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1 year ago

Find the smallest 4 digit number which is exactly divisible by 72 and 108with explaination

Mathematics

1 answer:

likoan [24]1 year ago

5 0

The smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

The Least common multiple of both the numbers 72 and 108 is 216. Since 216 is the least common multiple of both the numbers. Therefore, the four-digit number needs to be a multiple of 216 to be divisible by both the numbers. Thus, when 216 is multiplied by 5 the result is 1080, which is divisible by both 72 and 108. Hence, the smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

Learn more about Least Common Multiple:

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Find the distance between these points.<br> R(-1,0), S(8,6)<br> V(26)<br> V(85)<br> 3V(13)

Thepotemich [5.8K]

Answer:

The distance is equal to $3\sqrt{13}\ units$

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$R(-1,0)\\S(8,6)$

substitute the values

$d=\sqrt{(6-0)^{2}+(8+1)^{2}}$

$d=\sqrt{(6)^{2}+(9)^{2}}$

$d=\sqrt{36+81}$

$d=\sqrt{117}\ units$

Simplify

$d=3\sqrt{13}\ units$

4 0

3 years ago

What is the sign of a.

posledela

As a = 0 , there is no sign . Its only 0. Thus the answer is (c)

6 0

3 years ago

The average American spent $8,508 on health care in 2011. The cost of health care is projected to rise about 5.8% per year for t

klio [65]

<h3>The projected amount the average American spent on health care in 2014 is $ 10075.91</h3>

<em><u>Solution:</u></em>

Given that,

The average American spent $8,508 on health care in 2011

The cost of health care is projected to rise about 5.8% per year for the years 2012-2022

<em><u>The increasing function is given as:</u></em>

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate in decimal

t is number of years

From given,

a = 8508

$r = 5.8 \% = \frac{5.8}{100} = 0.058$

t = 2011 to 2014 = 3 years

<em><u>Substituting the values, we get,</u></em>

$y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91$

Thus the projected amount the average American spent on health care in 2014 is $ 10075.91

4 0

3 years ago

Researchers claim that 8% of people have blue eyes. Suppose the researchers' claim is true. Mrs. Greene has a Geometry class wit

vovikov84 [41]

Answer:

Probability that exactly 5 of them have blue eyes is 0.1165.

Step-by-step explanation:

We are given that Researchers claim that 8% of people have blue eyes. Suppose the researchers' claim is true. Mrs. Greene has a Geometry class with 40 students.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 40 students

r = number of success = exactly 5

p = probability of success which in our question is % of people

having blue eyes, i.e; 8%

<em>LET X = Number of students having blue eyes</em>

So, it means X ~ $Binom(n= 40,p=0.08)$

Now, Probability that exactly 5 of them have blue eyes is given by = P(X = 5)

P(X = 5) = $\binom{40}{5}\times 0.08^{5} \times (1-0.08)^{40-5}$

= $658008 \times 0.08^{5} \times 0.92^{35}$

= 0.1165

Therefore, Probability that exactly 5 of them have blue eyes is 0.1165.

7 0

3 years ago

A married man filing serpartly with a taxable income of 167,000

erastovalidia [21]

Sorry I don't see a question here but .

Knowing your income tax rate can help you calculate your tax liability for unexpected income, retirement planning or investment income. This calculator helps you estimate your average tax rate, your tax bracket, and your marginal tax rate for the current tax year.

4 0

2 years ago

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Find the smallest 4 digit number which is exactly divisible by 72 and 108with explaination​

Find the smallest 4 digit number which is exactly divisible by 72 and 108with explaination