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Questions in mathematics

📝 Answered - The grade distribution of the students in a geometry class is as follows. | Grade | A | B | C | D | F | | :---- | :- | :- | :- | :- | :- | | Frequency | 28 | 35 | 56 | 14 | 7 | Find the probability that a student earns a grade of B. [tex]P(B)=?[/tex]

📝 Answered - Let $f$ be a function such that $f^{\prime}(x)=2 \cos (2 x)$ and $f\left(\frac{2 \pi}{3}\right)=-\frac{\sqrt{3}}{2}$. Use the tangent line approximation of $f(x)$ at $x=\frac{2 \pi}{3}$ to estimate the value of $f(\pi)$. a $-\frac{\sqrt{3}}{2}-\frac{\pi}{3}$ b $-\frac{5 \pi}{3}+\frac{1}{2}$ c $\frac{2 \pi}{3}-\frac{2}{\sqrt{3}}$ d $-\frac{\sqrt{3}}{3}$ e $\frac{2 \pi}{3}$

📝 Answered - Question 3 (5 points) Listen [tex]$9 / 11=? / 22$[/tex]

📝 Answered - If [tex]$f(x)=-2[x]+8$[/tex], what is [tex]$f(-1.8)$[/tex]? A. 4 B. 6 C. 10 D. 12

📝 Answered - Which terms are like terms in the following expression? [tex]3 x+3 x y-2 x+5 y+5 x^2[/tex] A. [tex]3 x, 3 x y,-2 x[/tex] and [tex]5 y[/tex] B. [tex]3 x[/tex] and [tex]-2 x[/tex] C. [tex]3 x,-2 x[/tex] and [tex]5 x^2[/tex] D. All terms are alike.

📝 Answered - Subtract. $\begin{array}{r} 2-7= \\ -6-2= \end{array}$

📝 Answered - $\operatorname{curl} u =\nabla \times u$ $=\left|\begin{array}{ccc} e _1 & e _2 & e _3 \\ \frac{\partial}{\partial x_1} & \frac{\partial}{\partial x_2} & \frac{\partial}{\partial x_3} \\ u_1 & u_2 & u_3 \end{array}\right|$

📝 Answered - Find the standard form equation of the line that passes through the points (2,-10) and (7,-9).

📝 Answered - What is the true solution to the logarithmic equation below? [tex]$\log _4\left[\log _4(2 x)\right]=1$[/tex] A. [tex]$x=2$[/tex] B. [tex]$x=8$[/tex] C. [tex]$x=64$[/tex] D. [tex]$x=128$[/tex]

📝 Answered - What is the standard form of the equation of a parabola that opens up or down? A. $x=a(y-y)^2+h$ B. $x=a y^2+b y+c$ C. $y=a(x-h)^2+v$ D. $y=a x^2+b x+c$