Answer:
The last answer; 12.
Step-by-step explanation:
In order to solve this, use substitution. Since it gives you an equation for y, substitute that equation in the other formula as y. This will give you:
Then simplify:
Since 6x - 6x cancels out, you are left with 12.
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
<h3>What is Riemann sum?</h3>
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
Learn more about Riemann sum here:
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Answer: e. .0950
Step-by-step explanation:
Let X be the number of people that can be cure from disease.
Since each people independently has a 40% chance of contracting the disease.
So ,
A hospital has the capacity to handle at most 8 cases of the disease.
Binomial distribution formula :
Then , the probability that the hospital’s capacity will be exceeded
Hence, the probability that the hospital’s capacity will be exceeded is e. .0950.
Thus , the correct option is e. .0950.