Your formula for the probability checks out.

This is what I am getting for the expectation

where the horizontal axis is the waiting time and the vertical is the expected time to wait. But it was done while I am half asleep and needs some checking.

The formula that produces this graph is the piecewise function:

Surprisingly this says that the expected waiting time is 10 after t >= 30.

]]>I don't know G well enough to do anything clever, like somehow using (coding?) it to actually give the solution. Would be nice to include that, if it can be done.

Until I saw that I could plug figures into point E (the string vertex), I just grabbed E and manipulated it vertically (while also adjusting display size) towards or away from the earth until the sum of the length of the two tangents was as close to 100 feet greater than the length of the earth's arc between the tangents as I could get it.

I'd have to think about it...

]]>I am pasting the question in on behalf of my son, he has gone to bed.

I hope this makes sense

"Erica and William enjoy playing the game Snakes and Ladders.
In one game they noticed that after they had both thrown twice they were both at the foot of the same ladder which took them to square 53.

After two more throws each, they both arrived at the head of a snake and moved down to square 4.

Each time, they threw completely different numbers. The total of the first two throws was 4 more than the total of the second two throws. Also, in the four throws, Erica did not roll the same number more than once and neither did William.

Which numbered square was at the foot of the ladder and which square was at the top of the snake? "

Thank you for your help

]]>Of these 7, due to juvenile bird mortality rates 3 come of age at 3 years old and go on to produce their own off spring for their breeding life.

Is that mortality rate yearly?

]]>[math]

For the first problem, I'm compelled to just add up the numbers, but that doesn't seem right... .

]]>

Hi! I need help. How should you convert the summation of 5n-3 into an equation?

You mean into an expression.?

]]>I have seen this type of question but in it AD was the median if it is the median then

in triangle ABC

(AB)²+(AC)²=(BC)²=81

in triangle ACD

angle ADC is 90 degree as AD is median

x²+36=(AC)² x²=(AC)²-36

and similarly triangle ABD

x²+9=(AB)² x²=(AB)²-9

(AB)²=(AC)²-36+9=(AC)²-27

(AB)²-(AC)²=-27

(AB)²+(AC)²=81

adding equations

2(AB)²=81-27

AB=3√3

x=3√2

I think you are considering AD as altitude, not a median.

If AD is altitude AD^2=BD*CD which gives the result quickly.This was derived considering similar triangles but a problem set on Pythagoras theorem has to be done accordingly.

Note that the sign would acually be if you included 0 in your definition of natural numbers.]]>sorry i do not know to work it out from here i tried factorising but didnt get anywhere

Please help answer these.

State whether the following are given, unfounded or covered by a particular definition. Provide the explanation for your selection:

1. If I have two coplanar lines, I must have a plane.

2. There are two adjacent angles whose outside edges form a straight line. The measure of the first angle is 100 degrees, so the measure of the other must be 80 degrees

3. I have drawn a polygon with eight sides, so it must be an octagon.

4. A square has two diagonals.

5. If the diameter of the circle is 12, the radius must be 6.

Use the following images for questions 6 through 10:

6. In the figure above, line segment MC is equal to imaginary line segment MI.

7. In the figure above, line segment EJ is equal to line segment JM.

8. In the figure above, the measure of angle AMC is 90 degrees.

9. In the figure above, the measure of arc AC is 90 degrees

10. In the figure above the measure of angle AME is x degrees, then the measure of angle EMB is 180-x degrees.

11. In a right triangle where one side is 3, and the hypotenuse is 5, the remaining side must be 4.

12. In a triangle, if I have two angles that add up to 50 degrees, the remaining angle must be 130 degrees.

13. The diameter of a circle always passes through the midpoint of the circle.

14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.

15. The area of a sphere is 4 times the area of a circle with the same radius.

16. If a radius bisects a chord, then the lengths of the parts of the radius on either side of the chord are equal.

17. If a circle has a central point M, and both point A and point D are on the circle, then ls_MA and ls_MD will be equal.

18. If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53).

19. The given points (4, -8), (4, -5), and (-2, -6) make a right triangle.

20. The given points (2, -3), (-7, -7), (2, -7), and (-7, -2) make a square.

The diagram we have sen a few days back.

]]>Bob

]]>-2 is not yet a factor as the 2 in the second term is + not -

But two minuses make a plus ie. -- is the same as + so I can re-write the expression as

Now -2 and y are common factors so we can move them to a single expression outside a bracket for the remainder.

Notice I have put in an extra x 1 so that there is something in the second part of the bracket and not just an empty space or worse still a zero.

You can test whether you have factorised correctly by multiplying out:

Hope that helps.

Bob

]]>