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kati45 [8]
3 years ago
5

From a deck of five cards numbered 2, 4, 6, 8, and 10, respectively, a card is drawn at random and replaced. this is done three

times. what is the probability that the card numbered 2 was drawn exactly two times, given that the sum of the numbers on the three draws is 12?
Mathematics
1 answer:
Serga [27]3 years ago
3 0

Since the sum of the numbers on the three draws is 12, if we want the card numbered 2 to be drawn exactly two times, the third card can only be numbered 8. In fact, 2+2+8 = 12, and there are no other possibilities, unless you consider the various permutations of the terms.

So, we have three favourable cases: we can draw 2,2,8, or 2,8,2, or 8,2,2. This are the only three cases where the card numbered 2 is drawn exactly two times, and the sum of the number on the three draws is 12.

Now, the question is: we have three favourable cases over how many? Well, we have 5 possible outcomes with each draws, and the three draws are identical, because we replace the card we draw every time.

So, we have 5 possible outcomes for the first draw, 5 for the second and 5 for the third. This leads to a total of 5 \times 5 \times 5 = 5^3 = 125 possible triplets.

Once we know the "good" cases and the total number of possible cases, the probability is simply computed as

P = \cfrac{\text{number of favourable cases}}{\text{number of all possible cases}} = \cfrac{3}{125}

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in a poll 303 students voted . nominee d received 2/3 of the votes how many votes did nominee d receive​
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Answer:

Nominee d receive 202 votes.​

Step-by-step explanation:

Given : In a poll 303 students voted. Nominee d received \frac{2}{3} of the votes.

To find : How many votes did nominee d receive​ ?

Solution :

The number of votes = 303

Nominee d received \frac{2}{3} of the votes.

i.e. n=\frac{2}{3}\times 303

n=2\times 101

n=202

Therefore, nominee d receive 202 votes.​

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A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
creativ13 [48]

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

r=\frac{18}{2+\theta}

step 2

Find the value of s

s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

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3 years ago
I need help please it’s due today I forgot how to do this :(
choli [55]

Answer:

Samantha payed 12.71$ for her purchase.

Step-by-step explanation:

I may have misunderstood the question, but it looks like you can use a calculator for this!

6.19 + 2.85 + 2.29 + 1.38 =

12.71

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