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dmitriy555 [2]
3 years ago
8

The Perimeter of rectangle DEFG is 120, ED=X, and FE=4x. What is the value of x?

Mathematics
2 answers:
Mazyrski [523]3 years ago
6 0

Perimeter=120

ED=x (length)

FE=4x (breadth)

Perimeter of rectangle= 2(l+b)

Given,

2(x+4x)=120

2x+8x=120

10x=120

x=120÷10

x=12

Therefore, value of x is 12

tensa zangetsu [6.8K]3 years ago
6 0

Answer: 12

<u>Step-by-step explanation:</u>

You are given that perimeter = 120, length (FE) = 4x, and width (ED) = x

 P  =    2L  + 2w    (P = perimeter, L = length, w = width)

120 = 2(4x) + 2(x)

120 =   8x   +  2x

120 =       10x

<u>÷10 </u>    <u>   ÷10    </u>

12  =          x

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Answer:

a)

\bf H_0: The mean of adults aged 18 to 32 that continue to be  dependent on their parents is 0.3

\bf H_a: The mean of adults aged 18 to 32 that continue to be  dependent on their parents is greater than 0.3

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c) practically 0

d) Reject the null hypothesis.

Step-by-step explanation:

a)

Since an individual aged 18 to 32 either continues to be dependent on their parents or not, this situation follows a Binomial Distribution and, according to the previous research, the probability p of “success” (depend on their parents) is 0.3 (30%) and the probability of failure q = 0.7

According to the sample, p seems to be 0.34 and q=0.66

To see if we can approximate this distribution with a Normal one, we must check that is not too skewed; this can be done by checking that np ≥ 5 and nq ≥ 5, where n is the sample size (400), which is evident.

<em>We can then, approximate our Binomial with a Normal </em>with mean

\bf np = 400*0.34 = 136

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\bf \sqrt{npq}=\sqrt{400*0.34*0.66}=9.4742

Since in the current research 136 out of 400 individuals (34%) showed to be continuing dependent on their parents:

\bf H_0: The mean of adults aged 18 to 32 that continue to be  dependent on their parents is 0.3

\bf H_a: The mean of adults aged 18 to 32 that continue to be  dependent on their parents is greater than 0.3

So, this is a r<em>ight-tailed hypothesis testing. </em>

b)

According to the sample the proportion of "millennials" that are continuing to be dependent on their parents is 0.34 or 34%

c)

Our level of significance is 0.05, so we are looking for a value \bf Z^* such that the area under the Normal curve to the right of \bf Z^* is ≤ 0.05

This value can be found by using a table or the computer and is \bf Z^*= 1.645

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s = standard deviation of the sample

n = size of the sample

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d)

Since the z-score provided by the sample falls far to the left of  \bf Z^* we should reject the null hypothesis and propose a new mean of 34%.

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