Answer:
The standard form is :
Step-by-step explanation:
A polynomial in standard form will be in decreasing powers of the variable.
The given polynomial is
We rearrange the terms in descending powers of y.
We start with the term with the highest degree and end with the term with the least degree.
Answer:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 10% of data from the top 90% is 64.08.
The graph attached illustrate the situation.
ANSWER
The general solution is , where
is an integer
<u>EXPLANATION</u>
In order to solve the linear congruence;
We need to determine the inverse of (which is a Bézout coefficient for 33).
To do that we must first use the Euclidean Algorithm to verify the existence of the inverse by showing that;
Now, here we go;
The greatest common divisor is the last remainder before the remainder of zero.
Hence, the .
We now express this gcd of 1 as a linear combination of 33 and 280.
We can achieve this by making all the non zero remainders the subject and making a backward substitution.
Equation (2) in equation (1) gives,
The above linear combination tells us that is the inverse of
.
Now we multiply both sides of our congruence relation by .
This implies that;
.
Since this is modulo, the solution is not unique because any integral addition or subtraction of the modulo (280 in this case) produces an equivalent solution.
Therefore the general solution is,
, where
is an integer