The statements are true about the graphs of all nth degree polynomials are B and D.
B. It goes up and down at most a total of n times.
D. The number of x-intercepts is at most n.
Answer:
A + B + C = π ...... (1)
...........................................................................................................
L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
...........................................................................................................
In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
72 is the length d of how deep end in feet}
Answer:
The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).
Step-by-step explanation:
A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.
The (1 - <em>α</em>) % confidence interval for the population proportion (<em>p</em>) is given by:

The information provided is:

*Use a <em>z</em>-table for the critical value.
Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:

Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).
Answer:

$29619.13
Step-by-step explanation:
a. Tara has $14375 in credit card debt and the interest rate is 5.3%.
Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then
......... (1)
Again Tara borrows $570 each month for rent from her parents without any interest.
If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write
g(t) = 570 × 12t = 6840t ........ (2)
Therefore,
b. So, for t = 2 years,
= $29619.13
So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)