Answer:
see below and attached
Step-by-step explanation:
To solve a system of quadratic equations:
- Equal the equations then rearrange so that it is set to zero.
- Use the quadratic formula to solve.
I have done this (see attached workings) but cannot get any of the solutions you've provided. I have even graphed the two functions, and the points of intersection concur with my workings (see attached graph).
Answer:
![\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & {64} & {63-65} & {1} & {67} & {66-68} & {11} & {70} & {69-71} & {8} &{73} & {72-74} & {7} & {76} & {75-77} & {3} & {79} & {78-80} & {1}\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%7BMidpoint%7D%20%26%20%7BClass%7D%20%26%20%7BFrequency%7D%20%26%20%7B64%7D%20%26%20%7B63-65%7D%20%26%20%7B1%7D%20%20%26%20%7B67%7D%20%26%20%7B66-68%7D%20%26%20%7B11%7D%20%26%20%7B70%7D%20%26%20%7B69-71%7D%20%26%20%7B8%7D%20%26%7B73%7D%20%26%20%7B72-74%7D%20%26%20%7B7%7D%20%20%26%20%7B76%7D%20%26%20%7B75-77%7D%20%26%20%7B3%7D%20%26%20%7B79%7D%20%26%20%7B78-80%7D%20%26%20%7B1%7D%5C%20%5Cend%7Barray%7D)
Using the frequency distribution, I found the mean height to be 70.2903 with a standard deviation of 3.5795
Step-by-step explanation:
Given
See attachment for class
Solving (a): Fill the midpoint of each class.
Midpoint (M) is calculated as:
![M = \frac{1}{2}(Lower + Upper)](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28Lower%20%2B%20Upper%29)
Where
Lower class interval
Upper class interval
So, we have:
Class 63-65:
![M = \frac{1}{2}(63 + 65) = 64](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2863%20%2B%2065%29%20%3D%2064)
Class 66 - 68:
![M = \frac{1}{2}(66 + 68) = 67](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2866%20%2B%2068%29%20%3D%2067)
When the computation is completed, the frequency distribution will be:
![\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & {64} & {63-65} & {1} & {67} & {66-68} & {11} & {70} & {69-71} & {8} &{73} & {72-74} & {7} & {76} & {75-77} & {3} & {79} & {78-80} & {1}\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%7BMidpoint%7D%20%26%20%7BClass%7D%20%26%20%7BFrequency%7D%20%26%20%7B64%7D%20%26%20%7B63-65%7D%20%26%20%7B1%7D%20%20%26%20%7B67%7D%20%26%20%7B66-68%7D%20%26%20%7B11%7D%20%26%20%7B70%7D%20%26%20%7B69-71%7D%20%26%20%7B8%7D%20%26%7B73%7D%20%26%20%7B72-74%7D%20%26%20%7B7%7D%20%20%26%20%7B76%7D%20%26%20%7B75-77%7D%20%26%20%7B3%7D%20%26%20%7B79%7D%20%26%20%7B78-80%7D%20%26%20%7B1%7D%5C%20%5Cend%7Barray%7D)
Solving (b): Mean and standard deviation using 1-VarStats
Using 1-VarStats, the solution is:
![\bar x = 70.2903](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2070.2903)
![\sigma = 3.5795](https://tex.z-dn.net/?f=%5Csigma%20%3D%203.5795)
<em>See attachment for result of 1-VarStats</em>
How do we graph anything? Make a table of values for x and y and then plot each point. After plotting each point on the xy-plane, connect each point with a straight line or curve (depending on the function).
In this case, we must first isolate y.
y = (-4/3)x + 8y
y - 8y = (-4/3)x
-7y = (-4/3)x
y = (-4/3)x ÷ (-7)
y = (4/21)x
Now follow the steps above.
Sorry but I can’t see the picture
Answer:
82
Step-by-step explanation:
because 63% of 130 is 81.9
and since the question is asking approximately which means rounding, so you round 81.9 to get 82.