Fiona’s number:

when shrek asks fiona for her telephone number, fiona is a bit coy about it, and tells shrek the following information:

my telephone number has 10 digits.
there are no repeated digits in my telephone number.
the first three digits are in ascending order.
the second three digits are in descending order.
both the last four digits and the last two digits are multiples of sixty.
my last four digits are not a multiple of 43.
my first three digits are the square of an integer less than twenty.
the sum of the second three digits is 14.

what number should shrek dial?

He should dial 289-743-1560

Step-by-step explanation:

The first three digits:  "My first three digits are the square of an integer less than twenty"

Step 1:   We can get the first three by looking at the squares of the integers from 1 to 19.  We need a three digit number, so starting with 10, since 10² = 100, we list the squares of the integers from 10 to 19

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

Step 2:  "The first three digits are in ascending order" and no digits can repeat, so we eliminate the answers above that don't satisfy both of these condintions.  This leaves just 3 choices:

13² = 169

16² = 256

17² = 289

*We will come back to this once we have more information.

The last 2 numbers: "the last two digits are multiples of sixty".  

The only 2 digit number that is a multiple of 60 is 60, so 6 and 0 are the last 2 digits.  This rules out two answers from Step 1 since no digits can repeat.  Only 289 works since 169 and 256 each have a 6 in them.  So now we know the first 3, and last 2 numbers!

                                     2 8 9 _ _ _ _ _ 6 0

The last 4 numbers: "the last 4 digits are multiples of sixty"

We want to find a 4 four digit number that has 60 as the last 2 digits.  Notice a pattern when you multiply 60 by certain digits...

60 x 1 = 60

60 x 2 = 120

...

60 x 6 = 360

60 x 11 = 660

60 x 16 = 960     (these all don't work since they are not 4 digits)

60 x 21 = 1260     (this is the first 4 digit result, but it doesn't work because

                              there is a '2' in it, and 2 has already been used as the

                               first digit of the number)

60 x 26 = 1560     (this number could work, so lets try it and see if we can

                               satisfy the rest of the statements)

Now our number is

  2 8 9 _ _ _ 1 5 6 0

The second three digits:  "The second three digits are in descending order"  and "The sum of the second three digits is 14"

If we assume that 1, 5, 6 and 0 are the last four digits, we know that 2, 8 and 9 are the first three digits, this leaves 3, 4 and 7 as the three remaining digits.  

3 + 4 + 7 = 14     so that condition is satisfied.   We just need to write then in descending order, so our final number is

289-743-1560

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

ddd

step-by-step explanation: