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Olegator [25]
2 years ago
13

Suppose a bag contains many marbles, 54% of which are purple. You draw 5 marbles from the bag with replacement.

Mathematics
1 answer:
dolphi86 [110]2 years ago
6 0

Part A

Use the binomial probability distribution formula.

p = 0.54 = probability of getting a purple marble

n = 5 = sample size

x = 2 = number of purple we want to get

P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}\\\\P(2) = \frac{5!}{2!(5-2)!}*0.54^2*(1-0.54)^{5-2}\\\\P(2) = 10*0.54^2*0.46^3\\\\P(2) = 0.283831776\\\\

The \frac{n!}{x!(n-x)!} portion is from the nCr combination formula. The exclamation marks indicate a factorial.

Alternatively, you could use Pascal's Triangle for that portion.

<h3>Answer: 0.283831776</h3>

This decimal value is exact. Round it however you need to.

============================================================

Part B

To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.

n*p = 5*0.54 = 2.7

<h3>Answer: 2.7</h3>
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5 0
2 years ago
The arithmetic sequence a; is defined by the formula:
Morgarella [4.7K]

Answer:

The sum of the first 650 terms of the given arithmetic sequence is 2,322,775

Step-by-step explanation:

The first term here is 4

while the nth term would be ai = a(i-1) + 11

Kindly note that i and 1 are subscript of a

Mathematically, the sum of n terms of an arithmetic sequence can be calculated using the formula

Sn = n/2[2a + (n-1)d)

Here, our n is 650, a is 4, d is the difference between two successive terms which is 11.

Plugging these values, we have

Sn = (650/2) (2(4) + (650-1)11)

Sn = 325(8 + 7,139)

Sn = 325(7,147)

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3 years ago
The diagram shows four graphs match the graphs to the equations
cluponka [151]

Answer:

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2 years ago
Describe the pattern
krek1111 [17]

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negative linear

Step-by-step explanation:

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3 0
2 years ago
Select the solution to the graph from the following points. Select all that apply.
stellarik [79]

Answer:

The solutions are:

(-15 , -4) ⇒ 1st

(3 , 2) ⇒ 3rd

(21 , 8) ⇒ 5th

Step-by-step explanation:

To find the solution of the graph let us make the equation of the line by using any two points on the line

The form of the linear equation is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept (value y at x = 0)

The formula of the slope is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

From the figure

∵ The line passes through points (-3 , 0) and (0 , 1)

- Find the slope of the line

∴ m=\frac{1-0}{0--3}=\frac{1}{3}

- Substitute the value of m in the form of the equation

∴ y = \frac{1}{3} x + b

∵ b is the value of y at x = 0

∵ y = 1 at x = 0 ⇒ y-intercept

∴ b = 1

∴ y = \frac{1}{3} x + 1

Lets substitute the x-coordinate of each point to find the y-coordinate, if the y-coordinate is equal to the y-coordinate of the points, then the point is a solution

Point (-15 , -4)

∵ x = -15

∴ y = \frac{1}{3} (-15) + 1

∴ y = -5 + 1 = -4 ⇒ same value of the point

∴ (-15 , -4) is a solution

Point (-6 , 1)

∵ x = -6

∴ y = \frac{1}{3} (-6) + 1

∴ y = -2 + 1 = -1 ⇒ not the same value of the point

∴ (-6 , 1) is not a solution

Point (3 , 2)

∵ x = 3

∴ y = \frac{1}{3} (3) + 1

∴ y = 1 + 1 = 2 ⇒ same value of the point

∴ (3 , 2) is a solution

Point (12 , 9)

∵ x = 12

∴ y = \frac{1}{3} (12) + 1

∴ y = 4 + 1 = 5 ⇒ not the same value of the point

∴ (12 , 9) is not a solution

Point (21 , 8)

∵ x = 21

∴ y = \frac{1}{3} (21) + 1

∴ y = 7 + 1 = 8 ⇒ same value of the point

∴ (21 , 8) is a solution

6 0
2 years ago
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