Awesomeguy

Because the box is indistinguishable, we can use the reccurence relation. \(B(n,k)=B(n−1,k−1)+kB(n−1,k)\)with \(B(n,1)=1B(n,1)=1\) and \(B(n,n)=1B(n,n)=1\). For your case, you need the sum \(B(4,1)+B(4,2)+B(4,3)\). I trust you can use the formula to complete the problem.

Putting all with a base of 2,

2^10 * 2^40 * 2^120 = 2^n

Add up exponents, n = 170

January 8th, 15th, and 22nd would also be a Monday as we can add 7 to get the same day of the week. 1 day before Monday is Sunday, the 21st.

Rearranging line L_1 into intercept form, 
y = -5/8x - 9/8

If line L_2 is perpendicular, it would have slope 8/5,
y = 8/5x + b
 

Plugging in (10, -10), 

-10 = 16 + b 

b = -26

Therefore m+b is 8/5 + (-26) = -24.4 or -24 2/5

The Pascal's Triangle for (m+n)^7 has coefficients, 1, 7, 21, 35, 35, 21, 7, 1. If both m and n are odd, then either of them to the power of anything would result in an odd number. Because odd * odd is odd, and all of the coefficients are odd, I think all 8 terms would be odd

To be a multiple of 2, it would have to have a one's digit of 2, 4, 6, 8. (0 is not included as you cannot have a hundredths digit with a 0.) This makes all the possible palindromes xyx, where x is one of these digits, and y is any digit. This gives 4 possibilities for x, and 10 possibilities for y, creating 40 even palindromes. To find all of the 3 digit palindromes, it is again in format xyx, but in this case x can be any number giving 100 possibilities (10*10). 40/100 = 2/5 probability.

Because a quadrilateral angles sum up to 360 degrees, A, B, C, and D must sum to 360.

Since it's a arithmetic sequence with B being 72, we can write them as 

A, B, C, D
72-x, 72, 72+x, 72+2x

Add them all up to get, 288+2x = 360. Simplify to get x = 36, and angle D was equal to 72 + 2x, so angle D is 144 degrees.

It's already in standard form? a = 2, b = 7, c = 3

The answer is 109. We know that a supplementary angles are two angles that add up to 180, and A and B follow this rule. This means, 8x - 27 + 4x + 3 = 180. Adding like terms, we get 12x - 24 = 180, 12x = 204, and finally, x = 17. But the problem is asking for the degree measure of angle A, so, 8*17 - 27 = 109.

It would be 4 seconds. We want to find out how many seconds it will take until the ball hits the ground, making our h = 0. Adding \(-16t^2\)to both sides, we get \(16t^2 = 64t\). Dividing both sides by \(16t\) we get, \(t = 4\).