Found this on google to help you out but it states “ Find the first derivative of a function f(x) and find the critical numbers. Then, find the second derivative of a function f(x) and put the critical numbers. If the value is negative, the function has relative maxima at that point, if the value is positive, the function has relative maxima at that point.”
m x H = ![\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%2637.5%26-12.5%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Step 1; Multiply 5 with this matrix ![\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%5C%5C4%268%5C%5C%5Cend%7Barray%7D%5Cright%5D)
and we get a matrix ![\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%2610%5C%5C20%2640%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Multiply the fraction 
with the matrix and we get ![\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2m%7D%7B5%7D%20%26%5Cfrac%7B4m%7D%7B5%7D%20%5C%5C%5Cfrac%7B8m%7D%7B5%7D%20%26%5Cfrac%7B16m%7D%7B5%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step2; Now equate corresponding values of the matrices with each other.
-5 = 
and so on. By equating we get the value of m as 
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get ![\left[\begin{array}{ccc}2&9&-9\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%269%26-9%5C%5C%5Cend%7Barray%7D%5Cright%5D)
.
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
![\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%266%26-8%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
. Equating the matrices from step 3 and 4 we get the value of H as ![\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%26-1%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step 5; Now to find the value of m x H we need to multiply the value of with the matrix
Step 6; Multiplying we get the matrix m x H = [ -25 
]
Answer:
60.2
Step-by-step explanation:
8.6pounds×7gallons
=60.2pounds
The answer is 5 gallons
Its very simple.
Turn 60% and 10% into decimals ( .60 and .10)
Multiply 8 gallons ( brand A ) by .60 and you get 4.8 gallons
Multiply 2 gallons ( brand B ) by .10 and you get .2 gallons
Add them up and you get 5 gallons.
Given:
μ = 89 ng/ml, population mean
σ = 23 ng/ml, population standard deviation
Random variable, x = 100
To test P(x < 100), calculate the z-score.
z = (x-μ)/σ = (100 - 89)/23 = 0.4783
From standard tables, obtain
P(x < 100) = 0.6838 = 68.4%
Answer: 68.4%
