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3 years ago

Identify the series 2 + 5 + 8 + 11 + 14 + . . . as arithmetic, geometric or neither.

Mathematics

2 answers:

rusak2 [61]3 years ago

4 0

2, 5, 8, 11, 14 is an arithmetic sequence

$a_1=2;\ d=3;\ a_n=2+(n-1)\cdot3=2+3n-3=3n-1$

nignag [31]3 years ago

3 0

Answer:

Arithmetic Series

Step-by-step explanation:

We are given a series 2 + 5 + 8 + 11 + 14 + . . .

We need to choose which series this one.

For geometric: The common ration is equal.

For arithmetic: The common difference is equal.

Series: 2 + 5 + 8 + 11 + 14 + . . .

Common difference : 5 - 2 = 8 - 5 = 14 - 11 = 3

Here, The common difference is equal.

Hence, The series is arithmetic.

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It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute

Genrish500 [490]

Answer:

a) 0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes

b) 0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mildly obese:

Mean 376 minutes and standard deviation 67 minutes, which means that $\mu = 376, \sigma = 67$

Sample of 6

This means that $n = 6, s = \frac{67}{\sqrt{6}} = 27.35$

Lean

Mean 520 minutes and standard deviation 110 minutes, which means that $\mu = 520, \sigma = 110$

Sample of 6

$n = 6, s = \frac{110}{\sqrt{6}} = 44.91$

A) What is the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for mildly obese people. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{420 - 376}{27.35}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463

1 - 0.9463 = 0.0537

0.0537 = 5.37% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes.

B) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?

This is 1 subtracted by the pvalue of Z when X = 420, using the mean and standard deviation for lean people. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{420 - 520}{44.91}$

$Z = -2.23$

$Z = -2.23$ has a pvalue of 0.0129

1 - 0.0129 = 0.9871

0.9871 = 98.71% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes

5 0

3 years ago

A daycare charges a base fee of 3 dollars plus 0.50 dollars per minute for late (after closing time) pick-ups. Albin had to pay

natali 33 [55]

Answer:

The variable a is how many minutes late Albin is.

Step-by-step explanation:

10.50=0.50a+3

The 10.50 is the charge for the late pickup

The 3 dollars is a flat fee for being late

The 0.50 dollars per minute for being late

The variable a is how many minutes late Albin is.

6 0

4 years ago

Read 2 more answers

A bird is 7 feet above the ground what interger would you use to represent the distance that the bird needs to fly to get back t

Lelechka [254]

-7 because it is integers so it’s going below sea level :) your welcome

4 0

3 years ago

Simplify the Matrix Operation <br> 4[-4 5 -6]

Doss [256]

Answer:

[-16 20 -24].

Step-by-step explanation:

4[-4 5 -6]

= [4*-4 4*5 5*-6]

= [-16 20 -24].

4 0

3 years ago

Can someone tell me how to do 18 is ______ % of 30? Also please be specific. I want the work.

jonny [76]

Answer:

60%

Step-by-step explanation:

18 is 60% of 30.

18/30 as a decimal is 0.6

0.6 to a percent is 0.6*100 is 60

Therefore 60% is the answer <3

8 0

4 years ago