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taurus [48]
3 years ago
9

Is 1 a rational number?

Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0
Yes 1 is a rational number, because it can be expressed as the quotient of two integers
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Which equation gives the value of the circumference, C, of a circle with a diameter of 56 feet?
Keith_Richards [23]

Answer:175.84 ft

Step-by-step explanation: the equation would be diameter times pi

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3 years ago
The graph shows the number of chairs made in a factory during one day .
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Answer:

C) the factory produces 25 chairs per hour

                     

Step-by-step explanation:

Let's find the rate of change (slope):  

let:\\(x1,y1) =(2,50)\\(x2,y2)=(4,100)\\m=\frac{100-50}{4-2} =\frac{50}{2} =25 \\

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3 years ago
Luella has a pond in her yard. She wants to surround it with 330 feet of fencing. Fencing is sold by the yard. How many yards sh
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Answer:

110 yards

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1yard =3 feet

Step-by-step explanation:

if you multiply 3 to 110=330

or 330 divided by 3=110 yards.

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2 years ago
What's the solution to the equation x/3 + x/6 = 7/2
marta [7]

Step-by-step explanation:

x/3+x/6=7/2

We simplify the equation to the form, which is simple to understand

x/3+x/6=7/2

Simplifying:

+ 0.333333333333x+x/6=7/2

Simplifying:

+ 0.333333333333x + 0.166666666667x=7/2

Simplifying:

+ 0.333333333333x + 0.166666666667x=+3.5

We move all terms containing x to the left and all other terms to the right.

+ 0.333333333333x + 0.166666666667x=+3.5

We simplify left and right side of the equation.

+ 0.5x=+3.5

We divide both sides of the equation by 0.5 to get x.

x=7

4 0
2 years ago
Read 2 more answers
A search committee is formed to find a new software engineer. (a) If 100 applicants apply for the job, how many ways are there t
vagabundo [1.1K]

These are three questions with three complete answers.

Answers:

(a) C(100,6) = 100! / [ 9! × (100 -9)! ] =

              = (100×99×98×97×96×95×94×93×92) / (9×8×7×6×5×4×3×2×1) =

              = 1,902,231,808,400

(b) C(9,6) = 9! / [ 6! * (9 - 6)! ] = 9! / [6! 3!] = (9 × 8 × 7 × 6!) (6! × 3 × 2 × 1) =

          =  (9 × 8 × 7 × 6!) (6! × 3 × 2 × 1) =  (9 × 8 × 7 ) / (3 × 2 × 1) = 84

(c) P(6,3) = 6! / (6 - 3)! = 6! / 3! = (6 × 5 × 4 × 3!) / 3! = 120

Step-by-step explanation:

(a) If 100 applicants apply for the job, how many ways are there to select a subset of 9 for a short list?

This is the formula for combinations: C (m,n) = m! / [n! (m - n)! ].

We will also use the formula for permutations, only as an intermediate step, to explain the solution. The formula for permutations is: P (m,n) = m! / (m - n)!

Next you will see why the final formula that you can use to solve the problem is that of combinations (because the order in which you make the list does not matter) and how you use it.

You have to select a subset of 9 candidates from a list of 100 applicants.

The first candidate may be chosen from the 100 different applicants, the second candidate may be chosen from the 99 left applicants, the third candidate from 98 applicants, and so on, which leads to:

  • 100 × 99 × 98 × 97 × 96 × 95 × 94 × 93 × 92 possible variants.

Note that this is the permutation of 100 candidates taken from 9 in 9:

P(100,9)  = 100! (100 - 9)! = 100! / (91!) =

              = 100 × 99 × 98 × 97 × 96 × 95 × 94 × 93 × 92 × 91! / 91! =

              = 100× 99 × 98 × 97 × 96 × 95 × 94 × 93 × 92.

But you have to eliminate the repetitions!

Suppose that A, B, C, D, E, F, G, H, I represents the set formed by nine selected members whose names are A, B, C, D, E, F, G, H and I. So, any combination of those same names, written in different order, represents the same set (list). That means that there are 9! = 9× 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 equivalent lists.

That is why you must divide the first result (possible ways in which you can select nine candidates) by the number of ways that represent the same list for every set.

So, the conclusion is that the number of different lists of nine candidates is:

C(100,6) = 100! / [ 9! × (100 -9)! ] =

              = (100×99×98×97×96×95×94×93×92) / (9×8×7×6×5×4×3×2×1) =

              = 1,902,231,808,400

(b) If 6 of the 9 are selected for an interview, how many ways are there to pick the set of people who are interviewed? (You can assume that the short list is already decided).

Since, the short list, i.e. the  subset of 9 candidates is already decided, you will select 6 candidates to interview from 9 possible candidates.

So, your final set of candidates to interview will be the combination of 9 candidates taken from 6 in 6. The order of the names A, B, C, D, E, F, and G, is not relevant, and, therefore, the formula to use is that of combinations:

  • C (m,n) = m! / [n! (m - n)! ]

  • C(9,6) = 9! / [ 6! * (9 - 6)! ] = 9! / [6! 3!] = (9 × 8 × 7 × 6!) (6! × 3 × 2 × 1) =

                   =  (9 × 8 × 7 × 6!) (6! × 3 × 2 × 1) =  (9 × 8 × 7 ) / (3 × 2 × 1) = 84

(c) Based on the interview, the committee will rank the top three candidates and submit the list to their boss who will make the final decision. (You can assume that the interviewees are already decided.) How many ways are there to select the list from the 6 interviewees?

Ranking the top three candidates means that the order matters. Because it is not the same A, B, C than A, C, B, nor B, A, C, nor B, C, A, nor C, A, B, nor C, A, B.

Hence, you have to use the formula for permutations (not combinations).

The formula is: P(m,n) = m! / (m - n)!

Here, you must rank (select) 3 names, from a set (list) of 6 names, and the formula yields to:

  • P(6,3) = 6! / (6 - 3)! = 6! / 3! = (6 × 5 × 4 × 3!) / 3! = 120

4 0
3 years ago
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