Answer:
The chance of completing the entire package installation in under 12 minutes is 0.1271.
Step-by-step explanation:
We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.
To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.
Utilizing 
, we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.
Given the symmetry of the standard normal distribution density function, we ascertain 
.
Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.
To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.
200 miles = (6 miles/day)x + (10 miles/day)y
where x signifies the days she spent running and y represents the days bike riding.
If the minimum biking days are set to be 15, indicated by y = 15, we have:
200 miles = (6 miles/day)x + (10 miles/day)(15 days)
Solving for x gives:
200 = 6x + 150
50 = 6x
x = 8.3333 days
Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.
Answer:
Error made by Andrew: He identified incorrect factors based on the roots.
Step-by-step explanation:
The roots of the polynomial consist of: 3, 2 + 2i, 2 - 2i. By the factor theorem, if a is a root of the polynomial P(x), then (x - a) must be a factor of P(x). According to this premise:
(x - 3), (x - (2 + 2i)), (x - (2 - 2i)) represent the factors of the polynomial.
<pBy simplification, we obtain:
(x - 3), (x - 2 - 2i), (x - 2 + 2i) as the respective factors.
This is where Andrew's mistake occurred. Factors should always be in the form (x - a), not (x + a). Andrew expressed the complex factors incorrectly, resulting in an erroneous conclusion.
Thus, the polynomial can be expressed as:
<span><span>Response
26 1/2 does not correspond to an integer but can be rounded to 27, which is an integer.
Clarification
An integer comprises whole numbers only. It does not include fractions.
253/2=25+3/2=25+1 1/2=26 1/2
</span><span>26 1/2 does not correspond to an integer but can be rounded to 27, which is an integer.
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