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yanalaym [24]
3 years ago
9

Please help: A box contains 5 yellow balls, 3 blue, and 1 red ball. Two balls are drawn at random. Find the probability that:

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
8 0

Answer:

a) 0.2778

b) 0.3611

c) 0.1389

d) 0.0833

Step-by-step explanation:

We have a total of 5 + 3 + 1 = 9 balls

a) First ball being yellow: we have 5 yellow balls, so P1 = 5/9

Second ball being yellow after one yellow was drawn: we have 4 yellows and 8 balls, so P2 = 4/8 = 1/2

Both yellows: P = P1 * P2 = 5/18 = 0.2778

b) Both blues:

P1 = 3/9 = 1/3

P2 = 2/8 = 1/4

P = P1 * P2 = 1/12 = 0.0833

Both yellows or both blues: 5/18 + 1/12 = 0.2778 + 0.0833 = 0.3611

c) First yellow: P1 = 5/9

Second red: P2 = 1/8

Pa = P1 * P2 = 5/72

or

First red: P3 = 1/9

Second yellow: P4 = 5/8

Pb = P3 * P4 = 5/72

P = Pa + Pb = 10/72 = 5/36 = 0.1389

d) First blue: P1 = 3/9 = 1/3

Second red: P2 = 1/8

Pa = P1 * P2 = 1/24

or

First red: P3 = 1/9

Second blue: P4 = 3/8

Pb = P3 * P4 = 1/24

P = Pa + Pb = 2/24 = 1/12 = 0.0833

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35/40 reducing fractions
laila [671]

Answer: 7/8

What you have to do here is to find the highest number which can be divided by both. Or you have to divide both the numerator and denominator until it can not be divided by any number anymore. You can do this by finding the highest common factor (<u>HCF)</u> of both the number, 35 and 40.

Highest Common Factor: HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.

So, the highest number which divides 35 and 40, is 5. Now 35 divided by 5 is 7 and 40 divided by 5 is 8. The final answer is 7/8 and there is no more numbers which can divide both of them by a specific number.


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2 years ago
Graph this rational equation. Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asy
irakobra [83]

Step-by-step explanation:

We have given,

A rational function : f(x) = \frac{x-2}{x-4}

W need to find :

Point of discontinuity : - At x = 4, f(x) tends to reach infinity, So we get discontinuity point at x =4.

For no values of x, we get indetermined form (i.e \frac{0}{0}), Hence there is no holes

Vertical Asymptotes:

Plug y=f(x) = ∞ in f(x) to get vertical asymptote   {We can us writing ∞ = \frac{1}{0}}

i.e ∞ = \frac{x-2}{x-4}

or \frac{1}{0}=\frac{x-2}{x-4}

or x-4 =0

or x=4, Hence at x = 4, f(x) has a vertical asymptote

X -intercept :

Plug f(x)=0 , to get x intercept.

i.e 0 = \frac{x-2}{x-4}

or x - 2 =0

or x = 2

Hence at x=2, f(x) has an x intercept

Horizontal asymptote:

Plug x = ∞ in f(x) to get horizontal asymptote.

i.e f(x) = \frac{x-2}{x-4} = \frac{x(1-\frac{2}{x} )}{x(1-\frac{4}{x} )}

or f(x) = \frac{(1-\frac{2}{∞} )}{(1-\frac{4}{∞} )}

or f(x) = 1 = y

hence at y =f(x) = 1, we get horizontal asymptote





4 0
3 years ago
Which point is a solution to the system of linear equations?
Sloan [31]

The ordered pair which is a solution to the system of linear equations is: A. (3, 0).

<h3>How to determine the solution?</h3>

In order to determine a solution to the system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (3, 0), we have:

y = −x + 3

0 = -3 + 3

0 = 0 (True).

2x − y = 6

2(3) - 0 = 6

6 - 0 = 6

6 = 6 (True).

For ordered pair (3, -1), we have:

y = −x + 3

-1 = -3 + 3

-1 = 0 (False).

For ordered pair (0, 3), we have:

y = −x + 3

3 = 0 + 3

3 = 3 (True).

2x − y = 6

2(0) - 3 = 6

0 - 3 = 6

-3 = 6 (False).

For ordered pair (-1, 3), we have:

y = −x + 3

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3 = 2 (False).

Read more on ordered pairs here: brainly.com/question/12179097

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6 0
1 year ago
In the diagram, which angles are vertical angles? Check all that apply.
dybincka [34]
The vertical angles made is ABE and CBD, Thus meaning that your answer is B
5 0
2 years ago
Read 2 more answers
California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive ma
Elanso [62]

Answer:

a) The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is P=0.7788

b) The probability that at least 7 months elapsed before the first earthquake of destructive magnitude occurs knowing that 3 months have already elapsed is P=0.7165

Step-by-step explanation:

Tha most appropiate distribution to model the probability of this events is the exponential distribution.

The cumulative distribution function of the exponential distribution is given by:

P(t

The destructive earthquakes happen in average once a year. This can be expressed by the parameter λ=1/year.

We can express the probability of having a 3 month period (t=3/12=0.25) without destructive earthquakes as:

P(t>0.25)=1-P(t

Applying the memory-less property of the exponential distribution, in which the past events don't affect the future probabilities, the probability of having at least 7 months (t=0.58)  elapsed before the first earthquake given that 3 months have already elapsed, is the same as the probability of having 4 months elapsed before an earthquake.

P(t>0.58)/P(t>0.25)=P(t>0.33)

P(t>0.33)=1-P(t

8 0
3 years ago
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