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Inessa [10]
3 years ago
13

How many positive integers less than 1000 a) aredivisibleby7? b) are divisible by 7 but not by 11? c) are divisible by both 7 an

d 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f) aredivisiblebyneither7nor11? g) havedistinctdigits?
Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

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

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Answer:

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For the second example.

If there are 550 bison in the heard this year, and this year was a decrease of 10% from last year we can express last year's number like this.

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Step-by-step explanation:

When we talk about mathematical language, the <u>difference </u>between two numbers, quantities or terms is the <u>substraction operation.</u>

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hey there!

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first you have to find the reciprocal for 2 / 5 can do that by flipping 2 / 5 you'll then get 5 / 2 now the rest is simple all you have to do is multiply 7/12 by 2/5 so you multiply 7 by 2 and you get 14 that's your numerator 10 divide 12 by 5 and you'll get 60 so now you have 14 / 60 7 / 30 now you simplify and you get

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