First off, there are 6 choices: 1, 2, 3, 4, 5, and 6
The probability of getting a 6 is 1/6
The probability of getting a prime number is 1/2
Multiply them and you get 1/12
The probability is 1/12.
Hope this helped!
The slope is 3, and the y-intercept is 9
Segment AB is a diameter of the sphere.
diameter = AB = 16 in.
radius = r = (16 in.)/2 = 8 in.
Volume of a sphere:
V = (4/3) * pi * r^3
V = (4/3) * (22/7) * (8 in.)^3
The water inside the bowl occupies half of the bowl, so the volume of the water is half the volume of the bowl.
Volume of water:
V = (1/2)(4/3)(22/7)(8^3) in.^3
Answer: Second choice.
Answer:
-13
Step-by-step explanation:
Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
