Questions in mathematics

Questions in mathematics

📝 Answered - $\frac{27^{-6}}{125^{-3}} \div \frac{9^{-2}}{25^{-4}}$

📝 Answered - A barista wants to use Arabica and Robusta beans to make a cup of coffee containing less than 280 milligrams of caffeine. Each ounce of Arabica beans contains 40 milligrams of caffeine and each ounce of Robusta beans contains 60 milligrams of caffeine. If the barista is required to use twice as many Arabica beans as Robusta beans, which inequality gives all possible values for the amount [tex]$a$[/tex], in ounces, of Arabica beans the barista could use? (A) [tex]$0\ \textless \ a\ \textless \ 1 \frac{3}{4}$[/tex] (B) [tex]$0\ \textless \ a\ \textless \ 2$[/tex] (C) [tex]$0\ \textless \ a\ \textless \ 3 \frac{1}{2}$[/tex] (D) [tex]$0\ \textless \ a\ \textless \ 4$[/tex]

📝 Answered - $\begin{array}{ll} n_1=16 & n_2=22 \\s_1^2=4.875 & s_2^2=1.449\end{array}$ The confidence interval for the ratio of two population variances is given by $\left(\frac{s_1^2}{s_2^2} \cdot \frac{1}{F_{\frac{a}{2}}}\right)<\frac{\sigma_1^2}{\sigma_2^2}<\left(\frac{s_1^2}{s_2^2} \cdot \frac{1}{F_{\left(1-\frac{a}{2}\right)}}\right)$ where $F_{\frac{-}{2}}$ and $F_{\left(1-\frac{4}{2}\right)}$ are the critical values for the level of confidence $c=1-\alpha$ and the $F$-distribution with $n_1-1$ numerator degrees of freedom and $n_2-1$ denominator degrees of freedom. Use the $F$-distribution table to find the confidence interval for the ratio of the population variances. Round the endpoints of the interval to four decimal places, if necessary. Lower Endpoint = $\square$ Upper Endpoint = $\square$

📝 Answered - What is the least common denominator that can be used to solve this equation? [tex]\frac{1}{3}+\frac{2}{x-3}=5[/tex] A. [tex]$x(x-3)$[/tex] B. [tex]$5 x(x-3)$[/tex] C. [tex]$x$[/tex] D. [tex]$x-3$[/tex]

📝 Answered - What is the solution to this inequality? $-16 x>-80$ A. $x<-5$ B. $x<5$ C. $x>5$ D. $x>-5$

📝 Answered - Which of the following expressions is equivalent to $(3 x)(4+y)-2.5 x$? A. $12 x-0.5 x y$ B. $14.5 x+3 y$ C. $9.5 x+3 x y$ D. $7 x -2.5 y$

📝 Answered - Points lie on the graph of the function [tex]f(x)=\lceil x\rceil+2[/tex]? Check all that apply. (-5.5, -4) (-3.8, -2) (-1.1, 1) (-0.9, 2) (2.2, 5) (4.7, 6)

📝 Answered - Multiply $(2 x+1)(2 x-3)$ a. $4 x^2-4 x-3$ b. $4 x^2+6 x-3$ c. $4 x^2-4 x+3$ d. $4 x^2+4 x-3$

📝 Answered - One factor of [tex]6 x^2-12 x+18[/tex] is A. [tex]6(x-6)[/tex] B. [tex]x^2-2 x+3[/tex] C. [tex]x+6[/tex] D. [tex]x^2-12 x+18[/tex]

📝 Answered - The domain of a quadratic function is all real numbers and the range is $y \leq 2$. How many $x$-intercepts does the function have?