I need help with this please. I need to find the volume. For number 7

larisa86 [58]

Part A
To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, $\frac{3}{5}$ and $\frac{2}{3}$ equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

Part B
To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

$1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} 
$

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

$\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}$

Now, we can simply add our numerators.

$25+24=49$

We know that he needs $\frac{49}{15}$ gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

$\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}$

Using that logic, we can see that the painter needs exactly $3 \frac{4}{15}$ gallons of paint.

4 0

3 years ago

How to solve 14x+2=9

shusha [124]

Answer:

14x + 2 = 9

-2 -2

14x = 7

/14 /14

X = 7/12

6 0

3 years ago

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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 $).

A)

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

Which of the following means the same as 2(3x – 4) ?

Lorico [155]

Answer:

6x - 8

Step-by-step explanation:

2(3x – 4)

Distribute

2*3x - 2*4

6x - 8

8 0

3 years ago

I urgently need the answer plzzzzzzz with explanation too plzzzzz

Eddi Din [679]

The pizza is fresh and the doe is fresh made

3 0

4 years ago

Read 2 more answers