What is the vertex of the parabola graphed below?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

At the beginning of year 1, carlos invests $600 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 5? what is, the balance?

Determine the required value of the missing probability to make the distribution a discrete probability distribution. x p(x) 3 0.23 4 ? 5 0.51 6 0.08 p(4) = nothing  (type an integer or a decimal.)