All Answers 358201 Answers

The sum of the numbers is 540.

The median is 61.

No number is larger than 179.

There is only one mode.

Try this:  179, 178, 61, 61, 61.

Hugo, he does not owe me an appology.

His response was a perfectly appropriate  one. I considered it polite.  Thanks for the response Kas120W.

Do you notice I use the pronoun 'he' even though I could be talking about a female. 

There are an inadequate number of gender neutral pronouns available for use in the English language.

Besides, in my culture, 'you're right man"  IS  gender neutral.

In a circle, equal central angles create equal chords.

Angle(BEC) = angle(AED) because they are vertical angles; therefore, their chords are congruent.

You have three sums of 17 each, for a total of  3 x 17  =  51.

Yet, if you sum all the digits from 1 through 9, you only get 45.

This means that there is an overlap of 6  (51 - 45  =  6).

The overlap occurs because the three end numbers are each counted twice.

The three numbers that total to 6 are 1, 2, and 3.

So, the sum of the three corner digits is 6.

The original equation (the absolute value equation) can be graphed in parts:

If  x  <=  -23, then the equation is:    y  =  -(x + 23) - (x - 5) - (x - 48)  =  -3x + 30

If  -23  <=  x  < = 5, the equation is:  y  =  (x _ 23) - (x - 5) - (x - 48)  =  -x + 76

If  5  <= x  <= 48, the equation is:     y  =  (x + 23) + (x - 5) - (x - 48)  =  x + 66

if  x  >=  58, then the equation is:      y  =  (x + 23) + (x - 5) + (x - 48)  =  3x - 30

If you graph these, you will see that a line with a slope of 2 will intersect this graph in one point only if the

point is the intersection of the two parts:  y  =  x + 66  and  y  =  3x - 30  which occurs at  (48, 114).

For  y  =  2x + k  --->   114  =  2(48) + k   --->  k  =  18.

Att:  Hugo

Have you actually drawn the Venn diagram for yourself ?

I suspect that you have not.

If you give people suggestions you must either have solved it that way for yourself

OR

You must state clearly that it is a suggestion but you have not actually done the question or seen if your suggestion is any real value.

There is nothing more frustrating than trying to follow the obscure instruction of an answerer and then finding out later that they were totally wasting your time.  

I do not care so much where the question came from.

I am happy to help people but I want to see that they have tried to help themselves first.

You claim you have, please show me what you have done.

How to read this table:

Reading across the top row (the "has a dog" row):

--  16 persons both have a dog and have a cat

--  6 persons have a dog but do not have a cat

--  there is a total of 22 persons who have a dog

Reading across the next row (the "does not have a dog" row):

--  4 persons do not have a dog but do have a cat

--  3 persons have neither a dog nor a cat

--  there is a total of 7 persons who do not have a dog

Reading down the first column (the "has a cat" column):

--  16 persons have both a dog and a cat

--  4 persons have a cat but no dog

--  there is a total of 20 persons who have a cat

Reading down the next column (the "does not have a cat" column):

--  6 persons do not have a cat but they do have a dog

--  3 persons have neither a dog nor a cat

--  9 person do not have a cat

The 29 in the lower right-hand corner box shows the total number of people.

To answer the first question:  22 out of 29 have a dog, for a probability of 22/29.

To answer the second question:  only 3 do not have either a cat or a dog, so 26 have one or the other (or both):  26/29

Hello! Im sorry if this seems like a dumb mistake but I am pretty sure I plotted it incorrectly and I am not sure what I did wrong.

Since MN is a median of the trapezoid, MA will be the middle line of triangle(PRS) and equal to one-half the base.

This makes MA = 10.

Also BN will be the middle line of triangle(QRS) and equal to 10.

MA + BN  =  10 + 10  =  20; but they have an overlap of 7   --->   MN  =  13.

13 is one-half the sum of the two bases; since one base is 20, the other base must be 6.

Show us what you have tried.

x + y  =  10     --->     x  =  10 - y

x² + y²  =  56     --->     (10 - y)² + y²  =  56

                                     (100 - 2y + y²) + y²  =  56

                                     100 - 2y + 2y²  =  56

                                     2y² - 2y + 44  =  0

                                       y² - y + 22  =  0

Using the quadratic formula:  y  =  5 +/- sqrt(3)

                                               x  =  5 -/+ sqrt(3)

Answers:   ( 5 + sqrt(3), 5 - sqrt(3) )   and   ( 5 - sqrt(3), 5 + sqrt(3) ) 

First    sec = 1/ cos      to have a negative sec   cos must be negative (Q II and III)

- 2 sqrt 3/3  is the same as  -2/sqrt 3    and this is   1/ cos

     so cos (3x) = -sqrt 3/2

               3x = 5pi/6     and    7pi/6     

                  x = 5 pi/18            7 pi/18

x³ + y³  =  (x + y)(x² - xy + y²)

Since  x³ + y³  =  b     --->     (x + y)(x² - xy + y²)  =  b

Since  x + y  =  a         --->           a·(x² - xy + y²)  =  b     --->     x² - xy + y²  =  b/a     (equation #1)

Since  x + y  =  a     --->     (x + y)²  =  a²    

and  (x + y)²  =  x² + 2xy + y²      --->     x² + 2xy + y²​  =  a²     (equation #2)

Combining equation #2 and equation #1:     x² + 2xy + y²​  =  a² 

                                                                      x²  -   xy + y²  =  b/a 

Subtracting:                                                           3xy         =   a² - b/a

Rewriting:                                                               3xy        =  (a³ - b)/a

Dividing:                                                                   xy         =  (a³ - b) / (3a)

The modulus of complex number  a + bi  is  sqrt( a²+ b² )..

The modulus of  6 - 4i  is  sqrt( 6² + (-4)² )  =  sqrt(  36 + 16 )  =  sqrt( 52 ).

I'll leave it to you to place it into reduced radical form ...

q iii

t  i u

q iv

What is a sixth of a cupcake 

A bite.  Not a byte, a bite.

_.