Answer: b) 84
Step-by-step explanation:
Let p be the prior estimate of the required proportion.
As per given , we have
p =0.5 (The probability of getting heads on a fair coin is 0.5)
Significance level : 
Critical z-value (using z-value table ) : 
Confidence interval width : w= 0.18
Thus , the margin of error : 
Formula to find the sample size ( if prior estimate of proportion is known.):-
Substitute the values , we get
Simplify ,
[Round of to the next whole number.]
Hence, the number of times we would have to flip the coin =<u>84</u>
hence, the correct answer is b) 84
First, we can convert both of them to improper fractions.
We do that by multiplying the denominator to the whole number, adding it to the numerator, and keeping the denominator.
2 5/3 - 2 3/2
So we have:
11/3 - 7/2
Convert both of them to denominators of 6:
22/6 - 21/6
Subtract the numerators and keep the denominators:
1/6
The angle between two vectors is given by:
cos (x) = (v1.v2) / (lv1l * lv2l)
We have then:
v1.v2 = (2, -5). (4, -3)
v1.v2 = (2 * 4) + (-5 * (- 3))
v1.v2 = 8 + 15
v1.v2 = 23
We look for the vector module:
lv1l = root ((2) ^ 2 + (-5) ^ 2)
lv1l = 5.385164807
lv2l = root ((4) ^ 2 + (-3) ^ 2)
lv2l = 5
Substituting values:
cos (x) = (23) / ((5.385164807) * (5))
x = acos ((23) / ((5.385164807) * (5)))
x = 31.33 degrees
Answer:
The angle between the two vectors is:
x = 31.33 degrees
Find the common ratio for the following sequence. 27, 9, 3, 1, ... = 1/3
Find the common ratio for the following sequence. 1/2, -1/4, 1/8, -1/16, ... = -1/2
Find the common ratio for the following sequence. 1/2, -1/4, 1/8, -1/16, ...
= -1/2
