Use your plan to find the temperature at the top of Mt Everest.

The water level of a certain reservoir is depleted at a constant rate of 1000 units daily. The reservoir is refilled by randomly

Aloiza [94]

Answer:

The probability that the reservoir will be empty in the next ten days is 0.476

Step-by-step explanation:

In 10 days, the reservoir will have 10000 units of water depleted. Since the reservoir starts with almost 5000, then by gaining 8000 units it wont get emptied. It also wont get emptied if it gains 5000 or more units twice, thus, if it rains during 2 days it shoudnt get emptied.

However, note that the reservoir could get emptied if it doesnt rain in the first five days, because it will lose 5000 units, exceding its starting amount. Thus, there are only 2 possibilities for the reservoir to be emptied:

If it doesnt rain in the first five days
If it rains only once in the fisrt five days providing only 5000 units of water, and during the second period of five days it doesnt rain.

We know that the rainfall distribution is Poisson with rate 0.2 per day. In five days the rate is 0.2*5 = 1; lets call X this random variable. The probability to not have any rainfalls in 5 days is

$P_X(0) = \frac{e^{-1} 1^0}{0!} = e^{-1} = 1/e$

Also, the probability for it to rain just once in five days is the probability of X being equal to one

$P_X(1) = \frac{e^{-1} 1^1}{1!} = 1/e$

Therefore, the probability of the event 'it doesnt rain in the first five days' is 1/e, and the probability of the other event 'it rains once in the first five days, also that rain adds 5000 units of water and it doesnt rain in the other five days' is

1/e*0.8*1/e (we multiply 1/e foe the probability that the rain gives 5000 units of water and then by the probability that it doesnt rain in the last five days).

Summing both disjoint events, we obtain that the probability that the reservoir is emptied is

1/e+ 1/e*0.8*1/e = 0.476

5 0

3 years ago

In the magic square shown, the sums of the numbers in each row, column and diagonal are the same. What are the values of x, y, z

garri49 [273]

$v=23$ , $w=19$ , $x=22$ , $y=26$ , $z=20$ ;; to find the answer, set the expressions equal to each other, since the sum of the numbers should be the same.

Use $v+w+24=v+43$ and solve for $w$ , which would result in $w=19$ .

You can also use $x+z+24=z+46$ to find $x$ – or $x=22$ .

Plug in the values for $x$ and $w$ , and find $y$ using $25+22+19=y+40$ or $66=y+40$ and results in $y=26$ .

After plugging in the $y$ value, you can easily find $v$ and $z$ .

$v+18+25=66$ – since 66 is the sum of a full row, and the sums of the numbers in each row, column, and diagonal are the same, so therefore, $v+43$ should also equal 66. This results in $v=23$ , and, using the same value for the sum of $z+21+25$ , or $z+46=66$ , we find that $z=20$ .

The final answer is $v=23$ , $w=19$ , $x=22$ , $y=26$ , $z=20$ .

Sorry it took so long;; I hope this helps :)

5 0

4 years ago

Charles Miller invested his textbook royalty income in two accounts, one paying 3% annual simple interest and the other paying 2

yKpoI14uk [10]

Answer:

The amount invested at 3% is 300 &

The amount invested at 2% is 100.

Step-by-step explanation:

Total yearly interest for the two accounts is: $11

Let x be the amount invested at 3%

& y be the amount invested at 2%

From the question we can get 2 equations as;

x = 3y --------------------------Equation 1

0.03x + 0.02y = 11 ----------Equation 2

Substitute for x in Equation 2 we get;

0.03 (3y) + 0.02y = 11

0.09y + 0.02y = 11

0.11y = 11

Divide the above equation by 0.11, we get;

y = $\frac{11}{0.11}$

y = 100

Let us substitute the value of y in Equation 1 we get;

x = 3(100)

x = 300

Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:

0.03 x 300 + 0.02 x 100

= 9 + 2

= 11

Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.

6 0

4 years ago

Which partial quotients could be added to find 396 ➗ 12?

Nookie1986 [14]

The answer is C. All you have to do it’s divide 396 by 12 then choose C because you add 30 and 3 to get the quotient

6 0

3 years ago

Read 2 more answers

40 POINTS PLEASE HELP Joe and Bill are working on building a stone wall that will be 120 feet long. Joe works from one end and i

andrew-mc [135]

Answer:

26.67 hours or 26 hours and 40 minutes.

Step-by-step explanation:

To find out how long will it take for Joe and Bill to finish building the wall together, first find their individual work rates in feet per hour:

Bill:

$B = \frac{10\ ft}{4 h} \\B = 2.5\frac{\ ft}{h}$

Joe:

$B = \frac{10\ ft}{5 h} \\B = 2.0\frac{\ ft}{h}$

Their combined work rate is:

$W =J+B\\W = 2.5\frac{\ ft}{h}+2.0\frac{\ ft}{h}\\W=4.5\frac{\ ft}{h}$

Then, divide the total size of the wall by their work rate to find the time spent to finish it:

$t = \frac{120\ ft}{2.5\frac{\ ft}{h}} \\t= 26.67\ h$

3 0

4 years ago