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3 years ago

PLEASE HELP WITH THIS CONDITIONAL PROBABILITY QUESTION AND PLEAS COULD YOU SHOW A STEP BY STEP EXPLANATION.

1 answer:

5 0

Hello I know this may be difficult on your end but you don’t always have to get the answer from someone you can contact a teacher and get help this keep be very helpful keep this in your head you are intelligent no matter what anyone tells you ask your teacher a question about the problem tell them you don’t get how to do it if you have to just whatever it takes for you to learn how to do it have a wonderful day or night bye!!!...

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Can anyone explain why this two is being added before the integral? Does it have something to do with integral symmetry?

PIT_PIT [208]

Yes it's exactly due to symmetry. Specifically, symmetry about the x axis.

Simply writing $\displaystyle \int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx$ , without the 2 out front, will only get you the area of the portion shown in red (see diagram below).

The blue region has equal area of the red region due to symmetry.

So,

$\displaystyle 2\int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx$

represents the red and blue regions combined.

The portion in green is $\displaystyle \int_{-4}^{8}\left[\sqrt{x+8} - \frac{x}{2} \ \right]dx$ which is the integral of the difference of the upper and lower curves over the interval $-4 \le x \le 8$

---------------

In all honesty, it's probably easier to integrate with respect to y since the given functions are in terms of y initially. Also, there isn't a junction point in which the curves swap places in terms of which one is larger. However, it doesn't hurt to have practice in integrating with respect to x.

If you're curious about what the y integral looks like, then it would be

$\displaystyle \int_{-2}^{4} \bigg[ (2y) - (y^2-8)\bigg] dy$

You can use a tool like WolframAlpha to check that both integral expressions result in 36 to help confirm that they represent the same overall area (just in different ways of course).

5 0

2 years ago

Read 2 more answers

Which graph represents the solutions to the inequality |2x − 4| less than or equal to 14?

atroni [7]

The graph that represents the solutions to the inequality |2x − 4| less than or equal to 14 or |2x - 4| ≤ 14 is a number line with a closed circle on negative 5, shading to the right and a closed circle on 9, shading to the left. The answer is letter B. The less than or equal to symbol or '≤' represents that all integers less than or equal to 9 are all solutions to the given inequality.

5 0

3 years ago

Which mixed number is equivalent to 9/7? A. 1 2/9. B. 1 2/7. C. 2 1/7 D. 2 1/9

saveliy_v [14]

In mixed form, it would be equal to 1 2/7

In short, Your Answer would be Option B

Hope this helps!

8 0

3 years ago

Read 2 more answers

Emanuel is renting a car for 1week in Charleston, South Carolina. The rental car agency is charging $175 for the rental and 15%

Semenov [28]

Answer:

201.25 (im not 100% sure)

Step-by-step explanation:

If its correct please mark me as brainliest

6 0

2 years ago

Read 2 more answers

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

3 years ago