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3 years ago

A: The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5]

Mathematics

1 answer:

spayn [35]3 years ago

6 0

we analyze the table

From the table we can see that f(x) values are larger than g(x) values till x= 4

When x=5 the g(x) is greater than f(x)

So we can say the graph of f(x) exceeds g(x) over the interval [0,4]

Over the interval [4,5] g(x) exceeds f(x), it means there is a intersection point between 4 and 5

The graph of g(x) exceeds the graph of f(x) after some point of intersection between 4 and 5

Answer is : c: The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x).

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3 years ago

Suppose ten students in a class are to be grouped into teams. (a) If each team has two students, how many ways are there to form

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(a) There are 113,400 ways

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Step-by-step explanation:

The number of ways to from k groups of n1, n2, ... and nk elements from a group of n elements is calculated using the following equation:

$\frac{n!}{n1!*n2!*...*nk!}$

Where n is equal to:

n=n1+n2+...+nk

If each team has two students, we can form 5 groups with 2 students each one. Then, k is equal to 5, n is equal to 10 and n1, n2, n3, n4 and n5 are equal to 2. So the number of ways to form teams are:

$\frac{10!}{2!*2!*2!*2!*2!}=113,400$

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Replacing k by 4, n by 10, n1 and n2 by 2 and n3 and n4 by 3, we get:

$\frac{10!}{2!*2!*3!*3!}=25,200$

So, If each team has either two or three students, The number of ways form teams are:

113,400 + 25,200 = 138,600

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3 years ago