An equation has solutions of m= -5 and m = 9. Which could be the equation?
2 answers:
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Answer:
700 lei
Step-by-step explanation:
You have a geometric sequence for which you know the common ratio and the last term.
There are only three terms, so you can solve the problem in either of two ways.
1. The brute force method (easiest for only a few terms)
Each term is half the one before it, so each term is double the one after it.
3rd term = 100 lei
2nd term = 200
1st term = 400
Total = 700 lei
Oana spent 700 lei
2. Using formulas (best for longer sequences)
The general formula for your sequence is
aₙ = a₁rⁿ⁻¹
For your sequence,
a₃ = 100; r = 0.5
(a) Calculate a₁
Set the last term equal to the general formula.
a₃ = a₁(0.5)ⁿ⁻¹
100 = a₁(0.5)² = 0.25a₁
a₁ = 100/0.25 = 400
(b) Calculate the sum
The general formula for the sum of a geometric sequence is
Oana spent 700 lei.
Answer:
a. 0.692 or 69.2%; b. 0.308 or 30.8%.
Step-by-step explanation:
This is the case of <em>the probability of the sum of two events</em>, which is defined by the formula:
(1)
Where represents the probability of the union of both events, that is, the probability of event A <em>plus</em> the probability of event B.
On the other hand, represents the probability that both events happen at once or the probability of event A times the probability of event B (if both events are independent).
<em>Notice the negative symbol for the last probability</em>. The reason behind it is that we have to subtract those common results from event A and event B to avoid count them twice when calculating .
We have to remember that a <em>sample space</em> (sometimes denoted as <em>S</em>)<em> </em>is the set of the all possible results for a random experiment.
<h3>Calculation of the probabilities</h3>From the question, we have two events:
Event A: <em>event</em> <em>subscribers rented a car</em> during the past 12 months for <em>business reasons</em>.
Event B: <em>event subscribers rented a car</em> during the past 12 months for <em>personal reasons</em>.
With all this information, we can proceed as follows in the next lines.
The probability that a subscriber rented a car during the past 12 months for business <em>or</em> personal reasons.
We have to use here the formula (1) because of the sum of two probabilities, one for event A and the other for event B.
Then
Thus, <em>the</em> <em>probability that a subscriber rented a car during the past 12 months for business or personal reasons</em> is 0.692 or 69.2%.
The probability that a subscriber <em>did not </em>rent a car during the past 12 months for either business <em>or</em> personal reasons.
As we can notice, this is the probability for <em>the complement event that a subscriber did not rent a car during the past 12 months</em>, that is, the probability of the events that remain in the <em>sample space. </em>In this way, the sum of the probability for the event that a subscriber <em>rented a car</em> <em>plus</em> the event that a subscriber <em>did not rent</em> a car equals 1, or mathematically:
As a result, the requested probability for <em>a subscriber that did not rent a car during the past 12 months for either business or personal reasons is </em>0.308 or 30.8%.
We can also find the same result if we determine the complement for each probability in formula (1), or:
Then
