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3 years ago

72b384 is a number in which one of its digits is ‘b'. If the number is a multiple of 9, what is the numerical value of ‘b'?

Mathematics

1 answer:

Maslowich3 years ago

7 0

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

So, the sum of the digits of your number is

$7+2+b+3+8+4 = 24+b$

Since b ranges from 0 to 9 (it is a digit and it can't have any other values), 24+b ranges from 24 to 33. The only multiple of 9 in this range is 27, which we obtain by choosing b=3.

So, the only way to choose a value for b in order to make your number divisible by 9 is choosing b=3 and thus getting the number 723384, and indeed we have

$\dfrac{723384}{9}=80376$

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The populations of Cities A and B are 1.6 x 10^5 and 1,070,000, respectively. The population of City C is twice the population

Semenov [28]

Answer:

13.375 times

Step-by-step explanation:

1,070,000 times 2=2,140,000. 2,140,000 divided by 160,000=13.375.

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3 years ago

Can someone give me the answers and step by step instructions please??

professor190 [17]

Answer:

$-1,4,-7,10,...$ neither

$192,24,3,\frac{3}{8},...$ geometric progression

$-25,-18,-11,-4,...$ arithmetic progression

Step-by-step explanation:

Given:

sequences: $-1,4,-7,10,...$

$192,24,3,\frac{3}{8},...$

$-25,-18,-11,-4,...$

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For $-1,4,-7,10,...$ :

$4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)$

Hence,the given sequence does not form an arithmetic progression.

$\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}$

Hence,the given sequence does not form a geometric progression.

So, $-1,4,-7,10,...$ is neither an arithmetic progression nor a geometric progression.

For $192,24,3,\frac{3}{8},...$ :

$\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}$

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For $-25,-18,-11,-4,...$ :

$-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)$

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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3 years ago

Melissa used 4 cups of sugar to bake 54 cookies. If she’s only used 1 cup of sugar, what would be an equivalent ratio of cups to

daser333 [38]

Answer:

$\frac{2}{27}$

Step-by-step explanation:

We have given that melissa used 4 cups of sugar to bake 54 cookies.

That means 1 cup of sugar will be used to bake $\frac{54}{4}=\frac{27}{2}$ by unitary method

We have to find the ratio of cups to the cookies

We are using 1 cup of sugar

And cookies will be $\frac{27}{2}$

$\text{equivalent ratio}=\frac{1}{\frac{27}{2}}=\frac{2}{27}$

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3 years ago

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The volume of rectangular prism is the product of its length, width and height.
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3 years ago

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Answer:

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