Answer:
1. Parameter because the value is a numerical measurement describing a characteristic of a population
Step-by-step explanation:
A parameter is a fixed measure which <u>describes the whole population</u> while a statistic is a <u>characteristic of a sample</u> (which is a portion of the target population).
In a study of all 1963 employees at a college, it is found that "40%" own a computer.
The study involved the entire population of employees in the college, therefore the result describes the computer owning <u>characteristics of the whole population under study</u>. It is therefore a parameter.
<u>The correct option is 1.</u>
Answer:
1.148698
Step-by-step explanation:
Answer:
(a) 9
Step-by-step explanation:
![\sf t^3 - r + 20 \div r](https://tex.z-dn.net/?f=%5Csf%20t%5E3%20-%20r%20%2B%2020%20%5Cdiv%20%20r)
substitute r = 4, t = 2
![\sf (2)^3 - 4 + 20 \div 4](https://tex.z-dn.net/?f=%5Csf%20%282%29%5E3%20-%204%20%2B%2020%20%5Cdiv%204)
simplify
![\sf (2)^3 - 4 + 5](https://tex.z-dn.net/?f=%5Csf%20%282%29%5E3%20-%204%20%2B%205)
cubic of 2 is 8
![\sf 8 - 4 + 5](https://tex.z-dn.net/?f=%5Csf%208%20-%204%20%2B%205)
simplify
![\sf 9](https://tex.z-dn.net/?f=%5Csf%209)
PEMDAS tells us to use multiplication and division before addition and subtraction.
<u>-5(8) </u>÷ 10 - <u>14 ÷ 7</u> - <u>(-2)(3)</u>
<u> -40 ÷ 10</u> - 2 - -6
<u>-4 - 2 </u> + 6 <em>two negatives make a positive so - - 6 = + 6</em>
<u> -6 +6</u>
0
Answer: 0
b must be equal to -6 for infinitely many solutions for system of equations
and ![-3 x+\frac{1}{2} y=-3](https://tex.z-dn.net/?f=-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3)
<u>Solution:
</u>
Need to calculate value of b so that given system of equations have an infinite number of solutions
![\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7By%3D6%20x%2Bb%7D%20%5C%5C%5C%5C%20%7B-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3%7D%5Cend%7Barray%7D)
Let us bring the equations in same form for sake of simplicity in comparison
![\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7By%3D6%20x%2Bb%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow-6%20x%2By-b%3D0%20%5CRightarrow%20%281%29%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow-3%20x%2B%5Cfrac%7B1%7D%7B2%7D%20y%3D-3%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20-6%20x%2By%3D-6%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20-6%20x%2By%2B6%3D0%20%5CRightarrow%282%29%7D%5Cend%7Barray%7D)
Now we have two equations
![\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B-6%20x%2By-b%3D0%5CRightarrow%281%29%7D%20%5C%5C%5C%5C%20%7B-6%20x%2By%2B6%3D0%5CRightarrow%282%29%7D%5Cend%7Barray%7D)
Let us first see what is requirement for system of equations have an infinite number of solutions
If
and
are two equation
then the given system of equation has no infinitely many solutions.
In our case,
![\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Ba_%7B1%7D%3D-6%2C%20%5Cmathrm%7Bb%7D_%7B1%7D%3D1%20%5Ctext%20%7B%20and%20%7D%20c_%7B1%7D%3D-%5Cmathrm%7Bb%7D%7D%20%5C%5C%5C%5C%20%7Ba_%7B2%7D%3D-6%2C%20%5Cmathrm%7Bb%7D_%7B2%7D%3D1%20%5Ctext%20%7B%20and%20%7D%20c_%7B2%7D%3D6%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7B-6%7D%7B-6%7D%3D1%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B1%7D%3D1%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D%3D%5Cfrac%7B-b%7D%7B6%7D%7D%5Cend%7Barray%7D)
As for infinitely many solutions ![\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D)
![\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%201%3D1%3D%5Cfrac%7B-b%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow6%3D-b%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20b%3D-6%7D%5Cend%7Barray%7D)
Hence b must be equal to -6 for infinitely many solutions for system of equations
and