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it was marked as wrong when i entered two...

incorrect answer deleted.  See answer #4

we put Alice and Andrew on opposite teams.

We then have \(\dbinom{6}{3}=20\) ways to select 3 players from the remaining six for one of the teams.

Once those 3 are selected the other 3 are automatically on the other team.

In your working you treated permutations of players within a team as important.  They aren't.

Thanks @emraldwonder. I did a bit of research and also chloroplasts contain a pigment known a chloropyll. And the chloropyll absorbs all light colors but green. So the green light is then reflected onto the plant showing parts like stems and leaves green.

Again thanks for your help, I really appreciate it!

1)

The total circumference is 10 * 2pi = 20pi, and the whole circle is 360 degrees, so the answer is pi / 20 pi x 360 = 1/20 x 360 = 18 degrees.

2)

Keep in mind that the measure of each degree is 108. Because the circles have radius 1, they will not overlap with each other, and each circle's blue region is 108/360 of its whole area, or 3/10. Since there are 5 circles and each one has area pi, the answer is 3pi/2.

3)

Let's call the radius of the small circle r. Then, the side length of the square is 2r, and the diameter of the large circle is 2rsqrt2, and its radius is rsqrt2. The gray region is the large circle's area minus the small circle's. We know that pir^2 = 12, and subtracting the areas gives pir^2, so our answer is 12.

4) 

Draw lines that split the hexagon in two equal congruent pieces and go through two vertices. You will end up with 6 equaliteral triangles, so the radius of the circle is 36 / 6 = 6. This means that the circumference is 6 * 2pi = 12pi.

5) 

Call the radius of circle A r and the radius of circle B s. Then, 55r/360 = 40s/360 => 55r = 40s => 11r = 8s.

We want the ratio of the areas, and since it is 2D, we just want r^2/s^2, or (8/11)^2 = 64 / 121.

Hoping this helped,

asdf334

The answer to number one is 11, as the q(x) cannot cancel an exponent of 11 from p(x).

For number 2, let's find the ways to make an x^2 term. We can pair the -4x^2 and -7 together, the 2x and tx together, and then -5 and x^2 together. This gives 28 + 2t - 5 = 0, so 2t + 23 = 0 and t = -11.5.

Hoping this helped,

asdf334

Thank you very much for explaining it step by step! 

asdf335: You made a mistake in your "3 digits" summation. You should get: 12,600. And also in your "4 digit" summation. You should get: 166,500.

0 to 9 =45
10 to 99 =855
100 to 999 =12,600
1000 to 9999 =166,500
45 + 855 + 12,600 + 166,500 =180,000 - Sum of ALL digits from 0 to 9999.

Thanks asdf334!

If you made a mistake in your previos post, you are able to edit it :)

Also, I notice that you have images that have 'waiting for moderation" all over them. If this is happening for you, you can right click on the image you want to see select copy image address, and then go to a new tab in your browser and then paste your copied image address. Then you can see the image.

Hope this helps! :)

Could you type out the questions? :)

For number one, the parallelogram is a rhombus as one angle is 60 degrees (because equaliteral triangle), and since the triangle's perimeter is 1, the sides are 1/3 and the area is sqrt3 / 36. So, the area of the rhombus is sqrt3 / 12. We can cut it into two equaliteral triangle with area sqrt3 / 24 each, so each side is sqrt6 / 6, and the perimeter is 2sqrt6 / 3.

For number 2, we can draw a rectangle with the shorter base as one of its sides that is in the trapezoid. We know that the longer base is 18 x 2 = 36, so the part of it not contained by the rectangle's side is (36 - 18) / 2 = 9. Now we use the pythagorean theorem to get that the two congruent sides are 15, so the perimeter is 15 + 15 + 18 + 36 = 54 + 30 = 84 cm.

For number 3, if the angle between the two strips is 30 degrees, then one of the angles of the parallelogram is 30. The parallelogram is obviously a rhombus as all four sides are equal, and its area is found by multiplying the two diagonals and dividing by 2. A simple way to solve this (with some trigonometry), we noting that sine 15 and cosine 15 are (sqrt6 plus or minus sqrt2)/4, so the area of one of the triangles that the diagonals split the rhombus into is 1/2. Multiply this by 4 to get 2 sq in.

For number 4, you should define which median, as there are several medians. :)

Hoping this helped,

asdf334

Hey Android4EVER,

The images that you insterted say "Waiting for Moderation" answerers can't see the diagrams and answer. 

You should try this:

If you "right click"  on the image and select  "Copy Image Address".....you can open up a new browser  window and paste this address into it......hit "Enter"  and you should be able to see the image

Hope this Helps :)

Let's take it case by case, for when X = -2, -1, 0, and 1. Also, let the form (a, b) mean the number a on the red and b on the blue.

When X = -2, we can have (1, 3), (2, 4), (3, 5), and (4, 6).

When X = -1, we can have (1, 2), (2, 3), (3, 4), (4, 5), and (5, 6).

When X = 0, this is just doubles, so it is just when a = b, or 6 ways.

When X = 1, we just reverse a and b when X was -1, to get another 5 ways. So, there are 4 + 5 + 6 + 5 = 20 ways. To find the probability, there are 6 x 6 = 36 ways total, so the answer is 20/36 = 5/9.

Hoping this helped, 

asdf334

I assume you may have meant to say smallest, as I have seen those kinds of questions before, so I will answer both.

For largest, because a is a constant, it cannot make the largest exponent any higher, so the answer is 4.

For smallest, we want to cancel some exponents, so we can multiply g(x) by -1/2 and add to get x^4 - 3x^2 + 2 - x^4 + 3x^2 - x + 1/2 = -x + 5/2, so the degree is 1.

Hoping this helped, 

asdf334

Let's do it case by case: 1 digits, 2 digits, 3 digits, and 4 digits.

1 digit: The numbers are 1, 2, 3, 4, 5, 6, 7, 8, and 9. The digits sum to 45.

2 digits: For each group of ten numbers, there are 10 times the tens digit used plus 45. For example, 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3 + 1 + 4 + 1 + 5 + 1 + 6 + 1 + 7 + 1 + 8 + 1 + 9 = (10 x 1) + 45. Repeat this to get (10 x 1 + 10 x 2 + 10 x 3 + 10 x 4 + 10 x 5 + 10 x 6 + 10 x 7 + 10 x 8 + 10 x 9) + 45 x 9 = 10 x 45 + 45 x 9 = 19 x 45.

3 digits: We know that each group of 100's last two digits sum to 19 x 45 (above), so we just add 100 x the hundreds digit. This is 100 x 45 for each one, and then we have 100 x 45 + 19 x 9 x 45 = 171 x 45 + 100 x 45 = 271 x 45.

4 digits: Do the same process we did above to get 9 x 271 x 45 + 1000 x 45 = 3439 x 45.

Add these up to get 20 x 45 + 271 x 45 + 3439 x 45 = 291 x 45 + 3439 x 45 = 3730 x 45 = 167850.

Hoping this helped, 

asdf334

$145,000 x 20% =$29,000.00 - down payment required.
$145,000 - $29,000 =$116,000 - amount of mortgage to be borrowed.
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1} - This is the formula you would use to calculate the monthly payment:
$587.75 - The monthly payment on the mortgage. 
$587.75 x 360 months = $211,590.00 - Principal + interest that must be paid over a period of 30 years or 360 months.
$211,590.00 - $116,000 =$95,590.00 - Total amount of interest on the mortgage.

To have the shortest possible and maximum angle of elevation, we want the incline to have the maximum ratio, 12:1. So, we know that it is a right triangle with base 1 and height 12. So, our answers are tan^-1(12) and sqrt145.

Hoping this helped, asdf334

b - $45,000/12 =$3,750 - Your gross monthly income
$3,750 x 5% =$187.50 - Monthly contribution @ 5%
$3,750 x 4% =$150 - Monthly contribution @ 4%
FV =PMT{[1 + R]^N - 1 / R} - This is the formula you would use to compare the two invetments.
1 - $187.50 @ 2% for 15 years =$39,321.20
2 - $150.00 @ 4% for 15 years =$36,913.57
c - $40,000/12 =$3,333.33 - Your gross monthly income
$3,333.33 x 5% =$166.67 - Your monthly contribution @ 5%.
$3,333.33 x 4% =$133.33 - Your monthly contribution @ 4%.
1 - $166.67 @ 2% for 25 years =$64,804.82
2 - $133.33 @ 4% for 25 years =$68,548.89
d - $45,000/12 =$3,750 - Your gross monthly income
$3,750 x 4% =$150.00 - Your monthly contribution @ 4%.
$150.00 @ 4% for 25 years = $77,119.43 - Balance of your account after 25 years @ 4% comp. monthly.

I have edited the question to correct spelling and added clarification.  We are studying Right Angle Trigonometry.

(0, 4000, 8000, 12000, 16000, 20000, 24000, 28000, 32000, 36000)>>Total Sum = 180,000
(2890, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000, 4000) >>>Total Number = 38,890

We know that if \(x\) is a factor of \(n\), then \(\frac{n}{x}\) is also a factor of \(n\). Because \(90\) is not a perfect square, we can pair up the \(x\)'s and the \(\frac{n}{x}\)'s and multiply them to get \(n\). Because this is true for every number, we can count the number of factors of \(90 = 2 \cdot 3^2 \cdot 5\). We can choose 2 ways for the exponent of 2, 3 for the exponent of 3, and 2 for the exponent of 5. So, there are \(2 \cdot 3 \cdot 2 = 12\) factors. This means there are \(\frac{12}{2}=6\) paris that multiply to \(90\), and their products together is \(90^6\), so the answer is \(\boxed{k=6}\).

Hoping this helped, 

asdf334