geno3141

(3 - z) / (z + 1)  >= 1

I want to multiply both sides by (z + 1) but I have to be careful because I'll have to change the direction of the inequality sign

if I multiply by a negative. So I get two cases.

Case 1:  (z + 1)  >  0     --->     [ (3 - z) / (z + 1) ] · (z + 1)  >=  1 · (z + 1)

                      z  > -1                                                  3 - z  >=  z + 1

                                                                                      2  >=  2z

                                                                                      1  >=  z     --->     z  <= 1

              Final answer for this case:  -1 < z  and  z <= 1     or     -1 < z <=1     or     (-1, 1]

Case 2:  (z + 1)  <  0     --->     [ (3 - z) / (z + 1) ] · (z + 1)  <=  1 · (z + 1)        (switch the inequality sign)

                       z  < -1                                               3 - z  <=  z + 1

                                                                                     2  <=  2z   

                                                                                     1   <= z     --->     z >= 1

                 This is impossible because z can't be both < -1 and >= 1 at the same time.

The final answer is what we got in case 1.

I may have misunderstood the problem; if the problem is -5 < x <= 2, then the answer is (-5, 2]

Round brackets if not included; square brackets if included.

If the problem is:  -5 < x   then  x > -5    --->    (-5, infinity)

Use parentheses because the -5 is not included; infinity always gets a parenthesis.

You are to add the number that you got from spinner A (the number in the left-hand column) to the number that you

got from spinner B (the number in the top row).

So, the answer in the first empty box is the answer you get when you add the "1" from spinner A to the "2" that you 

get from spinner B.

Similarly, the answer in the next open box is the answer that you get when you add the "3" from spinner A to the "4"

from spinner B.

Etc.

a)  The way that they found that the relative frequency of rolling a 1 was by dividing the number of times that 1 occurred (11)

      by the total number of times that they rolled the die (50):  11/50  =  0.22

       To calculate the relative frequency of rolling a 4, divide the number of times that 4 occurred (9) by the total number of

       times that they rolled the die (50):  9/50  =  ????

b)  First, find the relative frequency of rolling a 5:  12/50  =   ????

      and, then, multiply that answer by the number of times that you roll the die (3000):     ?????

c)  When a fair die is rolled, each number should come up as often as any of the other numbers; since there are 6 numbers

     on a die, each number should come up about 1/6^th of the time.

     To find the number of times that you expect a 5 to come up when you roll a die 3000 times, multiply (1/6) x 3000  =   ?????

By the way, if you have only one, it is called a "die"; "die" is the singular, "dice" is the plural. You have 1 die or you

have 2 dice, or 3 dice, or ...

2)  Since she picked 100 balls and the probability that a ball is yellow is 0.10, multiply the probability times

              the total number of balls.  Number of yellow balls  =  0.10 x 100  =  ???

              Place this answer into the table.

     Since she picked a total of 100 balls and you now know the number of blue balls, red balls, and yellow

               balls, subtract to find the number of green balls.

               Place this answer into the table.

     To find the relative frequency of the blue balls, divide the number of blue balls (32) by the total number 

               of balls (100) and place this decimal into the table.

      To find the relative frequency of the red balls, divide the number of red balls (20) by the total number 

               of balls (100) and place this decimal into the table.

      Do the same process to find the relative frequency of green balls.

     If she picks another 250 balls, she should expect to get about 0.20 x 250  =  ???  more red balls.

     The total number of red balls expected would be the number you just calculated added to 20, the

       number that she already had.

1)  To estimate the number of left-handed girls in the school, take the probability that a girl is left-handed

                 and multiply it by the number of girls in the school:  0.20 x 320  =       

      To estimate the number of left-handed boys in the school, take the probability that a boy is left-handed

                 and multiply it by the number of boys in the school:  0.10 x 250  =       

      To find the final answer, add these two values together.

There are 360^o around each point.

Subtract the 72^o to get 288^o.

These degrees will be equally divided between the two polygons:  144^o.

Using the  formula for the number of degrees in each interior angle of a regular polygon: 

                    [ (n - 2)·180^o ] / n  =  144^o

Solving:                (n - 2)·180^o  =  144^o·n

                         180^o·n - 360^o  =  144^o·n

                                      36^o·n  =  360^o

                                             n  =  10

                                                                                                                            2x² - 11x + 14  =  0

Move the constant term to the other side:                                                             2x² - 11x        =  -14

Divide all terms by the coefficient of the x²-term:                                                 x² - (11/2)x      =  -7

Complete the square by

  1)  dividing the coefficient of the x-term by 2:  (-11/2) / 2  =  -11/4

  2)  squaring that number:  (-11/4)²  =  121/16

  3)  adding this term to both sides of the equation:                                   x² - (11/2)x + 121/16  =  -7 + 121/16 

Factor and combine numbers:                                                                                    (x - 11/4)²  =  9/16

Find the square root of both sides:                                                                                 x - 11/4   =   +/- 3/4

Finish:                  x - 11/4  =  3/4            x - 11/4  =  -3/4

                                      x  =  14/4                     x  =  8/4  

                                      x  =  7/2                       x  =  2

WA = WN    --->  call this length "a"

LA = LK       --->  call this length "b"

KR = RO     --->  call this length "c"

OU = UN     --->  call this length "d"

WL  =  a + b  =  12                     WL + RU  =  a + b + c + d  =  34

LR  =  b + c  =  18                                                 b + c        =  18                                (subtracting)

RU  =  c + d  =  22                                           -------------------------

UW  =  a + d  =  ?                                           a              + d  =  16

Will it always be the case that a quadrilateral that is curcumsribed around a circle will have sides such that

one pair of opposite sides will have the same total length as the other pair of opposite sides?