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joja [24]
3 years ago
7

The length of a rectangle is 4 inches more than the width. the perimeter is 32 inches. find the length and width.

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
The length of the rectangle is 10 inches, and the width is 6 inches.

10 + 10 + 6 + 6 = 32


And that's your answer! ^ I hope this helped! c:
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A van,a moving company charges 50.00 plus 5.50 by per mile. The table shows the total cost for the number of miles drivin
Anna71 [15]

y = 55/10x + 50 is the equation to represent this situation

8 0
2 years ago
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa
Sladkaya [172]

Answer:

The null hypothesis is H_0: \mu = 2.5.

The alternative hypothesis is H_1: \mu > 2.5

Step-by-step explanation:

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years.

At the null hypothesis, we test if the mean is of 2.5 years, that is:

H_0: \mu = 2.5

A study was then done to see if the mean time has increased in the new century.

At the alternative hypothesis, we test if the mean has increased, that is, if it is above 2.5 years. So

H_1: \mu > 2.5

8 0
3 years ago
What is the value for Q1
Sever21 [200]

Answer:

its 5 and 1/2

Step-by-step explanation:

6 0
3 years ago
Lena will use 7 cups of apples to make 4 batches of applesauc. Which expression shows the number of cups of apples in each batch
astraxan [27]

Answer:  1 3/4 cups of apples in each batch

Step-by-step explanation:

STEP  1

Writing out the equation to represent if 7 cups of  apples make 4 batches   One batch is as a result of how many  cups of apples

LET x be number of cups of apples to make each batch

7 cups of  apples = 4 Batches

        x cups of apples = 1 Batch

STEP 2  Solving by cross multiplication

1 batch x 7 cups of apples = 4 batches  X x cups of apples

x cups of apples=1 batch x 7 cups of apples / 4batches

x   = 7 / 4 =  1 3/4

number of cups of apples to make each batch=  1 3/4

8 0
3 years ago
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
3 years ago
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