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Gala2k [10]
3 years ago
13

The function y = 3 squared - x - 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
3 0

Answer: Y < = 144

Step-by-step explanation:

Given that the function y = 3 squared - x - 3 is graphed only over the domain of {x | –8 < x < 8}

That is, y = 3x^2 - 3

Since x is greater than -8, the minimum value of x will be -7.

Also, x is less than 8, the maximum value of x will be 7

Substitute the two values into the given function.

When x = -7

Y = 3(-7)^2 - 3

Y = 3(49) - 3

Y = 147 - 3

Y = 144

When x = 7

Y = 3(7)^2 - 3

Y = 3(49) - 3

Y = 147 - 3

Y = 144

The range of the graph is therefore, Y less than or equal to 144. That is,

Y < = 144

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Answer:

1716 ;

700 ;

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Step-by-step explanation:

Given that :

Number of members (n) = 13

a. How many ways can a group of seven be chosen to work on a project?

13C7:

Recall :

nCr = n! ÷ (n-r)! r!

13C7 = 13! ÷ (13 - 7)!7!

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b. Suppose seven team members are women and six are men.

Men = 6 ; women = 7

(i) How many groups of seven can be chosen that contain four women and three men?

(7C4) * (6C3)

Using calculator :

7C4 = 35

6C3 = 20

(35 * 20) = 700

(ii) How many groups of seven can be chosen that contain at least one man?

13C7 - 7C7

7C7 = only women

13C7 = 1716

7C7 = 1

1716 - 1 = 1715

(iii) How many groups of seven can be chosen that contain at most three women?

(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)

Using calculator :

(15 * 35) + (6 * 21) + (1 * 7)

525 + 126 + 7

= 658

c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?

(First in second out) + (second in first out) + (both out)

13 - 2 = 11

11C6 + 11C6 + 11C7

Using calculator :

462 + 462 + 330

= 1254

d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?

Number of ways with both in the group = 11C5

Number of ways with both out of the group = 11C7

11C5 + 11C7

462 + 330

= 792

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