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3 years ago

Emily's bill for dinner at a restaurant was $61. She left an 18% tip. What was the amount of the tip?

1 answer:

7 0

You cross multiply. So 61 over 18 = x over 100. You multiply 61 and get the answer of 1600. Now with what you have left, you divide that with 18 and you should get your answer of <span>338.888889. Make sure to round it to whatever it tells you to round to!</span>

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If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

kvasek [131]

Answer:

Step-by-step explanation:

Given that:

If C(x) = the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x) = $\dfrac{C(x)}{x}$

We are to consider a given function:

$C(x) = 54,000 + 130x + 4x^{3/2}$

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

$C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}$

$C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )$

$C(1000) = 54,000 + 130000 + 4(31622.7766)$

$C(1000) = 54,000 + 130000 + 126491.1064$

$C(1000) = $310491.1064$

$\mathbf{C(1000) \approx $310491.11 }$

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x) = $\dfrac{C(x)}{x}$

SO;

$c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}$

Using the law of indices

$c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}$

$c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}$

c(1000) =$ 310.49 per unit

The marginal cost is C'(x)

Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:

$C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}$

$C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}$

$C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}$

$C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}$

$C'(1000) = 319.7366596$

$\mathbf{C'(1000) = \$319.74 \ per \ unit}$

(d) Find the production level that will minimize the average cost.

the average cost per unit is c(x) = $\dfrac{C(x)}{x}$

$c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}$

the production level that will minimize the average cost is c'(x)

differentiating $c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}$ to get c'(x); we have

$c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }$

$c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }$

Also

$c''(x)= \dfrac{108000}{x^3} -x^{-3/2}$

$c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0$

$x^2 = 27000\sqrt{x}$

$\sqrt{x} (x^{3/2} - 27000) =0$

x= 0; or $x= (27000)^{2/3}$ = $\sqrt[3]{27000^2}$ = 30² = 900

Since production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

$c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}$

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

8 0

3 years ago

Ramon surveyed his friends about their favorite snacks.he found that 1/6 of his friends prefer trail mix.what is the equivalent

Alex

<span>Students could also give the answers as green to blue, blue to green, truck , car to truck, blue to total, and green to total.Some students may write part to part ratios. When the class comes back together, this could be a good time to discuss why a part to whole ratio is more useful when comparing statements that include percents. Students may need to be reminded that percents are a form of a part to whole comparison where the whole is 100.hoose different pairs of small groups to post diagrams and explain how the diagram helped them to see the relationship between the fractions, percents, and decimals.</span>

5 0

3 years ago

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I’m really having trouble on this, can anyone help?

NikAS [45]

Answer:

the first box is proportional but the second is not

thus; y is (4/3)x for the first illustration

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2 years ago

Which of the following expressions is equivalent to 2/ 5 ÷ 7 /8 ?

Sonja [21]

You haven't provided expressions, so I can work out the problem for you. When we divide fractions, remember always "keep, switch, flip!" That's what we're gonna do here. We keep the 2/5, switch the sign to multiplication, and flip the 7/8 to 8/7. Therefore, we have 2/5*8/7. That gives us 16/35. Hope this helps!

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3 years ago

Use the table to write a proportion.

Tanya [424]

Answer:

Step-by-step explanation:

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3 years ago