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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.

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Step-by-step explanation:

3 0
2 years ago
Megan surveyed a random sample of 60 students at her school and found that 42 of them ride the bus to school each day. if there
Dmitry_Shevchenko [17]
42/60, x/320. 320/60=5.33333, 42*5.33333=224. So, about 224 students would ride the bus.
4 0
3 years ago
. Which ordered pairs in the form (x, y) are solutions to the equation 7x – 5y = 28?
Brut [27]

we know that

If a ordered pair (x,y) is a solution of the equation, then the ordered pair must satisfy the equation

we have the equation

7x-5y=28

Let's verify all the cases to determine the solution to the problem.

<u>case A)</u> point (-6,-14)

Substitute the values of x and y in the equation

x=-6\\y=-14

7(-6)-5(-14)=28

-42+70=28

28=28 -------> is  true

therefore

The point  (-6,-14) is a solution of the equation

<u>case B)</u> point (-1,-7)

Substitute the values of x and y in the equation

x=-1\\y=-7

7(-1)-5(-7)=28

-7+35=28

28=28 -------> is  true

therefore

The point  (-1,-7) is  a solution of the equation

<u>case C)</u> point (4,10)

Substitute the values of x and y in the equation

x=4\\y=10

7(4)-5(10)=28

28-50=28

-22=28 -------> is not true

therefore

The point (4,10) is not a solution of the equation

<u>case D)</u> point (7,9)

Substitute the values of x and y in the equation

x=7\\y=9

7(7)-5(9)=28

49-45=28

4=28 -------> is not true

therefore

The point  (7,9) is not a solution of the equation

therefore

<u>the answer is </u>

(-6,-14)

(-1,-7)

8 0
3 years ago
Read 2 more answers
What if its "greater than 9"
goblinko [34]

Answer:

its gotaa be a number thats atleast 10

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the range of this data set? {14, 25, 61, 18, 30, 32, 28, 45, 21} 47 28 7 I don't know.
kati45 [8]

The range of the dataset = 47

What is the range of a dataset?

The range of a set of data is the difference between the greatest number and least number

The given data set is:

{14, 25, 61, 18, 30, 32, 28, 45, 21}

The greatest number = 61

The least number = 14

The range of the dataset = Greatest Number - Least Number

The range of the dataset = 61  -  14

The range of the dataset = 47

Learn more on range of a distribution here: brainly.com/question/4679134

3 0
2 years ago
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