Did I do number 3 Part A right? If not may someone please explain? Thanks
1 answer:
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Answer:
The area and the perimeter of the picture are:
- <u>Area = 160 cm^2</u>
- <u>Perimeter = 67.31 cm</u>
Step-by-step explanation:
To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:
- Area of a rectangle = base * height
As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:
- Area of a rectangle = 16 cm * 12 cm
- Area of a rectangle = 192 cm^2
Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:
- Area of a triangle = (base * height) / 2
The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:
- Area of a triangle = (8 cm * 8 cm) / 2
- Area of a triangle = (64 cm^2) / 2
- Area of a triangle = 32 cm^2
We subtract to the found area:
- Area of the picture = 192 cm^2 - 32 cm^2
- <u>Area of the picture = 160 cm^2</u>
To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:
Where:
- a = Opposite leg (8 cm)
- b = Adjacent leg (8 cm)
So, we replace in the theorem:
(and we clear c)
-
- c = 11.3137085 cm
- c ≅ 11.31 cm
At last, we add all the sides of the picture begining by the base and going by the left side:
- Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
- <u>Perimeter of the picture = 67.31 cm approximately</u>.
The probability that the transistor will last between 12 and 24 weeks is 0.424
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
X~gamma()
E(X)=
=
=6 weeks
V(x)=
=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X, ,
, False)
P()
P()
P()
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
To learn more about probability click here:
#SPJ4
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder, is V = π r^2 h. It shows that the diameter is 5. But we need the radius. The radius is half of the diameter. So, 5/2. This gets you 2.5.
The equation is now:
V = π(2.5)^2h
This is the answer.