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I am Lyosha [343]
1 year ago
11

For the arithmetic sequence 42, 32, 22, 12... find the 18th term.

Mathematics
1 answer:
Stella [2.4K]1 year ago
7 0

Answer:

The18th term of the given sequence is -128

Explanation:

To find the 18th term of the sequence:

42, 32, 22, 12, ..., we need to find the nth term of the sequence first.

The nth term of a sequence is given be the formula:

T_n=a+(n-1)d

Where a is the first term, and d is the common difference.

Here, a = 42, d = 32 - 42 = -10

\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}

To find the 18th terem, substitute n = 18 into the nth term

\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}

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Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 5% of all
Gnom [1K]

Answer:

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

Step-by-step explanation:

For each visitor of the website, there are only two possible outcomes. Either they are looking for the website, or they are not. The probability of a customer being looking for the website is independent of other customers. This means that the binomial probability distribution is used 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.

5% of all visitors to the website are looking for other websites.

So 100 - 5 = 95% are looking for the website, which means that p = 0.95

Find the probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

This is P(X = 2) when n = 4. So

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

P(X = x) = C_{4,2}.(0.95)^{2}.(0.05)^{2} = 0.0135

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

5 0
2 years ago
Solve (x + 5)2 = 48.
natita [175]

Answer:

x = -5  ±4sqrt(3)

Step-by-step explanation:

(x + 5)^2 = 48

Take the square root of each side

sqrt((x + 5)^2) = ±sqrt(48)

x+5 = ±sqrt(16*3)

x+5 = ±4sqrt(3)

Subtract 5 from each side

x = -5  ±4sqrt(3)

7 0
3 years ago
Tom was in elementary school from 1997 to 2002 how much time was that in years
Sindrei [870]
Tom was in elementary school for about 5 years 
7 0
3 years ago
Read 2 more answers
Miss Howe has 3/5 of a chocolate candy bar she eats 3/4 of it later as a snack what fraction of the whole candy bar did she cons
Alla [95]

Answer:

9/20

Step-by-step explanation:

First you'd do 3/5 x 3/4 because the denominators aren't the same. When you multiply them you get 9/20. That's your answer! If your not satisfied look it up on Google lol.

6 0
3 years ago
A young boy let’s out 30 feet of string on his kite. If the angle of elevation from the boy to his kite is 27”, how high is the
const2013 [10]

Answer:

The height of the kite from the ground is 13.617 feet  

Step-by-step explanation:

Given as :

The measure of the string = 30 feet

The angle of elevation from the boy to his kite = 27°

Let the height of the kite from ground = H feet

So, From Triangle

Sin angle = \dfrac{\textrm perpendicular}{\textrm Hypotenuse}

Or, Sin 27° =  \dfrac{\textrm H}{\textrm 30}

or, H = 30 ×  Sin 27°

I.e H = 30 × 0.4539

∴ H = 13.617 feet

Hence the height of the kite from the ground is 13.617 feet   Answer

7 0
3 years ago
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