used to compare two rates. It's as simple as that. I don't know a simpler way to say it! lol I hope this helps! Please mark as brainliest! :D

4 0

3 years ago

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