Susan purchased company ABC's stock and invested the balance in her money market account. ABC's stock yielded 13% last year and
1 answer:
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Step-by-step explanation:
Susan purchased company ABC's stock and invested the balance in her money market account
- ABC's stock yielded 13% last year and her money market account yielded 5% last year
- Susan's initial investments amount to $15000, and the annual income is $1070
We need to find how much money is invested in stock and how much is invested in her money market account
Assume that she invested $x in ABC's stock and $y in her money market account
∵ She invested $x in ABC's stock
∵ She invested $y in her market account
∵ Her initial investments amount is $15000
∴ x + y = 15000 ⇒ (1)
The interest formula is I = Prt, where P is the initial investment, r is the rate of interest in decimal and t is the time
In ABC's stock:
∵ She invested $x
∴ P = x
∵ The rate is 13%
∴ r = 13% = 13 ÷ 100 = 0.13
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = x(0.13)(1)
∴ = 0.13x
In her market account:
∵ She invested $y
∴ P = y
∵ The rate is 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = y(0.05)(1)
∴ = 0.05y
∵ Her annual income is $1070
- Add the interest of ABC's stock and the interest of her market
account, equate the sum by 1070
∴ 0.13x + 0.05y = 1070 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.05 to eliminate y
∵ -0.05x - 0.05y = -750 ⇒ (3)
- Add equations (2) and (3)
∴ 0.08x = 320
- Divide both sides by 0.08
∴ x = 4000
- Substitute value of x in equation (1) to find y
∵ 4000 + y = 15000
- Subtract 4000 from both sides
∴ y = 11000
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
#LearnwithBrainly
You might be interested in
Answer:
Answer is 2
Step-by-step explanation:
We know that average rate of change of a function f(x) in the interval (a,b) is
Using this we can say that
Using properties of integration we have
3 to 6 integral = 20-5 =15
0 to2 integral = -3=5 =-8
Thus integral form 0 to 6 would be = -8+15+5 = 12
Average rate of change form 0 to 6 =
Answer is 2
Answer:
y = -1/10x^2 +2.5
Step-by-step explanation:
The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:
-1 -4 = -5
So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).
The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...
y = (1/(4p))(x -h) +k
y = -1/10x^2 +2.5
_____
You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.
