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Delvig [45]
3 years ago
8

How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

Mathematics
1 answer:
erastovalidia [21]3 years ago
6 0
Find total number of integers.

a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51

Find how many integers is divisible by 2.

a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>

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22

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An urn contains 8 green and 9 white balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, a
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Answer:

The probability is 0.022

Step-by-step explanation:

Firstly, we need to get the total number of balls in the urn

mathematically, we have this as ;

8 + 9 = 17

now, the probability of selecting a white ball will be the number of white balls divided by the total number of balls

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4 0
3 years ago
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Answer:

The point C is 12.68 km away from the point A on a bearing of S23.23°W.

Step-by-step explanation:

Given that AB is 50 km and BC is 40 km as shown in the figure.

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The length of y-component of AC = |AB cos 80° - BC sin 20°|

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tan\theta= 5/11.65

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AC= \sqrt{5^2+11.65^2}=12.68 km

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8 0
2 years ago
3x - 20 = 4 PLEASE EXPLAIN HOW YOU GOT THE ANSWER IN STEPS!
sammy [17]

Answer:

x = 8

Step-by-step explanation:

3x - 20 = 4

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GarryVolchara [31]

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f(x) = 4x2 – 8x + 4

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=  4t^2 - 32t + 64.

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3 years ago
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