Answer:
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C
Step-by-step explanation:
∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗
Let 1st=arctan(x)
And 2nd=1
∫▒〖arctan(x).1 dx=arctan(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗
As we know that
derivative of arctan(x)=1/(1+x^2 )
∫▒〖1 dx〗=x
So
∫▒〖arctan(x).1 dx=arctan(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1
Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now
Let 1+x^2=u
du=2xdx
Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get
1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)
1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)
1/2 ∫▒(2xdx/u) =1/2 ln(u)+C
1/2 ∫▒(2xdx/u) =1/2 ln(1+x^2 )+C
Putting values in Eq1 we get
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C (required soultion)
Ok so cos(x) = sin(90-x) so using that you can get sin(7x-15) = sin(90-(3x+5)) so 7x-15 = -3x+85. 10x = 100 and x = 10. Use that to find the 2 angles are 55 and 35
Answer:
43cm
Step-by-step explanation:
96-10 (5 x2 sides)=86
86/2 sides=43 longest side
According to the Central Limit Theorem, the distribution of the sample means is approximately normal, with the mean equal to the population mean (1.4 flaws per square yard) and standard deviation given by:
The z-score for 1.5 flaws per square yard is:
The cumulative probability for a z-score of 1.11 is 0.8665. Therefore the probability that the mean number of flaws exceeds 1.5 per square yard is
1 - 0.8665 = 0.1335.
Complete question :
It is estimated 28% of all adults in United States invest in stocks and that 85% of U.S. adults have investments in fixed income instruments (savings accounts, bonds, etc.). It is also estimated that 26% of U.S. adults have investments in both stocks and fixed income instruments. (a) What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to decimal places. (b) What is the probability that a randomly chosen U.S. adult invests in stocks, given that s/he invests in fixed income instruments?
Answer:
0.929 ; 0.306
Step-by-step explanation:
Using the information:
P(stock) = P(s) = 28% = 0.28
P(fixed income) = P(f) = 0.85
P(stock and fixed income) = p(SnF) = 26%
a) What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to decimal places.
P(F|S) = p(FnS) / p(s)
= 0.26 / 0.28
= 0.9285
= 0.929
(b) What is the probability that a randomly chosen U.S. adult invests in stocks, given that s/he invests in fixed income instruments?
P(s|f) = p(SnF) / p(f)
P(S|F) = 0.26 / 0.85 = 0.3058823
P(S¦F) = 0.306 (to 3 decimal places)
