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Questions in mathematics

[Answered] Answer the following. Round your answers to the nearest hundredth. (a) Convert [tex]$\frac{2 \pi}{11}$[/tex] radians to degree measure. [ ] ° (b) Convert [tex]$288^{\circ}$[/tex] to radian measure. [ ] radians

[Answered] Complete the table for the function [tex]$y=\log _{\frac{1}{3}}(x)+4$[/tex]. | x | y | |---|---| | [tex]$\frac{1}{9}$[/tex] | | | [tex]$\frac{1}{3}$[/tex] | | | 1 | | | 3 | | | 9 | | Graph the function [tex]$y=\log _{\frac{1}{T}}(x)+4$[/tex]. Plot two points with integer coordinates to graph the function.

[Answered] Subtract and simplify if necessary. $\begin{array}{l} 1 \frac{3}{10}-\frac{9}{10}=N \quad 2-7 \frac{4}{9}-\frac{7}{9}=N \quad 3 \cdot \frac{3}{4}-1 \frac{3}{4}=N \\ 8 \frac{2}{5}-2 \frac{3}{5}=N \quad \text { s. } 11 \frac{2}{7}-6 \frac{5}{7}=N \end{array}$

[Answered] Which one of the following is true when [tex]f(x)=x^3+5 x^2-x+8[/tex] divided by [tex]g(x)=x^2+2[/tex]? A. The degree of the remainder is 1. B. The remainder is [tex]x+5[/tex] C. The quotient is [tex]3 x+2[/tex]. D. The constant term of the quotient is -2.

[Answered] Choose all that apply. Which of the following happens if you increase the value of [tex]$b$[/tex] in any exponential function of the form [tex]$y=a b^x$[/tex] where [tex]$b\ \textgreater \ 0$[/tex]? I. The domain changes. II. The range changes. III. The [tex]$y$[/tex] values increase more quickly.

[Answered] If an object is propelled off a cliff, its height above the ground after [tex]$t$[/tex] seconds is given by the equation [tex]$s(t)=-9.8 t^2+148.6 t+30$[/tex], measured in meters. What is the average rate of change of the position of the object for the time period [tex]$t=1$[/tex] to [tex]$t=5$[/tex] seconds? The average rate of change of the object is $\square$ meters per second.

[Answered] What is the $x$-intercept of the graph of the function $f(x)=x^2-16 x+64 ?$ A. $(-8,0)$ B. $(0,8)$ C. $(8,0)$ D. $(0,-8)$

[Answered] What can each term of the equation be multiplied by to eliminate fractions? [tex]$\frac{1}{2} x-\frac{5}{4}+2 x=\frac{5}{6}+x$[/tex]

[Answered] Graph the equation. [tex]y=-4|x+5|[/tex]

[Answered] A pharmaceutical company is running tests to see how well its new drug lowers cholesterol. Fifteen adults volunteer to participate in the study. The total cholesterol level of each participant (in [tex]$mg / dL$[/tex]) is recorded once at the start of the study and then again after three months of taking the drug. The results are given in the following table. Construct a [tex]$90 \%$[/tex] confidence interval for the true mean difference between the cholesterol levels for people who take the new drug. Let Population 1 be the initial cholesterol level and Population 2 be the cholesterol level after three months. Round the endpoints of the interval to one decimal place, if necessary. | Total Cholesterol Levels (in mg/dL) | |---|---| | Initial Level | Level after Three Months | | 185 | 202 | | 193 | 206 | | 191 | 217 | | 182 | 220 | | 190 | 183 | | 198 | 214 | | 190 | 217 | | 203 | 218 | | 189 | 183 | | 226 | 210 | | 185 | 186 | | 204 | 209 | | 183 | 208 | | 227 | 211 | | 197 | 208 |