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Maksim231197 [3]
3 years ago
9

Calculate a_57 for the sequence {a_n}={-6,-9/2,-3,-3/2,0}

Mathematics
1 answer:
Archy [21]3 years ago
3 0

Answer:the 57th term is 78

Step-by-step explanation:

The sequence is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 6

d =3/2

n = 57

We want to determine the value if the 57th term, T57. Therefore,

T57 = - 6 + (57 - 1) ×3/2

T57 = - 6 + 56 × 3/2 = - 6 + 84

T57 = 78

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A factory makes car batteries. The probability that a battery is defective is 1/14. If 400 batteries are tested, about how many
Rufina [12.5K]

Answer:

28.6, that is, about 29 are expected to be defective

Step-by-step explanation:

For each battery, there are only two possible outcomes. Either it is defective, or it is not. The probability of a battery being defective is independent of other betteries. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

The probability that a battery is defective is 1/14.

This means that p = \frac{1}{14}

400 batteries.

This means that n = 400

How many are expected to be defective?

E(X) = np = 400*\frac{1}{14} = 28.6

28.6, that is, about 29 are expected to be defective

3 0
3 years ago
Factor of 42a5b3, 35a3b4, and 42ab4
Scrat [10]
Can u explain it a little more clearly...
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An equation of the line of best fit for a data set is y=0.54x+3.04. Describe what happens to the line of best fit when each y-va
Ghella [55]

Answer:

The slope decreases and the y-intercept decreases.

Explanation:

Red is original, blue is when y is doubled.

5 0
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Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (13, 84) lies
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Answer:

If P = (x,y) then formulas for each trigonometric functions are:

sin x = y/r

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tan x = y/x

cot x = x/y

sec x = r/x

cosec x = r/y

where r = √(x²+y²).

First find r:

r = √(13²+84²)=√(169+7056)=√7225=85.

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Answer:

67

Step-by-step explanation:

GOOD LUCK!!

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