Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet$ $f(x)+2$ is divisible by $(x+1)^3$. Write your answer in expanded form (that is, do not factor $f(x)$).

If t17 = 3 (t5) in an arithmetic progression, find t1 in terms of d.

In 2000 the average price of a football ticket was $48.28. during the next 4 years, the proce increased an average of 6% each year. a) write a model giving the average price (p), in dollars, of a ticket (t) in years after 2000.b) graph the model. estimate the year when the average ticket price was about $60

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.