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Leona [35]
3 years ago
8

the width of a rectangle is 12 units less than the length. The perimeter is 108 units. Find the length

Mathematics
1 answer:
sukhopar [10]3 years ago
3 0
Length = x
Width = 2 x - 12

Equation Formation
2 (x) + 2(2 x - 12) = 108
2 x + 4 x - 24 = 108
6 x - 24 = 108
6 x = 132
x = 22

Length = 22 units
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Here is the full question:

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(b) 0.2510

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Step-by-step explanation:

Given that:

The sample size = 10

Sample proportion= 60% 0.6

Let X represents the no of streaked-shell snails.

X \sim Binom (n =1 0, p = 0.60)

The Probability mass function (X) is:

P(X =x)= (^n_x) p^x(1-p)^{n-x}; x = 0,1,2,3...

The Binomial probability with mean μ = np

= 10 * 0.6

= 6

Standard deviation σ = \sqrt{np(1-p)}

= \sqrt{10*0.6*(1-0.6)}

= 1.55

The probability that the percentage of the streaked-shelled snails in the sample will be:

a)

P(X = 0.5) = ^nC_x p^x (1 -p) ^{(n-x)}

= ^{10}^C_5 * (0.6)^5(1-0.6)^{10-5}

= \dfrac{10!}{5!(10-5)!} * (0.6)^5(1-0.6)^{10-5}

= 0.2007

b)

P(X = 0.6) = ^nC_x p^x (1 -p) ^{(n-x)}

= ^{10}^C_6 * (0.6)^6(1-0.6)^{10-6}

= \dfrac{10!}{6!(10-6)!} * (0.6)^6(1-0.6)^{10-6}

= 0.2510

c)

P(X = 0.7) = ^nC_x p^x (1 -p) ^{(n-x)}

= ^{10}^C_7 * (0.6)^7(1-0.6)^{10-7}

= \dfrac{10!}{7!(10-7)!} * (0.6)^7(1-0.6)^{10-7}

= 0.2150

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