Ng the Zero Product Property Warm-Up Which are solutions of the equation (x + 5)(x-3) = 0?
1 answer:
For this case we have a factorized quadratic equation. We equal each factor to zero and thus find the roots:
Subtracting 5 from both sides we have:
Thus, the first solution of the equation is:
On the other hand we have:
Adding 3 to both sides:
Thus, the second solution of the equation is:
Answer:
The solutions of the equation are:
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Use a proportion to find how many seconds are needed to fold 5 shirts.
We are given that he takes 28 seconds to fold 2 shirts:
28 sec : 2 shirts
We are not given the amount of time needed for 5 shirts, which we need to solve:
x seconds : 5 shirts
Express in a fraction:
Cross multiply and simplify:
Therefore, he needs 70 seconds to fold 5 shirts.
Answer: 11.5%
Explanation:
Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.
Now, we get the z-score for 720 seconds by the following formula:
where
So, the z-score of 720 seconds is given by:
Let
t = time for the auditor to finish his work
z = z-score of time t
Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:
Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.
Explanation:
Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.
Now, we get the z-score for 720 seconds by the following formula:
where
So, the z-score of 720 seconds is given by:
Let
t = time for the auditor to finish his work
z = z-score of time t
Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:
Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.