Identify the principle that best describes a rose window's repeating pattern around a central point. Options: balance, emphasis, harmony, rhythm, variety.
Three integers have a negative product. If multiplying this product by two other integers results in a positive product, then the other two integers must have the same sign.
Proof: Let a,b,c be the three integers with negative product. If ab(c)(d)(e)>0, then d and e must have the same sign.
A manufacturer's item lengths are normally distributed with μ=14.2 inches and σ=2.3 inches. Find the probability that the mean length of 35 randomly chosen items exceeds 13.6 inches. (Round to 4 decimal places)
Calculate the variance of payout per policy holder for an insurance company with 1580 customers and payout scenarios: $690000 (0.001), $120000 (0.05), and 0 (0.949).
Martha wrote a quadratic function f(x)=5x3+2x2+7x−3. Two corrections: 1) Eliminate the 5x3 term, 2) Change the exponent of 2x2 to 3 and combine with 5x3.
Find the rate of change of monthly revenue R with respect to the number of completed responses x when x=1000, given R(x)=−12000+155x2+30x and the number of responses is increasing by 5 per month.
Tomic and Brooke play a free throw shooting game. Each basket is worth 221 points, and each miss is worth −43 points. They make 16 out of 30 free throws. Part A: Tomic incorrectly calculated their score as 5021 points. Explain his likely error. Part B: What is the correct number of points Tomic and Brooke scored?
Find the number of students per van and bus given that High School A rented 16 vans and 8 buses with 752 students, and High School B rented 5 vans and 5 buses with 380 students, where each van and bus carried the same number of students.
Find the equation of the line passing through (2,2) and parallel to the tangent line of y=−3x3−2x at (−1,5), where y=21−x2 and the tangents are perpendicular.