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3 years ago

Determine the value of x for which rls if A)10 B)0.75 C)1.25 D)20

Mathematics

2 answers:

DedPeter [7]3 years ago

8 0

Answer:

Step-by-step explanation:

Since R and S are parallel lines, this means that Angle 1 and Angle 2 must be equivalent because they are corresponding angles. So:

$\angle 1 =\angle 2$

Substitute the equations:

$20-8x=30-16x$

Add 16x to both sides:

$20+8x=30$

Subtract 20 from both sides:

$8x=10$

Divide both sides by 8:

$x=10/8=5/4=1.25$

So, our answer is C.

And we're done!

lesantik [10]3 years ago

7 0

Answer:

x = 1.25

Step-by-step explanation:

<1 and <2 are corresponding angles and if the lines are parallel, corresponding angles are equal

<1 = <2

20-8x = 30-16x

Add 16x to each side

20-8x+16x = 30-16x+16x

20 +8x = 30

Subtract 20 from each side

20+8x-20 = 30-20

8x= 10

Divide by 8

8x/8 = 10/8

x = 5/4

x = 1.25

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3 years ago

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:

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