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Molodets [167]
3 years ago
12

In any 15-minute period in a statistics class, the probability of observing at least one mistake made by professor Doe is 5%. Wh

at is the probability of observing at least one mistake made by this professor in this 60-minute long class
Mathematics
1 answer:
777dan777 [17]3 years ago
3 0

Hey there!

We can set this up a proportion to figure out the percent we need.

\frac{mins}{percent} = \frac{15}{5} =\frac{60}{p}

If you can see, the second numerator is four times the first. So, we multiply the bottom by four and we get 20.

Therefore, the probability if observing at least one mistake made by this professor is 20%.

I hope this helps!

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mixas84 [53]

The given system of equation that is 2x+y=3 and 6x=9-3y has infinite number of solutions.

Option -C.

<u>Solution:</u>

Need to determine number of solution given system of equation has.

\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}

Let us first bring the equation in standard form for comparison

\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}

\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

To check how many solutions are there for system of equations a_{1} x+b_{1} y+c_{1}=0 \text{ and }a_{2} x+b_{2} y+c_{2}=0, we need to compare ratios of \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}

In our case,  

a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3

a_{2}  = 6, b_{2} = 3,\text{ and }c_{2} = -9

\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}

As \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}, so given system of equations have infinite number of solutions.

Hence, we can conclude that system has infinite number of solutions.

5 0
3 years ago
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