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ValentinkaMS [17]
2 years ago
13

Help needed!!! Please

Mathematics
1 answer:
Sliva [168]2 years ago
7 0

Answer:

<em>The correct option is:  C. x=6\sqrt{3}, y=12</em>

Step-by-step explanation:

The two angles of the triangle are given as 60° and 60°

As the sum of all three angle in any triangle is always 180°, so the measure of the third angle will be: 180°-(60°+60°) = 180° - 120° = 60°

Now each angle of the triangle is 60°, it means the triangle is equilateral.

The base of the triangle is given as 12. So, the length of each side will be 12.

That means, the value of y=12

Now in the left right triangle.....

Sin(60)=\frac{x}{y} \\ \\ \frac{\sqrt{3}} {2}=\frac{x}{12} \\ \\ 2x=12\sqrt{3} \\ \\ x=6\sqrt{3}

So, the value of x = 6\sqrt{3}

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The following data were collected by counting the number of operating rooms in use atTampa general Hospital over a 20-day period
arlik [135]

Answer:

a)

Operating room x    1         2      3       4

P(x)                          0.15  0.25  0.4   0.2

b)

The graph of probability distribution is in attached image.

c)

All the probabilities lies in the range (0 to 1) and the probabilities add up to 1 so, the computed probability distribution is the valid probability distribution.

Step-by-step explanation:

Number of operating rooms   Days

1                                                  3

2                                                 5

3                                                 8

4                                                 4

a)

Sum of frequencies=1+2+3+4=10

Operating rooms x   frequency f  Relative frequency

1                                    3                    3/20=0.15

2                                   5                   5/20=0.25

3                                   8                   8/20=0.4

4                                   4                   4/20=0.2

So, using the relative frequency approach, a discrete probability distribution for number of operating rooms in use on any given day is

Operating room x    1         2      3       4

P(x)                          0.15  0.25  0.4   0.2

b)

The graph of probability distribution is in attached image.

c)

There are two conditions for a probability distribution to be valid

1. All probability must ranges from 0 to 1.

2. All probabilities must add up to 1.

We can see that all the probabilities lies in the range (0 to 1), so, condition 1 is satisfied.

For condition 2,

sum[p(x)]= 0.15+0.25+0.4+0.2=0.4+0.6=1.

As the probabilities add up to 1, so the condition 2 is also satisfied.

Thus, the computed probability distribution is the valid probability distribution.

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