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Questions in mathematics

[Done] Express $(x-1)(x+2)(x-3)$ in standard form.

[Done] A circle centered at the origin contains the point $(0,-9)$. Does $(8, \sqrt{17})$ also lie on the circle? No, the distance from the center to the point ($8, \sqrt{17}$) is not the same as the radius. No, the radius of 10 units is different from the distance from the center to the point $(8, \sqrt{17})$. Yes, the distance from the origin to the point ($8, \sqrt{17}$) is 9 units. Yes, the distance from the point $(0,-9)$ to the point ($8, \sqrt{17}$) is 9 units.

[Done] Use either the ratio test or the root test as appropriate to determine whether the series [tex]$\sum_{n=1}^{\infty} a_n$[/tex] with given terms [tex]$a_n$[/tex] converges, or state if the test is inconclusive. [tex]$a_n=\frac{n!}{1 \cdot 3 \cdot 5 \cdots(2 n-1)}$[/tex] A. The series converges. B. The series diverges. C. The test is inconclusive.

[Done] What is the vertical distance between (5, -12) and (5, 17)?

[Done] Simplify the radical expression. Write your answer in the simplest form. [tex]2 \sqrt{48}+\sqrt{200}-\sqrt{75}-4 \sqrt{32}[/tex]

[Done] A line intersects the points $(6,-4)$ and $(7,4)$. Write the equation of this line in point-slope form using the point $(6,-4)$. $y-[?]=\square(x-\square)$

[Done] A bank features a savings account that has an annual percentage rate of $4.1 \%$ with interest compounded semiannually. Jayden deposits \$2,500 into the account. How much money will Jayden have in the account in 1 year? Answer = $\$\square$ Round answer to the nearest penny. What is the annual percentage yield (APY) for the savings account? $APY=$ $\square$ \%. Round to the nearest hundredth of a percent.

[Done] [tex]\frac{2 x+1}{4}\ \textgreater \ \frac{x+3}{3}[/tex]

[Done] Work out $\frac{1}{8}+\frac{3}{4}$. Give your answer in its simplest form.

[Done] This table shows how many sophomores and juniors attended two school events. \begin{tabular}{|l|l|l|l|}\hline & Jazz band concert & Volleyball game & Total \\\hline Sophomore & 35 & 42 & 77 \\\hline Junior & 36 & 24 & 60 \\\hline Total & 71 & 66 & 137 \\\hline\end{tabular} What is the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game? Round your answer to two decimal places. A. 0.26 B. 0.56 C. 0.31 D. 0.48