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VARVARA [1.3K]
3 years ago
14

Consider the following statement: If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's an

d Fred's. Write the To Prove statement:
Mathematics
2 answers:
vovangra [49]3 years ago
8 0

Answer & Step-by-step explanation:

To prove statement: Prove that Bill's age is between Paul's and Fred's. The to prove statement of a conditional in found in the conclusion of the conditional.

<h2>___________________________________________________</h2><h2><em>I AM ALWAYS HAPPY TO HELP :)</em></h2>
sveticcg [70]3 years ago
7 0

Explanation:

It is given than Paul is older than Bill.

Let age of Bill= x years, as x is a  natural number.

Then, age of Paul = (x + a) Years, where a is any natural number.

And, Fred is younger than Bill.

So, age of Fred= x - k, where k is any natural number.

So, if we arrange the ages of Fred, Bill and Paul, their ages would be

Fred < Bill < Paul

x-k < x < x+a

Hence, we can say that , Paul is eldest, and Fred is smallest member between  three.

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The domain of a graph of a function is  x ∈ [-8, 9] and the range of a graph of a function will be y ∈ [7, 0]

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It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function shown in the picture.

As we can see in the graph there are two bold dots are shown which represents at these points the function value exist.

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At x = 9, y = 6

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The domain of a function is x ∈ [-8, 9]

The range of a function is y ∈ [7, 0]

Thus, the domain of a graph of a function is  x ∈ [-8, 9] and the range of a graph of a function will be y ∈ [7, 0]

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A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses whic
Galina-37 [17]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:

30x + 15y ≤ 450

They are only 20 drivers, therefore only 20 buses can be used. It is represented by:

x + y ≤ 20

They  are only 19 small buses and 18 large buses:

x ≤ 18

y ≤ 19

After plotting the graph, the minimum solution to the graph are at:

A (15,0), B(18,0), C(10, 10), D(18, 2).

The cost function is given as:

The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.

​

F(x, y) = 225x + 100y

At point A:

F(x, y) = 225(15) + 100(0) = $3375

At point B:

F(x, y) = 225(18) + 100(0) = $4050

At point C:

F(x, y) = 225(10) + 100(10) = $3250

At point D:

F(x, y) = 225(18) + 100(2) = $4250

The minimum cost is at point C(10, 10) which is $3250

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