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IrinaK [193]
3 years ago
14

Solve the system of equations using any method.

Mathematics
1 answer:
fenix001 [56]3 years ago
8 0
In addition or subtraction?
Y+8=4
Y-12=2x-8
+12
—————-
Y=2x+14
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What are the vertex, axis of symmetry, maximum or minimum value, and range of y = 3x^2 + 6x − 1?
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The vertex is when x=-b/2a, which is also the line of symmetry. 
in this case, b=6, a=3, so x=-6/6=-1
when x=-1. y=3-6-1=-4

another way to do it is to write the equation into vertex form by making a square:
3x²+6x-1
3(x²+2x-1/3)
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3(x+1)²-4

Either way, 
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Complete question :

Birth Month Frequency

January-March 67

April-June 56

July-September 30

October-December 37

Answer:

Yes, There is significant evidence to conclude that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

Step-by-step explanation:

Observed value, O

Mean value, E

The test statistic :

χ² = (O - E)² / E

E = Σx / n = (67+56+30+37)/4 = 47.5

χ² = ((67-47.5)^2 /47.5) + ((56-47.5)^2 /47.5) + ((30-47.5)^2/47.5) + ((37-47.5)^2/47.5) = 18.295

Degree of freedom = (Number of categories - 1) = 4 - 1 = 3

Using the Pvalue from Chisquare calculator :

χ² (18.295 ; df = 3) = 0.00038

Since the obtained Pvalue is so small ;

P < α ; We reject H0 and conclude that there is significant evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

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