You convert a decimal to a fraction by putting the digits to the right of the decimal point over "1" followed by the same number of zeros. (Most folks learn this in 3rd or 4th grade.)
0.66 = 66/100 . . . . . 2 decimals, so the denominator is 100
Then you reduce the fraction by canceling common factors. It helps to know your times tables and divisibility rules. (Or you can have your calculator do it.)
0.66 = 66/100 = 33/50
1.00 = 100/100 = 1
I pray to hod for yourgood day
Answer:
Matias divided 7.6 by 10 raised to the power of -2.
Step-by-step explanation:
Given : Matias preformed an operation with 7.6 and a number. He ended up moving the decimal point in 7.6 two places to the left.
To find : Matias divided 7.6 by 10 raised to the power of ?
Solution :
Matias preformed an operation with 7.6 and a number.
He ended up moving the decimal point in 7.6 two places to the left we have to multiply it with 0.01
i.e. ![7.6\times 0.01=\frac{7.6}{100}=0.076](https://tex.z-dn.net/?f=7.6%5Ctimes%200.01%3D%5Cfrac%7B7.6%7D%7B100%7D%3D0.076)
So, Matias divided 7.6 by 10 raised to the power of -2.
Option a:
is the right answer
Step-by-step explanation:
The given expression is:
![\frac{5}{x-2} - \frac{3}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7Bx-2%7D%20-%20%5Cfrac%7B3%7D%7Bx-2%7D)
As the denominators of both terms are same, the LCM will be x-2
so
![\frac{5-3}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B5-3%7D%7Bx-2%7D)
Subtracting
![\frac{2}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx-2%7D)
Hence,
Option a:
is the right answer
Keywords: Polynomials, fractions
Learn more about polynomials at:
#LearnwithBrainly
A scatter diagram has points that show the relationship between two sets of data.
We have the following data,
![\left\begin{array}{ccccccc}\mathrm{x}&3&7&15&32&74\\\mathrm{y}&40&35&30&25&17\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5Cbegin%7Barray%7D%7Bccccccc%7D%5Cmathrm%7Bx%7D%263%267%2615%2632%2674%5C%5C%5Cmathrm%7By%7D%2640%2635%2630%2625%2617%5Cend%7Barray%7D%5Cright)
where <em>x</em> is the average number of employees in a group health insurance plan and <em>y</em> is the average administrative cost as a percentage of claims.
To make a scatter diagram you must, draw a graph with the independent variable on the horizontal axis (<em>in this case x</em>) and the dependent variable on the vertical axis (<em>in this case y</em>). For each pair of data, put a dot or a symbol where the x-axis value intersects the y-axis value.
Linear regression is a way to describe a relationship between two variables through an equation of a straight line, called line of best fit, that most closely models this relationship.
To find the line of best fit for the points, follow these steps:
Step 1: Find
and
as it was done in the below table.
Step 2: Find the sum of every column:
![\sum{X} = 131 ~,~ \sum{Y} = 147 ~,~ \sum{X \cdot Y} = 2873 ~,~ \sum{X^2} = 6783](https://tex.z-dn.net/?f=%5Csum%7BX%7D%20%3D%20131%20~%2C~%20%5Csum%7BY%7D%20%3D%20147%20~%2C~%20%5Csum%7BX%20%5Ccdot%20Y%7D%20%3D%202873%20~%2C~%20%5Csum%7BX%5E2%7D%20%3D%206783)
Step 3: Use the following equations to find intercept a and slope b:
![\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 147 \cdot 6783 - 131 \cdot 2873}{ 5 \cdot 6783 - 131^2} \approx 37.05 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 5 \cdot 2873 - 131 \cdot 147 }{ 5 \cdot 6783 - \left( 131 \right)^2} \approx -0.292\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%20%20%20%20%20%20%20a%20%26%3D%20%5Cfrac%7B%5Csum%7BY%7D%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BXY%7D%20%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%3D%20%20%20%20%20%20%20%20%20%20%20%20%20%5Cfrac%7B%20147%20%5Ccdot%206783%20-%20131%20%5Ccdot%202873%7D%7B%205%20%5Ccdot%206783%20-%20131%5E2%7D%20%5Capprox%2037.05%20%5C%5C%20%5C%5Cb%20%26%3D%20%5Cfrac%7B%20n%20%5Ccdot%20%5Csum%7BXY%7D%20-%20%5Csum%7BX%7D%20%5Ccdot%20%5Csum%7BY%7D%7D%7Bn%20%5Ccdot%20%5Csum%7BX%5E2%7D%20-%20%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%7D%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7B%205%20%5Ccdot%202873%20-%20131%20%5Ccdot%20147%20%7D%7B%205%20%5Ccdot%206783%20-%20%5Cleft%28%20131%20%5Cright%29%5E2%7D%20%5Capprox%20-0.292%5Cend%7Baligned%7D)
Step 4: Assemble the equation of a line
![\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~37.05 ~-~ 0.292 \cdot x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20y~%26%3D~a%20~%2B~%20b%20%5Ccdot%20x%20%5C%5Cy~%26%3D~37.05%20~-~%200.292%20%5Ccdot%20x%5Cend%7Baligned%7D)