Answer: 3x+3, 5x+40, 4x+24
Answer:
Step-by-step explanation:
You could use the scores of a football game: 13:22 points
Or how many boys and girls are in your class: There are 12 girls to 13 boys, 12:13 or 12/13
Or you could say how many dogs and cats there are in an animal shelter: There are 11 dogs to 24 cats, 11:24, 11 dogs/24 cats
Step 1: Arrange the data given in ascending order, that is from least to greatest.
<u>Given data:</u>
![42, \; 51, \; 54, \; 46,\; 49, \; 53,\; 52, \; 37, \; 33, \; 36, \; 50, \; 41,\; 50,\; 38\\ \\](https://tex.z-dn.net/?f=%2042%2C%20%5C%3B%2051%2C%20%5C%3B%2054%2C%20%5C%3B%2046%2C%5C%3B%20%2049%2C%20%5C%3B%2053%2C%5C%3B%20%2052%2C%20%5C%3B%2037%2C%20%5C%3B%2033%2C%20%5C%3B%2036%2C%20%5C%3B%2050%2C%20%5C%3B%2041%2C%5C%3B%20%2050%2C%5C%3B%20%2038%5C%5C%20%5C%5C%20%20)
<u>Data in ascending order:</u>
![33, \; 36, \; 37, \; 38, \; 41, \; 42,\; 46, \; 49,\; 50, \; 50,\; 51,\; 52,\; 53, \; 54](https://tex.z-dn.net/?f=%2033%2C%20%5C%3B%2036%2C%20%5C%3B%2037%2C%20%5C%3B%2038%2C%20%5C%3B%2041%2C%20%5C%3B%2042%2C%5C%3B%20%2046%2C%20%5C%3B%2049%2C%5C%3B%20%2050%2C%20%5C%3B%2050%2C%5C%3B%20%2051%2C%5C%3B%20%2052%2C%5C%3B%20%2053%2C%20%5C%3B%2054%20)
Step 2: Find the median (Q2). The median is the value exactly in the middle of an ordered set of numbers .If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
Since in our problem we have 14 datas, we need to pick the middle most numbers and find the average of the same.
![Median =\frac{46+49}{2} =\frac{95}{2} =47.5](https://tex.z-dn.net/?f=%20Median%20%3D%5Cfrac%7B46%2B49%7D%7B2%7D%20%3D%5Cfrac%7B95%7D%7B2%7D%20%3D47.5%20)
The median is called Q2 and equal to 47.5
Step 3: Find the lower quartile (Q1). Considering the values to the left of the median(Q2), the median to those values is the Q1 and called as Lower quartile.
![Q1=38](https://tex.z-dn.net/?f=%20Q1%3D38%20)
Step 4: Find the upper quartile (Q3). Considering the values to the right of the median(Q2), the median to those values is the Q3 and called as Upper quartile.
![Q3=51](https://tex.z-dn.net/?f=%20Q3%3D51%20)
Conclusion:
Using the above details we need to plot the box and whisker plot attached with this problem.
Answer:
possible values of 4th term is 80 & - 80
Step-by-step explanation:
The general term of a geometric series is given by
![a(n)=ar^{n-1}](https://tex.z-dn.net/?f=a%28n%29%3Dar%5E%7Bn-1%7D)
Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term
- Given, 5th term is 40, we can write:
![ar^{5-1}=40\\ar^4=40](https://tex.z-dn.net/?f=ar%5E%7B5-1%7D%3D40%5C%5Car%5E4%3D40)
- Given, 7th term is 10, we can write:
![ar^{7-1}=10\\ar^6=10](https://tex.z-dn.net/?f=ar%5E%7B7-1%7D%3D10%5C%5Car%5E6%3D10)
We can solve for a in the first equation as:
![ar^4=40\\a=\frac{40}{r^4}](https://tex.z-dn.net/?f=ar%5E4%3D40%5C%5Ca%3D%5Cfrac%7B40%7D%7Br%5E4%7D)
<em>Now we can plug this into a of the 2nd equation:</em>
<em>
</em>
<em />
<em>Let's solve for a:</em>
<em>
</em>
<em />
Now, using the general formula of a term, we know that 4th term is:
4th term = ar^3
<u>Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:</u>
![ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80](https://tex.z-dn.net/?f=ar%5E3%5C%5C1.%28640%29%28%5Cfrac%7B1%7D%7B2%7D%29%5E3%3D80%5C%5C2.%28640%29%28-%5Cfrac%7B1%7D%7B2%7D%29%5E3%3D-80)
possible values of 4th term is 80 & - 80