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2 years ago

5

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

1 answer:

cricket20 [7]2 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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3 years ago

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3 years ago

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3 years ago

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amm1812

3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

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169 = 169

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8 0

3 years ago

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect

ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

$Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}$

Now the points A(−3, 4) and B(7, 2)

$AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}$

$AB = \sqrt{(10)^{2} +(-2)^{2}}$

$AB = \sqrt{100+4}$

$AB = \sqrt{104}$

$AB = 2\sqrt{26}\units$

Thus

$CD= 2\sqrt{26}\units$

Now the points

A (−3, 4) , D (−4, −1)

$AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}$

$AD = \sqrt{(-1)^{2} +(-5)^{2}}$

$AD = \sqrt{1 + 25}$

$AD = \sqrt{26}\units$

Thus

$BC = \sqrt{26}\units$

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

$Length = 2\sqrt{26}\ units$

$Breadth = \sqrt{26}\ units$

$Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})$

$Perimeter\ of\ rectangle = 2(3\sqrt{26})$

$Perimeter\ of\ rectangle = 6\sqrt{26}$

$\sqrt{26} = 5.1 (Approx)$

$Perimeter\ of\ rectangle = 6\times 5.1$

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

8 0

3 years ago