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Vilka [71]
3 years ago
12

Nate solves the equation _ x 5=15 by writing and solving 15/5=_. Explain why Nates method works.

Mathematics
1 answer:
Crazy boy [7]3 years ago
3 0
This is because Nate is isolating the variable. For example, in the equation 10x=40, you would divide both sides by 10 in order to get the variable by itself, just as Nate did. Nate is also performing the inverse operation, which allows for one to undo/unravel the question to find the answer.
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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
sleet_krkn [62]

This question is incomplete, the complete question is;

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.

In other words, how many 5-tuples of integers  ( h, i , j , m ), are there with  n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?

Answer:

the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Step-by-step explanation:

Given the data in the question;

Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1

this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.

So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'

Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;

\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right]

= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]

= [( n + 4 )!] / [ 5!( n-1 )! ]

= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

4 0
3 years ago
You saved 300 to spend over summer. You decide to budget 50 to spend each week. Write and equation that represents the situation
Anestetic [448]
Y=300-50x
Y= total $
X= number of weeks
5 0
3 years ago
Read 2 more answers
catriona earned 16 more stickers than Peter. she earned 35 stickers. how many stickers did Peter earn?​
expeople1 [14]

Answer:

19

Step-by-step explanation:

If Catriona has 16 more stickers than Peter than the only thing you have to do is subtract and find the difference

5 0
3 years ago
You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean i
notsponge [240]

The question given is incomplete, I googled and got the complete question as below:

You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean in the world. Crab populations and commercial catch rates are highly variable, but the fishery is under constant pressure from over-fishing, habitat destruction, and pollution. These days, you tend to pull crab pots containing an average of 2.4 crabs per pot. Given that you are economically challenged as most commercial fishermen are, and have an expensive boat to pay off, you’re always interested in projecting your income for the day. At the end of one day, you calculate that you’ll need 7 legal-sized crabs in your last pot in order to break even for the day. Use these data to address the following questions. Show your work.

a. What is the probability that your last pot will have the necessary 7 crabs?

b. What is the probability that your last pot will be empty?

Answer:

a. Probability = 0.0083

b. Probability = 0.0907

Step-by-step explanation:

This is Poisson distribution with parameter λ=2.4

a)

The probability that your last pot will have the necessary 7 crabs is calculated below:

P(X=7)=  {e-2.4*2.47/7!} = 0.0083

b)

The probability that your last pot will be empty is calculated as:

P(X=0)=  {e-2.4*2.40/0!} = 0.0907

8 0
3 years ago
Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt
Agata [3.3K]

Answer:

60 minutes.

Step-by-step explanation:

Distance = Rate × Time

14 miles = 14mph × ?

Hence, time = 14 miles ÷ 14 mph = 1 hour

1 hour = 60 minutes.

He rode his bike for 60 minutes.

8 0
3 years ago
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