How many positive integers less than 1000 a) aredivisibleby7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f) aredivisiblebyneither7nor11? g) havedistinctdigits?

a.142 b.130 c.12 d.220 e.208 f.779 g.720

Step-by-step explanation:

How many positive integers less than 1000 (from 1 to 999)

a) are divisible by 7?

999/7=142,71

then there are 142 integers that are divisible by 7

7*1=7

7*2=14

7*3=21

...

7*141=987

7*142=994

b) are divisible by 7 but not by 11?

as 7 and 11 are prime numbers

7*11=77

999/77=12.97

142-12=130

c) are divisible by both 7 and 11?

999/77=12.97

then there are 12 integers that are divisible by both 11 and 7 below 1000

d) are divisible by either 7 or 11?

999/7=142.71

999/11=90.81

then the numbers that are divisible either by 7 or 11 is

142+90-12(the numbers that are counted in both grups 'divisible by 7' and 'divisible by 11')

220

e) are divisible by exactly one of 7 and 11?

[142('divisible by 7')-12('divisible by both')]+[90('divisible by 11')-12('divisible by both')]

208

f) are divisible by neither 7 nor 11?

999('all the positive integers below 1000)-220('are divisible by either 7 or 11')

779

g) have distinct digits?

For evey digit x from 0 to 9

0xx,1xx,2xx,3xx,4xx,5xx,6xx,7xx,8xx,9xx 10 options

xx0,xx1,xx2,xx3,xx4,xx5,xx6,xx7,xx8,xx9 10 options

x0x,x1x,x2x,x3x,x4x,x5x,x6x,x7x,x8x,x9x 10 options

and xxx one option

for each of the first three rows we have to sustract the option in wich the three digits are the same digit.

for the 0 we have to sustract the 000 of the fourth row as it is not a positive number.

10 (different digits)*(9+9+9+1)(different combinations for each number)-1(the 000)=279

999-279=720

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98