Answer:
There are 685464 ways of selecting the 5-card hand
Step-by-step explanation:
Since the hand has 5 cards and there should be at least 1 card for each suit, then there should be 3 suits that appear once in the hand, and one suit that apperas twice.
In order to create a possible hand, first we select the suit that will appear twice. There are 4 possibilities for this. For that suit, we select the 2 cards that appear with the respective suit. Since there are 13 cards for each suit, then we have
possibilities. Then we pick one card of all remaining 3 suits. We have 13 ways to pick a card in each case.
This gives us a total of 4*78*13³ = 685464 possibilities to select the hand.
Gradient of line,m=(17-6)/(20-0)=11/20
finding equation of line using a point (20,17)
y-17=11/20(x-20)
y-17=(11/20x)-11
y=11/20x+(17-11)
y=(11/20)*x+6
Answer:
The volume is decreasing at the rate of 1.396 cubic inches per minute
Step-by-step explanation:
Given
Shape: Cone
--- rate of the radius
--- rate of the height


Required
Determine the rate of change of the cone volume
The volume of a cone is:

Differentiate with respect to time (t)

Substitute values for the known variables









The volume is decreasing at the rate of 1.396 cubic inches per minute
The solution is 2sqrt77/77. You just fill in 2/3 for the x's. When you do that, you do that you get (2/3)/sqrt(9-[2/3]^2) which, simplified, is (2/3)/sqrt(9-[4/9]). Now use the common denominator under the radical of 9 to get (2/3)/sqrt([81-4]\9). Simplifying even further gives you (2/3)/([sqrt(77)]/3). Now do that division by multiplying 2/3 by the reciprocal of ([sqrt(77)]/3) to get 2/sqrt77. I rationalized the denominator to get that result up there.