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Alina [70]
3 years ago
15

Compare and contrast the absolute value of a real number to that of a complex number.

Mathematics
2 answers:
Yuki888 [10]3 years ago
7 0

The definition of complex, real and pure imaginary number is as follows:

A \ \mathbf{complex \ number} \ is \ written \ in \ \mathbf{standard \ form} \ as:\\ \\ \ (a+bi) \\ \\ where \ a \ and \ b \ are \ real \ numbers. \ If \ b=0, \ the \ number \ a+bi=a \\ is \ a \ \mathbf{real \ number}. \ If \ b\neq 0, \ the \ number \ (a+bi) \ is \ called \ an \\ \mathbf{imaginary \ number}. \ A \ number \ of \ the \ form \ bi, \ where \ b\neq 0, \\ is \ called \ a \ \mathbf{pure \ imaginary \ number}

The absolute value of this number is given by:

|a+bi|=\sqrt{a^{2}+b^{2}}

So, the absolute value of a complex number represents the distance between the origin and the point in the complex plane. On the other hand, the absolute value of a real number means only<em> how far</em> a number is from zero without considering any direction.

sveticcg [70]3 years ago
4 0
The absolute value of a real number is a positive value of the number. Which means that the absolute value is the distance from zero of the number line. However, that of the complex numbers is the distance from the origin to the point in a complex plane. 
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The table shows the number of medical clinics and the number of bowling alleys in several cities.
DedPeter [7]

Answer:

Step-by-step explanation:

a) to create a scatter plot for the data, let data for clinics be x and that one for Bowling alleys be y then plot x values with corresponding y values on a graph tool.

<u>x                     y</u>

14                   12

1                      3

6                     6

5                     7

10                    7

6                      8

11                      9

8                      15

6                       7

16                     12

The scatter plot is attached below

b) a cluster is a group of data that is close together. From the plot, the ordered pairs forming a cluster are;

(6,6), (6,7), (5,7), and (6,8)

c) An outlier is a point in a plot which lies very far from the other values. In this case, point its  point (8,15)

d)The linear regression equation is one written in the form of

Y=a+bX where ;

Y=the dependent variable

X=the explanatory variable

a=the intercept, which is the value of y when x=o

b=slope of the line

The formula to apply here is ;

a=(∑y)(∑x²)-(∑x)(∑xy) / n(∑x²)-(∑x)² where n is number of samples

b= n(∑xy)-(∑x)(∑y) / n(∑x²)-(∑x)²

Form a table like below

<u>x                     y               xy               x²                 y²</u>

14                   12              168            196              144

1                      3                 3               1                   9

6                     6                 36            36                 36

5                     7                 35             25                49

10                    7                 70             100              49

6                      8                 48             36              64

11                      9                99             121               81

8                      15               120             64            225

6                       7                42               36              49

16                     12                192            256            144

83                     86              813           871               850------------sum

∑x=83   ∑y=86  ∑xy=813  ∑x²=871  ∑y²=850 and n=10

Applying the formula

a=(∑y)(∑x²)-(∑x)(∑xy) / n(∑x²)-(∑x)²

a=[(86 * 871) - (83*813) ]/ 10 (871-83²)

a=[74906 - 67479] / 10(-6018)

a=[7427] / -60180

a= - 0.1234

b= n(∑xy)-(∑x)(∑y) / n(∑x²)-(∑x)²

b=10(813)-(83*86) / 10 (871)-(83²)

b=[8130-7138] / 8710 -6889

b= 992/1821

b=0.5448

The liner regression equation will be;

Y=a+bX

Y= -0.1234 + 0.5448 X

e) correlation coefficient r is given by;

r= n∑xy - (∑x)(∑y) / √n(∑x²)-(∑x)² × √n(∑y²)-(∑y)²

r=10*813 - (83*86) / √10 *871 -83² ×√10*850 - 86²

r=8130-7138 / √8710-6889 × √8500-7396

r= 992 / (√1821 × √1104)

r=992/ 42.67×33.23

r=992/1417.9

r=0.6996

f) r² is important because it shows you the proportion of the variance of one variable that is predictable from the other variable.

r=0.6996

r²=0.6996² =0.4894

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