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1 year ago

What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?.

Mathematics

1 answer:

Tems11 [23]1 year ago

7 0

10080 is the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8.

Divisibility is being able to divide a number evenly and result to a whole number. Divisibility rules are set of rules to test if one number is divisible by another without doing much computation.

#1: divisibility by 2

A number is divisible by 2 if its last digit is even.

# 2: divisibility by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3.

# 3: divisibility by 4

A number is divisible by 4 if the number represented by its last two digits is divisible by 4.

#4: divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

# 5: divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

# 6: divisibility by 7

Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.

#7: divisibility by 8

A number is divisible by 8 if the number represented by its last three digits is divisible by 8.

#8: divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

# 9: divisibility by 10

A number is divisible by 10 if its last digit or the digit in the ones place is 0.

To get the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8, consider first the numbers that are divisible by 5(numbers ending in 5 or 0) and narrow it down to numbers ending in 0 since numbers ending in 5 is not divisible by 2, thus making it indivisible by 6.

The process goes on by narrowing the list by checking its divisibility by 3, 4, 7 and 8.

To know more about divisibility rules, visit brainly.com/question/9462805.

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An iron cube measures 10cmx10cmx10cm. what is its volume?

Andrei [34K]

Volume of a cube is sides a3

so 10x10x10

V=1000cm

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3 years ago

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Midd

zavuch27 [327]

Given:

Total number of students at Colfax Middle School = 270

Ratio of boys to girls is 5:4.

Total number of students at Winthrop Middle School = 180

Ratio of boys to girls is 4:5.

The two schools hold a dance and all students from both schools attend.

To find:

The fraction of the students at the dance are girls

Solution:

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.

$5+4=9$

Number of boys $=270\times \dfrac{5}{9}=150$

Number of girls $=270\times \dfrac{4}{9}=120$

There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.

$4+5=9$

Number of boys $=180\times \dfrac{4}{9}=80$

Number of girls $=180\times \dfrac{5}{9}=100$

Now,

Total number of students in both schools $= 270+180$

$= 450$

Total number of girls in both schools $= 120+100$

$= 220$

The fraction of the students at the dance are girls is

$\text{Required fraction}=\dfrac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}$

$\text{Required fraction}=\dfrac{220}{450}$

$\text{Required fraction}=\dfrac{22}{45}$

Therefore, the required fraction is $\dfrac{22}{45}$ .

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3 years ago

Find all values of x for which the series converges. (enter your answer using interval notation. ) [infinity] (4x)n n = 1

andreyandreev [35.5K]

The series converges to 1/(1-9x) for -1/9<x<1/9

Given the series is ∑ $9x^{n} x^{n}$

We have to find the values of x for which the series converges.

We know,

∑ $ar^{n-1}$ converges to (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ $(9x)^{n}$ is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to 1/1-9x for -1/9<x<1/9

For more information about convergence of series, visit

brainly.com/question/15415793

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