What expression shows the relationship between the value term n

Mathematics

1 answer:

ruslelena [56]3 years ago

4 0

<span>-5n + 15 is the answer I think
I understand if it's not</span>

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A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure anti

Murrr4er [49]

With amounts measured in gallons, let

x = amount of 65% antifreeze

y = amount of 90% antifreeze

1 gal of the 65% brand contains 0.65 gal of pure antifreeze; x gal would contain 0.65x gal. Similarly, y gal of the 90% brand contains 0.90y gal of pure antifreeze.

To obtain 120 gal of 80% antifreeze solution (which contains 0.80•120 = 96 gal of pure antifreeze), we must have

x + y = 120 … … … … … [total volume of antifreeze solution]

0.65x + 0.90y = 96 … [total volume of pure antifreeze]

Solve the first equation for y :

y = 120 - x

Substitute this into the second equation and solve for x :

0.65x + 0.90 (120 - x) = 96

0.65x + 108 - 0.90x = 96

0.25x = 12

x = 48

Solve for y :

y = 120 - 48

y = 72

6 0

2 years ago

An English teacher needs to pick 9 books to put on his reading list for the next school year, and he needs to plan the order in

Nikitich [7]

Answer: $4.37\times10^3$

Step-by-step explanation:

Given : Number of choices for novels = 4

Number of choices for plays = 6

Number of choices for poetry books = 5

Number of choices for nonfiction books = 5

Total books =4+6+5+5=20

If he wants to include all 4 novels, then the number of books left to select = 9-4=5

Remaining choices for books = 20-4=16

Number of combinations of n things taking r at a time : $\dfrac{n!}{r!(n-r)!}$

Then, the number of different reading schedules are possible :_

$^4C_4\times^{16}C_5\\\\=\dfrac{4!}{4!(4-4)!}\times\dfrac{16!}{5!(16-5)!}\\\\=(1)\times\dfrac{16\times15\times14\times13\times12\times11!}{120\times11!}\\\\=4368=4.368\times10^3\approx4.37\times10^3$