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3 years ago

The length of a rectangle is three times it’s width. The perimeter is 100. What are the dimensions

Mathematics

1 answer:

JulijaS [17]3 years ago

3 0

The length of rectangle is 37.5 and width is 12.5

Step-by-step explanation:

Given,

Width of rectangle = w

Length of rectangle = 3w

Perimeter of rectangle = 100

Perimeter = 2(Length+Width)

$100=2(3w+w)\\100=2(4w)\\100=8w\\8w=100$

Dividing both sides by 8

$\frac{8w}{8}=\frac{100}{8}\\w=12.5$

Width of rectangle = 12.5

Length of rectangle = 3(12.5) = 37.5

The length of rectangle is 37.5 and width is 12.5

Keywords: Rectangle, perimeter

Learn more about perimeters at:

#LearnwithBrainly

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The Apple, Inc. sales manager for the Chicago West Suburban region is disturbed about the large number of complaints her office

ankoles [38]

Answer:

0.6856

Step-by-step explanation:

$\text{The missing part of the question states that we should Note: that N(108,20) model to } \\ \\ \text{ } \text{approximate the distribution of weekly complaints).]}$

Now; assuming X = no of complaints received in a week

Required:

To find P(77 < X < 120)

Using a Gaussian Normal Distribution ( $\mu =$ 108, $\sigma$ = 20)

Using Z scores:

$Z = \dfrac{77-108}{20} \\\\ Z = -\dfrac{35}{20} \\ \\ Z -1.75$

As a result X = 77 for N(108,20) is approximately equal to to Z = -1.75 for N(0,1)

SO;

$Z = \dfrac{120-108}{20} \\ \\ Z = \dfrac{12}{20}\\ \\ Z = 0.6$

Here; X = 77 for a N(108,20) is same to Z = 0.6 for N(0,1)

Now, to determine:

P(-1.75 < Z < 0.6) = P(Z < 0.6) - P( Z < - 1.75)

From the standard normal Z-table:

P(-1.75 < Z < 0.6) = 0.7257 - 0.0401

P(-1.75 < Z < 0.6) = 0.6856

3 0

3 years ago

Because library books are read many times, glue is often applied to the spine of a book to keep the pages tight. A glue is consi

Kipish [7]

Answer:

a. The p-value is less than α, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Step-by-step explanation:

It is given that the library books are often glued for keeping the pages stick and intake. A glue is considered successful if it is able to make the pages of the book intake for at least six months.

It is given that the value of α is = 0.01

and the value of p is = 0.006

Thus when the p-value is less than the value of α, it results in the null hypothesis to get rejected. And there is no convincing support claim that the proportion of the books glued with G lasted for 6 months is different from the proportion of the books that lasted for 6 months when it is glued with K brand.

6 0

3 years ago

Read 2 more answers

Can someone help me with this with step by step explanation plssss

liberstina [14]

Answer:

m = - 16/10

= - 1.6

Step-by-step explanation:

m2 + 8m

(the - 16 here is divided into 10 m's as you can see in m2 and 8m)

So, in order to find out what 1m is, you have to <em>divide</em> - 16 by 10, which gives you - 1.6

Good luck!

5 0

3 years ago

The time a randomly selected individual waits for an elevator in an office building has a uniform distribution with a mean of 0.

Amiraneli [1.4K]

Answer:

The mean of the sampling distribution of means for SRS of size 50 is $\mu = 0.5$ and the standard deviation is $s = 0.0409$

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

Step-by-step explanation:

To solve this problem, 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size, of at least 30, can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 0.5, \sigma = 0.289$

What are the mean and standard deviation of the sampling distribution of means for SRS of size 50?

By the Central Limit Theorem

$\mu = 0.5, s = \frac{0.289}{\sqrt{50}} = 0.0409$

The mean of the sampling distribution of means for SRS of size 50 is $\mu = 0.5$ and the standard deviation is $s = 0.0409$

Does it matter that the underlying population distribution is not normal?

By the Central Limit Theorem, since we have of sample of 50, which is larger than 30, it does not matter that the underlying population distribution is not normal.

What is the probability a sample of 50 people will wait longer than 45 seconds for an elevator?

We have to use 45 seconds as minutes, since the mean and the standard deviation are in minutes.

Each minute has 60 seconds.

So 45 seconds is 45/60 = 0.75 min.

This probability is 1 subtracted by the pvalue of Z when X = 0.75. So

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

By the Central Limit Theorem

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

$Z = \frac{0.75 - 0.5}{0.0409}$

$Z = 6.11$

$Z = 6.11$ has a pvalue of 1

1-1 = 0

0% probability a sample of 50 people will wait longer than 45 seconds for an elevator.

8 0

3 years ago

Una caja en forma de prisma rectangular tiene 10cm3 de volumen.Si la longitud de cada arista se multiplica por 4, ¿cual sera el

Salsk061 [2.6K]

40cm. Por que 10 e 4

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3 years ago