Answer: a) z=1.43
b) 0.1528
Step-by-step explanation:
The given set of hypothesis :


Since the alternative hypothesis
is two-tailed , so we perform two-tailed test.
Also, it is given that : A random sample of n=76 Americans found 28 with brown eyes.
Sample proportion: 
a) The z-statistic would be :-


b) P-value for two-tailed test = 2P(Z>|z|)= 2P(z>|-1.43|)
=2P(z>1.43)
=2(1-P(z≤1.43)
=2-2P(z≤1.43)
= 2-2(0.9236)[Using standard z-table]
= 2-1.8472=0.1528
Hence, the P-value of the test= 0.1528
USING PYTHAGORAS THEORAM,
x²+3²= 5²
x²+9= 25
x²= 25-9 = 16
x= √16
x= 4
OPTION D
X² - 4x + y² - 8y = 5
Complete the square:
x² - 4x + (4) + y² - 8y + (16) = 5 + (4) + (16)
→ (x - 2)² + (y - 4)² = 25
Center: (2,4)
radius: √25 = 5
Just square to find them to buy the answer by a dividend then the fraction of the answer then you get your answer