4. The Television Chocolate Room was painter

Mathematics

1 answer:

VashaNatasha [74]3 years ago

5 0

Answer:

Step-by-step explanation:

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Hiram earned a score of 83 on his semester algebra test. Ile needs to have a total of at least 180 points from his semester and

I am Lyosha [343]

Answer:

He needs 97 to ensure his A Grade.

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2 years ago

There are 14 tops you’d like to purchase, but you can only afford six. If you select tops at random, how many different groups o

Slav-nsk [51]

Answer:

3003 different groups of 6tops

Step-by-step explanation:

Using the combination formula, generally, when selecting r number of objects out of a pool of n numbers, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If there are 14 tops I'd like to purchase and I can only afford six, the number of ways I can choose this six at random from the 14tops can be done in 14C6 number of ways.

14C6 = 14!/(14-6)!6!

14C6 = 14!/8!6!

14C6 = 14×13×12×11×10×9×8!/8!×6×5×4×3×2

14C6 = 14×13×12×11×10×9/6×5×4×3×2

14C6 = 14×13×12×11/8

14C6 = 3003ways

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3 years ago

Show that if x and y may both be written as the sum of the squares of two rational integers, then their product xy may also be w

Georgia [21]

Answer:

See proof below

Step-by-step explanation:

One way to solve this problem is to "add a zero" to complete the required squares in the expression of xy.

Let $x=m^2+n^2$ and $y=l^2+k^2$ with $m,n,l,k\in \mathbb{Z}$ . Multiplying the two equations with the distributive law and reordering the result with the commutative law, we get $xy=(m^2+n^2)(l^2+k^2)=m^2l^2+m^2k^2+n^2l^2+n^2k^2=n^2l^2+m^2k^2+m^2l^2+n^2k^2$

Now, note that $0=2lkmn-2lkmn=2nkml-2nlmk$ by the commutativity of rational integers. Add this convenient zero the the previous equation to obtain $xy=n^2l^2-2nlmk+m^2k^2+m^2l^2+2nkml+n^2k^2=(nl-mk)^2+(ml+nk)^2$ , thus xy is the sum of the squares of $nl-mk,ml+nk\in \mathbb{Z}$ .