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\(\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:6\:\\ \:\mathrm{Interval\:Notation:}&\:[6,\:\infty \:)\end{bmatrix}\)

https://web2.0calc.com/questions/fractions_65115

You DO see they were posted at about the same time. don't you?    The first answer was posted while I was writing my solution and I didn't see it, silly!

BTW   should be    d = - 4      

Largest such number = 111
(1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 52, 53, 54, 55, 60, 61, 62, 63, 69, 70, 71, 77, 78, 79, 86, 87, 94, 95, 103, 111) >Numbers you CANNOT make up

(8, 16, 17, 24, 25, 32, 33, 34, 40, 41, 42, 48, 49, 50, 51, 56, 57, 58, 59, 64, 65, 66, 67, 68, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115..........etc.) >Numbers you CAN make up 

1. The side length of the base is 320 feet.

2. It will take 360 seconds.

3. Prism B has volume 1200 m^3.

4. The volume is 15,400 miles^3.

5. The space not taken is 400 - 80*pi cm^3.

6 , 12 , 21 , 24 , 27 , 36 , 42 , 45 , 48 , 54 , 60 , 63 , 69 , 72 , 84 , 96 , 102 , 114 , 120 , 123 , 126 , 129 , 132 , 141 , 147 , 156 , 162 , 165 , 168 , 174 , 186 , 192 , 201 , 204 , 207 , 210 , 213 , 216 , 219 , 231 , 234 , 237 , 240 , 243 , 246 , 249 , 255 , 258 , 261 , 264 , 267 , 270 , 273 , 276 , 279 , 285 , 288 , 291 , 294 , 297 , 306 , 312 , 321 , 324 , 327 , 336 , 342 , 345 , 348 , 354 , 360 , 363 , 369 , 372 , 384 , 396 , 402 , 405 , 408 , 411 , 417 , 420 , 423 , 426 , 429 , 432 , 435 , 438 , 450 , 453 , 456 , 459 , 462 , 465 , 468 , 471 , 477 , 480 , 483 , 486 , 489 , 492 , 495 , 498 , 504 , 516 , 525 , 528 , 534 , 540 , 543 , 546 , 549 , 552 , 561 , 564 , 567 , 576 , 582 , 594 , 600 , 603 , 609 , 612 , 615 , 618 , 621 , 624 , 627 , 630 , 633 , 639 , 642 , 645 , 648 , 651 , 654 , 657 , 672 , 675 , 678 , 681 , 684 , 687 , 690 , 693 , 699 , 702 , 714 , 720 , 723 , 726 , 729 , 732 , 741 , 747 , 756 , 762 , 765 , 768 , 774 , 786 , 792 , 804 , 816 , 825 , 828 , 834 , 840 , 843 , 846 , 849 , 852 , 861 , 864 , 867 , 876 , 882 , 894 , 906 , 912 , 921 , 924 , 927 , 936 , 942 , 945 , 948 , 954 , 960 , 963 , 969 , 972 , 984 , 996 , >>Total = 195 such multiples.

Why would you post this when the answer was already given?

1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11

There are:2,  4,  6,  8,  10 ==5 even numbers.

The probability is: 5/11  x  4/10  x  3/9  x  2/8  x  1/7 ==1 / 462

For what value y of is the slope of the line through P and Q equal to 1/7?

Hello Guest!

\(m=\frac{y_Q-y_P}{x_Q-x_P}\)

\(\frac{1}{7}=\frac{y-4}{4-(-3)}\\ y-4=\frac{4+3}{7}\\ y=\frac{4+3}{7}+4\\ \color{blue}y=5\)

  !

15 , 22 , 29 , 36 , 43 , 50 , 57 , 64 , 71 , 78 , 85 , 92 >>Total==12 such integers.

a5/a3 = 7/2.

Sorry.....it is correct :

    in 5 minutes   A will fill  5/20 th of the cistern    B will fill 5 / 15 th of the cistern and  C will fill 5 /12 ths of the cistern

                                         5/20                            +             5/15                                              + 5/12        = 1 complete cistern 

That answer is wrong.

840       arithmetic series   d = 4

842      geometric series   r = 1/2

840 is the original number

A three-digit even number is given such that the hundreds, tens, and unit digits respectively form a decreasing arithmetic sequence. When two is added to the number, the same order of the digits now forms a geometric sequence. What is the original number?   

840 will work.  Arithmetic sequence, the difference is –4   

842                 Geometric sequence, the multiplier is 1/2  

I complain about people who give only the answer, without explaining the steps which led to that answer. 

Sorry; I have no steps.  I just contemplated this for a little while and an answer sort of fell out of the sky. 

_.

Kelvin had some money. If he buys 3 books, he will have $12 left. If he buys 5

books, he will be short of $4. Find the cost of a book.    

Let M stand for Kelvin's money, and let B stand for the price of a book.  

M – 3B = 12      (equation 1)  

M – 5B = –4      (equation 2)  

Subtract eq 2 from eq 1  

2B = 16  which means  B = 8  i.e., The cost of one book is $8. 

You can go on to determine that Kelvin started with $36 but the problem doesn't ask for that. 

_.

YW, but your methodology was correct versus mine.  I think I made a mistake when I "rewrote" the sequence.  I think I converted it to an exponential sequence rather than a geometric sequence.  I'm not sure of that, though. 

_.

AB = 5       ra + rb = 5            (ra = radius of circle 'a'   etc)

AC = 6       ra + rc = 6

BC = 8       rb + rc = 8        

solve for the radii then you can comput the areas

ra = 5 - rb    sub into second equation

5-rb + rc = 6      multiply   eq 3  by -1   and add to this equation to get:

5 - 2 rb = -2

rb = 3.5     the ra = 1.5     rc =4.5    <============Take it from here !

p + j = 924 (2) = 1848

p = j + 232         so p = 1040     and j = 808

a = p + 172 = 1212

j / a = 808 / 1212   = 2/3

Multiply the denominator and numerator by 1-2i

(11-2i) /  5     or        11/5   - 2/5 i

1/ ( 1/20 + 1/15 + 1/12) = 120/24 minutes = 5 minutes

Rationalizing the denominator, we get

\(\displaystyle \frac{3 + 4i}{1 + 2i} = \frac{3}{2} - \frac{1}{2} i\)

The probability is 1/4.

\(57=\sqrt { (2+0!)!!+2 \over . \overline 2 } \text { by Lewis Baxter }\)