Solve by the linear combination method (with or without multiplication).

Mathematics

1 answer:

Dima020 [189]3 years ago

5 0

The first step is to name the equations to make the process of solving them easy.

$6x+7y=-4....(1)\\5x-3y=-21....(2)$

The second step is to multiply each of the equations by the coefficient of the x term in the other equation. In this case, we will multiply equation (1) by 5 to get equation (3) and then multiply equation (2) by 6 to get equation (4).

$-30x-35y=20...(3)\\30x-18y=-126...(4).$

The next step is to add equation equation(3) and (4) together to get equation (5) as shown below;

$-53y=-106....(5)\\=> y= 2.$

The next step is to take the value of y and substitute it into any of the equations above. For this solution, I pick equation (1). The work done to solve for x is shown below.;

$6x+7y=-4\\=>6x+7(2)=-4\\=>6x=-18\\=>x=-3$

The solution for this system of equations is $(-3,2)$

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About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil

Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

$P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}$

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$