Answer:
A. Simple Random Sampling
B. Cluster Sampling
C. Convenience Sampling
D. Systematic Sampling
E. Stratified Sampling
Step-by-step explanation:
Simple Random Sampling is the sampling when samples are chosen randomly, where each unit has an equal chance of being selected in a sample.
If the population is divided into a different group called cluster and clusters are selected as a sample then it is Cluster Sampling.
In Convenience sampling, observers collect the sample as his\her convenience.
In Systematic Sampling sample is chosen by some criteria like he\she is taken every 10th unit as a sample from the population.
In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.
Here is the equation you need:
3(x + 9) = 2x - 7
You finish.
![\boxed{(x - a)(x - b) = 0}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%28x%20-%20a%29%28x%20-%20b%29%20%3D%200%7D)
The equation above is the intercept form. Both a-term and b-term are the roots of equation.
![x = - \frac{1}{3} \\ x = 5](https://tex.z-dn.net/?f=x%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5C%5C%20x%20%3D%205)
These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.
![(x + \frac{1}{3} )(x - 5) = 0](https://tex.z-dn.net/?f=%28x%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%28x%20-%20%205%29%20%3D%200)
Here we can convert the expression x+1/3 to this.
![x + \frac{1}{3} = 0 \\ 3x + 1 = 0](https://tex.z-dn.net/?f=x%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%200%20%5C%5C%20%203x%20%2B%201%20%3D%200)
Rewrite the equation.
![(3x + 1)(x - 5) = 0](https://tex.z-dn.net/?f=%283x%20%2B%201%29%28x%20-%205%29%20%3D%200)
Simplify by multiplying both expressions.
![3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%20-%2015x%20%2B%20x%20-%205%20%3D%200%20%5C%5C%203%20%7Bx%7D%5E%7B2%7D%20%20-%2014x%20%20-%205%20%3D%200)
<u>Answer</u><u> </u><u>Check</u>
Substitute the given roots in the equation.
![3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0](https://tex.z-dn.net/?f=3%20%7B%285%29%7D%5E%7B2%7D%20%20-%2014%285%29%20%20-%205%20%3D%200%20%5C%5C%2075%20-%2070%20-%205%20%3D%200%20%5C%5C%2075%20-%2075%20%3D%200%20%5C%5C%200%20%3D%200)
![3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0](https://tex.z-dn.net/?f=3%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%5E%7B2%7D%20%20-%2014%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%29%20-%205%20%3D%200%20%5C%5C%203%28%20%5Cfrac%7B1%7D%7B9%7D%20%29%20%2B%20%20%5Cfrac%7B14%7D%7B3%7D%20%20-%205%20%3D%200%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%2B%20%20%5Cfrac%7B14%7D%7B3%7D%20%20-%20%20%5Cfrac%7B15%7D%7B3%7D%20%20%3D%200%20%5C%5C%20%20%5Cfrac%7B15%7D%7B3%7D%20%20-%20%20%5Cfrac%7B15%7D%7B3%7D%20%20%3D%200%20%5C%5C%200%20%3D%200)
The equation is true for both roots.
<u>Answer</u>
![\large \boxed {3 {x}^{2} - 14x - 5 = 0}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%20%7B3%20%7Bx%7D%5E%7B2%7D%20%20-%2014x%20-%205%20%3D%200%7D)