Tutor profile: Yongy S.

Calculate the following integral: $(\int_{2}^{5} -20(x + 5) \ dx$)

$(\int_{2}^{5} -20(x + 5) \ dx$) $(=\int_{2}^{5} -20x - 100 \ dx$) $(=\left[-10x^2-100x\right]_2^5$) $(=(-10 * 25 - 100 * 5) - (-10 * 4 - 100 * 2))$) $(=-250 - 500 + 40 + 200$) $(=-510$)

The Houston Chronicle polls a random sample of 330 voters, finding 114 who say they will vote "yes" on the upcoming school budget. Create a 95% confidence interval for actual sentiment for all voters. Interpret your confidence interval.

Given $$\hat{p} = \frac{114}{330}$$ and $$n = 330$$: $$n\hat{p} = 114 > 5$$ and $$n(1 - \hat{p}) = 186 > 5$$ so the normal approximation to binomial can be used. Confidence interval = $$\hat{p} \pm z\sqrt\frac{\hat{p}(1 - \hat{p})}{n}$$ where $$z = invNorm(0.975) = 1.96$$ Confidence interval = $$\frac{114}{330} \pm 1.96\sqrt\frac{\frac{114}{330}(1 - \frac{114}{330})}{330}$$ Confidence interval = (0.38, 0.49)

$(\frac{1}{1 + \frac{1}{1 - \frac{1}{x}}} = 4$) Solve for $$x$$.

$(\frac{1}{1 + \frac{1}{1 - \frac{1}{x}}} = 4$) $(1 = 4(1 + \frac{1}{1 - \frac{1}{x}})$) $(1 = 4 + \frac{4}{1 - \frac{1}{x}}$) $(-3 = \frac{4}{1 - \frac{1}{x}}$) $(\frac{-3}{4} = \frac{1}{1 - \frac{1}{x}}$) $(\frac{-3}{4}(1 - \frac{1}{x}) = 1$) $(\frac{-3}{4} + \frac{3}{4x} = 1$) $(\frac{3}{4x} = \frac{7}{4}$) $(12 = 28x$) $(\frac{3}{7} = x$)