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xz_007 [3.2K]
3 years ago
12

the length of a rectangle is 3 feet more than twice the width. if the width is increased by four feet the perimeter of the new r

ectangle is 68 feet. find the area of the original rectangle
Mathematics
1 answer:
densk [106]3 years ago
5 0

Answer:

The area of the original rectangle  = 189 sq ft.

Step-by-step explanation:

Let, the width of the rectangle = m feet

So, the length of the rectangle =  (2 m + 3)  ft

Now, new width w'  = (m + 4)

Perimeter of new rectangle (P')   = 68 ft

Perimeter of a rectangle = 2 (LENGTH + WIDTH)

⇒68 ft   = 2( L + W')  

or, 68 ft   = 2 [( 2m + 3) + (m + 4)]

or, 2 (3m + 7)  = 68

or, 3m + 7 = 68/2  = 34

⇒ 3m = 34 - 7 = 27

⇒ m = 27/3 = 9

or, m = 9 ft

Hence, the original width  of the rectangle =  9 ft

Original Length of the rectangle = 2m  + 3  = 2(9) + 3 = 21 ft

Now, Area of the Rectangle = LENGTH X WIDTH

=  21 ft  x  9 ft  = 189 sq ft

Hence,the area of the original rectangle  = 189 sq ft.

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GrogVix [38]

Answer:

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So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

If the score is lower than 30.3 we consider this score as risk averse

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(49.5,15)  

Where \mu=49.5 and \sigma=15

We are interested in the bottom 10% of the data.

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.9   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.28

And if we solve for a we got

a=49.5 -1.28*15=30.3

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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.

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