Pick 1: 6 yellow out of 15 total marbles = 6/15 = 2/5
Pick 2: 6 yellow out of 15 total marbles = 6/15 = 2/5
Pick 1 AND Pick 2
2/5 x 2/5 = 4/25
C D and F because it’s a set rate. 50miles PER hour $10 EACH pizza 5 points for EVERY CORRECT test question. It shows a direct correlation.
Answer:
a = 1, b = 2, c = 3
Step-by-step explanation:
Answer:
2/5 or 2:5
Step-by-step explanation:
Face Card:
The face cards in a deck are the Jack, Queen, and King. There are 4 of each card (1 in each suit), for a total of 12 face cards.
Spade:
1/4 of all the cards in a deck are spades, so 52/4= 13 spades.
When added, the numerator of the probability is 25, however, because the Jack, Queen, and King of Spades are duplicated, we have to subtract 3.
25-3=22
22/55
when simplified: 2/5
The dimensions of a box that have the minium surface area for a given Volume is such that it is a cube. This is the three dimensions are equal:
V = x*y*z , x=y=z => V = x^3, that will let you solve for x,
x = ∛(V) = ∛(250cm^3) = 6.30 cm.
Answer: 6.30 cm * 6.30cm * 6.30cm. This is a cube of side 6.30cm.
The demonstration of that the shape the minimize the volume of a box is cubic (all the dimensions equal) corresponds to a higher level (multivariable calculus).
I guess it is not the intention of the problem that you prove or even know how to prove it (unless you are taking an advanced course).
Nevertheless, the way to do it is starting by stating the equations for surface and apply two variable derivation to optimize (minimize) the surface.
You do not need to follow with next part if you do not need to understand how to show that the cube is the shape that minimize the surface.
If you call x, y, z the three dimensions, the surface is:
S = 2xy + 2xz + 2yz (two faces xy, two faces xz and two faces yz).
Now use the Volumen formula to eliminate one variable, let's say z:
V = x*y*z => z = V /(x*y)
=> S = 2xy + 2x [V/(xy)[ + 2y[V/(xy)] = 2xy + 2V/y + 2V/x
Now find dS, which needs the use of partial derivatives. It drives to:
dS = [2y - 2V/(x^2)] dx + [2x - 2V/(y^2) ] dy = 0
By the properties of the total diferentiation you have that:
2y - 2V/(x^2) = 0 and 2x - 2V/(y^2) = 0
2y - 2V/(x^2) = 0 => V = y*x^2
2x - 2V/(y^2) = 0 => V = x*y^2
=> y*x^2 = x*y^2 => y*x^2 - x*y^2 = xy (x - y) = 0 => x = y
Now that you have shown that x = y.
You can rewrite the equation for S and derive it again:
S = 2xy + 2V/y + 2V/x, x = y => S = 2x^2 + 2V/x + 2V/x = 2x^2 + 4V/x
Now find S'
S' = 4x - 4V/(x^2) = 0 => V/(x^2) = x => V =x^3.
Which is the proof that the box is cubic.
