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Answer:
The Graph for Both is attached below.,
For line , y = 4x + 2 ......Red color Line on Graph
For line , y = -x + 7 ............Purple color Line on Graph.
Point of Intersection is ( 1 , 6 ) ....Orange Color
Step-by-step explanation:
Assume, y = 4x+2
Given:
For y = 4x + 2
Let the points be point A, and point B
To Find:
Point of Intersection of Two given lines= ?
Solution:
For Drawing a graph we require minimum two points but we will have here three points.
For y = 4x + 2
For point A( x₁ , y₁)
Put x = 0 in the given equation we get
y=4(0) + 2 =2
y=2
∴ y = 2
∴ point A( x₁ , y₁) ≡ ( 0 ,2)
For point B( x₂ , y₂)
Put y= 0 in the given equation we get
0= 4x+2
∴ point B( x₂ , y₂) ≡
Therefore,
The two points for the line 2x - 4y = 20 are
point A( x₁ , y₁) ≡ ( 0 ,-5)
point B( x₂ , y₂) ≡ (2 , 0)
Similarly,
For y = -x + 7
Put x = 0 in the given equation we get
y=-(0) + 7 =7
y=7
∴ y = 7
∴ point C( x₁ , y₁) ≡ ( 0 , 7)
For point D( x₂ , y₂)
Put y= 0 in the given equation we get
0= -x+7
∴ x = 7
∴ point D( x₂ , y₂) ≡ ( 7 , 0 )
For line , y = 4x + 2 ......Red color Line on Graph
point A( x₁ , y₁) ≡ ( 0 ,2) .....Green color point on graph
point B( x₂ , y₂) ≡ ..........Blue color point on graph
For line , y = -x + 7 ............Purple color Line on Graph
point C( x₁ , y₁) ≡ ( 0 , 7 ) .....Black color point on graph
point D( x₂ , y₂) ≡ ( 7 , 0 ) ...Red color point on graph
Point of Intersection is ( 1 , 6 ) ....Orange Color
Answer:
There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.
Step-by-step explanation:
To solve this problem, we run a hypothesis test about the population proportion.
Proportion in the null hypothesis (p0) = 0.2
Sample size (n) = 75
Sample proportion (sp) = 24/75 = 0.32
Significance level = 0.01
H0: p = 0.2
Ha: p 0.2
Test statistic = (sp - p0) / sqrt ((p0) (1-p0) / n)
Left critical Z value (for 0.01) = -2.5758
Right critical Z value (for 0.01) = 2.5758
Calculated statistic = (0.32 - 0.2) / sqrt ((0.32) (1-0.32) / 75) = 2.2278
Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.