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murzikaleks [220]
3 years ago
12

involving the election of officers on a committee. Assume that the committee consists of 14 members including Tasha. The same th

ree offices are to be filled. (1) In how many different ways can the offices be filled if each person can hold at most one office?
Mathematics
1 answer:
Yanka [14]3 years ago
5 0

Answer:

There are 364 ways of filling the offices.

Step-by-step explanation:

In this case, the order of filling of the offices does not matter, so, we can figure out the different ways of filling the offices by using the combination formula:

C^{n} _{r}=\frac{n!}{(n-r)!r!}

where n=14 (number of members)

r=3 number of offices

n!=n·(n-1)·(n-2)·...·3·2·1

C^{14} _{3}=\frac{14!}{(14-3)!3!}=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(11*10*9*8*7*6*5*4*3*2*1)*(3*2*1)}=\frac{14*13*12}{3*2*1} =364

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A quadratic function is defined by
ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

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Step-by-step explanation:

The given quadratic function is given in vertex  form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

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a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

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After the shifting the graph 6 units down, c = 23 - 6 = 17

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How do I solve this equation?
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x≤-4 or x≥0.5

Step-by-step explanation:

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