CPhill

If we exclude "0" as a beginning digit, we have 4 * 4!  = 96 possible numbers

The "6"  and "8"   in either the tens or thousands positions will each be larger than their neighboring digits.....

And they can be arranged in two ways.....

And given that the 6 and 8  occupy these positions....the first number can be chosen in two ways and the remaining digits can be arranged in 2 ways

So.......2 * 2 * 2  = 8 numbers are possible

So.....the probability is    8/96   =  1/12

If we subtract the "2" from both sides, we have that

√[ x + 1 ]  =  - 2

But this is impossible.....the radical will either always produce an answer  ≥ 0.....never a negative!!!!

(2/3)t - 1 < t+ 7 ≤ -2t + 15

First, we have

(2/3) t - 1 < t + 7     multiply through by 3

2t - 3 < 3t + 21    subtract  21, 2t from both sides

-24 < t

Then, we have

t + 7 ≤  -2t+ 15     add 2t to both sides, subtract 7 from both sides

3t ≤ 8    divide both sides by 3

t ≤  8/3

So......the answer is

(- 24, 8/3 ]

Total number of whiskers  =  7 *41  = 287

Take away the one with  17 whiskers  =  270 / 6  =  45 whiskers avg on the other six

Avg for 1st 10 days :

( 84 +88 + 91 + 92 + 96 + 94 + 89 + 78 + 87 + 81) / 10  =

880/10  =

88°  =   

6° above average

For 30 days....if the average temp each day was 80...then the sum of the temps must have been

(30 *80)  =  2400

So......subtracting the sum of the temps for the first 10 days - 880 -  from this we have  =  1520

So....this is the sum of the temps for the last 20 days of the month....so.....the average temp for these days  is just

1520 / 20   =     76°

Total number of people  =  5000 (2.26)   =  11300

Subtract out the 1400 single-person households [1400 people]   and we are left with

[11300 - 1400] persons /  [ 5000 - 1400] households  =

9900 / 3600  =   2.75 people in each multi-person household

14.31 (1.07)   ≈  $ 15.31

Average before removal   = ( 9 + 13+ 15+ 17+19+ 23 + 31+ 49)  / 8  = 22

Median before removal =  (17 + 19) / 2  =  18

Avg  after removal  =   24

Median after removal  = 20

19 must have been one of the numbers removed because  (17 + 23) / 2  = 20

So.....if the new average is 24......the sum of the numbers must be 24 * 6  = 144

So....the sum of the 7 numbers after 19 is removed is  157....so......13 must be the other number removed to have a sum of 144

Proof

9,15,17,23,31,49

Average = 24

Median  = 20

So...the product of the removed numbers is    19 * 13   =  247

S  =  35(x - 3)  ..... where  x  is the number put into the kiln and s is the money earned in sales

Same as the first one

S  = 12.99 ( x - 4)       where x is the number of pies made

Increase by  what  ????