Sharon draws a random card, from a

${\displaystyle \frac{{\mathbb{F}}_2[X,Y]}{(Y^2+Y+1,X^2+X+Y)}}$ and $\frac{{\displaystyle \left({\mathbb{F}}_2\right[Y]}}{{\displaystyle (Y^2+Y+1)}}\frac{{\displaystyle \left)\right[X]}}{{\displaystyle (X^2+X+\overline{Y})}}$ are isomorphic

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had

302

accurate orders and

69

that were not accurate.

a. Construct a

90​%

confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part​ (a) to this

90​%

confidence interval for the percentage of orders that are not accurate at Restaurant​ B:

0.164<p<0.238.

What do you​ conclude?

Suppose that you have a map on which 1 inch represents 25 miles. You cover a county on the map with a 1⁄8-inch-thick layer of modeling dough. Then you re-form this piece of modeling dough into a 1⁄8-inch-thick rectangle. The rectangle is 1 3⁄4 inches by 2 1⁄4 inches. Approximately what is the area of the county? Explain. 

For any vectors u, v and w, show that the vectors u+v, u+w and v+w form a linearly dependent set.

Simple Linear Regression - Difference between predicting and estimating?
Here is what my notes say about estimation and prediction:
Estimating the conditional mean
"We need to estimate the conditional mean ${\displaystyle {\beta }_0+{\beta }_1{x}_0}$ at a value ${\displaystyle x_0}$, so we use ${\displaystyle \widehat{Y_0}=\widehat{{\beta }_0}+\widehat{{\beta }_1}{x}_0}$ as a natural estimator." here we get
$\widehat{Y_0}~N({\beta }_0+{\beta }_1{x}_0,{\sigma }^2{h}_{00}) \text{where }{h}_{00}=\frac{1}{n}+\frac{{(x_0-\bar{x})}^2}{(n-1)s_x^2}$
with a confidence interval for ${\displaystyle E\left(Y_0\right)={\beta }_0+{\beta }_1{x}_0}$ is
${\displaystyle (\widehat{b_0}+\widehat{b_1}{x}_0-cs\sqrt{h_{00}},\widehat{b_0}+\widehat{b_1}{x}_0+cs\sqrt{h_{00}})}$
where ${\displaystyle c=t_{n-2,1-\frac{\alpha }{2}}}$ Where these results are found by looking at the shape of the distribution and at ${\displaystyle E\left(\widehat{Y_0}\right)}$ and ${\displaystyle var\left(\widehat{Y_0}\right)}$
Predicting observations
"We want to predict the observation ${\displaystyle Y_0={\beta }_0+{\beta }_1{x}_0+{ϵ}_0}$ at a value ${\displaystyle x_0}$"
$E(\widehat{Y_0}-Y_0)=0 \text{and }var(\widehat{Y_0}-Y_0)={\sigma }^2(1+h_{00})$
Hence a prediction interval is of the form
${\displaystyle (\widehat{b_0}+\widehat{b_1}{x}_0-cs\sqrt{h_{00}+1},\widehat{b_0}+\widehat{b_1}{x}_0+cs\sqrt{h_{00}+1})}$

find the derivative of sin((3pi x)/25)cos((pi x)/25)+15

A 6.0 cm diameter horizontal pipe gradually narrows to 2.0 centimeters. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow ?