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Amiraneli [1.4K]
3 years ago
14

The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number

. What is the original number?
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
7 0

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed  2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

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For the data set: 22, 40, 21, 18, 47, 22, 19, what is the mode?
SashulF [63]
Hello!

Mode : \fbox{it is the frequently occurIng value in the given set of observation}

Given observations are :-

22,40,21,18,47,22,19

Now , mode = \fbox{22}

The answer is 22 as it appears two times in the given set of observations.

Hope this is clear :)
Have a good day:)
7 0
2 years ago
Find the mean, the median, and all modes for the data in the given frequency distribution. (Round your answers to one decimal pl
kvasek [131]

Answer: Mean = 7.8

              Median = 9

             Mode = 2,9

Step-by-step explanation: <u>Mean</u> is the average value of a data set. Mean from a frequency table is calculated as:

E(X)=\frac{2(10)+3(9)+9(10)+11(7)+12(3)+15(4)+16(3)}{10+9+10+7+3+4+3}

E(X) = 7.8

Mean for the given frequency distribtuion is 7.8.

<u>Median</u> is the central term of a set of numbers. Median in a frequency table is calculated as:

1) Find total number, n:

n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46

2) Find position, using: \frac{n+1}{2}

\frac{n+1}{2}=\frac{47}{2} = 23.5

Median is in the 23.5th position.

3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9

Median for this frequency distribution is 9.

<u>Mode</u>  is the number or value associated with the highest frequency.

In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.

Mode for this distribution is 2 and 9.

7 0
3 years ago
A cubed-shaped box has its side lengths decreased by 3 cm, when this happens, the volume decreases by 1385cm^3. What is the side
mixer [17]

Answer:

Step-by-step explanation:

let side of cube=x cm

volume=x³ cm³

again side=(x-3) cm

volume=(x-3)³ cm³

x³-(x-3)³=1385

(a³-b³)=(a-b)(a²+ab+b²)

(x-x+3){x²+x(x-3)+(x-3)²}=1385

3(x^2+x²-3x+x²-6x+9)=1385

3(3x²-9x+9)=1385

9x²-27x+27=1385

9x²-27x+27-1385=0

9x²-27x-1358=0

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3 0
3 years ago
Greatest to least 1/3 1/2 3/4
schepotkina [342]
The answer will be 3/4, 1/2, and 1/3.
The bigger the fraction the smaller it is.
So 3/4 would be first .
The smaller the fraction the bigger it is.
So 1/3 would be last.
So that leaves you with 1/2 so that one would be in the middle of the set.
So the answer would be...:3/4, 1/2, and 1/3.
Hope that helped.
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Phantasy [73]

Answer:

I'm almost positive it's .A but I'm not sure

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