Questions in mathematics

Questions in mathematics

📝 Answered - In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red. If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second? $\frac{1}{8}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$

📝 Answered - What is the value of [tex]$x$[/tex] in the equation below? [tex]$1+2 e^{x+1}=9$[/tex] A. [tex]$x=\log 4-1$[/tex] B. [tex]$x=\log 4$[/tex] C. [tex]$x=\ln 4-1$[/tex] D. [tex]$x=\ln 4$[/tex]

📝 Answered - Look at this expression. [tex]24 x^4 y[/tex] [tex]3 x^{-4} y^{-1}[/tex] Which of the following is the simplest form of the expression above? A. 8 B. [tex]8 x^{-16} y^{-1}[/tex] C. [tex]8 x^{-1} y^{-1}[/tex] D. [tex]8 x^8 y^2[/tex]

📝 Answered - On a number line, the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the directed line segment from [tex]$Q$[/tex] to [tex]$S$[/tex] in a 3:5 ratio. Which expression correctly uses the formula [tex]$\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$[/tex] to find the location of point [tex]$R$[/tex]? A. [tex]$\left(\frac{3}{3+5}\right)(2-(-14))+(-14)$[/tex] B. [tex]$\left(\frac{3}{3+5}\right)(-14-2)+2$[/tex] C. [tex]$\left(\frac{3}{3+5}\right)(2-14)+14$[/tex] D. [tex]$\left(\frac{3}{3+5}\right)(-14-2)-2$[/tex]

📝 Answered - To rationalize the denominator of $\frac{2 \sqrt{10}}{3 \sqrt{11}}$, you should multiply the expression by which fraction? A. $\frac{\sqrt{10}}{\sqrt{10}}$ B. $\frac{\sqrt{11}}{\sqrt{11}}$ C. $\frac{2-\sqrt{10}}{2-\sqrt{10}}$ D. $\frac{3-\sqrt{11}}{3-\sqrt{11}}$

📝 Answered - Rewrite the following expression as a single logarithm: [tex]2 \log (x+3)+3 \log (x-7)-5 \log (x-2)-\log \left(x^2\right)[/tex] A. [tex] \log \left(\frac{(x+3)^2(x-2)^5}{(x-7)^3 x^2}\right)[/tex] B. [tex]\log \left(\frac{x^2(x+3)^2(x-7)^3}{(x-2)^5}\right)[/tex] C. [tex]\log \left(\frac{(x+3)^2(x-7)^3}{x^2(x-2)^5}\right)[/tex] D. [tex]\log \left(\frac{(x+3)^2(x-7)^3}{(x-2)^{-5} x^{-2}}\right)[/tex]

📝 Answered - Which phrase best describes the translation from the graph [tex]y=(x-5)^2+7[/tex] to the graph of [tex]y=(x+1)^2-2[/tex]? A. 6 units left and 9 units down B. 6 units right and 9 units down C. 6 units left and 9 units up D. 6 units right and 9 units up

📝 Answered - If [tex]f(x)=x^2+1[/tex] and [tex]g(x)=x-4[/tex], which value is equivalent to [tex](f \circ g)(10)[/tex] ? A. 37 B. 97 C. 126 D. 606

📝 Answered - By rounding to 1 significant figure, estimate the answers to these questions: a) [tex]$426 \times 894$[/tex] b) [tex]$657 \times 889$[/tex] c) [tex]$287 \times 494$[/tex]

📝 Answered - Find $\frac{3}{8}$ of 48.