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3 years ago

How would i find the explicit formula for the arithmetic sequence -11,-3,5,12

Mathematics

1 answer:

dimulka [17.4K]3 years ago

5 0

Arithmetic Sequence Formula:

$a_n=a_1+(n-1)d$

We have:

$a_1=-11,\ a_2=-3,\ a_3=5,\ a_4=12,\ ...$

$d=a_{n+1}-a_n\to d=-3-(-11)=-3+11=8$

Substitute:

$a_n=-11+(n-1)(8)=-11+8n-8=8n-19$

Answer: $a_n=8n-19$

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Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X

lbvjy [14]

Answer:

$\sigma = 1.8$

Step-by-step explanation:

Given

$\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}$

Required

The standard deviation

First, calculate the expected value E(x)

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2$

$E(x) = 2.7$

Next, calculate E(x^2)

$E(x^2) = \sum x^2 * P(x)$

So, we have:

$E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2$

$E(x^2) = 10.5$

The standard deviation is:

$\sigma = \sqrt{E(x^2) - (E(x))^2}$

$\sigma = \sqrt{10.5 - 2.7^2}$

$\sigma = \sqrt{10.5 - 7.29}$

$\sigma = \sqrt{3.21}$

$\sigma = 1.8$ --- approximated

5 0

3 years ago

How Is the 2 in the number 582 similar to and different from the 2 in a number 528

blsea [12.9K]

Answer:

it makes the answer larger. the 2 and the 8 are switched

3 0

3 years ago

Two students from a group of eight boys and 12 girls are sent to represent the school in a parade.

Deffense [45]

Answer

c. 62/95

Explanation

Probability is the chance of an event happening.

Probability = (favorable outcome)/(total outcome)

P(girl) = 12/20 × 11/19

= (12×11)/(20×19)

= 132/380

= 33/95

P( not a girl) = 1 - 33/95

= 62/95

8 0

3 years ago

Read 2 more answers

-6x - 24 = 10 -2x - 2 Please help & show you get to the answer

Zanzabum

Solve for x by simplifying both sides of the equation, the isolating the variable. x=-8

3 0

3 years ago

Read 2 more answers

Recall that two angles are complements of each other if

lbvjy [14]

Angle 1: 33, Angle 2: 147

Step-by-step explanation:

If I have angle x, and its supplement angle is 3 times its supplement increased by 48 degrees, then I know the following:

Angle 1 = x

Angle 2 = 3x+48

Both of these angles add to 180 degrees.

x+(3x+48)=180

= 4x+48=180

=4x=132

=x=33, Angle 1 = 33 degrees

So angle 1 is 33 degrees

that should mean that angle 2 is 147

4 0

3 years ago