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

Mathematics

1 answer:

sashaice [31]2 years ago

3 0

Answer:

130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

<h3>Divisible by 7</h3>

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

7n ≤ 1000

n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

<h3>Divisible by 7 and 11</h3>

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

77n ≤ 1000

n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

<h3>Divisible by 7, not 11</h3>

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

142 -12 = 130 integers divisible by 7, but not 11.

You might be interested in

simplify the mathematical expression to determine the appropriate india product or quotient in a scientific notation round round

Leno4ka [110]

From the power rules, the matching of each expression with its result is:

$(8.6*10^7)(9.1*10^{-8})=7.8$

$(6.9*10^5)(4.8*10^{-3})=3.3*10^3$

$\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}$

$\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7$

<h3>Power Rules</h3>

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and add the exponents.

2. Division with the same base: you should repeat the base and subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

From this for your question, you have:

$(8.6*10^7)(9.1*10^{-8})$ - From the distributive property of multiplication and power rules you can do: $(8.6*10^7)(9.1*10^{-8})=(8.6*9.1)*(10^7*10^{-8})=78.26*10^{-1}=7.8$

$(6.9*10^5)(4.8*10^{-3})$ - From the distributive property of multiplication and power rules you can do: $(6.9*10^5)(4.8*10^{-3})=(6.9*4.8)*(10^5*10{-3})=33.12*10^2=3.3*10^3$

$\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})}$ - From the distributive property of multiplication and power rules you can do:

$\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}$

$\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}$ - From the distributive property of multiplication and power rules you can do:

$\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7$