Answer:
Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Step-by-step explanation:
12a-(4b+4a)-b
12a-4b-4a-b
=> 8a-5b
Answer:
The number of movies purchased is 5
Step-by-step explanation:
40.00 + 3.50 = 43.50
43.50 + 3.50 = 47.00
47.00 + 3.50 = 50.50
50.50 + 3.50 = 54.00
54.00 + 3.50 = 57.50
so if you add 3.50 to 40, 5 times you'll get 57.50
Hope it helped
Answer: 
Step-by-step explanation:
See attached image.
Answer:
C. with 3000 successes of 5000 cases sample
Step-by-step explanation:
Given that we need to test if the proportion of success is greater than 0.5.
From the given options, we can see that they all have the same proportion which equals to;
Proportion p = 30/50 = 600/1000 = 0.6
p = 0.6
But we can notice that the number of samples in each case is different.
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size
po = Null hypothesized value
p^ = Observed proportion
Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.
Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis
