Sum of an infinite geometric sequence with the common ratio r, and the first term a1 is
![\frac{a_1}{1-r}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba_1%7D%7B1-r%7D%20)
we notice
-2 times -1/4=1/2,
1/2 times -1/4=-1/8
so a1=-2
r=-1/4 or -0.25
so the sum is
![\frac{-2}{1-(-0.25)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-2%7D%7B1-%28-0.25%29%7D%20)
=
![\frac{-2}{1+0.25}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-2%7D%7B1%2B0.25%7D%20)
=
![\frac{-2}{1.25}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-2%7D%7B1.25%7D%20)
=
![\frac{-8}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-8%7D%7B5%7D%20)
=
the sum is -8/5 or -1.6
Answer:
A.
Step-by-step explanation:
$15 rental fee added to the 12.75 per hour. you have to multiply the 12.75 times the amount of hours rented, which we don't know yet so that's variable x. then he has only $45 to spend so it has to be equal to or less than that.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Answer:
1) X stands for individual acts and y, group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) ![S=\left \{ 5,10 \right \}](https://tex.z-dn.net/?f=S%3D%5Cleft%20%5C%7B%205%2C10%20%5Cright%20%5C%7D)
Step-by-step explanation:
Completing with what was found:
<em> 1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30</em>
1. What do x and y represent in this situation?
X stands for individual acts and y, group acts.
Besides that, In the system of equation, they represent the time for x, and the time for y.
2. Do you agree that your classmate set up the equations correctly? Explain why or why not.
Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.
3. Solving the system by Elimination
![\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D12x%2B%206y%3D%20120%5C%5C%204x%2B%20y%3D%2030%5Cend%7Bmatrix%7D%5Cright.%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D12x%2B%206y%3D%20120%5C%5C%204x%2B%20y%3D%2030%5C%3A%2A%28-3%29%5Cend%7Bmatrix%7D%5Cright.%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D12x%2B%206y%3D%20120%5C%5C%20-12x%2B%20-3y%3D%20-90%5Cend%7Bmatrix%7D%5Cright.%5C%5C3y%3D30%5CRightarrow%20y%3D10%5C%5C4x%2B%2810%29%3D30%5CRightarrow%204x%3D20%5CRightarrow%20x%3D5%5C%5CS%3D%5Cleft%20%5C%7B%205%2C10%20%5Cright%20%5C%7D)
Answer:
20.3 units
Step-by-step explanation:
AB/CB = BD/AB
9/CB = 4/9
CB = 9×9/4
CB = 81/4 = 20¼ units
20.25 (20.3 units correct to 1 dp)