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Questions in mathematics

[Answered] Find the quotient. $3 \longdiv { 7 5 2 }$ $250 . \overline{6}$

[Answered] The expression $\frac{\log _{\frac{1}{3}} 2}{\log 2}$ is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression? A. $\log _{\frac{1}{3}} 2$ B. $\log _{\frac{1}{2}} 3$ C. $\log _2 \frac{1}{3}$ D. $\log _3 \frac{1}{2}$

[Answered] Evaluate the following, [tex]$\frac{a^2-b^2}{a-b}+\frac{2 a^2+b}{a+b}$[/tex] where [tex]$a=-1$[/tex] and [tex]$b=3$[/tex].

[Answered] Two events, A and B, are independent. If [tex]P(A)=0.3[/tex] and [tex]P(B)=0.2[/tex], what is [tex]P(A[/tex] and B)?

[Answered] Given two dependent random samples with the following results: | Population 1 | 19 | 26 | 26 | 30 | 48 | 33 | 31 | |---|---|---|---|---|---|---|---| | Population 2 | 24 | 38 | 40 | 38 | 39 | 41 | 29 | Use this data to find the $98 \%$ confidence interval for the true difference between the population means. Assume that both populations. Step 4 of 4: Construct the $98 \%$ confidence interval. Round your answers to one decimal place.

[Answered] What is the simplified value of the exponential expression $27^{\frac{1}{3}}$? A. $\frac{1}{3}$ B. $\frac{1}{9}$ C. 3 D. 9

[Answered] Simplify the following complex fraction: [tex]$\frac{1}{\frac{1}{P}+\frac{1}{S}}$[/tex]

[Answered] Solve the equations of each system by applying the reduction method and graph one of the systems on the Cartesian plane. a. [tex]\left\{\begin{array}{r}8 x+6 y=36 \\ 10 x-16 y=6\end{array}\right.[/tex] b. [tex]\left\{\begin{array}{l}6 x+8 y=34 \\ 10 x+6 y=40\end{array}\right.[/tex] c. [tex]\left\{\begin{array}{l}6 x+9 y=36 \\ 3 x-3 y=3\end{array}\right.[/tex] d. [tex]\left\{\begin{array}{l}20 x+28 y=200 \\ 20 x+24 y=80\end{array}\right.[/tex]

[Answered] Which function has the greatest $x$-intercept? $f(x)=3 x-9$ $g(x)=|x+3|$ $h(x)=2^x-16$ $j(x)=-5(x-2)^2$

[Answered] To determine if his teaching method increases students' learning, a professor administers a pretest to his class at the beginning of the semester and then a posttest at the end of the semester. The results from 10 randomly chosen students are given below. Let Population 1 be the Pretest scores and Population 2 be the Posttest scores. Test Scores Pretest, Posttest 50, 71 73, 82 64, 80 50, 62 86, 92 76, 71 60, 74 71, 80 76, 81 70, 68 Step 2 of 2: interpret the confidence interval obtained in Step 1.