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3 years ago

2 cubes thrown, what is probability one will land on a one and the other not a one

Mathematics

1 answer:

Sindrei [870]3 years ago

8 0

Answer:

The answer is 5/36.

Step-by-step explanation:

The probability that the first cube will land on a one is 1/6 and the probability that the second cube will land not on a one is 5/6.

So,you do 1/6*5/6=5/36.

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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

Madison arrived at work at 8:00 AM. She went out for lunch at 11:00 AM. She returned at 12:00 PM and worked until 4:00 PM. How m

goblinko [34]

C-7 hours, 0 minutes because between 8 and 11 are 3 hours and between 12 and 4 are 4 hours. 3+4= 7 hours

8 0

3 years ago

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What is a number increased by 7 multiplied by 4?

Lana71 [14]

Answer:

Step-by-step explanation:

9 + 7 is `16, and 16 is a multiple of 4

4 0

3 years ago

Gerry visited a farm and saw a total of 87 chickens and pigs. If there were a total of 248 legs between all of these animals, ho

Shkiper50 [21]

Answer: 37

Step-by-step explanation:

87 x 2 = 174

248 - 174 = 74

74 divided by 2 = 37

So, therefore you answer will be 37

:))

6 0

3 years ago

If x=3 calculate the value of x3-x

Dmitrij [34]

$x^3-x=3^3-3= \\\\ =27-3= \\\\ =\boxed{24}$

6 0

3 years ago

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