Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?

2022-05-01

Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?

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asked 2022-05-02

$\frac{{\mathbb{F}}_{2}[X,Y]}{({Y}^{2}+Y+1,{X}^{2}+X+Y)}$ 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

asked 2022-04-06

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?

asked 2022-03-25

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.

asked 2022-04-06

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

asked 2022-04-25

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 $\beta}_{0}+{\beta}_{1}{x}_{0$ at a value $x}_{0$, so we use $\hat{{Y}_{0}}=\hat{{\beta}_{0}}+\hat{{\beta}_{1}}{x}_{0}$ as a natural estimator." here we get

$\hat{{Y}_{0}}~N({\beta}_{0}+{\beta}_{1}{x}_{0},{\sigma}^{2}{h}_{00})\text{}\text{where}{h}_{00}=\frac{1}{n}+\frac{{({x}_{0}-\stackrel{\u2015}{x})}^{2}}{(n-1){s}_{x}^{2}}$

with a confidence interval for $E\left({Y}_{0}\right)={\beta}_{0}+{\beta}_{1}{x}_{0}$ is

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}})$

where $c={t}_{n-2,1-\frac{\alpha}{2}}$ Where these results are found by looking at the shape of the distribution and at $E\left(\hat{{Y}_{0}}\right)$ and $var\left(\hat{{Y}_{0}}\right)$

Predicting observations

"We want to predict the observation $Y}_{0}={\beta}_{0}+{\beta}_{1}{x}_{0}+{\u03f5}_{0$ at a value $x}_{0$"

$E(\hat{{Y}_{0}}-{Y}_{0})=0\text{}\text{and}var(\hat{{Y}_{0}}-{Y}_{0})={\sigma}^{2}(1+{h}_{00})$

Hence a prediction interval is of the form

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}+1},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}+1})$

asked 2022-05-11

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

asked 2022-04-04

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 ?