By just adding the given areas, we conclude that the definite integral is equal to 3.026
<h3>
How to calculate the definite integral?</h3>
The integral will be equal to the sum of the four areas between points a and c.
The areas above the horizontal axis are positive areas, these are A and C.
While the areas below the horizontal axis are negative areas, these are B and D.
Then the definite integral will be:
I = A - B + C - D
Here we know that:
A = 1.311
B = 2.229
C = 5.545
D = 1.601
Replacing that, we conclude that the definite integral is
I = 1.311 - 2.229 +5.545 - 1.601 = 3.026
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Answer:
The GCF is 6 and the lowest term is 2/5
Step-by-step explanation:
GCF is the greatest common factor. The highest number both of the numbers can be divided by.
12 can be divided by 6 and so can 30. This number can not go any higher so 6 is the GCF
Now divide the denominator and numerator by 6.
So:
12/6 = 2
30/6 = 5
Put it together
2/5
Reduced using the GCF, 12/30 is 2/5
Based on the information given, it should be noted that the mean and standard deviation of Y will be 0.4899 and 0.699 respectively.
<h3>Calculating the mean.</h3>
Based on the information given, it should be noted that the probability distribution for y will be:
Y 0 1. 2
Probability 0.63. 0.25. 0.12
The mean of Y will be:
= (0 × 0.63) + (1 × 0.25) + (2 × 0.12)
= 0 + 0.25 + 0.25
= 0.49
The variance will be 0.4899. Therefore, the standard deviation will be:
= ✓0.4899
= 0.699
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Answer:
C
Step-by-step explanation:
We know that the volume of a cylinder is given by the formula:
And we want to find the expression that represents the volume when the radius is (x+8) and the height is (2x+3).
So, let's substitute (x+8) for r and (2x+3) for h. This yields:
Let's expand.
Expand the square term first. We can use the perfect square trinomial pattern, which is:
Here, our a is x and b is 8. So:
Simplify:
Expand further. This time, we will use the distribute property. So:
Multiply:
Combine like terms:
Add:
Distribute the π:
So, our answer is C.
And we're done!
A linear inequality contains one of the symbols of inequality: < is less than. > is greater than. ≤ is less than or equal to.