A geometric series is written as 
, where 
is the first term of the series and 
is the common ratio.
In other words, to compute the next term in the series you have to multiply the previous one by .
Since we know that the first time is 6 (but we don't know the common ratio), the first terms are
.
Let's use the other information, since the last term is 
, we know that 
, otherwise the terms would be bigger and bigger.
The information about the sum tells us that
We have a formula to compute the sum of the powers of a certain variable, namely
So, the equation becomes
The only integer solution to this expression is 
.
If you want to check the result, we have
and the last term is
Answer:
4. 54- 8.5x>20
Step-by-step explanation:
Catherine only has $54, so she cannot spend more than that.
The canvas will cost at least $20, but we don't know how much exactly.
The tubes cost $8.50 each.
So, she starts with a total budget of $54, out of which she will buy paints (8.5x) and she wants to have at least $20 left for canvas.
So, we transpose those facts into the inequity:
54 - 8.5x > 20
Answer:
The probability of getting a sample with 80% satisfied customers or less is 0.0125.
Step-by-step explanation:
We are given that the results of 1000 simulations, each simulating a sample of 80 customers, assuming there are 90 percent satisfied customers.
Let 
= <u><em>sample proportion of satisfied customers</em></u>
The z-score probability distribution for the sample proportion is given by;
Z = 
~ N(0,1)
where, p = population proportion of satisfied customers = 90%
n = sample of customers = 80
Now, the probability of getting a sample with 80% satisfied customers or less is given by = P( 
80%)
P( 80%) = P( 
) = P(Z -2.24) = 1 - P(Z < 2.24)
= 1 - 0.9875 = <u>0.0125</u>
The above probability is calculated by looking at the value of x = 2.24 in the z table which has an area of 0.9875.
Answer:
<h2>Cubing both sides of an equation is reversible.</h2>
Step-by-step explanation:
Squaring both sides of an equation is irreversible, because the square power of negative number gives a positive result, but you can't have a negative base with a positive number, given that the square root of a negative number doesn't exist for real numbers.
In case of cubic powers, this action is reversible, because the cubic root of a negative number is also a negative number. For example
![\sqrt[3]{x} =-1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3D-1)
We cube both sides
![(\sqrt[3]{x} )^{3} =(-1)^{3} \\x=-1](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bx%7D%20%29%5E%7B3%7D%20%3D%28-1%29%5E%7B3%7D%20%5C%5Cx%3D-1)
If we want to reverse the equation to the beginning, we can do it, using a cubic root on each side
![\sqrt[3]{x}=\sqrt[3]{-1} \\\sqrt[3]{x}=-1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%3D%5Csqrt%5B3%5D%7B-1%7D%20%5C%5C%5Csqrt%5B3%5D%7Bx%7D%3D-1)
There you have it, cubing both sides of an equation is reversible.
<span>Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction. This is the answer which is C</span>
