The width is 2, because area you need to times the length with width.
B and C are the closest because they are only one apart. Hope this helps.
Answer: (a) 0.344578
(b) 0.211855
Step-by-step explanation: Let X represent Jill's score and Let Y represent Jack's score.
Jill's scores are approximately normally distributed with mean 170 and standard deviation 20 implies :
X ≈(170 , )
Also , since Jack's scores are approximately normally distributed with mean 160 and standard deviation, it implies
Y ≈ ( 160 , ).
It is given that their scores are independent which means that the outcome one one will not affect the outcome of the other, we the have:
Y - X ≈ N(-10 ,+ )
Y - X ≈ N(-10 ,625 )
Also , Y + X ≈ N ( 330 , 625 )
(a) We need to find the approximate probability that Jack's score is higher , that is
P ( Y > X)
=P(Y - X >0)
= P ( >
= 1 - Ф()
= 1 - Ф()
= 1 - Ф ( 0.4)
= 1 - 0.655422
= 0.344578
P ( Y > X) ≈ 0.345
(b) We need to calculate the approximate probability that their total score is above 350 , that is
P ( X + Y > 350)
= P ( > )
= 1 - Ф()
= 1 - Ф ( 0.8)
= 1 - 0.788145
= 0.211855
P ( X + Y > 350)≈ 0.212
Answer:
Step-by-step explanation:
Let's start with the equation of the volume of a cylinder:
Where:
- r is the radius of the cylinder (r=D/2=24/2=12 cm)
- h is the high of the cylinder (h = 60 cm)
We can us partial derivatives to find the differential of this volume. So we will have:
(1)
Now:
dr is a differential of the radius, so in our case it is 0.1 cm and dh, differential of the high, is 0.1*2 cm. We multiply by 2 because we need to consider the top and the bottom of the cylinder.
Now we just need to put all of this definitions in the equation (1).
I hope it helps you!
Answer:
add 9 to each side
Step-by-step explanation:
x^2 -6x = 5
Take the coefficient of the x term
-6
Divide by 2
-6/2=3
Square it
3^2 =9
Add 9 to each side
x^2 -6x+9 = 5+9
(x-3)^2=14