(1 point) How many ways can you give 9 (identical) apples to your 5 favourite Mathematics lecturers (without any restrictions)?

Mathematics

1 answer:

cricket20 [7]3 years ago

7 0

Answer:

126

Step-by-step explanation:

Total number of apples = 9

Number of favourite Mathematics lecturers = 5

To find number of ways in which 9 (identical) apples can be given to your 5 favourite Mathematics lecturers, find $C(9,5)$

Combination refer to selection of items such that order does not matter.

Use $C(n,p)=\frac{n!}{p!(n-p)!}$

Put $n=9,p=5$

$C(9,5)=\frac{9!}{5!(9-5)!}\\=\frac{9!}{5!4!}\\=\frac{9(8)(7)(6)5!}{5!4!} \\=\frac{9(8)(7)(6)}{4(3)(2)(1)}\\=126$

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Which of the following expressions is equal to -x2 - 36?

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A
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If g left parenthesis x right parenthesis equals 36 x squared minus 36 and h left parenthesis x right parenthesis equals 65 x,

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Given
g(x) = 36x² -36
h(x) = 65x

Find
x such that g(x) > h(x)

Solution
We can start by substituting the given information into the required relation.
36x² -36 > 65x
Subtracting the right side and factoring gives
36x² -65x -36 > 0
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The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
x < -4/9 or 9/4 < x