Questions in mathematics

Questions in mathematics

📝 Answered - Define spectrum and resolvent set of a bounded operator. Give an example of each.

📝 Answered - Consider two random variables X and Y with the joint p.d.f.: [tex]f(x, y) = \begin{cases} \frac{1}{50}(x^2 + y^2) & 0 \le x \le 2, 1 \le y \le 4 \\ 0 & \text{elsewhere} \end{cases}[/tex] 1) Find P(X + Y \le 4). 2) Find P(0.5 \le X \le 2).

📝 Answered - It is the method used to solve for the solutions/roots of a quadratic equation [tex]x^2 = k[/tex]. A. extracting square roots B. completing the square C. factoring D. quadratic formula

📝 Answered - A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be used to represent the data? A. The set must have a constant additive rate of change. B. The set must have a constant multiplicative rate of change. C. The values in the set must be positive. D. The values in the set must be increasing.

📝 Answered - What is the solution of $\sqrt{1-3 x}=x+3$? A. $x=-8$ or $x=-1$ B. $x=-8$ C. $x=-1$ D. no solution

📝 Answered - $3(6-4 x)<36-9 x$ Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The solution set expressed in interval notation is $\square$ . (Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is $\varnothing$.

📝 Answered - Write the equation in its equivalent exponential form. [tex]$5=\log _9 M$[/tex] What is the equivalent exponential form of the equation?

📝 Answered - Determine the domain and range of the function [tex]f(x)=2 \sqrt[3]{108}^{2 x}[/tex]. A. [tex] \{x \mid[/tex] all real numbers); [tex] \{y \mid y\ \textgreater \ 0\}[/tex] B. [tex] \{x-[/tex] all real numbers): [tex] \{y \mid y \geq 0\}[/tex] C. (x|x>0): (y| all real numbers) D. [tex] \{x \mid x \geq 0\} ;\{y \mid[/tex] all real numbers [tex]\}[/tex]

📝 Answered - Which multiplication expression is equivalent to [tex]$\begin{array}{c} \frac{2 x^2-5 x-3}{4 x^2+12 x+5} \div \frac{3 x^2-11 x+6}{6 x^2+11 x-10} \\ \frac{(x-3)(2 x+1)}{(2 x+1)(2 x+5)} \cdot \frac{(x-3)(3 x-2)}{(2 x+5)(3 x-2)} \\ \frac{(2 x+1)(2 x+5)}{(x-3)(2 x+1)} \cdot \frac{(2 x+5)(3 x-2)}{(x-3)(3 x-2)} \\ \frac{(x-3)(2 x+1)}{(2 x+1)(2 x+5)} \cdot \frac{(2 x+5)(3 x-2)}{(x-3)(3 x-2)} \end{array}$[/tex]

📝 Answered - Bao Yu is completing the square to solve the polynomial equation: [tex]x^2-x-3=0[/tex] What should be her first step? A. adding [tex]$-x$[/tex] to both sides of the equation B. adding -3 to both sides of the equation C. isolating the first term, [tex]$x^2$[/tex] D. isolating the constant, -3