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docker41 [41]
3 years ago
6

2. A function g(x) is defined by the diagram shown below.

Mathematics
1 answer:
skad [1K]3 years ago
8 0

Answer:

Step-by-step explanation:

diagram attached represents a function g(x).

Circle (1) (circle on the left) represents the set of domain (input values) and circle (2) represents the range (output values).

a). For input value x = 7, out put value of the function is y = 9.

   Therefore, g(7) = 9 will be the answer.

b). Range of the function g(x) is the set of output values.

    Range: {12, 9, 9, 17}

c). Inverse of the function g(x) will have,

   Domain: {12, 9, 9, 17}

   Range: {4, 7, 10, 15}

   For input value of x = 9, there are two output values y = 7, 10.

   Since, "a function can't have two output values for the same input value".

   Therefore, inverse of the function g(x) will not represent a function.

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There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.

Step-by-step explanation:

Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.

 The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is {11 \choose 3} = 165 . As a result, we have 165 ways to distribute the blackboards.

If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is {7 \choose 3} = 35. Thus, there are only 35 ways to distribute the blackboards in this case.

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