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oksian1 [2.3K]
3 years ago
11

So I have to compute the following but i don't know what they mean any help?

Mathematics
2 answers:
Gelneren [198K]3 years ago
7 0

Answer:

Step-by-step explanation:

This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr

i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.

I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.

Recall that

nCr=\frac{n!}{(r!)(n-r)!}

Consider question a) we are given (5 1) or ₅C₁

we can see that n = 5 and r = 1

If we substitute this into the formula:

₅C₁ = (5!) / [ (1!)(5- 1)!]

= (5!) / [ (5- 1)!]

= (5!) / (4!)

= (5·4·3·2·1) / (4·3·2·1)

= 5

hence ₅C₁ = 5

timama [110]3 years ago
4 0

Answer:

(a) 5

(b) 10

(c) 35

(d) 28

(e) 9

(f) 21

Step-by-step explanation:

(\frac{n}{k} )=\frac{n!}{k!(n-k)!}

(a)

(\frac{5}{1} )=\frac{5!}{1!(5-1)!} \\\\(\frac{5}{1} )=\frac{5*4*3*2*1}{1*4!} \\\\(\frac{5}{1} )=\frac{120}{1*4*3*2*1} \\\\(\frac{5}{1} )=\frac{120}{24} \\\\(\frac{5}{1} )=5

(b)

(\frac{5}{3} )=\frac{5!}{3!(5-3)!} \\\\(\frac{5}{3} )=\frac{5*4*3*2*1}{3*2*1*2!} \\\\(\frac{5}{3} )=\frac{120}{3*2*1*2*1}\\\\(\frac{5}{3} )=\frac{120}{12} \\\\(\frac{5}{3} )=10

(c)

(\frac{7}{4} )=\frac{7!}{4!(7-4)!} \\\\(\frac{7}{4} )=\frac{7*6*5*4*3*2*1}{4*3*2*1*3!} \\\\(\frac{7}{4} )=\frac{5040}{4*3*2*1*3*2*1} \\\\(\frac{7}{4} )=\frac{5040}{144} \\\\(\frac{7}{4} )=35

(d)

(\frac{8}{2}) =\frac{8!}{2!(8-2)!} \\\\(\frac{8}{2}) =\frac{8*7*6*5*4*3*2*1}{2*1*6!} \\\\(\frac{8}{2}) =\frac{40320}{2*1*6*5*4*3*2*1}\\\\(\frac{8}{2}) =\frac{40320}{1440} \\\\(\frac{8}{2}) =28

(e)

(\frac{9}{8} )=\frac{9!}{8!(9-8)!} \\\\(\frac{9}{8} )=\frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1} \\\\(\frac{9}{8} )=\frac{362880}{40320} \\\\(\frac{9}{8} )=9

(f)

(\frac{10}{4} )=\frac{10!}{4!(10-4)!} \\\\(\frac{10}{4} )=\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6!} \\\\(\frac{10}{4} )=\frac{3628800}{24*6*5*4*3*2*1} \\\\(\frac{10}{4} )=\frac{362880}{17280} \\\\(\frac{10}{4} )=21

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Anu and Aji solve an equation. In solving Anu commits a mistake in constant term and finds the roots 8 and 2. Aji commits a mist
vagabundo [1.1K]

The correct roots of the equation are (a) 9 and 1

From the complete question, their mistakes are:

<u>Anu</u>

  • Roots: 8 and 2
  • Wrong constant term

<u>Aji</u>

  • Roots: -9 and -1
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A quadratic equation is represented as:

ax^2 + bx + c = 0

Where:

\alpha\beta = \frac ca --- product of roots

\alpha + \beta = -\frac ba --- sum of roots

Anu made a mistake in the constant term, so we consider the sum of roots

Sum = 8 + 2

Sum = 10

Aji made a mistake in the coefficient, so we consider the product of roots

Product = -9 \times -1

Product = 9

The possible equations from the above sum and products are:

  • x^2 + 10x  + 9 =0.
  • x^2 - 10x  + 9 =0.
  • x^2 + 10x  - 9 =0.
  • x^2 - 10x  - 9 =0

Of all the above equations, the most likely equation is x^2 - 10x  + 9 =0, and it has a root of 9 and 1

Hence, the correct roots are (a) 9 and 1

Read more about roots of equations at:

brainly.com/question/3923172

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What is the solution to –4|–2x + 6| = –24?x = 0x = 0 or x = –6x = 0 or x = 6no solution
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The correct answers are the x = 6 and x = 0.

In order to find this, we can follow the order of operations.

–4|–2x + 6| = –24

Divide by -4

|–2x + 6| = 6

Since it is now equal to a absolute value, we have to solve for the positive and negative versions of the final answer. Let's start with the positive.

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4 0
3 years ago
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yulyashka [42]

<em>(4, -2)</em>

Step-by-step explanation:

For a reflection across the y-axis, you need to change the sign of the x to the opposite of what it was.

(x, y) to (-x, y)

If C has the coordinates of (-4, -2), to figure out the coordinates of C' after a reflection of the y-axis, we will change the sign of the x.

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