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There are actually 63 sequences of consecutive integers between 0 and 10,000 that sum up to: 645,645.

Sequences of consecutive integers:
1  - 322822  to 322823 = 645645
2  - 215214  to 215216 = 645645
3  - 129127  to 129131 = 645645
4  - 107605  to 107610 = 645645
5  - 92232  to 92238 = 645645
6  - 64560  to 64569 = 645645
7  - 58690  to 58700 = 645645
8  - 49659  to 49671 = 645645
9  - 46111  to 46124 = 645645
10  - 43036  to 43050 = 645645
11  - 30735  to 30755 = 645645
12  - 29337  to 29358 = 645645
13  - 24820  to 24845 = 645645
14  - 21507  to 21536 = 645645
15  - 19549  to 19581 = 645645
16  - 18430  to 18464 = 645645
17  - 16536  to 16574 = 645645
18  - 15352  to 15393 = 645645
19  - 14994  to 15036 = 645645
20  - 11712  to 11766 = 645645
21  - 9901  to 9965 = 645645
22  - 9750  to 9815 = 645645
23  - 9189  to 9258 = 645645
24  - 8347  to 8423 = 645645
25  - 8239  to 8316 = 645645
26  - 7465  to 7550 = 645645
27  - 7050  to 7140 = 645645
28  - 6097  to 6201 = 645645
29  - 5815  to 5924 = 645645
30  - 4941  to 5069 = 645645
31  - 4902  to 5031 = 645645
32  - 4444  to 4586 = 645645
33  - 4116  to 4269 = 645645
34  - 3831  to 3995 = 645645
35  - 3457  to 3638 = 645645
36  - 3214  to 3408 = 645645
37  - 2970  to 3179 = 645645
38  - 2896  to 3110 = 645645
39  - 2680  to 2910 = 645645
40  - 2374  to 2631 = 645645
41  - 2229  to 2501 = 645645
42  - 2115  to 2400 = 645645
43  - 1995  to 2295 = 645645
44  - 1792  to 2121 = 645645
45  - 1485  to 1869 = 645645
46  - 1461  to 1850 = 645645
47  - 1291  to 1719 = 645645
48  - 1287  to 1716 = 645645
49  - 1192  to 1646 = 645645
50  - 1167  to 1628 = 645645
51  - 1129  to 1601 = 645645
52  - 910  to 1455 = 645645
53  - 876  to 1434 = 645645
54  - 772  to 1373 = 645645
55  - 679  to 1323 = 645645
56  - 546  to 1260 = 645645
57  - 454  to 1223 = 645645
58  - 324  to 1181 = 645645
59  - 264  to 1166 = 645645
60  - 255  to 1164 = 645645
61  - 210  to 1155 = 645645
62  - 145  to 1145 = 645645
63  - 19  to 1136 = 645645

I assumed that  a^3*b =a^3b

ab^2 + 3a^3b - ab^2 + ab^2 - a^3b - 4a^3b + 2a^3b - ab^2

Group like terms together:

ab^2 - ab^2 + ab^2 - ab^2 + 3a^3b - a^3b - 4a^3b + 2a^3b

3a^3b - a^3b - 4a^3b + 2a^3b

[3a^3b + 2a^3b] - [a^3b - 4a^3b]

[5a^3b] - [5a^3b] = 0

Very poorly worded question !

I think what you want to say is:

What consecutive integers between 0 and 10,000 sum up to: 645,645 ?

The answer is: all integers between 19 (inclusive) and 1,136 (inclusive) =645,645

645,645 mod 77 =0 - the remainder.

Your question does not make sense.

The equation is:

x = floor(x) + 8/3

This means that the value of x is equal to the greatest integer less than or equal to x, plus 8/3.

For example, if x = 1.5, then the solution is:

floor(1.5) + 8/3 = 1 + 8/3 = 5/3

Therefore, the value of x is 5/3.

2. Let the sides of the rectangular prism be l, b, and h. We know that the total surface area of the prism is 56, so we have:

2(lb+bh+lh)=56

We also know that the sum of all the edges of the prism is 64, so we have:

l+b+h=64

We can solve this system of equations to find that l=8, b=6, and h=4.

The length of the diagonal joining one corner of the prism to the opposite corner is given by:

sqrt(l^2+b^2+h^2​)=sqrt(8^2+6^2+4^2)​=sqrt(128)​=8*sqrt(2)​

Therefore, the length of the diagonal is 8*sqrt(2).

Like this:

F=Father,  S=Son

F/ 6  + S / 12 =F/9 + S/8, solve for S in terms of F

S = (4F) / 3

Since his father worked a total of: 6 + 9 = 15 hours, the son could do the same job in:

S =( 4*15) / 3 = 20 hours. 

It is also obvious that when the father works: 6+9=15 hours, the son works: 12 + 8=20 hours.

I got 4 because there are no restrictions on which point Franklin can go to and he can only move to 4 different points, not going diagonal.

thank you very much for answering but this is from practice exam where we get to see the correct answer, and the answer is 20(unless they're wrong). I just want to know how did they come up with 20. 

Seven years ago, Grogg's dad was 6 times as old as Grogg, and 4 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?

Call Grogg's age now "G" and his dad's age now "D"  

Seven years ago                           (D – 7)  =  6 * (G – 7)  

Four years ago                              (D – 4)  =  4 * (G – 4)  

Multiply them out                            D – 7  =  6G – 42          (eq 1)  

                                                       D – 4  =  4G – 16          (eq 2)  

Subtract (eq 2) from (eq 1)                – 3  =  2G – 26  

                                                           23  =  2G  

                                                             G  =  11.5  

Find D by

plugging G back into (eq 1)               D – 7  =  (6)(11.5) – 42 

                                                        D – 7  =  69 – 42  

                                                              D  =  27 + 7  

                                                              D  =  34  

Check answer by

plugging G back into (eq 2)                D – 4  =  (4)(11.5) – 16  

                                                         D – 4  =  46 – 16 

                                                               D  =  30 + 4  

                                                               D  =  34 

_.

Let's say that the father can dig a well in f hours, and the son can dig a well in s hours. We know that the father and son can dig a well if the father works 6 hours and the son works 12 hours, or they can do it if the father works 9 hours and the son works 8 hours. This means that:

61​+121​=f1​+s1​

and

91​+81​=f1​+s1​

We can solve this system of equations to find that f=18 and s=36. Therefore, it will take the son 36 hours to dig the well alone.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

Consider                                                                ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

ty so much!

Let x be your starting amount and y be your brothers. 

Then both the following equations are true. 

x-5 = y+5 

2(y-25) = x+25 

Starting with the 2nd one: 2(y-25) = x+25 

2y = x+75 

y = 1/2x + 37.5 

For the first one: x-5 = y+5 

x = y+10 

So we can plug that into our old equation. 

y = 1/2(y+10) + 37.5 

y = 1/2y+5+37.5

y = 1/2y + 42.5 

1/2y = 42.5 

y = 85

So logically, X should equal 95

The answer is 85. 

7200

By simple inspection:

a(1) = 2

a(3) = - 4

a(5) = - 10

[2  -  4  -  10] = - 12

[2 * - 4 * -10] = 80

[-4 - 2] = - 6 / 2 =- 3 - this is the common difference

So, your sequence looks like this:

2 , -1 , -4 , -7 , -10 , -13 , -16 , -19 , -22 , -25 , >>Number of terms = 10>>Total Sum == -115

So, the 10th term = -25 - with this solution. There may be others. Look for them!

The answer is 02:47.

Let the common difference of the arithmetic sequence be d. Then,

a1​+a3​+a5​=−12

a1​+(a1​+2d)+(a1​+4d)=−12

3a1​+6d=−12

a1​+2d=−4

a1​a3​a5​=80

8(a1​+2d)(a1​−2d)(a1​+4d)​=80

(a1​−2d)(a1​+2d)(a1​+4d)=64

(−4)(−2d)(−4+d)=64

8d(d−1)=64

d(d−1)=8

d=2,4

If d=2, then

a1​=−4−2d=−8

a10​=a1​+9d=−8+18=10​

If d=4, then

a1​=−4−4d=−16

a10​=a1​+9d=−16+36=20​

Therefore, the possible values of a10​ are 10,20​.

1 - LCM(2, 13) ==26. So, you could have 13 teams of 2 students each, or 2 teams of 13 students each.

But, the question says "more than 100 students signed up to participate in GB competition."

So, we have to find number > 100 that is divisible by both 2 and 13. 102 is not divisible by 13. Next 104 is divisible by both 2 and 13, because: 104 mod 13==0

Therefore, the fewest number of students that signed up was: 104 students.

Where is " as shown below" ? Learn to upload the picture with your question.

The probability of drawing ANY number is 100% or 20 / 20

The probability of the 2nd number matching the first number is: 1 / 19

Therefore, the probability of the cards matching is: 20/20 * 1/19 = 1/19 =~5.26%