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yuradex [85]
3 years ago
11

An urn contains 7 red marbles and 3 white marbles. three marbles are drawn from the urn one after the other. find the probabilit

y that the first two are red and the third is white.
Mathematics
1 answer:
vaieri [72.5K]3 years ago
5 0

7+3 = 10 total marbles

 1st pick = 7/10 for a red one

2nd pick = 6/9 reduces to 2/3 for a red one

3rd pick = 3/8 for a white one

7/10 x 2/3 =14/30 reduces to 7/15

7/15 x 3/8 = 21/120 reduces to 7/40

 probability = 7/40

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What is the approximate area of a sector given O= 56 degrees with a diameter of 12m?​
jeyben [28]

Area of sector is 17.584 meters

<em><u>Solution:</u></em>

Given that we have to find the approximate area of a sector given O= 56 degrees with a diameter of 12m

Diameter = 12 m

Radius = Diameter / 2 = 6 m

An angle of  56 degrees is the fraction \frac{56}{360} of the whole rotation

A sector of a circle with a sector angle of 56 degrees is therefore also the fraction \frac{56}{360} of the circle

The area of the sector will therefore also be  \frac{56}{360} of the area

\text{ sector area } = \frac{56}{360} \times \pi r^2\\\\\text{ sector area } = \frac{56}{360} \times 3.14 \times 6^2\\\\\text{ sector area } = 17.584

Thus area of sector is 17.584 meters

3 0
3 years ago
A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected.
dimulka [17.4K]

Answer:

a. 39.55%

b. 44.02%

Step-by-step explanation:

We have the following data:

n = 5

x = 1

p = 5/20 = 0.25

to. If the sampling is done with replacement.

We apply the binomial distribution formula, which is as follows:

P = nCx * (p ^ x) * ((1-p) ^ (n-x))

Where nCx, is a combination, and is equal to:

nCx = n! / x! * (n-x)!

replacing we have:

5C1 = 5! / 1! * 4! = 5

replacing in the main formula:

P = 5 * (0.25 ^ 1) * ((1- 0.25) ^ (5-1))

P = 0.3955

that is, without replacing the probability is 39.55%

b. if the sampling is done without replacement.

Here it is a little different from the previous one, but what you should do is calculate three cases,

the first was the one at point a, when n = 5 and x = 1

5C1 = 5! / 1! * 4! = 5

the second is when n = 20 and x = 5, this is all possible scenarios.

20C5 = 20! / 5! * 15! = 15504

and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged

15C4 = 15! / 4! * 11! = 1365

In the end, it would be:

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Which means that without replacing the probability is 44.02%

7 0
3 years ago
Complete the function table to find the function values of {-1, 7} for f(n) = 2n - 1.
allochka39001 [22]

Answer:

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Step-by-step explanation:

3 0
3 years ago
If a gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice
Norma-Jean [14]

Answer:

He needs 5x+56 ft

Step-by-step explanation:

To find how much of fencing he needs , we find the perimeter of the given figure

All sides are equal in a square

To find perimeter of the square we add all the sides

4 sides we have for the square

one side is x, so perimeter of square = x+x+x+x= 4x

Now we find perimeter of rectangle

Opposite sides of rectangle are equal

Here for rectangle we consider only three sides

because fourth side is common for rectangle and square

So perimeter of the rectangle (with 3 sides) = 28 +x+ 28 = 56+x

Total fencing = perimeter of square + perimeter of rectangle

4x + 56 + x= 5x+56


5 0
3 years ago
A little monkey had some peaches. On the first day he decided to keep ½ of his peaches. He gave the rest away. Then he ate one.
Hunter-Best [27]

Answer:

22

Step-by-step explanation:

Working backwards

1+1 then x2 is 4

4+1 then x2 is 10

10+1 then x2 is 22

8 0
2 years ago
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