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3 years ago

12

Rickey has 7 over 8 cup of cereal in a bowl. He then gave two 1 over 4 cups of cereal from his bowl to his little sister. Which

of the following best explains the amount of cereal left in Rickey's bowl?

1 answer:

NeX [460]3 years ago

5 0

Answer:

5/8 cup left

Step-by-step explanation:

7/8 - 1/4

1/4=2/8

7/8-2/8

5/8

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The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac

olya-2409 [2.1K]

Answer:

a) $\frac{74}{10025}$

b) $\frac{3x-2}{x(8x+1)}$

c) $\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Step-by-step explanation:

For total cost function $c(x)$ , average cost is given by $\frac{c(x)}{x}$ i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., $\left ( \frac{c(x)}{x} \right )'$

Given: $c(x)=\frac{3x-2}{8x+1}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

a)

At x = 50 units,

$\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}$

b)

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

c)

Marginal average cost:

Differentiate average cost with respect to $x$

Take $f=3x-2\,,\,g=8x^2+x$

using quotient rule, $\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}$

Therefore,

$\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}$

3 0

3 years ago

Big will's ice cream cone contains 16 grams of saturated fat. This is 80% of his total daily allowance. What big will's total da

Ahat [919]

Answer:

20 grams

Step-by-step explanation:

Let x be the total allowance of fat

16 grams is 80% of his total allowance

x * 80% = 16

Change percent to a decimal

x *.8 = 16

Divide each side by .9

.8x/.8 = 16/.8

x = 20

8 0

3 years ago

What is the orthocenter of a triangle with vertices A(−3,−2)A(−3,−2), B(−2,2)B(−2,2), and C(2,−2)C(2,−2)?

ExtremeBDS [4]

A(−3,−2), B(−2,2), C(2,−2)

The orthocenter is the meet of the altitudes. We see AC is parallel to the x axis so the perpendicular $x=-2$ is the altitude through B.

Between A and B we have slope (2 - -2)/(-2 - -3) = 4 so perpendicular slope -1/4 through C(2,-2):

$y+2 = -\frac 1 4 (x - 2)$

For the y coordinate of the orthocenter we substitute in x=-2.

$y+2 = -\frac 1 4(-2 - 2) = 1$

$y = -1$

So the orthocenter is (x,y)=(-2,-1)

Answer: (-2,-1)

8 0

3 years ago

Find the value of the lesser root of x 2-8x+7=0

mariarad [96]

Hi there! The answer is x = 1

${x}^{2} - 8x + 7 = 0$

$(x - 7)(x - 1)$
Rule AB = 0, gives A = 0 or B = 0

$x - 7 = 0 \: \: or \: \: x - 1 = 0 \\ x = 7 \: \: \: \: \: \: \: \: \: or \: \: x = 1$
Therefore, the smallest of both roots is x = 1.

7 0

3 years ago

Need Help fast, with steps

Hitman42 [59]

Answer:The solution is in the attached file below

Step-by-step explanation:

5 0

3 years ago