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I might be able to do the rest not so sure about 19 and 20 tho

2. An ammonia and water mixture fills a 5 gallon container. 80% of the mixture is ammonia but some of the mixture will be drained and replaced with pure water. If a 5 gallon mixture of fifty percent ammonia is desired, how many quarts of the mixture need to be drained before the water is added? (A quart is one-fourth of a gallon.) Express your answer as a decimal to the nearest tenth.

5 gallons  = 20 qts  ....and 80% ammonia   = 20% water

Let x be the number of quarts of mixture that we need to drain

So...when this is done we have    [20 -x] qts of 20% water

[20 (.20) - x(.20)]  =

[20 - x] .20

To this, we obviously need to add back  "x" quarts of  pure water  to get 20 qts of  50% water [ = 50% ammonia ]

So we have

[20 - x ] .20  +  x (1)  = 20(.50)  simplify

4  - .2x + x  = 10

.8x + 4  = 10    subtract  4 from each side

.8x + 6     dibide both sides by .8

6 / [8/10]  = x

60/ 8  = x

x  = 7.5

So...we need to drain 7.5 qts  of the 20%water soluiton...and then add back this many qts of pure water to get a 20 qt solution of 50% water

expand  (10 x^3 - 1/(2 x^2))^5=100,000 x^15 - 25,000 x^10 - 1/(32 x^10) + 2,500 x^5 + 25/(8 x^5) - 125 - the constant term.

ty but the others are different i still find it hard to understand >.<

1. We bought 2 pens and 6 pencils, the ratio of the amount we spent on pencils to the amount we spent on pens was 7:4. Later we went back and bought 4 pencils and 3 pens and spent 1 dollar less. How much money did we spend that time?

Let the cost of a pen  = x  and the cost of  a pencil  = y

So we have that  

6y / 2x  = 7 / 4

3y / x  = 7/4

3y  = (7/4)x

y = (7/12)x

And we know that

2x + 6y   = A        where A  is in dollars

2x + 6(7/12)x  = A

2x + (42/12)x  = A

2x + 3.5x  = A

5.5x   = A  = (11/2)x    (1)

And we also know that

3x + 4y  =  A  - 1

3x + 4(7/12)x  = A  - 1

3x + (28/12)x  = A  - 1

3x + (7/3)x   = A  - 1

(16/3)x  = A  - 1      sub( 1)  in for  A

(16/3)x = (11/2)x- 1    subtract (11/2)x from both sides

-1/6x  = -1

x  = 6 (dollars)  = cost of a pen

And y = (7/12)(6)  = 42/12 =  3.5  dollars = cost of a pencil

So...the first time we spent

2(6) + 6(3.5) = $33

And the second time we spent

3(6) + 4(3.5)  = $32

Let x  be the number  of software programs produced  and y be the number of video games produced

And we have these  inequalities

x <=250

y <=325

And 

x + y < = 450

And we wish to maximinze this objective proift function, P :

P  = 65x  + 40y

Here's  the graph : https://www.desmos.com/calculator/k7ivq8jnv2

The max profit will occur at the corner point  ( 250, 200)

So...produce 250 software programs and 200 video games 

Let  PQ  be one leg and QR  be the other leg

PQ  = sqrt  [ 6^2 + ( 9- 5)^2 ] =   sqrt [ 36  + 4^2 ] = sqrt [52]

QR  = sqrt [ (12 - 6)^2  + 9^2  ]  =  sqrt  [ 6^2 + 9^2 ] =  sqrt [ 117]

And the area of a right triangle  = (1/2) (product of the leg lengths)  =

(1/2)sqrt(52)sqrt(117)  = (1/2) sqrt(6084)  = (1/2) 78   =   39 units^2

(3)/(2)-(10)/(3)((13)/(2)n-(1)/(3))>=-(1513)/(18)

I'm gonig to assume  that this is :

(3/2) - (10/3)[ (13/2)n - (1/3) >=  - (1513/18)  distribute the (10/3)  over the terms in parentheses

(3/2) - (130/6)n  +  10/9  >=  - (1513 / 18)      multiply through by LCM  of  2, 6, 9 and 18  = 18

27  - 390n + 20  >= - 1513   combine like terms

47 - 390n  > = -1513       subtract 47 from  both sides

-390n > = -1560    divide both sides by -390  and reverse the ineqaulity sign

n <= 4

We have that

x + y  =  5.8  ⇒    y  = 5.8 - x    (1)

And note that rate  * time  = distance covered.....so..

5.5x + 13.5y  = 40    (2)      put (1)  into (2)  for  y   and we have

5.5x + 13.5(5.8 - x)   = 40    simplify

5.5x  + 78.3  - 13.5 x   =  40

-8x + 78.3  = 40       subtract  78.3 from both sides

-8x  = - 38.3      divide both sides by  -8

x ≈  4.8  hrs  running

And  y ≈  5.8 - x  =  5.8 - 4.8  ≈  1 hrs biking

Ohh alright! Thanks

Notice that, at 7.5 miles....that the cost of taxi "A"  becomes cheaper than the cost of taxi "B"

So...taxi "B"  is the better deal for the first 7 miles ⇒  "D"

15.  -3x ( 5x + 1) (8 - 2x)  = 

-3x ( 5x * 8 + 1*8 - 2x*5x - 2x*1) =

-3x ( 40x + 8  - 10x^2  - 2x)  =

-120x^2  - 24x  + 30x^3  + 6x^2  =

30x^3 - 114x^2  - 24x 

There's no magic to this.

There are  7 pairs that multiply to a multiple of 196.

There are 21 unordered pairs that can be made from the set.

P[product is a multiple of 196]=7/21 = 1/3

http://www.drdrum.com/

Can someone please answer this question?

Hint: .( target area of triamgle) / (whole area of triangle) = desired probability 

Answer: If you look at 6 months, the total cost is $150, (C).

Good job! You're correct, it is (A) because you have an initial fee of $2.15, then the taxi service charges $1.68 for each mile, so $2.15+1.68x, or 1.68x+$2.15! 

13. \((8x^3-6x^4+3)-(3x^3-3+8x^4)= 8x^3-6x^4+3-3x^3+3-8x^4\)\(=-14x^4+5x^3+3+3=-14x^4+5x^3+6.\)

Remember! When you have a negative sign before the parenthesis, the signs change in inside!

Ty but I still don't really understand >.<

13. When you have a negative sign before the parenthesis, the signs change in inside!

So, the answer is -14x^4+5x^3+6, after the calculations!

Use the same method for 14!

Thanks

Using the key, we find out 4|4=44, which is there! (C). 

Here is my solution:

1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000. That is 123 zeros following 1. 

I can't count that high lol

9) When you wrote No. 9 in "standard form", why did you change the signs from + to - or vice versa?

It should be: 4m^3 - 9m^2 - m + 25

10) 3/4k^5  -  1/2k^3 - you cannot separate the coefficients from variables.

11 and 12 are OK.