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1 - Before the boys arrived, the ratio of girls to boys was: 96 / B = 4/5, solve for B

B = 120 boys.

2 - After few more boys arrived, the ratio of girls to boys: 96 / B = 2 / 3, solve for B

B = 144 boys.

3 - 144 - 120 = 24 boys arrived.

4 - The unit ratio is 96:144 == 1: 1.5

That is nicely thought through guest.   

(I haven't checked the final answer)

lightweight   very strong    resists corrosion 

Modulus  of    -2  +  8i  =sqrt  [ (-2)^2  + 8^2  ]  = sqrt [ 4 + 64 ] =  sqrt [ 68]   = sqrt [ 4 * 17 ] =  2sqrt (17)

5 (-2 + 8i)  =  -10  +  40i

a positive real number

Do you want to count them?

Assuming the same letters are not distinguishable:

There are 7! = 5040 ways to arrange 7 different letters in a line. But, since T and E are both repeated twice, the letters are overcounted by a factor of 2*2=4. therefore, the answer is 5040/4=\(\boxed{1260}\)

A)  Horizontal compression

B)   By a factor of 2

Explanation?

arc length =       2 pi   5  ( 110 /360)  =  10 pi * (11/36)  =  (110/36)pi = (55 / 18)  pi

x^2 + y^2  = 1

x coordinate =  r cos θ =  1 cos θ =  cosθ

y coordinate =  r sin θ  =  1 sin θ  =  sin θ

cos^2 θ  +  sin^2 θ  =  1

-636 +  720  =  84°  = Q1

-83  +  360   =  277°  =   Q4

145°  = Q2

442  -  360    =  82°  =   Q1

.28 * 60   =   16.8  =    16 '

,8 * 60  =  48 "

135° 16' 48"

Call S  the  number of sessions that  will   equalize the cost

4S +  50   =  6S  +  30

50  - 30  =   6S  - 4S

20  =  2S     divide  both sides  by  2

10  = S   ......10 sessions will equalize the  cost

2x^2 + 42x  +  260   =  6x

2x^2  + 42x  -  6x  +  260  =   0

2x^2   +  36x  +  260  =  0                divide  through  by  2

x^2 +  18x  +  130  =   0            

take 1/2 of 18  = 9,,,,square it  = 81....add it and subtract it

x^2  +  18x  +  81  +  130  -  81  =   0       factor   the first three terms, simplify the rest

(x  + 9)^2  +  51  =  0 

(x + 9)^2   =   -51

This is simple proportions

Let's assign variables. Let x = # of dollars Cartos receives

43 pounds/$23.65 = 200 pounds/ $x

The amount of money is multiplied by 200/43

So we have to multiply the number of dollars by that

and we get  110 dollars

\((-\infty, -8)\cup(-8,-2)\cup(-2,\inf)\)

What about 16?

I believe there are 7 because \(​​​​\lfloor\sqrt{1000}\rfloor=31~\text{and}~\lfloor\frac{31}{4}\rfloor=7\)

33 pages per day

99 pages/3 days =   33 pages/day

3 days / 99 pages =   1/33 days/page

 A classmate read 99 pages in 3 days. What's the unit rate?

to find the unit rate we need to find how many pages he reads each day. 

We divide 99/3 to find the amount he read in one day. 

99/3 = 33

A classmate read 33 pages per day. 

If that is the position function.....the derivative will show the rate of change

-3

(or : this is the same thing as the slope of the line   :  -3)

Though I do not know what units are needed !

SIX ends of tanks     6 * pi * .7²       m²                           ( . 7 is the radius)

Three tank outsides   3 * pi * 1.4 * 1.9      m²               Add these together then divide by   5  m^2 / tin   (the paint coverage )

Not always...

I am a student...

but I would presume that a lot of teachers might help!

I don't really understand what you are asking but...

if x is 50 and y 1 and the ratio is x:y 

then is y is equal to 8  you get 

50x8 = 400

You can break up the two Figure  into 2 Shapes....

The first one is...

28x28 = 724 

The Second one is 

56x14 = 724

You can get the total area by adding these..

724 + 724 = 1448