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3 years ago

9

The probability line shows the probability of 5 chance events (A, B, C, D, and E) occurring. Which THREE statements BEST describ

e the likelihood of the event occurring?
A) Event A is certain to occur.
B) Event E is certain to occur.
C) Event D is certain to occur.
D) Event B is not likely to occur.
E) Event C has an even chance of either occurring or not occurring.

2 answers:

KatRina [158]3 years ago

6 0

Answer:

E

B

C

Step-by-step explanation:

Ulleksa [173]3 years ago

3 0

Answer:

The answer is:

B) Event E is certain to occur.

D) Event B is not likely to occur.

E) Event C has an even chance of either

Step-by-step explanation:

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What is 11 1/2 + 10 11/16=

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Hey!

To solve this equation, we must first convert the mixed numbers into improper fractions. To do that we'll multiply the denominator by the whole number and add the total to the numerator.

<em>Original Equation :</em>

$11\frac{1}{2} + 10\frac{11}{16} = ?$

<em>New Equation {Converted Mixed Numbers Into Improper Fractions} :</em>

$\frac{23}{2} + \frac{171}{16} = ?$

Now that we've successfully changed our equation, we'll move onto the next step. Next we'll have change the fractions one more time so that the denominators are the same. To do that we'll multiply two by eight to get sixteen. We'll also be multiplying the top portion of the fraction by eight, because whatever you do to the bottom must also be done to the top; And vise versa.

<em>Fraction Conversion :</em>

$\frac{23*8}{2*8} = \frac{184}{16}$

So, now that we have our new fraction we can go ahead and plug that into our equation so we can start adding. Remember, we don't add the denominators, just the numerators.

<em>Old Equation :</em>

$\frac{23}{2} + \frac{171}{16} = ?$

<em>New Equation {Input New Fraction With Common Denominator} :</em>

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$\frac{355}{16}$

Now I'm not exactly sure how your instructor will accept your answer, but most prefer the final answer to be in the simplest form. In other words, they don't want it in the form of an improper fraction. They'd most likely rather have it as a mixed number.

<em>New Solution {Converted to a Mixed Number} :</em>

$22\frac{3}{16}$

Since the fraction cannot be simplified anymore, this should be our final answer.

<em>So, this means that the answer to the equation is </em> $22\frac{3}{16}$ .

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sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let $y(t)$ be the depth of water in the barrel at time $t$ , where $y$ is measured in inches and $t$ in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

$\frac{dy}{dt}=-k\sqrt{y}$

where $k$ is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by $\frac{1}{\sqrt{y}}$

$\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k$

Multiply by $dt$

$\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt$

Take integral

$\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt$

Integrate

$2\sqrt{y}=-kt+C$

Isolate $y$

$y(t)=(\frac{C}{2} -\frac{k}{2}t)^2$

We know that the water level starts at 36, this means $y(0)=36$ . We use this information to find the value of $C$ .

$36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12$

$y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2$

At t = 1, y = 34

$34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}$

So our formula for the depth of water in the barrel is

$y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\$

To find the time, $t$ , at which all the water leaks out of the barrel, we solve the equation

$\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49$

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

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