Answer:
The highest common factor for both 102 and 153 is
GCF- 51
Step-by-step explanation:
51*3= 153
51*2=102
The complete table will be:
![Monday - 100\\ Tuesday-65\\ Wednesday- 120\\ Thursday-150\\ Friday-90\\ Saturday- 0\\ Sunday-175](https://tex.z-dn.net/?f=Monday%20-%20100%5C%5C%20Tuesday-65%5C%5C%20Wednesday-%20120%5C%5C%20Thursday-150%5C%5C%20Friday-90%5C%5C%20Saturday-%200%5C%5C%20Sunday-175)
<u><em>Explanation</em></u>
Suppose, the number of sit-ups in Sunday is ![x](https://tex.z-dn.net/?f=x)
Mean is the simple average of some numbers. <u>For finding the mean number</u> of sit-ups per day, we need to <u>divide the 'total number of sit-ups' by the 'total number of days'</u>.
Here the total number of days is 7 and the total number of sit-ups for 7 days ![= 100+65+120+150+90+0+x= 525+x](https://tex.z-dn.net/?f=%3D%20100%2B65%2B120%2B150%2B90%2B0%2Bx%3D%20525%2Bx)
Given that, the mean number of sit-ups per day is 100. So, the equation will be...
![\frac{525+x}{7}=100\\ \\ 525+x=700\\ \\ x= 700-525=175](https://tex.z-dn.net/?f=%5Cfrac%7B525%2Bx%7D%7B7%7D%3D100%5C%5C%20%5C%5C%20525%2Bx%3D700%5C%5C%20%5C%5C%20x%3D%20700-525%3D175)
So, the number of sit-ups you have to do Sunday is 175.
You combine the numbers that have the same letter attached to them. Then you add or subtract the bumbers from each other to. After that you make the numbers and the numbers with letters into one equation
Ex: 13+5r+7r= 13+12r
Step-by-step explanation:
2w+w=3w If theres a letter by itself it means theres a 1.
Answer:
40 Apple juice and 20 Orange juice
Step-by-step explanation:
From the diagram, you know that 4 OJ makes one drink, so to make 5 drinks, you need 5 times that, or 20 OJ. You can also see that you need twice as much AJ as OJ, so that means you need 40 AJ.
*OJ = Orange juice and AJ = Apple juice
Answer:
--- Standard deviation
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Explain how the standard deviation is calculated.
<u>Start by calculating the mean</u>
To do this, we divide the sum of the products of grade and number of students by the total number of students;
i.e.
![\bar x = \frac{\sum fx}{\sum f}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20fx%7D%7B%5Csum%20f%7D)
So, we have:
![\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B50%20%2A%201%20%2B%2057%20%2A%202%20%2B%2060%20%2A%204%20%2B%2065%20%2A%203%20%2B72%20%2A3%20%2B%2075%20%2A%2012%20%2B%2077%20%2A%2010%20%2B%2081%20%2A%206%20%2B%2083%20%2A%206%20%2B%2088%20%2A%209%20%2B%2090%20%2A%2012%20%2B%2092%20%2A%2012%20%2B95%20%2A%202%20%2B%2099%20%2A%204%20%2B%20100%20%2A%205%7D%7B1%20%2B%202%20%2B%204%20%2B%203%20%2B3%20%2B%2012%20%2B%2010%20%2B%206%20%2B%206%20%2B%209%20%2B%2012%20%2B%2012%20%2B2%20%2B%204%20%2B%205%7D)
![\bar x = \frac{7531}{91}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B7531%7D%7B91%7D)
![\bar x = 82.76](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2082.76)
Next, calculate the variance using the following formula:
![\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%20%5Cfrac%7B%5Csum%20f%28x%20-%20%5Cbar%20x%29%5E2%7D%7B%5Csum%20f%7D)
i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset
So, we have:
![\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%20%5Cfrac%7B1%20%2A%20%2850%20-%2082.76%29%5E2%20%2B...................%2B%205%20%2A%20%28100%20-%2082.76%29%5E2%7D%7B91%7D)
![\sigma^2 = \frac{11580.6816}{91}](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%20%5Cfrac%7B11580.6816%7D%7B91%7D)
![\sigma^2 = 127.26](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%20127.26)
Lastly, take the square root of the variance to get the standard deviation
![\sigma = \sqrt{\sigma^2}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Csigma%5E2%7D)
![\sigma = \sqrt{127.26}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B127.26%7D)
--- approximated
<em>Hence, the standard deviation is approximately 11.28</em>
Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.