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lara31 [8.8K]
3 years ago
8

A die is rolled. What is the probability that the number is a factor of 6 or more than 2? Does this scenario represent mutually

exclusive or mutually inclusive events?
Mathematics
1 answer:
goblinko [34]3 years ago
6 0

Factors of 6 are : 1,2,3 and 6.

Let us find probability of getting the number that is a factor of 6.

P(\text{ The number is a factor of 6})=\frac{4}{6} =\frac{2}{3}

Now let us find probability of getting a number more than 2 (3,4,5,6).

P(\text{ The number is a greater than 2})=\frac{4}{6} =\frac{2}{3}

We can see that these two events are mutually inclusive events. We can find probability of mutually inclusive events by formula P(\text{X or Y})=P(X)+P(Y)-P(\text{X and Y}).  

P(\text{ The number is a factor of 6 and greater than 2})=\frac{2}{6} =\frac{1}{3}

Now we will find probability of getting the number is a factor of 6 or more than 2 using above formula.

P(\text{ The number is a factor of 6 or greater than 2})=\frac{2}{3} +\frac{2}{3}-\frac{1}{3}    

P(\text{ The number is a factor of 6 or greater than 2})= \frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1  

Therefore, our probability will be 1 and this scenario represents mutually inclusive events.  

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Given that the point slope form of an equation is y = mx + b where m represents the gradient and b is the y-intercept. Then, you have to substitute the following values into the equation :

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let \: m =  \frac{3}{7} ,x = 7,y =  - 4

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All possible roots of x^3+2x^2-16x-32
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Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1
jek_recluse [69]

Answer:

S_{31}=71.3


Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

U_n=a_1+(n-1)d


We were given that the 9th term is 17.


\Rightarrow 17=a_1+(9-1)(-2.1)


\Rightarrow 17=a_1+(8)\times(-2.1)


\Rightarrow 17=a_1-\frac{84}{5}


\Rightarrow 17+\frac{84}{5}=a_1


\Rightarrow a_1=\frac{169}{5}


The sum of the first n-terms is given by the formula,


S_n=\frac{n}{2}(2a_1+(n-1)d)


To find S_{31}, we substitute n=31, a_1=\frac{169}{5} and d=-2.1.


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))



\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})


\Rightarrow S_{31}=\frac{713}{10}


\Rightarrow S_{31}=71.3


The correct answer is D















8 0
3 years ago
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PLEASE HELP ASAP!!!! WILL MARK BRAINLIEST !!!
Veronika [31]
The answer is D. The last one
6 0
3 years ago
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