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The cosecant function is positive in quadrant I .

The cosine function is negative in quadrant IV .

The tangent function is negative in quadrant II .

The cosine function is positive in quadrant ​ II ​.

The cotangent function is positive in quadrant ​ III ​.     

a =x =4.5

Use Pythagorean theorem for right triangles to find the hypotenuse (distance between the towns. d)

d^2 = 5^2   + 7 ^2       solve for 'd'  miles

rate  *  time = distance

(13-c) t   = 30      13t - ct =30

(13+c) t  = 48       13t + ct = 48     add these two equations together  :   26t = 78     t = 3  

                                                                 now subtitute this value of  't'  into one of the equations to solve for 'c'

Cost will be fixed costs and costs per unit * units

c(x) == 200 000  + 300x

average will be  c(x) /x      C = ( 200 000 + 300x )/x   = 200 000/x + 300

Plug in   500   and   2000   and  4000  into C to find the average cost will go down as the number of bikes produced is increased.....

Find the length of the median of trapezoid .PQRS.

numerator =    2 ( 3 ^2/3)

denominator =  1 + 3^1/3 + 3^2/3             Multiply numerator and denominator by (1-3^1/3)

and simplify to  (after all of the steps)   to    3 - 3^2/3       or   3 - \(\sqrt[3]{9}\)

174 tix total

a = adult tix                     revenue from adult tix = $ 8a

174-a = c = children tix   revenue from child tix =  $ 6 (174-a)      the revenues summed = $ 1342

8a  + 6 (174-a) = 1342    solve for 'a' the number of adult tix .....    then 174-a = child tix

Maximum will occur at x = -b/2a =  1/ (2 ( 32/70^2)) =   4900/64 = x = 76.563 feet

Substitute this value of 'x' in to the h(x) equation to find the height at this point......

You don't say what the probability is of the Bad News Bears winning each game!  However, a similar question was asked and answered here: https://web2.0calc.com/questions/help-please_92611#r1 .  You should be able to make use of that to answer your question.

This is an arithmetic sequence as follows:

N/2 * [2*1000000004 + 5*(N - 1)] =9900000002700000000, solve for N

N =1,800,000,000 - 10-digit numbers that are divisible by 5.

1.  If x is the side length of the square then the circumference of the circle is 50 - 4x rather than 50 - x.

2. However, note that the maximum possible area that can be achieved by a piece of wire 50 inches long is when the whole wire is used to make a circle.  This results in an area of \(\pi (\frac{50}{2\pi})^2 = 198.94... in^2\)  i.e. much less than 800 in².

Yes, I'm so sorry for the confusion.

Do you want the SUM of the 10-digit number to be divisible by 5? Example:1234567890=45 which is divisible by 5.

2.5 gal water  - 1/4 gal - 5/8 gal - Lettuce gal = 3/4

2.5 - 1/4 - 5/8 - L= 3/4     solve for L the amount (in gallons) used for lettuce

I meant to write:

How many 10 digit numbers are there, such that the sum of the digits is divisible by 5?

...or    Four point two - zero - nine.    Sometimes people will say   four point two- OH- nine

Sorry, I meant to write how many 10 digit numbers are there, such of the digits is divisible by 5? The digits can be repeated.

I suppose you are wondering the least number of each (buns and dogs packages) to have the same number of each :buns = dogs

LCM of 10 and 6 is 30     so Raf would buy 5 packs of hot dogs and 3 packs of buns.

Write your question accurately !!  How many what? 4-digit, 5-digit, 6-digit numbers? And is divisible by what number?

Four and two hundred nine thousandths.

\($\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}$\)

Above is the problem.

I think your total area should be 800 square inches NOT 80 square inches.
Let x = side length of the square.
50 - x =Circumference of the circle.
[50 - x] / 2pi =Radius of the circle
x^2 + [(50 -x)/(2pi)]^2*pi = 800, solve for x
x =27.567 inches - one side of the square.
50 - 27.567 =22.433 inches - Circumference of the circle.
So that:22.433/2pi =3.57 inches - radius of the circle. 
27.567^2 + [3.57^2*pi] =~800 sq.inches.
So, the 50-inch wire should be cut into 2 pieces:
27.567 inches - being one side of the square.
22.433 inches - being the circumference of the circle.

Can you clear up all of that LaTex.....  I can't read it..... 

From A choose 10      5 choices in list B     1   fits the criteria

                          20      5                       B      2

                          30      5                       B      4  fit criteria

15 choices   7 possibles

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