<h3>
Answer:</h3>
System
Solution
- p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>
Step-by-step explanation:</h3>
(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
Answer:
the mean is the average, so you would add up all the numbers and then divide by the amount of numbers
so the answer would be 67.5
Answer:
The complex number 
has Cartesian form
.
Step-by-step explanation:
First, we need to recall the definition of 
when 
is a complex number:
.
Then,
. (I)
Now, recall the definition of the complex exponential:
.
So,
(we use that 
.
Thus,
Now we group conveniently in the above expression:
.
Now, substituting this equality in (I) we get
.
Thus,
![\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]](https://tex.z-dn.net/?f=%5Cexp%5Cleft%28%5Ccos%282%2B3i%29%5Cright%29%20%3D%20%5Cexp%5Cleft%28%5Ccosh%203%5Ccos%202%5Cright%29%5Cleft%5B%20%5Ccos%28%5Csinh%203%5Csin%202%29-i%5Csin%28%5Csinh%203%5Csin%202%29%5Cright%5D)
.
203/3.5=58mi/h
243/4.5=54mi/h
(58+54)/2=56mi/h
The answer in 56mi/h
