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3 years ago

Which formula can be used to find the nth term of a geometric sequence where the fifth term isn1/16 and the common ratio is 1/4?

Mathematics

1 answer:

kati45 [8]3 years ago

7 0

1/16=a(1/4)^(5-1)

1/16=a(1/4)^4

1/16=a/256

256/16=a

16=a

So the initial term is 16 so our formula is:

a(n)=16(1/4)^(n-1)

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3 years ago

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3 years ago

At a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective pa

11Alexandr11 [23.1K]

Answer:

Probability that fewer than 2 of these parts are defective is 0.604.

Step-by-step explanation:

We are given that at a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective parts 19% of the time.

A random sample of 7 parts produced by this machine is chosen.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 7 parts

r = number of success = fewer than 2

p = probability of success which in our question is % of defective

parts produced by one of the machine, i.e; 19%

LET X = Number of parts that are defective

So, it means X ~ Binom(n = 7, p = 0.19)

Now, probability that fewer than 2 of these parts are defective is given by = P(X < 2)

P(X < 2) = P(X = 0) + P(X = 1)

= $\binom{7}{0}\times 0.19^{0} \times (1-0.19)^{7-0}+ \binom{7}{1}\times 0.19^{1} \times (1-0.19)^{7-1}$

= $1 \times 1 \times 0.81^{7} +7 \times 01.9^{1} \times 0.81^{6}$

= 0.604

Therefore, the probability that fewer than 2 of these parts are defective is 0.604.

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