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Grace [21]
3 years ago
11

A caterer provides a conference banquet for a price of $40 per person for 20 or fewer people but will decrease the price by $1 p

er person for everyone if there are more than 20 people. What number of people will produce the maximum revenue for the caterer?
Mathematics
1 answer:
mel-nik [20]3 years ago
7 0

Answer:

The maximum revenue is $900, obtained with 30 people

Step-by-step explanation:

Naturally, the answer should be a number equal or higher than 20, because up to 20 persons, each one pays the same. Lets define a revenue function for x greater than or equal to 20.

f(x) = x*(40-(x-20)) = -x²+60x

Note that f multiplies the number of persons by how much would they pay (here, assuming that there are more than 20).

f is quadratic with negative main coefficient and its maximum value will be reached at the vertex.

The value of the x coordinate of the vertex is -b/2a = -60/-2 = 30

for x = 30, f(x) = 30*(40-(30-20))=30*30=900

So the maximum revenue is $900.

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A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. suppose th
Volgvan

Answer:

We are given:

Confidence level = 99%. Therefore, the critical value at 0.01 significance level using the standard normal table is given below:

z_{\frac{0.01}{2}}=2.576

Margin of error is given in the question as:

E=0.05

Since the previous proportion is not given, therefore, we need to assume \hat{p} = 0.5

Therefore, the sample size is:

n=\hat{p}(1-\hat{p}) \left( \frac{z_{\frac{0.01}{2}} }{E} \right)

  =0.5(1-0.5) \left( \frac{2.576}{0.05} \right)

  =0.25 \times 51.52^2

  =663.6 \approx 664

Therefore, 664 sample observations are required.    

4 0
3 years ago
An area of 1000ft^2is not possible explain why this is true
statuscvo [17]
It isn't true.

A theoretical field of grass sized 100ft by 10ft will have an area of 1000ft^2.
3 0
3 years ago
hellppppp,mr. Raymond told students in a true-false quiz with 10 questions you are certain to get five correct if you just guess
Aleks [24]

Answer:

No

Step-by-step explanation:

Cause it just doesnt not making is sence

3 0
3 years ago
19) Suppose that there are 55 Democrats and 45 Republicans in the US Senate. A committee of seven senators is to be formed by se
andre [41]

Answer:

Probability = 0.12676992

Step-by-step explanation:

The probability of selecting committee of seven composed of all Democrats.

Total number = 45+55= 100

Number of Democrats = 55

Number of committee = 7

Probability= (55C7)/(100/7)

Where C represent combination sign

Probability = (202927725/1.60075608*10^10)

Probability = 0.12676992

7 0
3 years ago
You order a breakfast that costs $10.25 and a coffee that costs $3.45. You leave a 02% tip and the sales tax is 9.5%. What is th
Rasek [7]

Answer: the total cost of the meal is

$17.7415

Step-by-step explanation:

The original cost of the breakfast $10.25 and the original cost of the coffee is $3.45. This means that the total cost of the breakfast and the coffee was

10.25 + 3.45 = $13.7

You leave a 20% tip. This means that the amount of tip that you left is

20/100 × 13.7 = 0.2 × 13.7 = $2.74

The sales tax is 9.5%. This means that the amount of sales tax that you paid is

9.5/100 × 13.7 = 0.095 × 13.7 = $1.3015

Therefore, the total cost of the meal would be

13.7 + 2.74 + 1.3015 = $17.7415

7 0
3 years ago
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