Find the constant term in the expansion (1/(2x^3) + x)^20.

Find the constant term in the expansion of (1/(2x^3) + x)^20. [The constant term is the summand which does not involve any power of x. For example the constant term in 3x^2− 4x + 23 +9x^10 + 5/(3x^6) is 23.] [Note on notation: 2^3 means '2 to the power of 3', so 2^3 = 8] [The pdf file contains the question in pretty format, more readable]

combination

How many license plates can a state have if each license plate has 2 letters followed by 4 digits, if the first digit cannot be zero?

Product of two infinite series ( exponential series)

Prove the following product explicitly using infinite series expressions: (please see pdf for scanned handwritten question) Here inf = infinity ( Sum_{k=0}^inf u^k/k! ) ( Sum_{l=0}^inf v^l/l! ) = Sum_{m=0}^inf (u+v)^m/m!

Recursions

See attached

Construction of confidence interval for mean and population proportion.

* Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected. x1 = 57, n1 = 95 and x2 = 84, n2 = 96; Construct a 98% confidence interval for the difference between population proportions p1 - p2. ................................. Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected. A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample ... click for more