a student carres a bag weighing 5kg from the ground floor to his clas on the first floor that is 2m high. the work done by the b
2 answers:
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Answer:
Step-by-step explanation:
<u>Quadratic Function</u>
The quadratic function can be expressed in the following form:
Where a is a real number different from 0, and x1, x2 are the roots or zeroes of the function.
From the conditions stated in the problem, we know
x_1=1+\sqrt{2}, \ x_1=1-\sqrt{2}
Substitute in the general formula above:
Operate the indicated product
To find the value of a, we use the y-intercept which is the value of y when x=0, thus
It follows that
Thus, the required quadratic function is
Or, equivalently
Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a <em>normal distribution</em> with mean and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of 3 inches, hence
.
- The standard deviation is of 0.009 inches, hence
.
Nails that are <u>more than 0.02 inches</u> from the mean are unusable, hence:
The proportion is P(|Z| > 2.22), which is <u>2 multiplied by the p-value of Z = -2.22</u>.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
You can learn more about the normal distribution at brainly.com/question/24663213