heureka

Bryan transfers 3000J of energy in 6 hours. Keiran transfers 750J of energy in 75 minutes. Who is more powerful

$$\\ \small{\text{
Power of Brian
$ P_{Brian}= 3000\ J * \frac{1\ kWh}{3.6*10^6\ J } * \frac{10^3\ W}{1\ kW} * \frac{1}{6\ h} =0.13\overline{8}\ W
$
}}$\\\\$
\small{\text{
Power of Keiran
$ P_{Keiran}= 750\ J * \frac{1\ kWh}{3.6*10^6\ J } * \frac{10^3\ W}{1\ kW} * \frac{1}{1.25\ h} =0.1\overline{6}\ W
$
}}$$

Keiran is more powerful!

if rxy=-.7, what is the coefficient of determination

"The coefficient of determination is simply the squared value of the correlation coefficient."

Hi Rosala,

here all possibilities:

I. 

    Letter 1 put into envelope 1

    Letter 2 put into envelope 2              or          Letter 2 put into envelope 3

    Letter 3 must be in envelope 3                       Letter 3 must be in envelope 2

    we have:

                       1. Letter 1 in envelope 1

                           Letter 2 in envelope 2

                           Letter 3 in envelope 3

                        2. Letter 1 in envelope 1

                            Letter 2 in envelope 3

                            Letter 3 in envelope 2

we can change places 3 times. Letter 1 can start in envelope 1 or in envelope 2 or in envelope 3

so we have 2 * 3 = 6

What is 2.3 x 109 divided by 6.2 x 104 by using scientific notation and the quotient rule. Write answer in scientific notation rounded to two decimal places?

$$\samll{\text{
$
\frac{2.3 * 10^9 }{ 6.2 * 10^4 }
$
}}\\\\
\samll{\text{
$
=\frac{2.3 }{ 6.2} * 10^9 * 10^{-4}
$
}}\\\\
\samll{\text{
$
=\frac{2.3 }{ 6.2} * 10^{9-4}
$
}}\\\\
\samll{\text{
$
=\frac{2.3 }{ 6.2} * 10^{5}
$
}}\\\\
\samll{\text{
$
=0.37096774194 * 10^{5}
$
}}\\\\
\samll{\text{
$
=37.096774194 * 10^{3}
$
}}\\\\
\samll{\text{
$
=37.10 * 10^{3}
$
}}\\\\
\samll{\text{
$
\frac{2.3 * 10^9 }{ 6.2 * 10^4 } = 37.10 * 10^{3}
$
}}$$

Hi Rosala,

for example if Letter 1 is in envelope 1 then you can't put Letter 2 or Letter 3 into envelope 1.

Hi Rosala,

There are 6 different possibilities to put 3 letters into 3 envelopes. I have numbered serially them with from 1 to 6. Then I have looked which letters agree with which envelopes. There remain 2 possibilities in those all 3 letters in the envelopes are wrong franked. Then the probability is: 2/6

my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter put a letter into each envelope and sealed it. what is the probability that none of the letters was in the correct envelope?

$$\small{\text{
\textcolor[rgb]{0,1,0}{okay} \text{ \textcolor[rgb]{1,0,0}{false}
\begin{array}{|l|c|c|c|}
\hline
$n& letter 1 & letter 2 & letter 3 $ \\
\hline
$1& envelope\ \textcolor[rgb]{0,1,0}{1} & envelope\ \textcolor[rgb]{0,1,0}{2} & envelope\ \textcolor[rgb]{0,1,0}{3} $ \\
$2& envelope\ \textcolor[rgb]{0,1,0}{1} & envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{2} $ \\
$3& envelope\ \textcolor[rgb]{1,0,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{1} & envelope\ \textcolor[rgb]{0,1,0}{3} $ \\
$\textcolor[rgb]{1,0,0}{4}& envelope\ \textcolor[rgb]{1,0,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{1} $ \\
$\textcolor[rgb]{1,0,0}{5}& envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{1} & envelope\ \textcolor[rgb]{1,0,0}{2} $ \\
$6& envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{0,1,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{1} $ \\
\hline
\end{array}
}}$$

The probability that none of the letters was in the correct envelope is  $$\frac{2}{6} = \frac{1}{3} = 33.\overline{3}\ \%$$

How many bottles each holding 1/4 litre can be filled from 7 1/2 litres

$$7 \frac{1}{2} \text{ litres} \\\\
=\frac{15}{2}\text{ litres} \\\\
=\frac{15}{2}*\frac{2}{2} \text{ litres} \\\\
=\frac{30}{4} \text{ litres} \\\\
=30\times \frac{1}{4} \text{ litres}$$

30 bottles

-x to the -1 power

$$(-x)^{-1} \\\\
=\dfrac{1}{(-x)}\\\\
=\dfrac{1}{-x}\\ \\
=-\dfrac{1}{x}$$

Ein Handwerker kann eine Arbeit in 14 Tagen erledigen, wenn er täglich 8 Stunden arbeitet. Wie viele Stunden müsste er täglich arbeiten, um bereits in 12 Tagen fertig zu sein?

$$\small{
\text{
$14$ Tage $\quad * \quad 8 $ Stunden $ = 12 $ Tage $\quad * \quad x $ Stunden
} $\\\\$ \text{ $ x = \dfrac{14*8}{12} = \dfrac{7*8}{6} = \dfrac{7*4}{3} = \dfrac{9*3+1}{3} = \dfrac{9*3}{3} +\dfrac{1}{3} = 9 +\dfrac{1}{3} = 9 \dfrac{1}{3} $
}}$\\\\$
\small{
\text{
$ x = 9 $ Stunden und $ 20 $ Minuten
}}$$

Der Handwerker muss 9 Stunden und 20 Minuten arbeiten, um bereits in 12 Tagen fertig zu sein.