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3 years ago

Find the solution of x – 13 = 25, and verify your solution using substitution.

Mathematics

1 answer:

motikmotik3 years ago

8 0

Answer:

x = 38

Step-by-step explanation:

x-13 = 25

Add 13 to each side

x-13+13 = 25+13

x = 38

Check

38-13 = 25

25=25

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3 years ago

Maggie is practicing her penalty kicks for her upcoming soccer game. During the practice, she attempts 10 penalty kicks. If each

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Answer:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.65)$

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

Solution to the problem

For this case we want to find this probability:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

5 0

3 years ago