CPhill

210°  =    30°  reference angle in the  3rd quadrant.......the coordinates  are  ( -√3/2  ,-1/2)

-7pi /4  =   2pi - 7pi/4 =  8pi /4  - 7pi/4 =  pi / 4 = 45°  ....the coordinates are  (√2/2, √2/2)

34pi/3  = 11pi + pi/3  =  240°   = 60°refernce angle in the 3rd quadrant.....the coordinates are  ( -1/2, -√3/2)

Rate * Time  =  Distance

So....you just need to evaluate this :

90 * 3    +  1.5 ( 72)    =      Total Distance

Let the price  of a zucchini  = Z

Then....let the price of a kiwi  = Z  +  .25

And we know that

3 (Z + .25)  +   4(Z)  =  4.95     simplify

4Z +  3Z  +  .75  = 4.95         subtract  .75 from both sides

7Z  =  4.20     divide both sides  by  7

Z =  .60   = the price of a zucchini

Z + .25 =  .85  = the price of a kiiwi

The total possible arrangements  are  9!  = 362800   arrangements

If we  count the ones  where NO  women stand next to each other  ....then note that the women can occupy

positions   1 - 3 - 5 -7   or  2 - 4 -6 - 8   or   3 - 5 -7 - 9  =  3  ways

And for each of these the women can be arranged in 4! = 24 ways

And  for each of these the men can be arranged  in 5!   =120 ways

So....the    number of  arrangements where at least two of the women stand to each other  =

9!  -  (3) (24)(120)  = 

362800 - 8640  =

354,240  possible arrangements

Let the width   = W

Let the length =  W + 3

The perimeter  =  2 ( W + L)

So

58 =  2 ( W  + (W + 3) )      divide both sides by  2

29  = 2W + 3         subtract  3  from both sides

26  = 2W     divide both sides  by  2

13 = W  = the width

And the length  = W + 3   = 16

2)

Find a such that ax^2+15x+4 is the square of a binomial.

For this to be true.....we need to have that the discrimant  must  = 0

So

15^2  - 4a (4)   = 0

225  - 16a  = 0

225 =  16a

a =  225 /16

If we take the positive square root of this we have   15/4

And note that   (15/4 x + 2)^2 =  (225/16)x^2 + 2 (15/4)(2)x  + 4  =  (225/16)x^2 + 15 x + 4

(1)

(2x+7)(x-5) = -43 + jx       simplify the left side

2x^2 + 7x -10x  - 35  =  -43 + jx          rearrange as

2x^2  + (7 - j)x  + 8  = 0

If this has one real solution.....then the discriminant must   = 0

So

(7 -j)^2  - 4 (2)(8)   =0     

49 - 14j + j^2  - 64  =  0      rearrange as

j^2 -14j - 15  = 0      factor as

(j -15) ( j + 1)   = 0

Set both facotrs to 0   and solve for j  and we get that

j  =15      and j = -1

So....we will have one real solution when  j = -1  or j  =15

See the graph here to confirm this  :  https://www.desmos.com/calculator/dw6lnjpnm7

That was my original answer, too, Geno

But...as EP  pointed out to me,  we  both interpreted this as  eating all the chocolate chips  BEFORE eating ANY of the butter cookies....however......the question seems to be implying  that we want the probability of  eating all the chocolate chips  BEFORE eating ALL the butter cookies.......this answer is probably somewhat different

One number is 10 more than another.  The sum of twice the smaller plus three times the larger, is 55.  What are the two numbers?

Let  x  be the smaller number  and x + 10  the larger....so.....

2x +3(x +10)  = 55

5x + 30  = 55

5x  =25

x  = 5     =  the smaller

x + 10  = 15  =  the larger

It takes 23 minutes for 6people to paint 6 walls.  How many minutes does it take 9people to paint 9walls

In one minute,   the   6 people will  paint   6/23   of a wall

So....in one minute....one person  will  paint  1/23  of a wall

So.....9 people will paint  9/23  of a wall  in one minute

So.....in 23 minutes.....they will paint  9 walls