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2 years ago

A flag measures 90 feet by 60 feet. What is the perimeter of this flag?

Mathematics

1 answer:

Temka [501]2 years ago

4 0

300 feet you add 90 twice which gets you 180 and then add 60 twice which gets you 120 and 120 plus 180 is 300

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Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

Aleks04 [339]

Answer:

a) $\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) $P(\bar X \leq 77)=P(Z$

d) See figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

$E(X) = 75$

$sd(X) = 7$

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X \leq 77)=P(Z$

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

8 0

2 years ago

Can you please solve this equation?

zmey [24]

x = -52 4/17
the full answer in attachments

3 0

3 years ago

alisson separates her 23 stickers into 4 equal piles.how many stickers does she have left over? A27 B 19 C 5 D 3

klemol [59]

We need to find the remainder- the sticker left over

Divide 23 stickers into 4 piles = 23/4= 5 stickers per pile and 3 stickers left over

D. She would have 3 stickers left over

6 0

3 years ago

Kate runs 2/3 of a mile on Mondays, Wednesday's and Thursdays. She runs 4/5 of a mile on Tuesday and Fridays. How many miles doe

padilas [110]

Answer:

Therefore, we conclute that Kate run 1 mile and 7/15 of a mile for the week.

Step-by-step explanation:

We know that Kate runs 2/3 of a mile on Mondays, Wednesdays and Thursdays. She runs 4/5 of a mile on Tuesday and Fridays. We calculate how many miles does Kate run during the week.

Therefore, we get

$\frac{2}{3}+\frac{4}{5}=\frac{10+12}{15}=\frac{22}{15}=1+\frac{7}{15}$

Therefore, we conclute that Kate run 1 mile and 7/15 of a mile for the week.

8 0

2 years ago

A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. [

BigorU [14]

Answer:

i only understand part A:

a) Yes, the more time the plant spend in sunlight, the taller it grows. for example, the plant that spend no time in the sun only grows to 4cm while the plant that spent 9 hours in the sun grew to 31

4 0

2 years ago