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Questions in mathematics

[Answered] Complete the table for the function [tex]$y=\log (x)+3$[/tex]. | x | y | |---|---| | [tex]$\frac{1}{100}$[/tex] | | | [tex]$\frac{1}{10}$[/tex] | | | 1 | | | 10 | | Graph the function [tex]$y=\log (x)+3$[/tex]. Plot two points with integer coordinates to graph the function.

[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 | | 89 | 69 | | 92 | 72 | | 67 | 61 | | 98 | 91 | | 88 | 85 | | 98 | 84 | | 87 | 82 | | 67 | 76 | | 94 | 91 | | 71 | 62 | Step 1 of 2: Construct a $95 \%$ confidence interval for the true mean difference between the scores to determine if the teaching method increases students' knowledge of the course material. Round the endpoints of the interval to one decimal place, if necessary.

[Answered] Find $x$ in each of the following. a. $(x-2)\binom{1}{4}=(10)$ b. $\left(\begin{array}{ll}2 & x\end{array}\right)\binom{-3}{2}=(4)$ c. $\left(\begin{array}{ll}x & 1\end{array}\right)\binom{4}{x}=(-30)$ d. $(x-3)\binom{x}{-1}=(12)$ e. $\left(\begin{array}{ll}2 & x\end{array}\right)\binom{x}{1}=(9)$

[Answered] Which statements accurately describe the function $f(x)=3(\sqrt{18})^x$ ? Select three options. A. The domain is all real numbers. B. The range is $y>3$. C. The initial value is 3. D. The initial value is 9. E. The simplified base is $3 \sqrt{2}$.

[Answered] What are the [tex]$x$[/tex]-intercepts of the graph of the function [tex]$f(x) = x^2+4 x-12$[/tex]? A. [tex]$(-6,0),(2,0)$[/tex] B. [tex]$(-2,-16),(0,-12)$[/tex] C. [tex]$(-6,0),(-2,-16),(2,0)$[/tex] D. [tex]$(0,-12),(-6,0),(2,0)$[/tex]

[Answered] The system of equations is solved using the linear combination method. [tex]\begin{array}{l} \frac{1}{2} x+4 y=8 \rightarrow-2\left(\frac{1}{2} x+4 y=8\right) \rightarrow-x-8 y=-16 \\ 3 x+24 y=12 \rightarrow \frac{1}{3}(3 x+24 y=12) \rightarrow \frac{x+8 y=4}{0=-12} \end{array}[/tex] What does [tex]$0=-12$[/tex] mean regarding the solution to the system? A. There are no solutions to the system because the equations represent parallel lines. B. There are no solutions to the system because the equations represent the same line. C. There are infinitely many solutions to the system because the equations represent parallel lines. D. There are infinitely many solutions to the system because the equations represent the same line.

[Answered] Solve the system of equations: [tex] \begin{array}{l} y=x^2+4 x-50 \\ y=4 x+50 \end{array} [/tex] Write the coordinates in exact form. Simplify all fractions and radicals. ( , ) ( , )

[Answered] Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope-intercept form. I need the slope.

[Answered] [tex]\frac{4}{6} \times \frac{1}{2}=[/tex]

[Answered] Law of sines [tex]\frac{\sin (A)}{a}=\frac{\sin (B)}{b}=\frac{\sin (C)}{c}[/tex] How many distinct triangles can be formed for which [tex]m \angle A=75^{\circ}, a=2[/tex], and [tex]b=3[/tex] ? One triangle can be formed where angle [tex]B[/tex] is about [tex]15^{\circ}[/tex]. No triangles can be formed. Two triangles can be formed where angle [tex]B[/tex] is [tex]40^{\circ}[/tex] or [tex]140^{\circ}[/tex]. One triangle can be formed where angle about [tex]40^{\circ}[/tex].