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Questions in mathematics

[Answered] Solve for $a$. $-a+28=14$

[Answered] Simplify the expression. $(22+4-5) \div 7$

[Answered] Simplify: $\frac{5 x+7}{2 x-1}-\frac{3 x+8}{2 x-1}$

[Answered] \begin{aligned} f\left(\frac{\pi}{6}\right) & =-5 \\ f^{\prime}\left(\frac{\pi}{6}\right) & =11 \\ g(x) & =f(x) \sin (x), \text { and } \\ h(x) & =\frac{\cos (x)}{f(x)} \end{aligned} Find $g^{\prime}\left(\frac{\pi}{6}\right)$ and $h^{\prime}\left(\frac{\pi}{6}\right)$ (no rounding, give exact answers). $\begin{array}{l} g^{\prime}\left(\frac{\pi}{6}\right)=\square \\ h^{\prime}\left(\frac{\pi}{6}\right)=\square \end{array}$

[Answered] 11) [tex]$27 x^3-8$[/tex]

[Answered] Write the equation of the line that contains the points $(1,-3)$ and $(5,1)$ in slope-intercept form.

[Answered] Determine the minimum sample size required when you want to be 95​% confident that the sample mean is within one unit of the population mean and sigma equals 12.1. Assume the population is normally distributed.

[Answered] Use the limit definition of the derivative to find [tex]f^{\prime}(x)[/tex] when [tex]f(x)=-3 x^2[/tex] a.) [tex]f^{\prime}(x)=2 x[/tex] b.) [tex]f^{\prime}(x)=-6 x[/tex] c.) [tex]f^{\prime}(x)=0[/tex] d.) [tex]f^{\prime}(x)=-6 x-3 h[/tex]

[Answered] Suppose [tex]f(t)=\frac{3 t+7}{5}[/tex] (a) Evaluate [tex]f(12)[/tex]. [tex]f(12)=[/tex] (b) Solve [tex]f(t)=2[/tex]. [tex]t=[/tex]

[Answered] A sample proportion of 0.78 is found. To determine the margin of error for this statistic, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.78. The minimum sample proportion from the simulation is 0.62, and the maximum sample proportion from the simulation is 0.80. The margin of error of the population proportion is found using half the range. What is the interval estimate of the true population proportion? A. (0.72, 0.84) B. (0.64, 0.92) C. (0.74, 0.82) D. [tex]$(0.69,0.87)$[/tex]