Shop #1 has the best price for 21 pizzas because it is $105, while Shop #2 costs $147 for 21 pizzas which is a lot more money. they would save $42, which is 147-105=42. hope this helps:)
Answer:
3x3x12= volume of large prism= 108
1x1x12= volume of hole= 12
(Volume of prism)-(volume of hole)= 96
Step-by-step explanation:
You have to go past the decimal point in since the first number in the tenths place is a zero you can't really round here so you go to the hundreds place and not so three you round down because 3 is closer to 0 then it is 10 so it would be 1. 4
Let

be an arbitrary point on the surface. The distance between

and the given point

is given by the function

Note that

and

attain their extrema, if they have any, at the same values of

. This allows us to consider the modified distance function,

So now you're minimizing

subject to the constraint

. This is a perfect candidate for applying the method of Lagrange multipliers.
The Lagrangian in this case would be

which has partial derivatives

Setting all four equation equal to 0, you find from the third equation that either

or

. In the first case, you arrive at a possible critical point of

. In the second, plugging

into the first two equations gives

and plugging these into the last equation gives

So you have three potential points to check:

,

, and

. Evaluating either distance function (I use

), you find that



So the two points on the surface

closest to the point

are

.
A. 1/5 fish
We know that 2/5 of Mike's fish are clownfish. Therefore, 3/5 are not clownish as 5/5 – 2/5 = 3/5. Also, if you look at the model, there are five pieces. If we assume that model represents the whole of Mike's fish and you take away two pieces, you are left with 3/5. So we know that the remaining fish is 3/5
Next, we know that of these 3/5 fish, 1/3 is damselfish, so we need to find 1/3 of 3/5. To do this, we must multiply 1/3 by 3/5 as "of" means multiply in Math.
So: 1/3 • 3/5 = 1 • 3/3 • 5 = 3/15 3 ÷ 3 = 1 and 15 ÷ 3 = 5 3/15 = 1/5
1/5 of Mike's fish are damsel fish
B. 2/5 fish
Now we know that 1/5 of Mike's fish is damselfish, and 2/5 is clownfish. To find the fraction of his fish that are neither, therefore, we must subtract their sum from the whole.
First, we add 1/5 and 2/5 together. Adding the numerators, 1 and 2, we get 1/5 + 2/5 = 3/5
Next, we subtract: 5/5 – 3/5 = 2/5, so 2/5 of his fish are neither clownfish or damselfish
And if you look at the model again, you can see that if you cross out 1 piece for the damselfish, and 2 pieces for the clownfish, you are left with 2/5