This problem is half understanding the question and half just plugging in numbers.
Understanding the Question:So its saying that n = whole number bigger than one, making n = 2, 3, 4, 5, etc.
Now try plugging any number n into the
![a_n = 4a_{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%204a_%7Bn-1%7D)
equation. Let's use 2 to make it simple. If you plug in 2, you get:
![a_2 = 4a_{2-1}\\ a_2 = 4a_1](https://tex.z-dn.net/?f=a_2%20%3D%204a_%7B2-1%7D%5C%5C%0Aa_2%20%3D%204a_1)
Remember that the subscripts (the small numbers in the corner) are simply the term number.
![a_1](https://tex.z-dn.net/?f=a_1)
is term 1,
![a_2](https://tex.z-dn.net/?f=a_2)
is term 2, etc. The equation is saying that "term 2 = 4 times term 1."
If you keep plugging in random numbers for n, you'll see that the equation basically says, "a term = 4 times the term right before it." That makes it easy to plug and chug to get our answer.
Plugging and Chugging
Now we understand the question is asking for the first 4 terms, and each term is 4 times the last term. You're told that term 1,
![a_1](https://tex.z-dn.net/?f=a_1)
= 6. That makes the next four terms:
Term 2
![a_2 = 4a_{2-1}\\ a_2 = 4a_1\\ a_2 = 4(6)\\ a_2 = 24](https://tex.z-dn.net/?f=a_2%20%3D%204a_%7B2-1%7D%5C%5C%0A%20a_2%20%3D%204a_1%5C%5C%0A%20a_2%20%3D%204%286%29%5C%5C%0A%20a_2%20%3D%2024)
Term 3
![a_3 = 4a_{3-1}\\ a_3 = 4a_2\\ a_3 = 4(24)\\ a_3 = 96](https://tex.z-dn.net/?f=a_3%20%3D%204a_%7B3-1%7D%5C%5C%20a_3%20%3D%204a_2%5C%5C%20a_3%20%3D%204%2824%29%5C%5C%20a_3%20%3D%2096)
Term 4
![a_4 = 4a_{4-1}\\ a_4 = 4a_3\\ a_4 = 4(96)\\ a_4 = 384](https://tex.z-dn.net/?f=a_4%20%3D%204a_%7B4-1%7D%5C%5C%20a_4%20%3D%204a_3%5C%5C%20a_4%20%3D%204%2896%29%5C%5C%20a_4%20%3D%20384)
Your first 4 terms are 4, 24, 96, and 384.
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Answer: A) F
SOLUTION
From the question, we want to find the probability of selecting a slip of paper with the letter t on it, then selecting the letter r, with replacement.
This means the probability of selecting t and r.
That is
![P(t)\times P(r)](https://tex.z-dn.net/?f=P%28t%29%5Ctimes%20P%28r%29)
There are 12 letters (total outcomes). And there are 2r and 2t.
So probability becomes
![\begin{gathered} \frac{possible\text{ outcome}}{\text{total outcome }} \\ P(t)=\frac{2}{12} \\ P(r)=\frac{2}{12} \\ P(t)\times P(r)=\frac{2}{12}\times\frac{2}{12} \\ =\frac{1}{6}\times\frac{1}{6} \\ =\frac{1}{36} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bpossible%5Ctext%7B%20outcome%7D%7D%7B%5Ctext%7Btotal%20outcome%20%7D%7D%20%5C%5C%20P%28t%29%3D%5Cfrac%7B2%7D%7B12%7D%20%5C%5C%20P%28r%29%3D%5Cfrac%7B2%7D%7B12%7D%20%5C%5C%20P%28t%29%5Ctimes%20P%28r%29%3D%5Cfrac%7B2%7D%7B12%7D%5Ctimes%5Cfrac%7B2%7D%7B12%7D%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B6%7D%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B36%7D%20%5Cend%7Bgathered%7D)
Hence the answer is
Multiply it all together 3/4 is 0.75 2/3 is 0.66 1/2 is 0.5 now do in your calculator 0.75+0.66+0.5 and becase everything is in fractions remember that you have to convert your decimal into a fraction your answer is 1 91/100
Answer:
The volume of the prism is 27 cubic inches.
Step-by-step explanation:
In order to calculate the volume of the given prism, we need to apply the correct formula. The volume of the wedge prism is given by the following formula:
![Volume = \frac{1}{2}*b*h*l](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2Ab%2Ah%2Al)
Applying the data from the problem on the equation above, we have:
![Volume = \frac{1}{2}*6*4.5*2\\Volume = 6*4.5\\Volume = 27](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A6%2A4.5%2A2%5C%5CVolume%20%3D%206%2A4.5%5C%5CVolume%20%3D%2027)
The volume of the prism is 27 cubic inches.
28% is 28/100 as a fraction but the simplest form is 14/50 and it can be simplified to 7/25. the decimal is 0.28
fraction is 7/25
decimal is 0.28