Find the missing term of the arithmetic sequence 22, ___ , 34, ...
1 answer:
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Answer:
25 one-dollar coins, 16 half-dollar coins, and 164 quarters
Step-by-step explanation:
First, set up equations based on the information given:
Then, substitute <em>q</em> in the first equation with the expression from the third equation:
Next, substitute <em>h</em> in that equation with the expression from the second equation:
Solve for <em>d</em>, the number of one-dollar coins:
Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:
Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:
Then, verify that the coins total $74:
Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:
Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:
In order to determine if the events are independent or not we need to find the conditional probabilities.
The conditional probability of event A, given event B is denoted as P(A|B)
P(A*B) indicates P(A and B)
Using the values, we get:
Since P(A|B) is not equal to P(A) this indicates that occurrence of event B has an impact on the occurrence of event A. This shows that the two events are dependent.
Therefore, the correct option is the second one.
2. A and B are not independent events because P(A∣∣B)≠P(A)
The conditional probability of event A, given event B is denoted as P(A|B)
P(A*B) indicates P(A and B)
Using the values, we get:
Since P(A|B) is not equal to P(A) this indicates that occurrence of event B has an impact on the occurrence of event A. This shows that the two events are dependent.
Therefore, the correct option is the second one.
2. A and B are not independent events because P(A∣∣B)≠P(A)