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frez [133]
3 years ago
5

Find an equation for the nth term of the arithmetic sequence. -1, 2, 5, 8, ...

Mathematics
2 answers:
vladimir1956 [14]3 years ago
4 0

Answer:

The expression for the n-th term is a_n = -4+3n.

Step-by-step explanation:

We know that the n-th term of an arithmetic progression is given by a_n= a+nd. So we need to find the coefficients a and d. In order to do this, we substitute the values n=1 and n=2 in the expression for a_n:

a_1 = a+d    = -1,

a_2 = a+2d = 2.

Now, notice that we have two linear equations with two unknowns, which it is not difficult to solve. Thus, the solution is d=3 and a=-4.

Hence, the expression for the n-th term is a_n = -4+3n.

We can check that the expression is correct substituting the values n=3 which gives a_3 = 5 and n=4 which gives a_4 = 8, as it is given in the statement of the problem.

aev [14]3 years ago
3 0
-1 + 3(n-1)
hope this helps you

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Scores of an IQ test have a​ bell-shaped distribution with a mean of and a standard deviation of . Use the empirical rule to det
Oduvanchick [21]

Complete question is;

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 87 and 113​?

​(b) What percentage of people has an IQ score less than 74 or greater than 126​? ​

(c) What percentage of people has an IQ score greater than 139​?

Answer:

A) 68% of the people had an IQ score between 87 and 113

B) 5% of the people had IQ scores less than 74 and greater than 126.

C) 0.15% had an IQ score greater than 139

Step-by-step explanation:

We are given;

Mean; x¯ = 100

Standard deviation; σ = 13

According to the empirical rule in statistics;

>> 68% of the data lies within one standard deviation of the mean

>> 95% of the data lies within two standard deviations of the mean

>> 99.7% of the data lies within three standard deviations

A) We want to find the percentage of people with an IQ score between 87 and 113.

Within one standard deviation, we have;

x¯ ± σ

>> (100 - 13), (100 + 13)

>> (87, 113) which is the range we are looking for.

Thus, 68% of the people had an IQ score between 87 and 113

B) we want to find percentage of people has an IQ score less than 74 or greater than 126.

Let's first find those who had between 74 and 126.

Let's use two standard deviations within the mean.

x¯ ± 2σ

>> (100 - (2×13)), (100 + (2×13))

>> (74, 126) which is the range we are looking for.

So percentage that have IQ scores between 74 and 126 is 95%

Thus;

Percentage of those who had less than 74 and greater than 126 is;

P = 1 - 95%

P = 5%

C) we want to find the percentage of people that had an IQ score greater than 139.

Let's use the z-score formula;

z = (x¯ - μ)/σ

z = (139 - 100)/13

z = 39/13

z = 3

This means it is 3 standard deviations above the mean.

Thus;

Since it's one side outside the mean, then;

Percentage of people with an IQ score greater than 139 = (1 - 99.7%)/2 = 0.3%/2 = 0.15%

5 0
3 years ago
Find the height of a right cylinder with surface area 160pie square units and radius 5 units
jenyasd209 [6]

Given:

Radius of a cylinder = 5 units.

Surface area of the cylinder = 160\pi

To find:

The height of the right cylinder.

Solution:

Surface area of a cylinder is:

A=2\pi rh+2\pi r^2

Where, r is radius and h is the height of the cylinder.

Putting r=5, A=160\pi in the above formula, we get

160\pi =2\pi (5)(h)+2\pi (5)^2

160\pi =10\pi h+2\pi (25)

160\pi =10\pi h+50\pi

Subtract 50\pi from both sides.

160\pi -50\pi=10\pi h

110\pi=10\pi h

Divide both sides by 10\pi.

\dfrac{110\pi}{10\pi}=h

11=h

Therefore, the height of the cylinder is 11 units.

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Which is the graph of the inequality? 3y - 9x ≥ 9
Flura [38]

Step-by-step explanation:

Use this calculator to check your answers and help explain the equation step by step.

www.quickmath.com

5 0
3 years ago
Please show the work for it as well thank you
AlexFokin [52]

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

       

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Two angles adjacent angles that add up to 180 degrees
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