To be precise, the size of your sample space is <span><span>(<span>2410</span>)</span><span>(<span>2410</span>)</span></span>. This number does go on the bottom of the fraction, and what goes on top is the size of the event. Break up the event into independent events 1. choose the 2 defective bulbs, and 2. choose the remaining 8 bulbs. I don't have much choice in event 1. There is only one way to choose both of the defective balls. In other words, <span><span>(<span>22</span>)</span><span>(<span>22</span>)</span></span> (choosing 2 defective bulbs from a set of 2 defective bulbs). For event 2, there are <span><span>24−2=22</span><span>24−2=22</span></span> nondefective bulbs, and I must choose <span>88</span> of them, so that's <span><span>(<span>228</span>)</span><span>(<span>228</span>)</span></span>. Finally, since events 1 and 2 are independent, we multiply the answers for the combined event: <span><span><span>(<span>22</span>)</span><span>(<span>228</span>)</span></span><span><span>(<span>22</span>)</span><span>(<span>228</span>)</span></span></span>
<span><span>P=<span><span><span>(<span>22</span>)</span><span>(<span>228</span>)</span></span><span>(<span>2410</span>)</span></span></span><span>P=<span><span><span>(<span>22</span>)</span><span>(<span>228</span>)</span></span><span>(<span>2410</span>)</span></span></span></span>
Or, since <span><span><span>(<span>22</span>)</span>=1</span><span><span>(<span>22</span>)</span>=1</span></span>,
<span><span>P=<span><span>(<span>228</span>)</span><span>(<span>2410</span>)</span></span></span><span>P=<span><span>(<span>228</span>)</span><span>(<span>2410</span>)</span></span></span></span>
Hope this helps!
The sequence forms a Geometric sequence as the rule to obtain the value for the next term is by ratio
Term 1: 1000
Term 2: 200
Term 3: 40
From term 1 to term 2, there's a decrease by
![\frac{1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20)
From term 2 to term 3, there's a decrease also by
![\frac{1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20)
The rule to find the
![n^{th}](https://tex.z-dn.net/?f=n%5E%7Bth%7D%20)
term in a sequence is
![n^{th}=a r^{n-1}](https://tex.z-dn.net/?f=n%5E%7Bth%7D%3Da%20r%5E%7Bn-1%7D%20)
, where
![a](https://tex.z-dn.net/?f=a)
is the first term in the sequence and
![r](https://tex.z-dn.net/?f=r)
is the ratio
So, the formula for the sequence in question is
![n_{th}](https://tex.z-dn.net/?f=n_%7Bth%7D%20)
term =
![1000( \frac{1}{5} ^{n-1} )](https://tex.z-dn.net/?f=1000%28%20%5Cfrac%7B1%7D%7B5%7D%20%5E%7Bn-1%7D%20%29)
The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.
We can find a partial sum of the sequence using the formula
![S_{∞} = \frac{a}{1-r}](https://tex.z-dn.net/?f=S_%7B%E2%88%9E%7D%20%3D%20%5Cfrac%7Ba%7D%7B1-r%7D%20)
for -1<r<1
Substituting
![a=1000](https://tex.z-dn.net/?f=a%3D1000)
and
![r= \frac{1}{5}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B1%7D%7B5%7D%20)
we have
![S_{∞}](https://tex.z-dn.net/?f=%20S_%7B%E2%88%9E%7D%20)
=
![\frac{1000}{1- \frac{1}{5} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1000%7D%7B1-%20%5Cfrac%7B1%7D%7B5%7D%20%7D%20)
= 1250
Hence, the correct option is option number 1
Hello!
To find the side length of a square with the diagonal you use the equation
![a = \sqrt{2} \frac{d}{2}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B2%7D%20%20%5Cfrac%7Bd%7D%7B2%7D%20)
a is side length
d is diagonal length
Put in the values you know
![a = \sqrt{2} * \frac{32}{2}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B2%7D%20%2A%20%20%5Cfrac%7B32%7D%7B2%7D%20)
Divide
![a = \sqrt{2} * 16](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B2%7D%20%2A%2016)
Multiply
a = 22.6
All the sides are 22.6 feet
Add all the sides
22.6 + 22.6 + 22.6 + 22.6 = 90.4
The answer is 90.4
Hope this helps!
Answer:
the third or fourth one probably
Step-by-step explanation:
Answer:
More than half the students scored 81 or better on the test
There were 12 students who scored 80 on the test
The same number of students scored between 81 and 90 on the test as scored between 61 and 80.
Step-by-step explanation: Please think this through, I don't know if I'm correct. It is either all or one of these