Answer:
a) 
And we can find this probability with the complement rule:
b) 
And if we use the z score we got:
Step-by-step explanation:
Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:
Where 
and 
Part a
We are interested on this probability
And we can use the z score formula given by:
And using this formula we got:
And we can find this probability with the complement rule:
Part b
For this case we select a sample of n =44 and the new z score formula is given by:
And if we find the z score we got:
And if we use the z score we got:
For domain 2x sqrt(2+x)>0
x>0,2+x>0,x>-2 combining
we get x>2
f'(x)=[1/{2x sqrt(2+x)}][{2x/(2 sqrt(2+x))}+2 sqrt(2+x)]
Answer:
Below in bold.
Step-by-step explanation:
Area = 30 + 12x and area is also = to width * length so we need to look for factors of 30 + 12x.
30 + 12x = 6(5 + 2x)
So 6 and 5 + 2x is one possible answer.
3 and 10 + 4x is another.
12 and 2.5 + x is another.
If we multiply these pairs together we see that the result is
30 + 12x in each case.
Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:
can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267
Given:
10 yards required
5 2/3 yards on hand.
We need to subtract the yards on hand from the total yards required.
First, we need to convert the mixed fraction into an improper fraction.
5 2/3 = ((5*3)+2)/3 = (15+2)/3 = 17/3
Second, we need to multiply 10 by a fraction that will give us the denominator of 3.
10 * 3/3 = (10*3)/3 = 30/3
Third, we do subtraction using our derived fractions.
30/3 - 17/3 = (30-17)/3 = 13/3
Lastly, we simplify the improper fraction. Improper fraction is a fraction whose numerator is greater than its denominator. Its simplified form is a mixed fraction.
13/3 = 4 1/3
Arliss needs to buy 4 1/3 yards more to complete the required yard length.
