Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0
Median is the middle number
60, 60, 65, 70, 70, 85, 90
70 is your median
mode is the number(s) that show up the most
60 and 70 is your mode, since they show up twice (one more than the others)
Range is largest number minus the smallest
90 - 60 = 30, 30 is your range
Mean is all the numbers added together divided by the number of numbers there are
60 + 90 + 65 + 70 + 70 + 85 + 60 = 500
500/7 = 71.42
Mean = 71.42
hope this helps
Answer:
The requirements for the hypothesis test does satisfied the method for testing the claim that from two population proportions the rate of polio is less for children given the salk vaccine.
Step-by-step explanation:
The percentage of children in the treatment group was:
(201229/401974)*100 = 49.9%
The percentage of children given placebo was:
(200745/401974)*100 = 50.1%
The percentage of children that developed polio in the treatment group:
(33/200745)*100 = 0.0164%
The percentage of children that developed polio in the placebo group:
(115/201229)*100 = 0.0571%
The percentage difference between the two group:
((0.0571-0.0164)/0.0571) = 61.62%
Therefore:
The amount of children used for each group was almost divided into half of the total amount of children. The test revealed although very small percentages of the both group developed polio, 68.62% more children given placebo than the children that was given the salk vaccine. Therefore, the study shows that the rate of polio is less for children given the salk vaccine and the the hypthesis test is satisfied.
Step-by-step explanation:
