I think you mean "if the points <span>(2,5), (3,2) and (4,5) satisfy an unknown 3rd degree polynomial, what is the polynomial?"
Since 3 roots {2, 3, 4} are known, we might begin by assuming that this poly would have the form y = ax^3 + bx^2 + cx + d (which has three factors). Unfortunately, three roots are not enough to determine all four constants {a, b, c, d}.
So, let's assume, instead, that the poly would have the form y = ax^2 + bx + c. Three given points should make it possible to determine {a, b, c}.
(2,5): 5 = a(2)^2 + b(2) + c => 5 = 4a + 2b + c
(3,2): 2 = a(3)^2 + b(3) + c => 2 = 9a + 3b + 5 - 4a - 2b
(4,5): 5 = a(4)^2 + b(4) + c => 5 = 16a + 4b + 5 - 4a - 2b
Now we have two equations in a and b alone, which enables us to solve for a and b:
</span>2 = 9a + 3b + 5 - 4a - 2b becomes -3 = 5a + b
<span>and
</span>5 = 16a + 4b + 5 - 4a - 2b becomes 0 = 12a + 2b, or 0 = 6a + b, or 0=-6a-b
<span>
Adding this result to -3 = 5a + b, we get -3 = -a, so a =3.
Thus, since -3 = 5a + b, -3 = 5(3) + b, so b = -18
All we have to do now is to find c. Let's do this using </span>5 = 4a + 2b + c.
We know that a = 3 and b = -18, so this becomes 5 = 4(3) + 2(-18) + c.
Thus, 5 = 12 - 36 + c, or c = 29.
With a, b and c now known, we can write the poly as y = 3x^2 - 18x + 29.
Now the only thing to do remaining is to verify that each of the three given points satsifies y = 3x^2 - 18x + 29. Try this, please.
Its a rational number because whole numbers dont consist of decimals nor fractions
Using it's concept, it is found that there is a 0.3043 = 30.43% probability of at least one O-ring failing.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem, of the 23 flights, 7 had at least one failure, hence the probability is given by:
p = 7/23 = 0.3043.
More can be learned about probabilities at brainly.com/question/14398287
#SPJ1
The boxplots 1 and 2 represent the distribution of data using a five number summary for the male and the female attendance
<h3>(a) The IQR of the male's data</h3>
The first box plot represents the male's boxplot.
So, we have:
- Upper quartile (Q3) = 14
- Lower quartile (Q1) = 2
The IQR is the difference between the above values
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2 = 12
So: the IQR for the males' data is 12
<h3>(b) The difference in the median values</h3>
From the first and second boxplots, we have:
- Median male = 10
- Median female = 18
The difference (d) between these values is
d = 18 - 10
d = 8
So: the difference between the median values of each data set is 8
<h3>(c) The distribution of data</h3>
This is dependent on whether the dataset has an outlier or not.
From the figure, we have:
- Male's data: presence of an outlier - use median
- Female's data: absence of an outlier - use mean
So: the male dataset is measured by median, while the mean is a better measure of center for the female's data
<h3>(d) Reason for outliers</h3>
A possible reason for outliers is sampling problems
Read more about boxplots at:
brainly.com/question/26392028
#SPJ1
