Answer:
Between 19 and 55, inclusive
Step-by-step explanation:
70 < Average < 79 (inclusive)
4×70 < sum < 4×79 (inclusive)
280 < sum < 316
280 < 92 + 84 + 85 + X < 316
280 < 261 + X < 316
19 < x < 55
Fourth score can be between 19 and 55, inclusive
Answer:
1/10000
Step-by-step explanation:
10 ^ -4
a^ -b = 1/a^b
1 / 10^4
1/10000
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
<h3>What is a triangle?</h3>
A triangle is a 2-D shape with 3sides and angles. According to the question, we are to determine whether the given measures form sides of a triangle.
For the following measure to form the sides of a triangle, the sum of any two sides must be equal to the third as shown:
3 + 12 = 15 > 13
3 + 13 = 16 > 12
13 + 12 = 25 > 3
Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle
Learn more triangle here: brainly.com/question/2217700
#SPJ1
Answer:

Step-by-step explanation:
Given
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
Required
Find 
We have:
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
Using integration by parts

Where
and 
Solve for du (differentiate u)

Solve for v (integrate dv)

So, we have:




-----------------------------------------------------------------------
Solving

Integration by parts
---- 
---------- 
So:



So, we have:

![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7Bx%5E2%7D%7B4%7De%5E%7B-4x%7D%20%2B%5Cfrac%7B1%7D%7B2%7D%20%5B%20-%5Cfrac%7Bx%7D%7B4%7De%5E%7B-4x%7D%20%20-%5Cfrac%7B1%7D%7B4%7De%5E%7B-4x%7D%5D)
Open bracket

Factor out 
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7Bx%7D%7B8%7D%20-%5Cfrac%7B1%7D%7B8%7D%5De%5E%7B-4x%7D)
Rewrite as:
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7B1%7D%7B4%7Dx%5E2%20-%5Cfrac%7B1%7D%7B8%7Dx%20-%5Cfrac%7B1%7D%7B8%7D%5De%5E%7B-4x%7D)
Recall that:
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7B1%7D%7B64%7DAx%5E2%20-%5Cfrac%7B1%7D%7B64%7D%20Bx%20-%5Cfrac%7B1%7D%7B64%7D%20E%5DCe%5E%7B-4x%7D)
By comparison:



Solve A, B and C

Divide by 

Multiply by 64



Divide by 

Multiply by 64



Multiply by -64


So:


Answer:
x = 77 degrees
Step-by-step explanation:
To get the value of x, we use the angle arc relationship
Mathematically, we have this as follows;
x = (76 + 78)/2
x = 77