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2 years ago

Which term of the arthemetic sequence (1, 3, 5, 7) is equal to 141

Mathematics

2 answers:

Dmitry_Shevchenko [17]2 years ago

6 0

Answer:

71th term is 141

Step-by-step explanation:

$a_{1}=1\\\\common \ difference = d = second \ term - first \ term\\\\ = 3 - 1 = 2\\\\a_{n} = 141\\\\a + (n -1)*d = a_{n}$

1 + (n - 1)*2 = 141 {Use distributive property}

1 + 2n - 2 = 141

2n - 1 = 141

2n = 141 + 1

2n = 142

n = 142/2

n = 71

gregori [183]2 years ago

3 0

Answer:

71st term

Step-by-step explanation:

First, find the nth term: 2n - 1 (the difference is 2, and the 0th term or the number before the 1 is -1). Next, set the nth term equal to 141 and solve for n. 2n - 1 = 141. We would add one to both sides → 2n = 142, then divide both sides by 2. n = 71.

Hope this helps!

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jarptica [38.1K]

1 ) 6

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2 years ago

Solve the proportional equation 3/r = 5/r+3

romanna [79]

Answer:

r=9/2 or 4.5

Step-by-step explanation:

First of all our goal is to get R by itself

by cross multiplying we get,

(r+3)*3=5r

by distributive property we get

3r+9=5r

substracting 3r from both sides we get

9=2r

by dividing by 2 in both sides we get

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3 years ago

9. A large electronic office product contains 2000 electronic components. Assume that the probability that each component operat

Marysya12 [62]

Answer:

97.10% probability that five or more of the original 2000 components fail during the useful life of the product.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it works correctly, or it does not. The probability of a component falling is independent from other components. 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.

In this problem we have that:

$n = 2000, p = 1-0.995 = 0.005$

Approximate the probability that five or more of the original 2000 components fail during the useful life of the product.

We know that either less than five compoenents fail, or at least five do. The sum of the probabilities of these events is decimal 1. So

$P(X < 5) + P(X \geq 5) = 1$

We want $P(X \geq 5)$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{2000,0}.(0.005)^{0}.(0.995)^{2000} = 0.000044$

$P(X = 1) = C_{2000,1}.(0.005)^{1}.(0.995)^{1999} = 0.000445$

$P(X = 2) = C_{2000,2}.(0.005)^{2}.(0.995)^{1998} = 0.002235$

$P(X = 3) = C_{2000,3}.(0.005)^{3}.(0.995)^{1997} = 0.007480$

$P(X = 4) = C_{2000,4}.(0.005)^{4}.(0.995)^{1996} = 0.018765$

$P(X < 5) = P(X = 0) + `P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.000044 + 0.000445 + 0.002235 + 0.007480 + 0.018765 = 0.0290$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.0290 = 0.9710$

97.10% probability that five or more of the original 2000 components fail during the useful life of the product.

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3 years ago

The graph shows the level of ibuprofen, y units, in a patient’s bloodstream x hours after the ibuprofen was taken. Select the co

ElenaW [278]

The graph is missing, so i have attached it.

Answer:

From 0 hours to 2 hours.

Step-by-step explanation:

From the attached graph, we can see that on the y-axis, denotes the level of ibuprofen in the patient’s bloodstream while the x-axis denotes the amount of hours after the ibuprofen was taken.

Now, looking at the graph, we can see that the curve goes up from a time of 0 hours which corresponds to 0 mg of ibuprofen to a time of 2 hours which corresponds to 400 mg of ibuprofen.

After that point, the curve begins to to go down. Since we are concerned with increase, we will make do with the first statement.

Thus, we can say the period at which the level of ibuprofen increased was from 0 hours to 2 hours.

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3 years ago

Aron is given $2.50 by his uncle and twice as much by his aunt. How much has Aron given in total?

Ivan

$7.50 bihgvjutfrthvfyjcyhvg

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