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2 years ago

Type the correct answer in each box. Find the elements of matrix A. help PLS!!

Mathematics

1 answer:

horsena [70]2 years ago

4 0

Answer:

a = 2

b = 11

c = 11

d = -2

Step-by-step explanation:

$\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right]$

$\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right]$

On comparing to right side, we get,

22a + 6b = 110

Divide the entire equation by 2

11a + 3b = 55 ------------(I)

11a - 9b = -77 -------------(II)

Subtract equation (II) from (I)

11a + 3b = 55

11a - 9b = -77

- + + {Now subtract}

12b = 132

b = 132/12

$\sf \boxed{\bf \ b = 11}$

Substitute the value of b in eqaution (I)

11a + 3*11 = 55

11a + 33 = 55

11a = 55 - 33

11a = 22

a = 22/11

$\sf \boxed{\bf \ a = 2}$

22c + 6d = 230

Divide by 2

11c + 3d = 115 -----------------(III)

11c - 9d = -139 ------------------(IV)

Subtract (IV) from (III)

11c + 3d = 115

11c - 9d = 139

- + -

12d = -24

d = -24/12

$\sf \boxed{\bf \ d = -2}$

Plugin d = - 2 in equation (III)

11c + 3*(-2) = 115

11c - 6 = 115

11c = 115 + 6

11c = 121

c = 121/11

$\sf \boxed{\bf \ c = 11}$

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We use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

23% of the respondents have boycotted goods for ethical reasons.

This means that $p = 0.23$

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

This is P(X = 2) when n = 6. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

27.89% probability that two have ever boycotted goods for ethical reasons

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Either less than two have, or at least two. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

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$E(X) = np = 10*0.23 = 2.3$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.23*0.77} = 1.33$

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