Write words to match the expression. 3+(4*12)

Mathematics

1 answer:

denpristay [2]3 years ago

5 0

3 more than the product of 4 and 12.

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A company that produces fine crystal knows from experience that 17% of its goblets have cosmetic flaws and must be classified as

Alex73 [517]

Answer:

0.3891 = 38.91% probability that only one is a second

Step-by-step explanation:

For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So 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.

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

And p is the probability of X happening.

17% of its goblets have cosmetic flaws and must be classified as "seconds."

This means that $p = 0.17$

Among seven randomly selected goblets, how likely is it that only one is a second

This is P(X = 1) when n = 7. So

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

$P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891$

0.3891 = 38.91% probability that only one is a second

7 0

3 years ago

If x-1/x=5 find x^3+1/x^3=?

ipn [44]

$\dfrac{x-1}{x}=5\ \ \ \ /x\neq0\\\\\dfrac{x-1}{x}=\dfrac{5}{1}\ \ \ \ |\text{cross multiply}\\\\5x=x-1\ \ \ \ |-x\\\\5x=1\ \ \ \ |:5\\\\x=0.2\\\\\dfrac{x^3+1}{x^3}=\dfrac{x^3}{x^3}+\dfrac{1}{x^3}=1+\dfrac{1}{x^3}\to1+\dfrac{1}{0.2^3}=1+\dfrac{1}{0.008}\\\\=1+\dfrac{1}{\frac{8}{1,000}}=1+\dfrac{1,000}{8}=1+125=126\\\\\text{Answer:}\ \dfrac{x^3+1}{x^3}=126$