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3 years ago

Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1)

Mathematics

2 answers:

Serhud [2]3 years ago

8 0

Answer: The mid point of the line segment is (1.5,2.5).

Step-by-step explanation:

Since we have given that

A (5,4) and B(-2,1) are the end points of the line segment.

We need to find the mid point say 'C':

As we know the formula for "Mid point ":

$C=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\C=\dfrac{5-2}{2},\dfrac{4+1}{2})\\\\C=(\dfrac{3}{2},\dfrac{5}{2})\\\\C=(1.5,2.5)$

Hence, the mid point of the line segment is (1.5,2.5).

anyanavicka [17]3 years ago

3 0

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ 5}} &,&{{ 4}}~) 
% (c,d)
&&(~{{ -2}} &,&{{ 1}}~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{-2+5}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(\frac{3}{2}~~,~~\frac{5}{2} \right)\implies \left(1\frac{1}{2}~~,~~2\frac{1}{2} \right)$

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3 years ago

Members of the millennial generation are continuing to be dependent on their parents (either living with or otherwise receiving

Morgarella [4.7K]

Answer:

$\bf H_0:$ 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

b) 34%

c) practically 0

d) Reject the null hypothesis.

Step-by-step explanation:

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

$\bf np = 400*0.34 = 136$

and standard deviation

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

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>

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

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

<em>Applying the continuity correction factor (this should be done because we are approximating a discrete distribution (Binomial) with a continuous one (Normal)), we simply add 0.5 to this value and </em>

$\bf Z^*$ corrected is 2.145

Now we compute the z-score corresponding to the sample

$\bf z=\frac{\bar x -\mu}{s/\sqrt{n}}$