Please help! Trigonometry review
1 answer:
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Answer:
The 99% confidence interval for the 1999 mean incomes of Middletown householders is ($33,013.5, $33,892.5).
Step-by-step explanation:
Of the 40,000 persons, 2621 householders reported their income.
The sample size of the study is, <em>n</em> = 2621.
As the sample size is large, i.e. <em>n</em> > 30 use <em>z</em>-distribution to compute the confidence interval.
The confidence interval for mean is:
The mean of this sample is,
The standard deviation is,
The critical value of <em>z</em> for 99% confidence level is:
The 99% confidence interval for the 1999 mean incomes of Middletown householders is:
Thus, the 99% confidence interval for the 1999 mean incomes of Middletown householders is ($33,013.5, $33,892.5).
Answer:
The proof is given below.
Step-by-step explanation:
Given a parallelogram ABCD. Diagonals AC and BD intersect at E. We have to prove that AE is congruent to CE and BE is congruent to DE i.e diagonals of parallelogram bisect each other.
In ΔACD and ΔBEC
AD=BC (∵Opposite sides of parallelogram are equal)
∠DAC=∠BCE (∵Alternate angles)
∠ADC=∠CBE (∵Alternate angles)
By ASA rule, ΔACD≅ΔBEC
By CPCT(Corresponding Parts of Congruent triangles)
AE=EC and DE=EB
Hence, AE is conruent to CE and BE is congruent to DE
