The rectangle below has an area of 70 square meters. Find the dimensions of the rectangle. (x - 11) (x - 8)

Mathematics

1 answer:

aniked [119]3 years ago

7 0

Answer:

the dimensions of the rectangle are 10 and 7.

Step-by-step explanation:

Given;

area of the rectangle, A = 70 m²

dimensions of the rectangle, = x - 11 and x - 8

The area of rectangle is calculated as;

A = L x B

70 = (x - 11)(x - 8)

70 = x² - 8x - 11x + 88

0 = x² - 8x - 11x + 88 - 70

0 = x² - 19x + 18

0 = x² - x - 18x + 18

0 = x(x - 1) -18(x - 1)

0 = (x - 18)(x - 1)

0 = x - 18 or

0 = x - 1

x = 18 or 1

The dimensions of the rectangle are calculated as;

L = 18 - 11 = 7

B = 18 - 8 = 10

Therefore, the dimensions of the rectangle are 10 and 7.

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Step-by-step explanation:

a) Since each question has 5 options, all of them equally likely, and only one correct answer, then the probability of having a correct answer is 1/5 = 0.2.

b) Let X be the number of correct answers. We will model this situation by considering X as a binomial random variable with a success probability of p=0.2 and having n=6 samples. We have the following for k=0,1,2,3,4,5,6

$P(X=k) = \binom{n}{k}p^{k}(1-p)^{n-k} = \binom{6}{k}0.2^{k}(0.8)^{6-k}$ .

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$P(X\geq 4) = P(X=4)+P(X=5)+P(X=6)=\binom{6}{4}0.2^{4}(0.8)^{6-4}+\binom{6}{5}0.2^{5}(0.8)^{6-5}+\binom{6}{6}0.2^{6}(0.8)^{6-6}= 0.01696$

c)The expected value of a binomial random variable with parameters n and p is $E[X] = np$ . IN our case, n=6 and p =0.2. Then the expected value of correct answers is $6\cdot 0.2 = 1.2$