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2 years ago

Y is inversely proportional to the square of x. If Y = 9 when x = 2, then what is y, when x is 10?

Mathematics

1 answer:

a_sh-v [17]2 years ago

5 0

Answer:

y = 0.36

Step-by-step explanation:

Given y is inversely proportional to x² then the equation relating them is

y = $\frac{k}{x^2}$ ← k is the constant of variation

To find k use the condition y = 9 when x = 2 , then

9 = $\frac{k}{2^2}$ = $\frac{k}{4}$ ( multiply both sides by 4 )

36 = k

y = $\frac{36}{x^2}$ ← equation of variation

When x = 10 , then

y = $\frac{36}{10^2}$ = $\frac{36}{100}$ = 0.36

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. At a clothing store, 12 people purchased blue sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 purchased

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The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

P(A)= the probability that they purchased a green sweater
P(B)= the probability that they purchased a gray sweater
Mutually exclusive events

You know:

8 purchased green sweaters
4 purchased gray sweaters
number of possible cases= 12 + 8 + 4+ 7= 21

So:

$P(A)=\frac{8}{31}$

$P(B)=\frac{4}{31}$

P(A⋂B) = 0

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= $\frac{8}{31}+ \frac{4}{31}$

P(A∪B)= $\frac{12}{31}$

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

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