Answer:
4250
Step-by-step explanation:
0.13 = 13%
1000×0.13=130
130×25= 3250 + 1000 = 4250
What I did:
You have to turn the percent to a decimal first
Then multiply the decimal by the first investment amount (1000)
then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with
Pacific time is 3 hours before Eastern time so subtract 3 hours from 11:00 am and you get 8:00 am
Well, let's first write these as points.
( 2 , 50 )
( 4 , 100 )
We can see that when "x" is reduced by 2, "y" is reduced by 50. This means that if we reduce "x" by 1, "y" will be reduced by 25. Thus, we can say that if "x" is 1, "y" will be 25.
( 1 , 25 )
What we know that 25 * 1 = 25, and that 2 * 25 = 50. We can see that multiplying "x" by 25 will give us our "y". We can now write this as an equation.
y = 25x
Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
Answer:
Og(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
To understand how the parent function is transformed, you have to look at a few things.
Firstly, is there a negative sign in front? If there is, then the function is flipped around the y-axis
Second, on the part where the x is included (in this case it is x+4) you have to see if there is a negative sign in front of this. If this is the case, then the formula is flipped around the x-axis
<em>Third, If the part with the x is being added to, then the graph is being translated to the left that many units. If it is being subtracted from, then it is being translated to the right that many units (in this case it is </em><u><em>x+4</em></u><em>, so we move to the left 4 units) ((it is the opposite of what would be common sense, I know))</em>
<em>Lastly, if the whole thing is being added to, move up that many units. If it is subtracted from, move down that many units (in this case it is 1/x+4 </em><u><em>- 6)</em></u><em> (( this one does follow common sense))</em>
There are other factors, such as leading coefficients (on just the x part or the whole thing) and other stuff I'm sure I don't remember )
For more information: https://mathhints.com/parent-graphs-and-transformations/