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madam [21]
3 years ago
14

(a) How many integers in the range 1 through 120 are integer multiples of 2, 3, or 5? keyboard_arrow_down Solution (b) How many

integers in the range 1 through 140 are integer multiples of 2, 5, or 7?
Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

(a) 88 integers

(b) 92 integers

Step-by-step explanation:

(a) integers whose last digits are divisible by 2 are multiples of two or numbers whose digits ends with zero. So for number 1-120 , all the even numbers which are sixty in number are are multiples of two.

For  3, numbers whose digits sum is divisible by three are multiples of three. 3,6,9,12,15,18,21,24,27,30 are multiples of three from numbers 1-30. we have four 30s in 120. which means numbers of integers will be 10*4 = 40integers. However out of these numbers , half are also integers of 2 which reduces the number added to 20integers.

For 5, numbers whose digits ends with 5 or 0 are multiples of 5. this gives us 24 integers for 1-120. but out of these 24integers, 16 are common integers of 2 and 3 which reduces the number added to 8integers.

Thus from 1-120 the intergers of 2,3 or 5 = 60+20+8 = 88integers.

(b) if we are considering from numbers 1-140;

for 2 we wil have 70 integers,

for 5 we will have 28 integers, but those integers that end with 0 are also integers of 2 which reduces the number added to 14.

For 7, numbers 7,14,21,28,35,42,49,56,63,70 are multiples of three from 1-70. This pattern is repeated from number 71-140. hence we have 20 integers in all. However 12 of the multiples are also multiples of either 2 or 5 which reduces the number to 8 integers.

Thus from 1-140, the integers of 2, 5, or 7 = 70+14+8 = 92integers

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GenaCL600 [577]

Answer:

69 Pieces of candy

Step-by-step explanation

So you get 3 pieces of candy at every house. And you do that 23 more times. We can right that out as 23*3. Which is 69.

6 0
3 years ago
A building 50 ft high casts a 75-ft shadow. Sarah casts a 6-ft shadow. The triangle formed by the building and its shadow is sim
Rom4ik [11]
Make each known side into a ratio like so...
75/6 
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and 50/x 
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Therefore, 
75    50
----  -----
 6      x

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8 0
3 years ago
Does any one understand these questions explain if you can.
maw [93]
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r=21.645
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A=πr²
A=π•21.645²
A=1471.855. answer C is closest. difference is in how they and I rounded

2) c, e, and f
3 0
3 years ago
(5x – 3y + 8) + (-3x + 6y - 3)​
Wewaii [24]

Answer:

2x+3y+5

Step-by-step explanation:

Firstly, we remove the parenthesis since there is nothing in front of it.

There is a “+” sign in front of the parenthesis, it stays the same.

Secondly, we combine like terms. We combine the x’s, the y’s, and the normal numbers without a variable.

Finally, after combining the like terms. You end up with “2x+3y+5”.

8 0
3 years ago
Find the sum of 12a + 7b, −6a − 9, and 14a − 12b.
Ivan
The answer is:  [A]:  " 20a − 5b − 9 " .
______________________________________
Explanation:
_______________________________________________
  (12a <span>+ 7b) + (−6a − 9) + (14a − 12b) =
 
   12a </span><span>+ 7b  +  1(−6a − 9) + 1(14a − 12b) =
</span>    
   12a + 7b + (1*-6a) + (1*-9) + (1*14a) + (1* -12b) =
      
    12a + 7b − 6a − 9 + 14a − 12b =  ?

Combine the "like terms:

12a − 6a  + 14a = 20a ; 

7b − 12b =  - 5b ;

and then we have "-9" ;
_____________________________________________________
So, write as:   " 20a − 5b − 9 " ;  which is:  Answer choice:  [A].
______________________________________________________
8 0
3 years ago
Read 2 more answers
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