Which is the graph of the system of equations Y=3x+6 and y=3x+1?

Find the sum of the arithmetic series given a1=8,a14=99,n=14.

Sergeu [11.5K]

Answer:

The sum of the series is 749

Step-by-step explanation:

Given

$a_1 = 8$

$a_{14} = 99$

$n = 14$

Required

The sum of the series

This is calculated using:

$S_n = \frac{n}{2}[a_1 + a_n]$

Substitute 14 for n

$S_{14} = \frac{14}{2}[a_1 + a_{14}]$

$S_{14} = 7[a_1 + a_{14}]$

Substitute values for a1 and a14

$S_{14} = 7[8 + 99]$

$S_{14} = 7*107$

$S_{14} = 749$

8 0

2 years ago

Richard wants to purchase a Jeep. The purchase price of the Jeep is $ 42 , 000. The dealership will allow him to pay cash or fin

laiz [17]

It will take him around 56 months to finish off his payment if he puts a down payment of 4,000 and pays $680 a month

7 0

1 year ago

Write a mix number that is greater than 3 but less than 4

Finger [1]

Lets find that number:
3 < x < 4
that can easily be thought as 3.5
3 < 3.5 < 4
now lets change the decimal to a mix number:
3.5 = 3 + 0.5
= 3 + 5/10
= 3 + 1/2
= 3 1/2

8 0

2 years ago

Read 2 more answers

Which of these pairs are like terms? 17, 3x 20x, 0.8x 0.5x, 0.5y 14x, 14

sukhopar [10]

B. 20x and .8x because they have the same variable

4 0

2 years ago

Read 2 more answers

Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length

Paladinen [302]

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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(also called standard error) $s = \frac{\sigma}{\sqrt{n}}$ .

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

In this problem, we have that:

$\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44$

a. What can we say about the shape of the distribution of the sample mean time?

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

$s = \frac{2}{\sqrt{21}} = 0.44$

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

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

By the Central Limit Theorem

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

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

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

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

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

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

X = 25.05

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

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

8 0

2 years ago