Determine whether each piece of given information alone is sufficient to prove quadrilateral ABCD is parallelogram. Justify your
answer. Yes/No? Reason... opposite side congruent, opposite angles congruent, opposite sides parallel, consecutive angles are supplementary, diagonals bisect each other, one pair of parallel and congruent sides, not enough information? (look at the image)
1 answer:
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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
