(7) m∠A = 52°
(8) m∠B = 117°
Solution:
(7) Let us first define the supplementary and complementary angles.
Supplementary angles: Two angles are said to be supplementary angles if their sum is add up to 180°
Complementary angles: Two angles are said to be complementary angles if their sum is add up to 90°
Given supplement of 142° = 180° – 142°
= 38°
Complement of ∠A = Supplement of 142°
⇒ Complement of ∠A = 38°
Measure of ∠A = 90° – 38°
= 52°
Hence m∠A = 52°.
(8) Given complement of 27° = 90° – 27°
= 63°
Supplement of ∠B = Complement of 27°
⇒ Supplement of ∠B = 63°
Measure of ∠B = 180° – 63°
= 117°
Hence m∠B = 117°.
Answer:
[0.875;0.925]
Step-by-step explanation:
Hello!
You have a random sample of n= 400 from a binomial population with x= 358 success.
Your variable is distributed X~Bi(n;ρ)
Since the sample is large enough you can apply the Central Limit Teorem and approximate the distribution of the sample proportion to normal
^ρ≈N(ρ;(ρ(1-ρ))/n)
And the standarization is
Z= ^ρ-ρ ≈N(0;1)
√(ρ(1-ρ)/n)
The formula to estimate the population proportion with a Confidence Interval is
[^ρ ±
*√(^ρ(1-^ρ)/n)]
The sample proportion is calculated with the following formula:
^ρ= x/n = 358/400 = 0.895 ≅ 0.90
And the Z-value is
≅ 1.65
[0.90 ± 1.65 * √((0.90*0.10)/400)]
[0.875;0.925]
I hope you have a SUPER day!