Questions in mathematics

Questions in mathematics

[Done] How do you multiply \(\frac{x^2 - 4}{x^2 - 1}\) by \(\frac{x + 1}{x^2 + 2x}\)?

[Done] A shirt is on sale at a 20% discount. The sales tax is 5%. A new sales clerk simply takes 15% off the original price. Is this correct? Why?

[Done] Six people can perform a task in 8 days. If we add 2 equally able people, how long would it take?

[Done] If a function \( f \) is continuous for all \( x \) and if \( f \) has a relative maximum at \((-1, 4)\) and a relative minimum at \((3, -2)\), which of the following statements must be true? A. The graph of \( f \) has a point of inflection somewhere between \( x = -1 \) and \( x = 3 \). B. \( f'(-1) = 0 \). C. This is wrong. D. The graph of \( f \) has a horizontal tangent line at \( x = 3 \). E. The graph of \( f \) intersects both axes. I understand why E is correct, but I do not get why A, B, and D are all wrong. Aren't B and D to be expected since they are relative max/min's? I also can't imagine a case in which "A" is incorrect. Can someone explain why they are wrong? Thank you!

[Done] What digit appears in the units place in the number obtained when [tex]2^{320}[/tex] is multiplied out?

[Done] Roxanne has \(\frac{1}{2}\) as many beads as Sherie. The number of beads Sherie has is \(\frac{4}{5}\) that of Marcos. Marcos has 165 beads. How many more beads does Marcos have than Roxanne?

[Done] The perimeter of a square is 1 meter. How many centimeters long is each side?

[Done] A car rental company sells accident insurance to 24% of its customers. Out of 550 customers, about how many customers are predicted to purchase insurance?

[Done] A baseball player reaches base 35% of the time. How many times can he expect to reach base in 850 at-bats?

[Done] Eric and Frank want to equally share [tex]\frac{4}{3}[/tex] feet of rope. What length of rope should each friend get? Explain how to use a drawing to help solve the problem.