In Alabama, 44% of the population favors the incumbent for governor. Find the probability that at least 72 out of 150 randomly sampled respondents favor the incumbent, using a normal approximation with continuity correction. X∼Binomial(n=150,p=0.44) P(X≥72) Y∼Normal(μ=66,σ=5.24) P(Y≥71.5) Use continuity correction Probability: 0.8001
Liv and 2 friends each have 61 of the original stack of programs. Show work: Liv has 21 of the stack, which she divides equally among herself and 2 friends, giving each 61 of the original stack.
Use synthetic division to simplify x−2x5−2x4+8x3−28x2+15x−9. Write the result as q(x)+d(x)r, where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. Simplify any fractions.
Estimate the proportion of oil tankers that had spills given a sample of 712 tankers, where 570 did not have spills. Enter the result as a fraction or decimal rounded to 3 decimal places.
A snowball's radius decreases at 0.1 cm/min. Find the rate of volume decrease when radius is 11 cm. (Round answer to 3 decimal places) dtdV=−4πr2dtdr=−4π(11)2(0.1)=−12.116mincm3
Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday.
Plan A: □ hour(s)
Plan B: □ hour(s)
a. Janessa paid $390.96 for a 2-year magazine subscription. After receiving 25 magazines in the second year, she cancelled. How many magazines will she receive a refund for? Round up to a whole number. b. Calculate the pro-rated refund Janessa should receive from the magazine company. Round up to the nearest cent.
1. Find n for arithmetic series: a) t1=8,tn=68,Sn=608 b) t1=−6,tn=21,Sn=75 2. Find t10 and S10 for series: a) 5+10+15+⋯ b) 10+7+4+⋯ c) (−10)+(−14)+(−18)+⋯ d) 2.5+3+3.5+⋯ 3. a) Sum of multiples of 4 between 1 and 999 b) Sum of multiples of 6 between 1 and 999
Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.