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Can you show your work?

The probability is 4/17.

See answers #1 and #2 here:  https://web2.0calc.com/questions/counting-probability

There are C(4,2)*C(4,2)*(10 - 1) = 6*6*9 = 324 swappy numbers.

CH is an altitude of the triangle ABC, m∠A = 60°, m∠B = 45°. Circle with the diameter CH intersects sides AC and BC at points N and M respectively. Find the area (exact value) of the quadrilateral CMHN if AN = 1.

Area of the quadrilateral CMHN = 5.598 u²  

Let the distance from his house to the airport=D
The distance from the airport to the office =200 - D

D / 40 + (200 - D) / 80 =4, solve for D
D = 120 miles - distance from his house to the airport.
200 - 120 = 80 miles - distance from the airport to the office.

∏ [ (2^n)^(3^-n), n, 1, ∞ ] =2^(3/4) =(2^3)^(1/4)

It's not easy if you don't know how to do it.

So, they're made moderators by the admin? nice.

My mistake... it's 65°  

By similar triangles, the probability is 7/8.

Carrie places a 10-foot ladder against a wall. If the ladder makes an angle of 65° with the level ground, how far up the wall is the top of the ladder?

Height  h = 10 * sin(60°)  

By symmetry, the vertex is (6, 12).

1)  If you don't want to get too deeply involved with fractions, assume that there are 100 games.

If they have finished 75% of the season, they will have played 75 games.

If they have won 40% of the games they have played, they will have won 40% of 75 games, which are 30 games.

This also means that they have lost 75 - 30  =  45 games.

Their record is now:  30 W  and  45 L

To have a final winning percentage, they will need to end with  50 W  and  50L.

So, they will need to win  20  games and lose only  5  games.

To win  20  out of the remaining  25  games, their winning percentage will have to be:  20 / 25 =  80%  of the remaining games.

This analysis will work no matter how many games were actually played.

2)  Since Jim brought  2  gallons and Kim brought  1.75  gallons, together they brought  3.75  gallons.

To divide this evenly:  3.75  divided by  3  means that each person would have  1.25  gallons.

So, Jim will have to give Lenny  0.75  gallons and Kim will have to give Lenny  0.50  gallons.

Of the total amount (0.75 + 0.50 = 1.25 gallons), Jim will give up 0.75 gallons:  0.75 / 1.25  =  0.60  (or 60%).

Kim will give up 0.50 gallons:  0.50 / 1.25  =   0.40  (or 40%).

Therefore, Jim should get 60% of $2.00, or $1.20

and Kim should get 40% of $2.00, or $0.80.

The quadratic inequality is x^2 - 2x + 3 > 0, so b + c = (-2) + 3 = 1.

Perimeter   P = 2 * 4.5 + ( 2 * 8 * pi * 50/360 ) + ( 2 * 3.5 * pi * 50/360 )  

For this parabola, a = 6 and b = 4, so c = sqrt(36 + 16) = 2*sqrt(13).  All points on the parabola satisfy \(|PF_1 - PF_2| = 4 \sqrt{13}\)

So PF_1 = 4*sqrt(13) + 7.

Let town A population =A

Let town B population =B

A + B = 4,800........................................(1)

0.06A + 0.12B =4800 * 0.105..............(2)

Use substitution to get:

A =1,200 - population of town A

B =3,600 - population of town B

See https://web2.0calc.com/questions/geometry-proof_5

Now, I'm assuming that any 4-letter "word" is valid such as: ACST. Ordinarily, if that is the case, then you would have: 26P4 =26 x 25 x 24 x 23 =358,800 "words".

But, because you want the first and last letters the same, then will use an example to illustrate what you want. Take the word "ROAR". You have 26 choices for the first "R", 25 choices for "O", 24 choices for "A", and because we are repeating the first "R" again, you have 26 choices.

So: 26 x 25 x 24 x 26 =405,600 "words"

Hi  Madyl,

Try watching this.    

They are made moderators by the operator (owner/developer) of the site.  He is almost never active as a participant, on the forum. 

Thank you for the answer, however what is rectangular form and can someone explain rectangular form more deeply? Thanks anyways... that's a heart from me!

I tried this answer and it is correct, one of the users above got the same answer as me