A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation. When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure.
The theorem should be same side interior
Step-by-step explanation:
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 35000
Alternative Hypothesis, Ha: μ < 35000
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (33450 - 35000)/(5978/sqrt(50))
z = -1.83
P-value Approach
P-value = 0.0336
As P-value >= 0.02, fail to reject null hypothesis.
There is not sufficient evidence to conclude that the average College tuition for a law degree costs at least thirty five thousand dollars.
Answer:
Option D. (x + 4)(x + 1)
Step-by-step explanation:
From the question given above, the following data were obtained:
C = (6x + 2) L
D = (3x² + 6x + 9) L
Also, we were told that half of container C is full and one third of container D is full. Thus the volume of liquid in each container can be obtained as follow:
Volume in C = ½C
Volume in C = ½(6x + 2)
Volume in C = (3x + 1) L
Volume in D = ⅓D
Volume in D = ⅓(3x² + 6x + 9)
Volume in D = (x² + 2x + 3) L
Finally, we shall determine the total volume of liquid in the two containers. This can be obtained as follow:
Volume in C = (3x + 1) L
Volume in D = (x² + 2x + 3) L
Total volume =?
Total volume = Volume in C + Volume in D
Total volume = (3x + 1) + (x² + 2x + 3)
= 3x + 1 + x² + 2x + 3
= x² + 5x + 4
Factorise
x² + 5x + 4
x² + x + 4x + 4
x(x + 1) + 4(x + 1)
(x + 4)(x + 1)
Thus, the total volume of liquid in the two containers is (x + 4)(x + 1) L.
