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bixtya [17]
2 years ago
5

Write a polynomial equation in standard form with roots of -3 and 4

Mathematics
1 answer:
liubo4ka [24]2 years ago
6 0

Answer:

I don't know the answer

Step-by-step explanation:

the most seats in guyan

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You can walk 1.75 miles in 30 minutes. What is your average speed?
Varvara68 [4.7K]

Answer:

The answer is 3.5 mph

Step-by-step explanation:

30 x 2 = 60 minutes = 1 hour

1.75 x 2 = 3.5 miles

So 3.5 miles in 1 hour

3.5 mph

3 0
3 years ago
MIKE NEEDS AT LEAST $100 TO BUY A NEW SUIT FOR THE DANCE.
Tanya [424]

Answer:

3x+10 = 100

or

100 - 10 = 3x

6 0
3 years ago
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
Consider the following polynomial. - 2x * y ^ 5 + 3x ^ 7 - 10x ^ 3 * y ^ 6 + 8x ^ 6 + 4 Which of the following statements are tr
Salsk061 [2.6K]

Option a: polynomial has 5 terms.

Option c: The constant term is 4.

Explanation:

The polynomial is -2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4

Option a: Polynomial has 5 terms

From the polynomial, we have,

1st term = -2 x y^{5}

2nd term = 3 x^{7}

3rd term = -10 x^{3} y^{6}

4th term = 8 x^{6}

5th term = 4

Hence, the polynomial has 5 terms.

Thus, Option a is the correct answer.

Option b: The leading coefficient is -2 and the degree of the polynomial is 7.

The leading coefficient is the coefficient of the variable with the largest degree.

The degree of the polynomial can be determine by the adding the powers of the variable.

degree of 1st term = -2 x y^{5} = 1+5=6

degree of 2nd term = 3 x^{7} =7

degree of 3rd term = -10 x^{3} y^{6} =3+6=9

degree of 4th term = 8 x^{6} =6

degree of 5th term = 4 =0

Thus, from these 5 terms the highest value is 9 which is the degree of the polynomial.

The polynomial -2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4 has a largest degree of 9 and the leading coefficient is -10.

Hence, Option b is not the correct answer.

Option c: The constant term is 4.

The constant term is a term in which variable will not occur.

From the polynomial -2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4, we can see that the constant term is 4.

Hence, Option c is the correct answer.

Option d: Polynomial is in decreasing degree order

The decreasing degree order is the degree in which each term is no larger than the degree of the preceding term.

From the polynomial, we have,

degree of 1st term = -2 x y^{5} = 1+5=6

degree of 2nd term = 3 x^{7} =7

degree of 3rd term = -10 x^{3} y^{6} =3+6=9

degree of 4th term = 8 x^{6} =6

degree of 5th term = 4 =0

where the degree of the 3rd term is not less than the 4th term.

Thus, the polynomial is not in decreasing degree order.

Hence, Option d is not the correct answer.

5 0
3 years ago
Which are equivalent to 3
Studentka2010 [4]

Answer: 9/12 is equivalent to 3/4.

Explanation: 3 times 12 = 36 and 4 times 9 = 36.

Hope this helps!

5 0
2 years ago
Read 2 more answers
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