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Questions in mathematics

[Done] The sum of two numbers is 1212 and their HCF is 101; find the numbers?

[Done] If you have 367 boxes of ribbons, and each box has 9 ribbons, how many ribbons do you have altogether?

[Done] Which of the following is *not* a possible value for a probability? A. 1/16 B. 1.001 C. 0.82 D. 10/100

[Done] How does sample size (n) affect SE (Standard Error)? As sample size increases, so does SE. As sample size decreases, so does SE. It doesn't. None of the above.

[Done] A parabola can be represented by the equation $y^2=-x$. What are the coordinates of the focus and the equation of the directrix? A. focus: $\left(-\frac{1}{4}, 0\right)$; directrix: $x=\frac{1}{4}$ B. focus: $\left(\frac{1}{4}, 0\right)$; directrix: $x=-\frac{1}{4}$ C. focus: $(-4,0)$; directrix: $x=4$ D. focus: $(4,0)$; directrix: $x=-4$

[Done] A tangent to the parabola [tex]y^2=12 x[/tex] makes an angle [tex]45^{\circ}[/tex] with the straight line [tex]x-2 y+3 \doteq 0[/tex]. Find its equation and the point of contact.

[Done] Find the derivative of [tex]$f(x)=x^3 \cos x$[/tex]

[Done] The series does not satisfy the hypotheses of the alternating series test as stated: [tex]$\frac{2}{3}-\frac{3}{5}+\frac{4}{7}-\frac{5}{9}+\ldots$[/tex] State which hypothesis is not satisfied. (Select all that apply.) A. The series is of the form [tex]$\sum_{n=1}^{\infty}(-1)^{n+1} b_n$[/tex] and [tex]$0 \leq b_{n+1} \leq b_n$[/tex] for all [tex]$n \geq 1$[/tex]. B. The series is of the form [tex]$\sum_{n=1}^{\infty}(-1)^{n+1} b_n$[/tex] and [tex]$\lim _{n \rightarrow \infty} b_n=0$[/tex]

[Done] Which points lie on the graph of [tex]f(x)=\log _9 x[/tex]? Check all that apply. [tex]\left(-\frac{1}{81}, 2\right)[/tex] [tex](0,1)[/tex] [tex]\left(\frac{1}{9},-1\right)[/tex] [tex](3,243)[/tex] [tex](9,1)[/tex] [tex](81,2)[/tex]

[Done] The first equation in the system models the height in feet, $h$, of a falling baseball as a function of time, $t$. The second equation models the height in feet, $h$, of the glove of a player leaping up to catch the ball as a function of time, $t$. Which statement describes the situation modeled by this system? $\left\{\begin{array}{l} h=35-16 t^2 \\ h=6+18 t-16 t^2 \end{array}\right.$ A. The height of the baseball is 18 feet at the moment the player begins to leap. B. The height of the baseball is 16 feet at the moment the player begins to leap. C. The height of the baseball is 35 feet at the moment the player begins to leap. D. The height of the baseball is 6 feet at the moment the player begins to leap.