All Answers 358504 Answers

There is a formula for summing up "Consecutive squares" , but it starts at 1 and up. You could sum them up in 2 tries: From 1 to 250 and from 1 to 124 and the subtract one from the other:

n = 250; a = 1/6 * (2*n + 1)*n*(n + 1) =5,239,625

n = 124; a = 1/6 * (2*n + 1)*n*(n + 1) =643,250

5,239,625 - 643,250 = 4,596,375 - the sum of your sequence from 125^2 to 250^2

Let the total number of students =T
0.40T + 30 =0.60T, solve for T
T = 150 total number of students.
0.6 x 150 =90 are girls
0.4 x 150 =60 are boys.
0.68 x 150 =102 students, which includes 30 boys, passed the exams.
102 - 30 boys = 72 girls who passed the exams.
90 girls - 72 girls = 18 girls who did NOT pass the exams.

18 girls / 150 students = 12% of the girl students who did NOT pass the exams.

OR: 18 girls /90 girl students =20% of ALL girls in school did NOT pass the exams.
 

Great! I got it right! Thank you so much for helping me with all of my problems!! :)

180 degrees in a triangle.

180-86 = 94.

4 *

4C = 72

C = 72/4 = 18.

ThusC is 18.

It is the distance light travels in a century.

A light century = 100 light years.

I think this is a case of "partitioning" of 8 identical bats onto 4 identical racks with at least 1 bat/rack. The result of this distribution is 5 ways as follows:

5 + 1 + 1 + 1 = 8
4 + 2 + 1 + 1 = 8
3 + 3 + 1 + 1 = 8
3 + 2 + 2 + 1 = 8
2 + 2 + 2 + 2 = 8

Sink = 12 Liters
Amount drained =D
12 - D =D - 6
12+6 =2D
D =18 / 2
D =9 liters drained out of the Sink

Oh ok. :) Let me work on that

Draw in diagonal ? Its not clear which diagonal. Thanks!

Here are hints to help you get started.

First draw diagonal EG meeting FH at point X.

Since the diagonals of a parralelogram bisect eachother EX = XG.

FX and GM are thus medians of EFG so P is the centroid of EFG.

Does this help>

Here are some hints from Geno,

https://web2.0calc.com/questions/hints-only-please

I'll give you some very worthwhile direction.

1)   Think of this as a coordinate geometry prob where A is at the origin, B is on the x axis and D is on the y axis.

2) What is the side length of the big square?

3) What is the equation of QN?  What is the half length of AB

4) Arc DQPB is a quarter of a circle.  What is the equation of that circle?

5) Find Q    (intersection of a circle and a line)

6)  What is the coordinates of the centre of the two squares?  Call it X

7)  What is the distance QX?

8)  What is the diagonal lengths of the little square?

9)  Now you have all the info you need to work out the area of the little square.

If you have questions you can ask but I will want you to show me that you have put some of your own effort in.

Please no one do this for guest. This is a teaching answer.