Answer:
Step-by-step explanation:
Alright, lets get started.
We have given the volume of a prism that is 2400 cubic centimeters.
we have not given which type of prism it is, so we are taking it as a rectangular prism.
The formula of volume of rectangular prism is :
Where l is length of base
w is width of base
h is height of prism
So, 
So, if we factor 2400 in two different manners, we could have two different dimensions of this prism having same volume that is 2400.
So, our first factor would be :
Means the prism has base of 20 and 20 centimeters and height of 6 centimeters.
Our second factor would be :
Means the prism has base of lenght 40 and width 30 and its height is 2 centimeters.
Hence we have two dimensions of prism, 20 20 6 and another one is 40 30 2. : Answer
Hope it will help :)
Answer:
There is significant evidence to conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.
Step-by-step explanation:
Given the data :
6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7
The hypothesis:
H0: μ = 3.2
H1 : μ > 3.2
n = sample size = 12
The sample mean, xbar = ΣX / n
xbar = 53.2 / 12
xbar = 4.43
Using calculator;
Sample standard deviation, s = 2.147
The test statistic :
(xbar - μ) ÷ (s/sqrt(n))
(4.43 - 3.2) ÷ (2.147/sqrt(12)
1.23 / 0.6197855
Test statistic = 1.985
The Pvalue using the Pvalue from Tscore calculator :
Tscore = 1.985 ; df = 12 - 1 = 11
Pvalue = 0.036
Since Pvalue < α ; We reject the Null
Hence, we conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.
Answer:
48
Step-by-step explanation:
In similar polygons, every side of one polygon is a certain number of times bigger than the corresponding side of the other polygon. This number is the scale factor. Since the perimeter of each polygon is the sum of the lengths of the sides of that polygon, the perimeters also have the same scale factor that the sides do.
For example, if a triangle has 3 sides measuring 5 cm each and a similar triangle has 3 sides measuring 10 cm each, you see that each side of the second triangle is 2 times the length of the corresponding side of the first triangle. The scale factor from the smaller triangle to the larger triangle is 2. Now look at the perimeters. Since 5 + 5 + 5 = 15 and 10 + 10 + 10 = 30, the perimeters are 15 cm and 30 cm, and again, the perimeter of the second triangle is the same 2 times bigger than the perimeter of the first triangle.
Now look at your problem.
The perimeter of the smaller flag to the right is 16.
We see a side on the larger flag is 15, but we don't see the same side length on the smaller flag, so 15 does not help us.
Now we see that a side of the smaller flag measures 4 and the corresponding side of the larger flag measures 12. We divide the larger side length by the corresponding smaller side length to find the scale factor.
12/4 = 3
The scale factor from the smaller flag to the larger flag is 3. The perimeters also have the same scale factor of 3.
perimeter = 3 * 16 = 48
Answer: 48
Basically you are trying to find two numbers that when they are added equals -2 and when multiplied equals -3. As you can see -3 plus +1 is equal to -2. And 1 times -3 equals -3. Therefore you have (x+1)(x-3). In order to check if these are the right numbers you will need to multiply (x+1)(x-3) and will end up with the first equation x^2-2x-3. Hope this helped! :)
Answer:
true
Step-by-step explanation:
