Answer:
There are 42 quarters (and 6 dimes).
Step-by-step explanation:
The given ratio is 2:14. But this does not tell us how many dimes nor how many quarters we have. Instead, it's a ratio. Modify this by multiplying numerator and denominator by n and then find n:
Number of dimes 2n
----------------------------- = -----
Number of quarters 14n
Then the total number of coins is 2n + 14n =48, implying that:
16n = 48, or n = 3.
Then the number of dimes is 2(n) = 2(3) = 6, and that of quarters is 14(n) =
14(3) = 42.
There are 42 quarters (and 6 dimes). Notice how the total of 42 and 6 is 48.
The Lagrangian for this function and the given constraints is
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
and
, and at the same time we find only one critical point at
.
Check the Hessian for
, given by
is positive definite, since
for any vector
, which means
attains a minimum value of
at
. There is no maximum over the given constraints.
The answer to your question would be -10
Answer:
The probability that the town has 30 or fewer residents with the illness = 0.00052.
Step-by-step explanation:
So, we have the following set of data or information or parameters given from the question above and they are; the number of people living in that particular society/community/town = 74,000 residents and the proportion of people that the diseases affected = .000215.
The first step to do is to determine the expected number of people with disease. Thus, the expected number of people with disease = 74,000 × .000215 = 15.91.
Hence, the probability that the town has 30 or fewer residents with the illness = 1.23 × 10^-7 × 15.91^30/ 2.65253 × 10^-32 = 0.00052.
Note the formula used in the calculating the probability that the town has 30 or fewer residents with the illness = e^-λ × λ^x/ x!
