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Few questions with this. First, in Melody's diagram, it says meters... it is supposed to be feet right? Also, the campsite is which point in the diagram?

This is a compound interest problem in a way, so we have 1/3 being the "interest". Since there are five times 1/3 is applied to the previous total, we can form the equation (1/3)^5 * 243 = (1/243) * 243 = 1.

Let  R  =  rate of the rower in still water.

Let  S  =  rate of the stream.

Downstream, the final rate is R + S.

Upstream, the final rate is R - S.

Using the formula  Distance  =  Rate x Time:

Downstream:  320  =  (R + S)(5)     --->     320  =  5R + 5S     --->     x2     --->     640  =  10R + 10S

Upstream:       320  =  (R - S)(10)    --->     320  =  10R - 10S

Combining the equations:     640  =  10R + 10S

                                              320  =  10R - 10S

Adding down the columns:   960  =  20R     --->     R  =  960 / 20  =  48 mph

To Find S:  320  =  5R + 5S     --->     320  =  5(48) + 5S     --->     320  =  240 + 5S     --->     80  =  5S     --->     S  = 16 mph     

The probability that the first marble is green:  5/20

The probability that after drawing the first green marble, the second marble will also be green:  4/19

The total probability:  5/20 x 4/19  =  20/380  =  0.0526      (you can round this answer)

If you mix 0.1 quart of oil for every 3.5 quarts of gasoline, you total mixture will be 3.6 quarts.

The percentage of oil is           0.1 / 3.6  =  0.0277777...

The percentage of gasoline is 3.5 / 3.6  =  0.9722222 ...

If there are 3 quarts of the mixture,

the amount of oil is            3 x 0.277777  =  0.0833333 quarts

the amount of gasoline is  3 x 0.972222  =  2.9166667 quarts.

If you divide the total sales from umbrellas by the revenue per umbrella you'll find the number of umbrellas.
To get the total sale from umbrellas simply subtract chair rentals (130) from the total revenue (567). Then divide the answer by the cost per umbrella (19).

Let x be number of umbrellas.

Since x*19=567-130 -> Number of umbrellas * cost = revenue 
It follows that x=(567-130)/19

Hope it helps. Cheers.

Let us say that each week, the company decreases the cost by $2.00 and the number sold will increase by 40.

Let  x  =  number of weeks

Then the number sold  =  800 + 40x

and the cost per phone  =  $80.00 - $2.00x

Revenue  =  (800 + 40x)(80 - 2x)

To graph this, rewrite as:  y  =  (800 + 40x)(80 - 2x)

 Multiply out:                     y  =  64000 + 1600x - 80x²                    (This is a parabola)

Find the vertex:                y - 64000  =  -80x² + 1600x

                                         y - 64000  =  -80(x² - 20x)

Complete the square:      y - 64000 - 8000  =  -80(x² - 20x + 100)

                                        y - 72000  =  -80(x - 10)²

So, after 10 weeks, the number sold will be 800 + 40(10)  =  1200

                                and the cost per phone will be  $80.00 - $2.00(10)  =  $60.00.

-½x + 3  =  4 - ¼x

Add ¼x to both sides:

-¼x + 3  =  4

Subtract 3 from both sides:

-¼x  =  1

The two solutions presented above are wrong.

Apologies:  I’m so use to seeing wrong answers, and the large drop in the x value (weight) are common for these types of questions;

I failed to check and verify my own work. 

These types of questions require careful reading to understand what it is asking for. 

 Such questions are common in science and statistics, both in academics and in the real-world.  

Has anyone else here found that the calculator is ironically limited, counting the fact that it is supposed to handle up to 60 digits?

Why ...Yes I have noticed that the calculator is ironically limited!

Just last week, I attempted to calculate the subtended angle of the diameter of a proton at a distance of 13.87786452158657931656064895234587541208515998456324875125489781395482315786541289653245874512458966521447802501478488219650257012045 light-years,

...and this bloody calculator just couldn’t do it with any precise accuracy! What a POS! I may as well use a slide rule. I’m ironically limited in slide rule usage –this amazingly accurate tool is decades before my time, but I have a 350 page book that explains how to use it. So, I best get to reading if I want an accurate answer.

GA

This will help

Here is a calc that will do it for you

it is not exactly 3 minutes

Nice diagram 

How do you know that answer is incorrect?

See https://web2.0calc.com/questions/help-please_82891.

Expand the following:
(x + 8)^3

(x + 8)^3 | = | sum_(k=0)^3 binomial(3, k) x^(3 - k)×8^k | 
 | = | binomial(3, 0) x^3 8^0 + binomial(3, 1) x^2 8^1 + binomial(3, 2) x^1 8^2 + binomial(3, 3) x^0 8^3 | : invisible comma 
binomial(3, 0) x^3 + 8 binomial(3, 1) x^2 + 64 binomial(3, 2) x + 512 binomial(3, 3)

The binomial coeffients comprise the 4^th row of Pascal's triangle:
=1 | | 3 | | 3 | | 1
x^3 + 3 8 x^2 + 3 8^2 x + 8^3

8^2 = 64:
x^3 + 8 3 x^2 + 64 3 x + 8^3

8^3 = 8×8^2:
x^3 + 8 3 x^2 + 64 3 x + 512

8^2 = 64:
x^3 + 8 3 x^2 + 64 3 x + 64 8

8×64 = 512:
x^3 + 8 3 x^2 + 64 3 x + 512

64×3 = 192:
x^3 + 8 3 x^2 + 192 x + 512

8×3 = 24:

x^3 + 24 x^2 + 192 x + 512

Let the distance she covered on her bike =D
Distance she walked to the cafe                =75 - D

D/9 + [75 - D] / 7 =9, solve for D
D =54 miles - that she walked !!

a +b =48, 

a=2b + 18, solve for a, b

Use substitution to get:

a = 38 and b = 10

If I understand your question !
You want to group the 10 digits from (0 to 9) in groups of 5 numbers in which 2 numbers will be of one kind and the other three of another kind. Example:00111. Is that right?

if so, then let us look at the numbers involved: Let us start with the same example as above: 00111. For the place of the first zero from the left, you have 10 choices. The same goes for the second zero. That is: 10 x 10= 100. The three "1s" can be any of the other 9 numbers, or: 9 x 9 x 9 =729. 

So, you would have: 100 x 729 =72,900. But each group of 5 numbers can have: 5! /3!2! =10 permutations.

Therefore the overall number would be:72,900 x 10 =729,000 such numbers.

Melody: Please check these numbers. Thanks.

Let the kids ticket cost = T
Adults' ticket will cost  = T + 60

347T + 225[T + 60] =33520, solve for T

T = $35 - price of a kid's ticket
$35 + $60 =$95 - price of an adult's ticket.

Let its speed upstrem =S
Its speed downstream =2S

[S + 2S] / 2 = 15,
[2S - S] / 2 = R, solve for S, R

S = 10 mph - its speed upstrem
10 x 2 =20 mph - its speed downstream
R =5 mph - the speed of the river's current.

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Hi there...

- Most Web-Browsers the last few years have "AD-Blocker"-function in their main code-base, such that people need not use 3rd-party plugins/add-ons which can be a security threat for users.
(The irony is astounding... (x-D) )

So if you take a look in your Web-Browser's settings/options there should be a way to disable this "AD-Blocker"-function.
Or at least a way for you to add "Web2.0Calc" to the "Whitelist", which then excludes it from being filtered by the "Ad-Blocker"-function.

Then you get access to the calculator yet again.

If you can't disable the "Ad-Blocker"-function or add "Web2.0Calc" to the "Whitelist", like f.ex. if a "Whitelist"-function doesn't exist in your current Web-Browser.
Then I would advise you to change over to another Web-Browser.


Kind regards...
BizzyX


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