Solve 4(x+3)=4x+12 for x
1 answer:
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We are given a triangle on the graph.
The vertices of the given triangle are (1,3), (-3,4) and (5,5).
The shown triangle is being transformed by the following rule
(x, y)→(x+3, y−2).
Let us apply same rule in each of the above coordinate
(1,3) →(1+3, 3 -2) → ( 4,1)
(-3,4) →(-3+3, 4 -2) → ( 0, 2)
(5,5) →(5+3, 5 -2) → ( 8, 3).
<h3>Therefore, coordinates of the transformed triangle are (4,1), (0,2) and (8,3).</h3>
Answer:
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays
against Ha : p1≠ p2 (claim) ( two sided)
The significance level is set at ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
or Z∝= 0.05/2= ± 1.96
The test statistic is
Z = p1-p2/√pq(1/n1 +1/n2)
p1= proportions of households decorating in city 1 = 45/60=0.75
p2= proportions of households decorating in city 2 = 40/50= 0.8
p = the common proportion on the assumption that the two proportion are same.
p =
Calculating
p =60 (0.75) + 50 (0.8) / 110
p= 45+ 40/110= 85/110 = 0.772
so q = 1-p= 1- 0.772= 0.227
Putting the values in the test statistic and calculating
z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)
z= -0.05/√ 0.175244 ( 110/300)
z= -0.05/0.25348
z= -0.197
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays