The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 900x − 40000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $60,000?
between 200 and 250; exclusive
between 200 and 250; inclusive
less than 250
more than 200

Answers

Answer 1

Solving the quadratic function, it is found that the range is of:

between 200 and 250; inclusive

The profit for x tours is modeled by the following equation:

[tex]p(x) = -2x^2 + 900x - 40000[/tex]

It is concave down, so the monthly profit will be of at least $60,000 between the two roots when [tex]p(x) = 60000[/tex]. Thus:

[tex]60000 = -2x^2 + 900x - 40000[/tex]

[tex]2x^2 - 900x + 10000 = 0[/tex]

Simplifying by 2:

[tex]x^2 - 450x + 50000 = 0[/tex]

Which has [tex]a = 1, b = -450, c = 50000[/tex]

Then:

[tex]\Delta = (-450)^2 - 4(1)(50000) = 2500[/tex]

[tex]x_{1} = \frac{-(-450) + \sqrt{2500}}{2} = 250[/tex]

[tex]x_{2} = \frac{-(-450) - \sqrt{2500}}{2} = 200[/tex]  

At least $60,000 includes $60,000, thus the interval is inclusive, and the correct option is:

between 200 and 250; inclusive

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The result of making the required variable the subject in both equation are :

p = w - cgh = - (m - r - 4d)

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5
Beena has a holiday in a villa in France.
The total cost of her travel is £349
Beena is on holiday for 2 weeks.
The cost of the villa is 650 euros per week.
While on holiday, Beena has 7 art lessons.
The cost of each art lesson is 45 euros.
Using an exchange rate of 1.12 euros = £1
(a) work out the total cost of Beena's travel, villa and art lessons.
Give your answer in pounds (£).

Answers

Answer:

The answer is 25 because they're both the same.

Mark me as brainliest please.

Step-by-step explanation:

The total cost of Beena's travel, villa and art lessons = £1790.97

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The total cost of her travel is £349

Beena is on holiday for 2 weeks.

The cost of the villa is 650 euros per week.

i.e. 2*650

  =1300 euros

  =1300/1.12

  =£1160.71

While on holiday, Beena has 7 art lessons.

The cost of each art lesson is 45 euros.

i.e. total cost = 7*45

                     =315

                     =315/1.12

                     =£281.25

[Using an exchange rate of 1.12 euros = £1]

Hence, The total cost of Beena's travel, villa and art lessons = £1790.97

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If you like my answer than please mark me brainliest

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

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