<span>the equation -2x² + 5x -3=0, we notice that the sum of the coefficient equals 0, -2+5-3=0, if such a case happens, the solution of the previous equation will be, x=1 (always) and x= c/a, a=-2, and c=-3, so x=-3/-2, finally, the answer is: the 2 in the denominator should be -2</span>
solution:
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
find the probability that (p∧ ≤ 0.06) , substitute the values of sample units (n) , and the probability of nonconformities (p) in the probability mass function of binomial distribution.
Consider x to be the number of non-conformities. It follows a binomial distribution with n being 50 and p being 0.03. That is,
binomial (50,0.02)
Also, the estimate of the true probability is,
p∧ = x/50
The probability mass function for binomial distribution is,
Where,
X=0,1,2,3,…..; q=1-p
The calculation is obtained as
P(p^ ≤ 0.06) = p(x/20 ≤ 0.06)
= 50cx ₓ (0.03)x ₓ (1-0.03)50-x
= (50c0 ₓ (0.03)0 ₓ (1-0.03)50-0 + 50c1(0.03)1 ₓ (1-0.03)50-1 + 50c2 ₓ (0.03)2 ₓ (1-0.03)50-2 +50c3 ₓ (0.03)3 ₓ (1- 0.03)50-3 )
=( ₓ (0.03)0 ₓ (1-0.03)50-0 + ₓ (0.03)1 ₓ (1-0.03)50-1 + ₓ (0.03)2 ₓ (1-0.03)50-2 ₓ (0.03)3 ₓ (1-0.03)50-3 )
Answer:
Option D : $20
Step-by-step explanation:
The average total cost to produce 100 oatmeal cookie = $0.25 per cookie.
So, total cost for 100 cookies will be = 
dollars
The company’s marginal cost is constant at $0.10 for all oatmeal cookies produced.
When 50 cookies are produced, the marginal cost will be = 
dollars
The total cost to produce 50 oatmeal cookies = 
dollars
Hence, option D is correct.
We can use Law of Cosines to solve for the angle of Z. The solution is shown below:
cos C=(a²+b²-c²)/2ab
cos Z = (yz² + xz² - xy² )/2*yz*xz
cos Z = (20² + 25 - 13²)/2*20*25
cos Z = 856 / 1000
Z=31.13°
The answer is angle 31.13°.
