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2 years ago

11

Chase buys a bag of cookies that contains 6 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cooki

es. What is the probability that Chase randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a chocolate chip cookie

1 answer:

Over [174]2 years ago

4 0

Answer:

0.0652173

Step-by-step explanation:

Given that :

6 chocolate chip cookies

6 peanut butter cookies

6 sugar cookies

6 oatmeal cookies

Total number of cookies purchased = (6+6+6+6) = 24

Probability, P= required outcome /total possible outcomes

This is a selection without replacement probability problem :

P(peanut butter cookies) = 6/24 = 1/4

Then ;

P(chocolate chip cookie) = 6/23

Hence,

P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173

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A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is

koban [17]

The expected length of code for one encoded symbol is

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha$

where $p_\alpha$ is the probability of picking the letter $\alpha$ , and $\ell_\alpha$ is the length of code needed to encode $\alpha$ . $p_\alpha$ is given to us, and we have

$\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}$

so that we expect a contribution of

$\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375$

bits to the code per encoded letter. For a string of length $n$ , we would then expect $E[L]=1.375n$ .

By definition of variance, we have

$\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2$

For a string consisting of one letter, we have

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4$

so that the variance for the length such a string is

$\dfrac{15}4-\left(\dfrac{11}8\right)^2=\dfrac{119}{64}\approx1.859$

"squared" bits per encoded letter. For a string of length $n$ , we would get $\mathrm{Var}[L]=1.859n$ .

5 0

2 years ago

Who is in 6th grade or 7th? <br> cause I swear hrw.com is horrible

LiRa [457]

Answer:

Not me

Step-by-step explanation:

im in high school lol

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1 year ago

Read 2 more answers

What is 2 2/15 - 1 2/3=<br> I ended up with 2 3/21 <br> Really need help with this!

QveST [7]

Answer:

$2 \frac{2}{15} - 1 \frac{2}{3}$

$= \frac{32}{15} - \frac{5}{3}$

$= \frac{32 \times 1 - 5 \times 5}{15}$

$= \frac{32 - 25}{15}$

$= \frac{7}{15}$

5 0

2 years ago

Pleeeeese help me as fast as you can!!!

Aleonysh [2.5K]

Answer:

A. $y=3x-10$

C. $y+6=3(x-15)$

Step-by-step explanation:

Given:

The given line is $6x+18y=5$

Express this in slope-intercept form $y=mx+b$ , where m is the slope and b is the y-intercept.

$6x+18y=5\\18y=-6x+5\\y=-\frac{6}{18}x+\frac{5}{18}\\y=-\frac{1}{3}x+\frac{5}{18}$

Therefore, the slope of the line is $m=-\frac{1}{3}$ .

Now, for perpendicular lines, the product of their slopes is equal to -1.

Let us find the slopes of each lines.

Option A:

$y=3x-10$

On comparing with the slope-intercept form, we get slope as $m_{A}=3$ .

Now, $m\times m_{A}=-\frac{1}{3}\times 3=-1$ . So, option A is perpendicular to the given line.

Option B:

For lines of the form $x=a$ , where, a is a constant, the slope is undefined. So, option B is incorrect.

Option C:

On comparing with the slope-point form, we get slope as $m_{C}=3$ .

Now, $m\times m_{C}=-\frac{1}{3}\times 3=-1$ . So, option C is perpendicular to the given line.

Option D:

$3x+9y=8\\9y=-3x+8\\y=-\frac{3}{9}x+\frac{8}{9}\\y=-\frac{1}{3}x+\frac{8}{9}$

On comparing with the slope-intercept form, we get slope as $m_{D}=-\frac{1}{3}$ .

Now, $m\times m_{D}=-\frac{1}{3}\times -\frac{1}{3}=\frac{1}{9}$ . So, option D is not perpendicular to the given line.

8 0

2 years ago

Passing through point (4, 9) and perpendicular to the line y= -1/5x -3

Ratling [72]

Answer:

y = 5x-11

Step-by-step explanation:

The slope intercept form of a line is y =mx+b where m is the slope

y = -1/5 x-3

The slope is -1/5

Lines that are perpendicular have negative reciprocal slopes

-1 /(-1/5)

-1 * -5/1

5

The slope of the line that is perpendicular is 5

y=5x+b

Using the point (4,9)

9 = 5(4)+b

9 = 20+b

9-20 =b

-11

y = 5x-11

6 0

2 years ago