A researcher wants to estimate the mean commute time of residents in Westchester County. The researcher samples 40 commuters and
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Answer:
(x-4)(x-3)
Step-by-step explanation:
multiply 1 and 12= 12
find two numbers that multiply to get twelve AND add together to get -7(the middle number)
the two numbers are -3 and -4 (they add up to get -7 AND multiply together to get 12)
plug in these numbers for -7x
x(x-3)-4(x-3)
the bolded is the first binomial and the second binomial is in the parenthesis.
(x-4)(x-3)
I hope this helps!
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