There are 15 students in a social studies class. Two students will be selected to present their term projects today. In how many different orders can two students be selected?

Answers

Answer 1

Answer: Given:
15 students
2 students must be chosen.
No repetition, no order

This is a combinations problem. We use this formula: n! / (n-r)!(r!)

n = 15 ; r = 2

15! / (15-2)!(r!) ⇒ 15! / 13! * 2! = 105

Answer 2

Answer:

Using the combination formula, it is found that the students can be selected in 105 ways.

The order in which the students are selected is not important, hence the combination formula is used to solve this question.

What is the combination formula?

The number of possible combinations of x elements from a set of n elements is given by:

$C_((n,x)) = (n!)/(x!(n-x)!)$

In this problem, two students are selected from a set of 15, hence the number of different orders is given by:

$C_(15,2) = (15!)/(2!13!) = 15 * 7 = 105$

More can be learned about the combination formula at brainly.com/question/25821700

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The sum of the page numbers of two facing pages in a book is 145. What are the page numbers?

Answers

The answer is 72 and 73. When you add 72+73 it equals 145.

Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistentnumber of miles

per gallon of gasoline and he has some gasoline in his tank already. Matthew writes the

equation 25(x + 3) = 424, where x represents the number of gallons of gasoline he will need to purchase to

complete the trip.

Identify the meaning of each of the constants in Matthew's equation in the context of the problem, then solve

the equation to determine how many gallons of gasoline he must purchase.

Answers

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

x = 13.96

x = 14

mathew needs to get 14 gallons of gasoline.

Look at the pattern below. What is the pattern rule? 3, 9, 27, 81, … Start at 3 and a) add 6 to get the next term b) m ultiply by 2 to get the next term c) m ultiply by 3 to get the next term d) m ultiply by itself to get the next term