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ddd [48]
2 years ago
10

Examine the system of equations.

Mathematics
1 answer:
MrMuchimi2 years ago
7 0

answer:

x =  - 2 \\ y = 2 \\  \\ ( - 2, \: 2)

explanation:

y =  -  \frac{1}{2} x + 1 \\ y = 2x + 6 \\ first \: equation \: add \:  \frac{1}{2} from \: both  \\  sides \\   \\ second \: equation \: subtract \: 2x \: from  \\  both \: sides \\  \\ y +  \frac{1}{2} x = 1 \\ y - 2x = 6 \\ solve \: the \: first \: equation \\  \\ y +  \frac{1}{2} x = 1 \\ subtract \:  \frac{x}{2} from \: both \: sides \\  \\ y =  -  \frac{1}{2} x + 1 \\ substitute \:  -  \frac{x}{2}  + 1 \: for \: y \: in \: the  \\ other \: equation \\  \\  -  \frac{1}{2} x + 1 - 2x = 6 \\ add \:   \frac{1}{2} x \: to \: 2x \\  \\  -  \frac{5}{2} x + 1 = 6 \\ subtract \: 1 \: from \: both \: sides \\  \\  -  \frac{5}{2} x = 5 \\ divide \: both \: sides \: by \:  -  \frac{5}{2}  \\  \\ x =  - 2 \\ substitute \: the \: value \: of \: x \: into \\ an \: equation \\  \\ y =  -  \frac{1}{2} ( - 2) + 1 \\ distribute \\  \\ y = 1 + 1 \\ add  \\  \\ y = 2 \\  \\ ( - 2, \: 2)

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Answer:

(a)\ P(x = 0) = 0.2725

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Step-by-step explanation:

Given

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This question is an illustration of binomial probability, and it is represented as:

P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}

Solving (a): P(x = 0) --- None has done one time fling

P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}

P(x = 0) = 1* 1 * (1 - 0.15)^{8}

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Solving (b): P(x \ge 1)

To do this, we make use of compliment rule:

P(x = 0) + P(x \ge 1) =1

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P(x \ge 1) =1 - P(x = 0)

P(x \ge 1) =1 - 0.2725

P(x \ge 1) =0.7275

Solving (c): P(x\le 2)--- Not more than 2 has one time fling

This is calculated as:

P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

We have:

P(x = 0) = 0.2725

P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}

P(x = 1) = 8* (0.15) * (1 - 0.15)^7

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P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}

P(x = 2) = 28* (0.15)^2 * (1-0.15)^6

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P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

P(x \le 2) = 0.2725 + 0.3847 + 0.2376

P(x \le 2) = 0.8948

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