f(x) is a multiple of the cosine function. g(x) is a multiple of the sine function. Both the cosine function and the sine function have a maximum value of 1, so the magnitude of the multiple will determine which function has the largest maximum value.
The multiple for f is 2; the multiple for g is 3, which is greater than 2. Hence g(x) has a larger maximum value than f(x).
Answer: the margin of error is 0.02
Step-by-step explanation:
Confidence interval for population proportion is written as
Sample proportion ± margin of error
If the confidence interval for this population proportion is (0.52, 0.56.), it means that the lower boundary is 0.52 and the upper boundary is 0.56
Let x represent the sample proportion and y represent the margin of error. Therefore,
x - y = 0.52
x + y = 0.56
Subtracting the second equation from the first equation, it becomes
- 2y = - 0.04
y = - 0.04/-2
y = 0.02
Answer:
5
Step-by-step explanation:
To evaluate (g ○ h)(9), evaluate h(9) , then use this value to evaluate g(x)
h(9) = = 3, then
g(3) = 2(3) - 1 = 6 - 1 = 5
Answer: (23.53, 25.47)
Step-by-step explanation:
The confidence interval for population mean(when population standard deviation is unknown) is given by :-
, where = sample mean
n = sample size.
s = sample standard deviation.
t* = Critical value.
Given :
s= 4.4
Confidence level = 90% =0.090
Significance level =
Sample size : n= 58
Degree of freedom : df= n-1= 57
Using t-distribution table , the critical value :
Then, the confidence interval will be :-
Hence, a 90% confidence interval for the population mean = (23.53, 25.47)