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Hunter-Best [27]

2 years ago

9

A rectangular board is 1.8 meters long and 1.25 meters wide. What is the area of the board in square millimeters? Do not round y

our answer.
=___square m

1 answer:

lilavasa [31]2 years ago

7 0

Answer:

2250000 mm^2 or 2.25 m^2

Step-by-step explanation:

Area=1.8*1.25=2.25 m^2=2250000 mm^2

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

A)

We want to find dy/dx.

So, let’s find our equation in terms of <em>x</em>. 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<em> </em>the <em>x</em> term to acquire:

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

Take the derivative of both sides with respect to <em>x: </em>

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

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 <em>x</em> is 30 and when <em>y</em> is $10,000.

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

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

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>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

2 years ago

Make sure to SHOW WORK

attashe74 [19]

9/4=2.25
2.25-1= 1.25

7 0

3 years ago

Read 2 more answers

stat: sample of 780 adults in the U.S.A., it was found that 80 of those had a pinworm infestation. You want to find the 99% conf

Anettt [7]

Answer: 554

Step-by-step explanation:

If prior population proportion is known, then the formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

As per given description, we have

p= 0.1

E=0.025

Critical z-value for 95% confidence : $z_{\alpha/2}=1.96$

Then,

$n=0.1(1-0.1)(\dfrac{1.96}{0.025})^2=553.1904\approx554$

Hence, the minimum sample size required = 554.

7 0

3 years ago

HELP ASAP 100 POINTS!!!

nikklg [1K]

<h3>Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>

===========================================================

Explanation:

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

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

Side notes:

Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
Choice 2 is not true. Point B is not on the parabola.
Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.

7 0

3 years ago

Read 2 more answers

When trying to write an equation in standard form, you first have to find the slope if it is not given. If the slope ends up bei

Elan Coil [88]

It is neither one. Division by zero is undefined in math, so if the slope ends up being 5/0, the line has undefined slope.

3 0

3 years ago