Part A.
1) Variables:
X: amount invested in AAA bonds
Y: amount invested in A bonds
Z: amount invested in B bonds.
2) Return:
4%* X + 6% * Y + 11% * Z = 1620
3) Investment:
X + Y + Z = 26,000
4) Ratio between AAA and B bonds.
X = 2*Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
2Z * 4% + Y * 6% + Z * 11% = 1620
=> 0.08Z + 0.06Y + 0.11Z = 1620
=> 0.19Z + 0.06Y = 1620
2Z + Y + Z = 26,000
=> 3Z + Y = 26,000 => Y = 26,000 - 3Z
Replace Y with 26,000 - 3Z
0.19Z + 0.06(26,000 - 3Z) = 1620
0.19Z + 1560 - 0.18Z = 1620
0.01Z = 1620 - 1560
0.01Z = 60
Z = 60 / 0.01 = 6000
=> X = 2*6000 = 12,000
=> Y = 26,000 - 12,000 - 6,000 = 8,000
Answer: 12,000 in bonds AAA, 8,000 in bonds A, and 6000 in bonds B.
Part B.
2) Return:
0.04X + 0.06 Y + 0.11Z = 2360
3) Investment:
X + Y + Z = 38,000
4) Ratio between AAA and B bonds.
X = 2Z
5) Solution of the system of equations:
Replace X with 2Z in the two first equations:
=> 0.08Z + 0.06Y + 0.11Z = 2360
=> 0.19Z + 0.06Y = 2360
2Z + Y + Z = 38,000
=> 3Z + Y = 38,000 => Y = 38,000 - 3Z
Replace Y with 38,000 - 3Z
0.19Z + 0.06(38,000 - 3Z) = 2360
0.19Z + 2280 - 0.18Z = 2360
0.01Z = 2360 - 2280
0.01Z = 80
Z = 80 / 0.01 = 8000
=> X = 2*8000 = 16,000
=> Y = 38,000 - 16,000 - 8000 = 14,000
Answer: 16,000 in AAA bonds, 14,000 in A bonds, and 8,000 in B bonds.
125000
Explanation:
(x= 1% of annual income)
15x+14x=36250
29x=36250
divide each side by 29
x=1250
1250x100=125000
To solve this problem, we must first find the discount amount, and then subtract this amount from the total price of the item.
To find the discount amount, we must find 35% of $40. To do this, we must first convert 35% to its decimal equivalent by dividing 35/100. We do this because percentages are parts out of a total 100 percent, thus this fraction represents an equivalent value that we can multiply by other numbers. Using our knowledge that 35/100 = 0.35, we can now set up our expression:
35% of $40 (keep in mind that the word "of" refers to multiplication in math)
0.35 * 40
To solve, we just multiply these two numbers together, which gives us 14.
This means that Kala got a discount of $14 off of the original price of $40. To find out how much she paid for it, we must subtract $14 from $40, as modeled below:
$40 - $14 = $26
Therefore, Kala paid $26 for the item.
Hope this helps!
Answer:
x = - 3
Step-by-step explanation:
If you have a look at the screenshot, the asymptote is equal to x=h.
In this case, we look at the bracket (x+3). The h is negative as it does not follow the standard (x-h) model. The value is 3. If we combine these two, the answer would be:
x = -3
<u>Answer:</u>
Using the pair of points (1, 1) and (0, 0) we have calculated the slope of the line
<u>Solution:</u>
Given that, we can use any two points from cartesian plane,
Let the two points be (0, 0) and (1, 1)
We have to find the slope of the line that, passes through the chosen two points.
Now, we know that, slope of a line that passes through 
is given by:
Substitute these values in "m" formula,
Hence, the slope of the line that passes through (1, 1) and (0, 0) is 1.
