What is probablity, and how would I be able to find? (Could you also show an example)

If events X and Y are independent, what must be true? Check all that apply.

larisa86 [58]

All these are true when X and Y are independent events:

1) The occurrence or lack of event X does not influence the occurrence of event Y, and the occurrence or lack of event Y does not influence the occurrence of event X.

2) P(X∩Y) = P(X) * P(Y)

3) P(X | Y) = P(X).... this is the probability of X given Y is equal to the probability of X.

4) P (Y | X) = P(Y)

5) P(A∪B) = P(A) + P(B) - P(A∩B)

6 0

2 years ago

Read 2 more answers

If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21

Ilya [14]

This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34 + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

$\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}$

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}$

and now let's use those 2 found folks, to get the 21st term,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104$

3 0

2 years ago

Quadrilateral QRST is similar to quadrilateral EDGF. What's the scale factor from EDGF to QRST

mart [117]

Answer:

C. $\frac{6}{5}$

Step-by-step explanation:

The ratio of the corresponding sides of a polygon is said to be equal. The ratio gives us the scale factor.

Therefore, assuming that quadrilateral QRST was the original polygon that was scaled up to give a similar polygon, EDGF, the scale factor would be expressed as $\frac{42}{35}$