e1s2kat26
2020-11-03
Answered

A middle school assigned a four digit ID number to each student. The number is made from the digits 123 and four and no digit is repeated if assigned randomly, what is the probability that an ID number will end with the number three

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doplovif

Answered 2020-11-04
Author has **71** answers

If the last digit must be a 3 and no digit can repeat, then there are 3 options (1, 2, and 4) for the first digit, 2 options for the second digit, 1 option for the third digit, and 1 option (a 3) for the last digit. The total number of outcomes that end with the number three is then

The total number of possible outcomes is

The probability an ID number will end with the number three is then

asked 2021-08-11

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function $h\left(t\right)=-16{t}^{2}+24t$ . Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

asked 2021-01-04

Write in words how to read each of the following out loud.

a. $\{x\in {R}^{\prime}\mid 0<x<1\}$

b. $\{x\in R\mid x\le 0{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}x\Rightarrow 1\}$

c. $\{n\in Z\mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

d. $\{n\in Z\cdot \mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

asked 2022-07-13

How do you solve $40+100x>120+29x$ ?

asked 2022-04-12

Let $(X,\mu )$ be a probability measure space. Suppose ${f}_{n}\to f$ pointwise and ${f}_{n}$ is dominated by some $\mu $-integrable function. Let $({A}_{n}{)}_{n}$ be a sequence of measurable sets converging to some measurable $S$ with $\mu (S)=1$.

Question. Is it true that ${\int}_{X}{f}_{n}{1}_{{A}_{n}}\phantom{\rule{thinmathspace}{0ex}}d\mu \to {\int}_{X}f\phantom{\rule{thinmathspace}{0ex}}d\mu $ ?

A half-baked idea

Define ${g}_{n}:={f}_{n}{1}_{{A}_{n}}$. In case,

Conjecture. ${1}_{{A}_{n}}\to {1}_{S}$ pointwise,

which I suspect to be true, then $|{g}_{n}|$ is dominated by a $\mu $-integrable function and so the Dominated Convergence Theorem gaurantees that ${\int}_{X}{g}_{n}\phantom{\rule{thinmathspace}{0ex}}dP\to {\int}_{X}f{1}_{S}\phantom{\rule{thinmathspace}{0ex}}dP={\int}_{X}f\phantom{\rule{thinmathspace}{0ex}}dP$ since $P(S)=1$.

Question. Is it true that ${\int}_{X}{f}_{n}{1}_{{A}_{n}}\phantom{\rule{thinmathspace}{0ex}}d\mu \to {\int}_{X}f\phantom{\rule{thinmathspace}{0ex}}d\mu $ ?

A half-baked idea

Define ${g}_{n}:={f}_{n}{1}_{{A}_{n}}$. In case,

Conjecture. ${1}_{{A}_{n}}\to {1}_{S}$ pointwise,

which I suspect to be true, then $|{g}_{n}|$ is dominated by a $\mu $-integrable function and so the Dominated Convergence Theorem gaurantees that ${\int}_{X}{g}_{n}\phantom{\rule{thinmathspace}{0ex}}dP\to {\int}_{X}f{1}_{S}\phantom{\rule{thinmathspace}{0ex}}dP={\int}_{X}f\phantom{\rule{thinmathspace}{0ex}}dP$ since $P(S)=1$.

asked 2022-05-21

Integration with partial fractions help please

I'm trying to work in my partial fractions chapter and some were easy but for whatever reason, I'm stuck now:

$\int \frac{-3}{x2+2x+4}dx$

What I tried: since my denominator is of higher order and a irreducible quadratic, I set it up to start like this:

$x-3=\int \frac{Ax+B}{x2+2x+4}+\frac{Cx+D}{x2+2x+4}dx$

I'm not really sure if that's right, the example in the book is a little different.

Anyway, after multiplying and collecting terms, I end up with

${x}^{5}(C)=0$

${x}^{4}(4C+D)=0$

${x}^{3}(A+12C+4D)=0$

${x}^{2}(2A+B+16C+12D)=0$

$x(4A+2B+16D+16)=1$

$4B+16D=-3$

but then when I tried to solve by substitution/addition methods, my numbers don't make sense. Am I even on the right track here? We just got started in this class and I feel like I'm behind already. Thanks for any help.

I'm trying to work in my partial fractions chapter and some were easy but for whatever reason, I'm stuck now:

$\int \frac{-3}{x2+2x+4}dx$

What I tried: since my denominator is of higher order and a irreducible quadratic, I set it up to start like this:

$x-3=\int \frac{Ax+B}{x2+2x+4}+\frac{Cx+D}{x2+2x+4}dx$

I'm not really sure if that's right, the example in the book is a little different.

Anyway, after multiplying and collecting terms, I end up with

${x}^{5}(C)=0$

${x}^{4}(4C+D)=0$

${x}^{3}(A+12C+4D)=0$

${x}^{2}(2A+B+16C+12D)=0$

$x(4A+2B+16D+16)=1$

$4B+16D=-3$

but then when I tried to solve by substitution/addition methods, my numbers don't make sense. Am I even on the right track here? We just got started in this class and I feel like I'm behind already. Thanks for any help.

asked 2021-08-07

What are the factors of ${m}^{2}-12m+20$ ?

1)$m-14$ and $m-6$

2)$m-10$ and $m-2$

3)$m-9$ and $m-3$

4)$m-5$ and $m-4$

1)

2)

3)

4)

asked 2022-02-09

How do you subtract $\frac{20}{33}-\frac{20}{33}$ ?