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
Reptile [31]
3 years ago
5

Help pls I'll give 25 points

Mathematics
1 answer:
RideAnS [48]3 years ago
5 0

Answer:

\text{C. }60

Step-by-step explanation:

<u>Question from image</u>:

"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."

Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.

Checkmarks mark where the 1 can be, the <em>x</em> marks where it cannot be.

\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}

Let's start with the first position:

\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in 3!=6 ways. Therefore, there are 4\cdot 6=\boxed{24} possible numbers when 1 is the first digit of the number.

Continue this process with the remaining possible positions for 1.

Second position:

\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in 3!=6 ways. Therefore, there are 3\cdot 6=\boxed{18} possible numbers when 1 is the second digit of the number.

The pattern continues. Next there will be 2 places to place the 2. For each of these, there are 3!=6 ways to rearrange the remaining 3 digits for a total of 2\cdot 6=\boxed{12} possible numbers when 1 is the third digit of the number.

Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still 3!=6 ways to rearrange the remaining three numbers. Therefore, there are 1\cdot 6=\boxed{6} possible numbers when 1 is the fourth digit of the number.

Thus, there are 24+18+12+6=\boxed{60} numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.

You might be interested in
Graph for the quadratic formula f(x) = (x - 3) ^2 +5
aksik [14]

Please see the attached graph to see f(x) = (x - 3) ^2 +5 graphed.

6 0
3 years ago
A store starts the day with 45 packages of cheese slices. Each package contains the same number of cheese slices. By the end of
Helen [10]

Answer

Step-by-step explanation:

5 0
3 years ago
How do I do it! Answer pls givin the brainliest
pychu [463]
Ok so she has to pay 30 percent more of the 20 dollars she already has to pay because of the tax and then the tip so you multiply 20 by .30 which is six then you add that to 20 which is 26
8 0
3 years ago
Read 2 more answers
How many solutions does the following equation have?<br> -7x-10-15x=-22x+83
Vlada [557]

Answer:

-22x-10=-22x+83

=-22x-10=-22x+83

=-10=83

x€⊙

4 0
3 years ago
If you borrow $894 for four years at an interest rate of 3%, how much interest will you pay?
Studentka2010 [4]

Answer:

$1006.20

Step-by-step explanation:

This is an example of compound interest.

To work this out you would first have to convert the percentage into a decimal, you can do this by dividing 3 by 100, which gives you 0.03. You are dividing by 100 as percentages are out of 100. Then you would add 1 to 0.03, which gives you 1.03. This is because you are finding percentage increases. Then you would multiply 894 by 1.03 to the power of 4, which gives you 1006.20. This is because you are finding 3 percent and adding it on and then finding 3 percent of that, this is why we put it to the power of how much time.

1) Divide 3 by 100.

3/100=0.03

2) Add 1 to 0.03.

0.03+1=1.03

3) Multiply 894 by 1.03 to the power of 4.

894*1.03^{4}=1006.20

3 0
3 years ago
Other questions:
  • Which side of ΔDEF is the longest?
    12·2 answers
  • To play his game, Charles must distribute 350 tokens, when there are 7 players. How many will he have to distribute for 11 playe
    8·2 answers
  • ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
    15·1 answer
  • Como se multiplican polinomios
    9·1 answer
  • An office manager recorded the number of reams of paper that were used for a printer each month for six months: 15, 10, 25, 19,
    10·1 answer
  • A student reads 56 pages in 4 hours. How many pages will the student read in 7 hours?
    5·1 answer
  • What is the equation of the line that Passes through (3,5) and is parallel to y=2x+6
    9·1 answer
  • Distribute -(6 - 4p) TWELVE POINTS FOR YOUR ANSWER!!
    10·2 answers
  • Solve the equation by completing the square
    7·1 answer
  • Multiply -9/8 by -14/15
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!