Given:
5) The expressions are
![16x+24y+32](https://tex.z-dn.net/?f=16x%2B24y%2B32)
![8(2x+3y+4)](https://tex.z-dn.net/?f=8%282x%2B3y%2B4%29)
![4(4x+24y+8)](https://tex.z-dn.net/?f=4%284x%2B24y%2B8%29)
7) The expression is
![7(3-x)+15x](https://tex.z-dn.net/?f=7%283-x%29%2B15x)
To find:
5) Whether the given expressions are equivalent.
7) simplified form of given expression.
Solution:
5)
First expression is
![16x+24y+32](https://tex.z-dn.net/?f=16x%2B24y%2B32)
Second expression is
![8(2x+3y+4)](https://tex.z-dn.net/?f=8%282x%2B3y%2B4%29)
![=8(2x)+8(3y)+8(4)](https://tex.z-dn.net/?f=%3D8%282x%29%2B8%283y%29%2B8%284%29)
![=16x+24y+32](https://tex.z-dn.net/?f=%3D16x%2B24y%2B32)
Third expression is
![4(4x+24y+8)](https://tex.z-dn.net/?f=4%284x%2B24y%2B8%29)
![=4(4x)+4(24y)+4(8)](https://tex.z-dn.net/?f=%3D4%284x%29%2B4%2824y%29%2B4%288%29)
![=16x+96y+32](https://tex.z-dn.net/?f=%3D16x%2B96y%2B32)
Therefore, the simplified forms of given expressions are
respectively. It means only first and second expressions and equivalent.
7)
We have,
![7(3-x)+15x](https://tex.z-dn.net/?f=7%283-x%29%2B15x)
![=7(3)+7(-x)+15x](https://tex.z-dn.net/?f=%3D7%283%29%2B7%28-x%29%2B15x)
![=21-7x+15x](https://tex.z-dn.net/?f=%3D21-7x%2B15x)
![=21+8x](https://tex.z-dn.net/?f=%3D21%2B8x)
Therefore, the simplified form of given expression is
.
P(rh-positive) = 95% = 0.95
Therefore,
P(rh-negative) = 1-P(rh-positive) = 1-0.95 = 0.05
Then,
P(rh-negative) for both parents = 0.05*0.05 = 0.0025
The formula is
![A=P(1+r)^t](https://tex.z-dn.net/?f=A%3DP%281%2Br%29%5Et)
A=future amount
P=present amount or princpal
r=rate in decimal
t=time in years
so
given
P=36000
r=4.75%=0.0475
t=6
![A=36000(1+0.0475)^6](https://tex.z-dn.net/?f=A%3D36000%281%2B0.0475%29%5E6)
![A=36000(1.0475)^6](https://tex.z-dn.net/?f=A%3D36000%281.0475%29%5E6)
use your calculator
A=47558.340
round to nearest cent
A=$47558.34
must pay back $47558.34
Answer:
∑ₙ₌₀°° (-3x)ⁿ / n!
R = ∞
Step-by-step explanation:
Maclaurin series is:
∑ₙ₌₀°° f⁽ⁿ⁾(0) xⁿ / n!
Find the nth derivative and evaluate at x=0:
f(x) = e⁻³ˣ
f⁽ⁿ⁾(x) = (-3)ⁿ e⁻³ˣ
f⁽ⁿ⁾(0) = (-3)ⁿ
The Maclaurin series is therefore:
∑ₙ₌₀°° (-3)ⁿ xⁿ / n!
∑ₙ₌₀°° (-3x)ⁿ / n!
Use ratio test to find the radius of convergence.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-3x)ⁿ⁺¹ / (n+1)!] / [(-3x)ⁿ / n!]│< 1
lim(n→∞)│(-3x) n! / (n+1)!│< 1
lim(n→∞)│3x / (n+1)│< 1
0 < 1
The radius of convergence is infinite.
____________________________________________________
Answer:
Your answer would be 1,385.44 ft²
____________________________________________________
Step-by-step explanation:
To find the area of a circle, we would use the equation ![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
In this case we have the diameter, and that's 42.
The radius of a circle is half of the diameter, therefore the radius would be 21.
Now we know the radius,we can plug that in to our equation.
Your equation should look like this:
![\pi (21)^2](https://tex.z-dn.net/?f=%5Cpi%20%2821%29%5E2)
Pi would be 3.14159
Now, you can solve.
![3.14159(21)^2\\\\3.14159*441\\\\=1,385.44](https://tex.z-dn.net/?f=3.14159%2821%29%5E2%5C%5C%5C%5C3.14159%2A441%5C%5C%5C%5C%3D1%2C385.44)
When you'r edone solving, you should get 1,385.44
1,385.44 ft² would be your FINAL answer.
____________________________________________________