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Questions in mathematics

[Done] Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times? [tex]P(k \text { successes }) = { }_n C_k p^k(1-p)^{n-k}[/tex] [tex]{ }_n C_k =\frac{n!}{(n-k)!\cdot k!}[/tex] A. [tex]{ }_7 C_5\left(\frac{1}{6}\right)^2\left(\frac{1}{6}\right)^5[/tex] B. [tex]{ }_7 C_5\left(\frac{1}{6}\right)^5\left(\frac{5}{6}\right)^2[/tex] C. [tex]{ }_7 C_2\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^5[/tex] D. [tex]{ }_7 C_2\left(\frac{2}{6}\right)^2\left(\frac{4}{6}\right)^5[/tex]

[Done] Which function has a vertex at $(2,-9)$? $f(x)=-(x-1)(x-5)$ $f(x)=(x+8)^2$ $f(x)=-(x-3)^2$ $f(x)=(x-5)(x+1)$

[Done] A quadrilateral has vertices $E(-4,2), F(4,7), G(8,1)$, and $H(0,-4)$. Which statements are true? Check all that apply. A. The slope of $\overline{ EH }$ is $-\frac{8}{5}$. B. The slopes of $\overline{ EF }$ and $\overline{ GH }$ are both $\frac{5}{8}$. C. $\overline{ FG }$ is perpendicular to $\overline{ GH }$. D. Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel. E. Quadrilateral EFGH is a rectangle because all angles are right angles.

[Done] In which triangle is the value of $x$ equal to $\tan ^{-1}\left[\frac{3.1}{5.2}\right]$? (Images may not be drawn to scale.)

[Done] What value of $c$ makes the statement true? $-2 x^3\left(c x^3+x^2\right)=10 x^6-2 x^5$ $c =$

[Done] Which best describes the graph of the function $f(x)=4(1.5)^x$? The graph passes through the point $(0,4)$, and for each increase of 1 in the $x$-values, the $y$-values increase by 1.5. The graph passes through the point $(0,4)$, and for each increase of 1 in the $x$-values, the $y$-values increase by a factor of 1.5. The graph passes through the point $(0,1.5)$, and for each increase of 1 in the $x$-values, the $y$-values increase by 4. The graph passes through the point $(0,1.5)$, and for each increase of 1 in the $x$-values, the $y$-values increase by a factor of 4.

[Done] Write the numbers. a) Seven thousand two hundred fifteen b) Eight thousand three hundred one c) Nine thousand thirteen d) Four thousand five hundred twelve e) Nine thousand f) One thousand six hundred seventy-seven g) Three thousand six hundred fourteen h) Five thousand eight hundred fifty-seven i) Seven thousand two hundred thirty-two j) Four thousand four hundred sixty-seven

[Done] The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator, the fraction increases by unity. The fraction is: (a) 3/5 (b) 1/3 (c) 7/9 (d) None of these

[Done] Which of the following numbers could be the sum of 234 and a 2-digit number? i) 230 ii) 295 iii) 346 iv) 335

[Done] What is the Kuhn-Tucker condition related to the Lagrange multipliers associated with equality constraints that are binding at the optimum? They are zero They are positive They are negative They are infinite