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UkoKoshka [18]
2 years ago
10

Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine

how many ways the prizes could be given out
Mathematics
1 answer:
mr Goodwill [35]2 years ago
5 0

We will use a combination formula to determine how many ways the prizes could be given out.

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

The formulas nCk is popularly known as counting formula.

Learn more about Combination:

brainly.com/question/4313883

#SPJ4

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Determine whether the given segments have the same length. Complete the justification of your answer,
Ratling [72]

Answer:

No does not contain the same length

Step-by-step explanation:

Given that

A(-4,2) , B (1,4), C (2, -1)

Now

AB would be

= \sqrt{(1-(-4))^2 + (4-2)^2} \\\\= \sqrt{29}

And, BC is

= \sqrt{(2-1)^2 + 1-(-4))^2} \\\\= \sqrt{26}

As we can see that the AB and BC are not equaled

So,

AB ≠ BC

Due to the different length

Therefore they do not contains the same length

We simply applied the distance formula due to which the length could be determined and the same is to be considered

5 0
3 years ago
Police records in the town of Saratoga show that 17 percent of the drivers stopped for speeding have invalid licenses. If 24 dri
Ymorist [56]

Answer:

Step-by-step explanation:

Given

17 % of the drivers stopped have invalid licenses

n=24 drivers are stopped

using Binomial distribution

^nC_r(p)^r(q)^{n-r}

here p=0.17

q=1-0.17=0.83

(a)none will have valid license i.e. r=0

P(r=0)^{24}C_0(0.17)^0(0.83)^{24}=(0.83)^{24}=0.0114

(b)Exactly one have invalid license i.e. r=1

P(r=1)=^{24}C_1(0.17)^1(0.83)^{23}=24\times 0.17\times (0.83)^{23}

=0.0561

(c)At least 2 will have invalid license i.e. r\geq 2

P(r\geq 2)=1-P(r=0)-P(r=1)

P(r\geq 2)=1-0.0114-0.0561

P(r\geq 2)=0.932

3 0
3 years ago
2. Evaluate f(x) = 3x+5/x-1<br> at x = 3
pashok25 [27]

Answer

Let f(x) = ax + b

Then

f(x + 1) = a(x + 1) + b

= ax + a + b

Hence, a = 3, and a + b = 5, b = 2

f(-2) = 3(-2) + 2

= -6 + 2

= - 4

f(2x) = 3(2x ) + 2

= 6x + 2

6 0
3 years ago
Write the equation of circle b with center B(-2,3) that passes through (1,2)
professor190 [17]

Answer:

(x+2)^2 + (y-3)^2 = 10

Step-by-step explanation:

The standard equation for circle is

(x-a)^2 + (y-b)^2 = r^2

where point (a,b) is coordinate of center of circle and r is the radius.

______________________________________________________

Given

center of circle =((-2,3)

let r be the radius of circle

Plugging in this value of center in standard equation for circle given above we have

(x-a)^2 + (y-b)^2 = r^2    \ substitute (a,b) \ with (-2,3) \\=>(x-(-2))^2 + (y-3)^2 = r^2  \\=>(x+2)^2 + (y-3)^2 = r^2    (1)

Given that point (1,2 ) passes through circle. Hence this point will satisfy the above equation of circle.

Plugging in the point (1,2 )  in equation 1 we have

\\=>(x+2)^2 + (y-3)^2 = r^2    \\=> (1+2)^2 + (2-3)^2 = r^2\\=> 3^2 + (-1)^2 = r^2\\=> 9 + 1 = r^2\\=> 10 = r^2\\=>  r^2  = 10\\

now we have value of r^2 = 10, substituting this in equation 1 we have

Thus complete equation of circle is =>(x+2)^2 + (y-3)^2 = r^2\\=>(x+2)^2 + (y-3)^2 = 10

7 0
3 years ago
A square family room has an area of 100 square meters. How long is each side?​
FromTheMoon [43]

Answer:

<em>Each side is 10 meters</em>

Step-by-step explanation:

Because since area is length times width, you would do 10x10 which is 100

4 0
3 years ago
Read 2 more answers
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