Melody

Hint:

They have both travelled    135/360   of a whole circumference.

The formula for the circumference of a circle is  2*pi *r

See what you can do that with and get back to us (with what you have done) if you need more help.

If you let

\(z=a+bi\qquad and \qquad w=q+ri\)           (where a,b,q and r are real)

then it is fairly easy to prove.  Just do the substitution.

for example,

\((z+\bar w)=[a+bi+q-ri]=[(a+q)+(b-r)i]\)

do the same for the other factor and then multiply them.  The answer is real;

Your formulas are not correct Pangolin     

The surface area of a sphere is A pi cm^2 and the volume of the sphere is B pi cm^3 where both A and B are three-digit whole numbers. Find the radius of the sphere. 

I get  r=6  or  r=9

If r= 6  then A=144  and B=288

If r=9  then   A=329     and     B=989

Symbols and Truth Values Let j represent _July is a warm month._ (True)
Let d represent _I am busy every day._ (False)
Let g represent _I work in my garden._ (True)
Let f represent _I like flowers._ (True)

j = July is a warm month
d = I am NOT busy every day.
g =I work in my garden.
f =I like flowers.

For each compound statement in symbolic form: a. Write a complete sentence in words to show what the symbols represent. b. Tell whether the compound statement is true or false.

I am not sure about your notation but this is my assumptions

a. j -> g               July is a warm month so I work in my garden
b. d -> ~g            I am not busy every day so I do NOT work in my garden
c. f -> g                I like flowers so I work in my garden
d. ~g -> ~j            I do NOT work in my garden so I do NOT like flowers.

e. (j _ f) -> d
f. (j _ g) -> f

Maybe 'so' can or should be replaces with some other word, like because, or hence ... 

You will have to tell me what the underscore symbol means.

Thanks Pangolin,

You forgot that the letters and numbers can be reversed so you will need to multiply your answer by 2.

Please proofread your questions and stop wasting everyone's time.

Thanks Ginger,

Unfortunately, I really do not understand the logic behind what you have done.

I roll a die and flip three coins at the same time, and repeat this multiple times. What is the probability that I flip three heads twice in a row before I roll two 6's twice in a row?

Here is my extremely dubious attempt.

For any individual turn 

   P(HHH)=1/8      P(not HHH)= 7/8

   P(6)=1/6            P(not 6) = 5/6

For any 2 consecutive turns

   P(HHH any number, HHH not 6 (or vise versa)) = 1/8 * 1* 1/8 * 5/6 *2 = 5/192

    P(6  any number of heads, 6 not all heads, (or vise versa)) = 1/6 *1 * 1/6 * 7/8 *2 = 7/144

I am only comparing these two things so the total for comparison is  5/192 + 7/144 = 43/576

Prob of favourable outcomes / prob or relevant outcome = 5/192  divided by  43/576 = 15/43

15/43 is approximately 0.3488

I doubt very much that mine is correct, Ginger seems more confident with her answer.

Suppose g(x)=4x^2+8x+13. Does g have an inverse? If so, find g^{-1}(25). If not, enter "undef".

g(x) only has an inverse if you restrict the domain.

g(x) is a concave up parabola.  At the vertex       \(x= \frac{-b}{2a}=\frac{-8}{8}=-1\)

So if you restrict the domain to x>-1   or   X<-1     then it will have an inverse, otherwise, it does not.

Since no restriction is given, the inverse is undefined.

Anyway,  I am being pedantic with the wording, which is appropriate in mathematics.

I can never remember how to do these. Would you like to answer it for us?