Prove that the diagonals of a rectangle bisect each other. the midpoint of is _____
1 answer:
In this attached picture, we can prove that triangles AOB and COD are congruent. ∠CDO and ∠ABO are equal because they are alternate angles. Similarly, ∠OAB and ∠OCD are equal because they are alternate angles, as well. We have a rectangle and in the rectangle, opposite sides are equal; AB = CD. Then, because of Angle-SIde-Angle principle, we can say that triangles AOB and COD are equal. If triangles are congruent, then OD = OB and OC = AO. Applying congruency to the triangles ACD and BCD, we can see that these triangles are also congruent. It means that the diagonals are equal. Since, OD = OB and OC = AO, it proves that the point O simultaneously is the midpoint and intersection point for the diagonals.
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Answer:
The calculated value z = 9.4451 > 1.96 at 5% level of significance.
Null hypothesis is rejected at 5% level of significance
yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance
Step-by-step explanation:
<u>Explanation</u>:-
<u>Step:- (1)</u>
The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart.
A student asked a random sample of teachers in 2018 and found 165 had smart-phones, 80 had a cell phone
The first sample proportion
A student asked a random sample of teachers in 2018 and found 165 had smart-phones,5 had no cell phone
The second sample proportion
<u>Step :-(ii)</u>
<u>Null hypothesis :H₀</u>: Assume that there is no difference in the distribution of types of cell phones for the teachers in 2018
H₀ : p₁ = p₂
<u>Alternative hypothesis :H₁</u>
H₁ : p₁ ≠ p₂
<u>Level of significance : ∝=0.05</u>
The tabulated value z=1.96
<u>Step:-(iii)</u>
The test statistic
where
q = 1-p
In given data n₁ = n₂ = n
on calculation , we get p = 0.2655
q =1-p = 1-0.2655
q = 0.7345
Z = 9.4451
The calculated value z = 9.4451 > 1.96 at 5% level of significance.
<u>Conclusion:</u>-
Null hypothesis is rejected at 5% level of significance
yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance