1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sattari [20]
3 years ago
7

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

mber. What is the original number?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0
Let X and Y be the digits.
If a two-digit number is written XY, then its value is 10x+y.
When the digits of the number are interchanged, it's YX, and its value is 10y+x.

The sum of the digits is 12.
The number formed by interchaning the digits is 54 more than the original number.

x+y=12 \\
10x+y+54=10y+x \\ \\
x+y=12 \\
10x-x+y-10y=-54 \\ \\
x+y=12 \\
9x-9y=-54 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 9 \\ \\
x+y=12 \\
\underline{x-y=-6} \\
x+x=12-6 \\
2x=6 \\
x=\frac{6}{2} \\
x=3 \\ \\
x+y=12 \\
3+y=12 \\
y=12-3 \\
y=9

The digits X and Y are 3 and 9, so the original number is 39.
You might be interested in
Which expression is equivalent to (4x^5+11)^2 ?
ale4655 [162]
The correct answer is c
7 0
3 years ago
Read 2 more answers
Round 1.5 to one decimal place
xxMikexx [17]
If the last digit in 1.50 is less than 5, then remove the last digit.

If the last digit in 1.50 is 5 or more and the second to the last digit in 1.50 is less than 9, then remove the last digit and add 1 to the second to the last digit.

If the last digit in 1.50 is 5 or more and the second to the last digit in 1.50 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.

When rounding 1.50 to one decimal place we use One Decimal Place Rule #1. Therefore, the answer to "What is 1.50 rounded to 1 decimal place?" is:

1.5
3 0
3 years ago
Read 2 more answers
The student population of a school consists of 300 girls and 500 boys
denis-greek [22]

Answer:

In all you have 800 students.

The ratio of girls to boys is 300:500

500 x 300 = 150000

Step-by-step explanation:

Hope this helps?

8 0
2 years ago
A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given th
taurus [48]

Answer:

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0518

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

In this question:

n = 27, s = 21.4. So

M = 2.0518\frac{21.4}{\sqrt{27}}

M = 8.45

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

5 0
3 years ago
At the Boston Marathon there were 20,000 runners who finished the race. Each runner ran a distance of 26 miles. If you add toget
andre [41]

Answer:

the runners have gone 20.8 times around the globe all together

Step-by-step explanation:

At the Bostom Marathon, we have a total of

N = 20,000 runners

We know that each runner ran a distance of

d = 26 miles

Therefore, the total distance travelled by all runners combined is:

D=Nd=(20,000)(26)=5.2\cdot 10^5 mi

We know that the circumference of the Earth is

c=2.5\cdot 10^4 mi

Here we want to find how many times around the globe would the marathon runners have gone. This can be found by calculating the following ratio:

n=\frac{D}{c}

And substituting the values, we find:

n=\frac{5.2\cdot 10^5}{2.5\cdot 10^4}=20.8

So, the runners have  gone 20.8 times around the globe all together.

4 0
3 years ago
Other questions:
  • · B__________8cm___________C·
    7·1 answer
  • Which is the graph of linear inequality 6x + 2y > –10? On a coordinate plane, a dashed straight line with negative slope goes
    7·1 answer
  • What could equal 16 if your x4
    8·2 answers
  • What percent of 22 is 58
    5·1 answer
  • 2.6 as a mixed number
    14·2 answers
  • Choose the graph of this equation y 2.5
    9·1 answer
  • Each day after school, Chelsey runs 2.8 miles farther than Kyle.
    14·2 answers
  • Need answer asap! Which set of points would result in a slope of 1/4?
    12·1 answer
  • Mr. Smith wants to build a rectangular gate with a diagonal as support. If the width and height are 4 ft and 3 ft respectively,
    11·1 answer
  • There are 713 boxes in the stores room, each having 12 bags of tikis in them. What is the total number if tiki bags are inside t
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!