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SOVA2 [1]
3 years ago
11

A bag contains 3 red marbles and 8 blue marbles. A marble is drawn from the bag, the color recorded, then the marble is put back

into the bag. This process is repeated ten times, and we are interested in the number of blue marbles drawn. What would be the probability of success in this experiment
Mathematics
1 answer:
Oksana_A [137]3 years ago
3 0

Answer:

0.0414

Step-by-step explanation:

Total number of marbles= 8+3= 11

8 blue and 3 red

Marbles are picked with replacement until 10 marbles are selected.

Probability of number of blue marbles choosen in 10 pick with replacement out of 11 marbles= ((8C1/11C1))^10

=(8/11)^10

=0.72723^10

= 0.0414

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Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
Nitella [24]

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

 

So what we have to do is to look for the values of the variables:

<span>For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9</span>

<span>
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49</span>

 

<span>By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2 </span>

<span>b^2 =  49 – 9</span>

<span>b^2  = 40

</span>

Therefore the equation of the hyperbola is:

<span>(x^2 / 9) – (y^2 / 40) = 1</span>

5 0
3 years ago
Read 2 more answers
Please help me, this is PEDMAS
rusak2 [61]

Answer:

1). 183

2). 83

3). 353

4). -2652

5). 59

6). 510

7). -293

8). 79

9). 78

10). 87

Step-by-step explanation:

Considering order of operation, parenthesis must be simplified first.

The solutions to the given questions are shown below;

1). \ \ 5+(7\times (3+2)^2) + 3=8 +  (7\times (5)^2)  = 8 + (7\times 25) = 8 + 175 = 183

2). \ 16+(8+ (6+2)^2) - 5=16-5 +  (8+ (8)^2)  = 11 + (8+64) = 11 + 72 = 83

3). \ (15+ 3)^2 + ((14+6)+3^2)= (18)^2 + ((20) + 9) = 324 + (29) = 353

4). \ ((11+ 2)-(24+2)^2)\times 2^2 = (13 - 676) \times 4  = (-663)\times 4 = -2652

5). \ ((4+3)^2+ 6) -5+3^2= (49 + 6) - 5 + 9= (49+6+9) - 5 = 64-5 = 59

6). \ (20+ 2)^2 +((15+7)+2^2)= (484) + (22+ 4)= 484 + 26 =510

7). \ ((12 + 4)- (15+3)^2+ 5^2 = (16 -  324) + 25 = -318 + 25 = -293

8). \ (6^2+ (24+ 3+5^2)) - 3^2= (36 + (52)) - 9 = (88) - 9 = 79

9). \ ((10-4)^2\times 2) + 2 + 2^2= ((6)^2 \times 2) + 2 + 4 = (36\times 2)+ 6 = 72 + 6 = 78

10). \ (7^2 + (16 + 8 + 2^2)) + 3^2 = (49 + 28) + 9 = 78 + 9 = 87

3 0
3 years ago
Solve the following quadratic by factoring.
Lina20 [59]

Answer:

4, -1

Step-by-step explanation:

We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:

x^2 - 3x - 4 = 0

Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.

(x + or - ?) ( x + or - ?) = 0

Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:

(x - 4) (x + 1) = 0

To test that this is equal to the original equation, simply multiply it out using FOIL.

x * x = x^2

x * 1 = x

x * -4 = -4x

-4 * 1 = -4

Putting each component into an equation:

x^2 + x - 4x - 4 = 0

Simplifying:

x^2 - 3x - 4 = 0

Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)

Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.

You can also check your answers by plugging them back into the original equation.

5 0
3 years ago
The Sharks have played 5 basketball games this seasons. Their scores are 65,63,67,60, and 65. If they only score 30 points in th
Digiron [165]
<span>The list of scores will be: 30 60 63 65 65 67. To get the median, you have to arrange the scores from lowest to highest. The middle number is the median. In this, case there are two numbers in the middle so you have to add the two and then divide by two.</span> <span>Therefore, 63 + 65 = 128 / 2 = 64.</span>
5 0
3 years ago
The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the
maxonik [38]

Answer:

a) 0.5 = 50% of flanges exceed 1 millimeter.

b) A thickness of 0.96 millimeters is exceeded by 90% of the flanges

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

P(X > x) = \frac{b - x}{b - a}

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

This means that a = 0.95, b = 1.05

(a) Determine the proportion of flanges that exceeds 1.00 millimeters.

P(X > 1) = \frac{1.05 - 1}{1.05 - 0.95} = \frac{0.05}{0.1} = 0.5

0.5 = 50% of flanges exceed 1 millimeter.

(b) What thickness is exceeded by 90% of the flanges?

This is x for which:

P(X > x) = 0.9

So

\frac{1.05 - x}{1.05 - 0.95} = 0.9

1.05 - x = 0.9*0.1

x = 1.05 - 0.9*0.1

x = 0.96

A thickness of 0.96 millimeters is exceeded by 90% of the flanges

4 0
3 years ago
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