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3 years ago

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The table shows the number of feathers Patsy the Peacock sold at each of the 8 festivals this year. Based on this data, what is

a reasonable estimate of the probability that Patsy sells fewer than 5 feathers next festival?

2 answers:

Readme [11.4K]3 years ago

4 0

Answer:75%

Step-by-step explanation:

liraira [26]3 years ago

3 0

Answer: 75%

Step-by-step explanation:

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent <em>p</em>-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

(c) The series

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0

2 years ago

Karls mother buys 60 party favors to give out as a fift during karls birthday party which number of guest will not let her divid

xeze [42]

THE answer is 15 just look it up

7 0

3 years ago

Read 2 more answers

The store currently has seven rackets of each version. What is the probability that all of the next ten customers who want this

Mila [183]

The probability that all of the next ten customers who want this racket can get the version they want from current stock is 0.821

<h3>How to solve?</h3>

Given: currently has seven rackets of each version.

Then the probability that the next ten customers get the racket they want is P(3≤X≤7)

<h3>Why P(3≤X≤7)?</h3>

Note that If less than 3 customers want the oversize, then more than 7 want the midsize and someone's going to miss out.

X ~ Binomial (n = 10, p = 0.6)

P(3≤X≤7) = P(X≤7) - P(X≤2)

From Binomial Table:

= 0.8333 - 0.012

= 0.821

To learn more about Probability visit :

brainly.com/question/25870256

#SPJ4

6 0

2 years ago

There are 30 students in a classroom. The ratio of boys to girls is 2:3.

Arisa [49]

<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Split 30 into the ratio 2 : 3

12 : 18

12 / 18 + x = 1/5

Cross multiply:

12(5) = 1(18 + x)

60 = 18 + x

Subtract 18 from both sides:

x = 42

42 girls entered the classroom

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0

2 years ago

-3y -9x =21. -18x +4y =32

Reil [10]

The value of x is -2 and the value of y is -1.

Step-by-step explanation:

Step 1; The given equations are taken as

-3y -9x =21 or -9x -3y = 21, take this as equation 1

-18x +4y =32, take this as equation 2

Step 2; We multiply equation 1 with 2 and equation 2 with 1 so we can cancel out the variable x in both equations. By doing this we get

-18x -6y =42, take this as equation 3

-18x +4y =32, this is the same as equation 2

If we subtract 3 with 2, we cancel out the x variable and can calculate the value of y.

10y = -10 , y = -10/10 = -1

Step 3; Substituting this value of y in any of the previous equations we will get x's value. Here this value of y is substituted in equation 2.

-18x +4(-1) =32, -18x -4 = 32 , -18x = 36, x=-2.

So we have x = -2 and y = -1.

5 0

2 years ago