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erma4kov [3.2K]
2 years ago
13

box contains five while balls, four red balls and three blue balls. Suppose that three balls are randomly selected. a. What is t

he probability that exactly two of the balls are white ? b. What is the probability that one ball of each color is selected ? c. What is the probability that all three of the selected balls have the same color ?
Mathematics
1 answer:
maria [59]2 years ago
7 0

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Number of white balls = 5

Number of red balls = 4

Number if blue balls = 3

Probability = required outcome / Total possible outcomes

Total possible outcomes (Total number of balls) = 5 + 4 + 3 = 12

a. What is the probability that exactly two of the balls are white?

(White, white, not white) or (not white, white, white) or (white, not white, white)

Assume balls were picked without replacement ;

P(white, white, not white) = (5/12 × 4/11 × 7/10) = 0.1060606

P(not white, white, white) = (7/12 × 5/11 × 4/10) = 0.1060606

P(white, not white, white) = (5/12 × 7/11 × 4/10) = 0.1060606

P(exactly 2 white balls) = 3×(0.1060606) = 0.3181818

b. What is the probability that one ball of each color is selected ?

(White, red, blue) or (red, white, blue) or (red, blue, white) or (blue, red, white), (white, blue, red), (blue, white, red)

P(white, red, blue) = (5/12 * 4/11 * 3/10) = 0.0454545

(0.0454545 × 3) = 0.272727

c. What is the probability that all three of the selected balls have the same color ?

P(white, white, white) or P(blue, blue, blue) or P(red, red, red)

P(white, white, white) = (5/12 * 4/11 * 3/10) = 0.0454545

P(blue, blue, blue) = (3/12 * 2/11 * 1/10) = 0.0045454

P(red, red, red) = (4/12 * 3/11 * 2/10) = 0.0181818

(0.0454545 + 0.0045454 + 0.0181818) = 0.0681817

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sergey [27]

Answer:

If the length is 50 yd, the width is  60 yd.

If the length is 40 yd, the width is  75 yd.

If the length is 48 yd, the width is  62.5 yd.

If the length is 36 yd, the width is 83.33 yd.

The length and the width vary inversely because when the length decreased the width increased

Step-by-step explanation:

<em>The area of any rectangle A = L × W, where</em>

  • L is its length
  • W is its width

<em>The relation is direct proportion if the quotient of two quantity equals constant  (y/x = k, when y and x increased) and inverse if the product of the two quantity equals constant (yx = k, when x increased y decreased and vice versa)  </em>

∵ The area of the rectangular plot of land = 3000 yards²

∴ A = 3000

∵ Its length = 50 yards

∴ L = 50

→ Substitute them in the rule above to find W

∵ 3000 = 50 × W

→ Divide both sides by 50 to find W

∴ 60 = W

∴ The width of the plot is 60 yards

∵ Its length = 40 yards

∴ L = 40

→ Substitute them in the rule above to find W

∵ 3000 = 40 × W

→ Divide both sides by 40 to find W

∴ 75 = W

∴ The width of the plot is 75 yards

∵ Its length = 48 yards

∴ L = 48

→ Substitute them in the rule above to find W

∵ 3000 = 48 × W

→ Divide both sides by 48 to find W

∴ 62.5 = W

∴ The width of the plot is 62.5 yards

∵ Its length = 36 yards

∴ L = 36

→ Substitute them in the rule above to find W

∵ 3000 = 36 × W

→ Divide both sides by 36 to find W

∴ 83. 33 = W

∴ The width of the plot is  83.33 yards

∵ The area is a constant value

∵ A = LW

→ The product of L and W equals the constant value, can you discover

   that from the values of L and W

∴  The length and the width of the rectangular plot vary inversely

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3 years ago
Write the equation of the line that passes through (-4,3) and is parallel to y = -2x - 8.
kobusy [5.1K]

Answer:

y = -2x - 5

Step-by-step explanation:

Let the equation if the line be y = mx + c

since the line is parallel to y = -2x - 8, their gradients/slope must be the same (aka m = -2)

sub (-4, 3):

3 = -2(-4) + c

c = -5

therefore, the equation of the line is y = -2x - 5

This is a question on coordinate geometry. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

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2 years ago
Original price: $50 Discount: 15% Sale price: $ <br> What is the sale price?
sasho [114]

Answer:

42.50

Step-by-step explanation:

If we get 15% off, we still have to pay (100-15) = 85% of the price

The sale price = original * percent we still have to pay

       sale price = 50 *.85

                            42.50

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3 years ago
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ololo11 [35]
The last option because he spent $135 or more
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2 years ago
Find the exact circumference of a circle with diameter equal to 8 ft. 8 ft. 16 ft. 64 ft.
maria [59]

ANSWER

8π ft

EXPLANATION

The circumference of a circle is calculated using the formula C=πd.

Where d=8 is the diameter of the circle.

We substitute d=8 into the formula to obtain,

C=8π ft.

Because we are looking for the exact circumference, we leave the answer in terms of π.

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3 years ago
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