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ss7ja [257]
2 years ago
11

the radius of Earth is 6400 km. the distance of the moon from the Earth's surface is 380000 km. find the radius of the moon whic

h subtends an angle of 20'at the centre of the earth​

Mathematics
1 answer:
-BARSIC- [3]2 years ago
4 0

Answer:

1100 km

Step-by-step explanation:

The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface.  Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.

Draw circle representing the moon and earth.  Draw tangent lines from the earth's center to the edge of the moon.  The angle between these lines is the subtended angle.  Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects.  Notice this forms a right angle.

(See attached diagram)

Using trigonometry:

sin(θ/2) = r / (R + h)

r = (R + h) sin(θ/2)

Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:

r = (6400 + 380000) sin(1/6 °)

r = 1100

The moon's radius is 1100 km.

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Harrison Water Sports has two retail outlets: Seattle and Portland. The Seattle store does 60 percent of the total sales in a ye
Anna11 [10]

Answer: P = 0.75

Step-by-step explanation:

Hi!

The sample space of this problems is the set of all the possible sales. It is divided in the disjoint sets:

S_s = {\text{sales made in Seattle }}\\S_p={\text {sales made in Portland}}

We have also the set of sales of boat accesories S_b, the colored one in the image.

We are given the data:

P(S_s) = 0.6\\P(S_b | S_s) = \frac{P(S_b\bigcap S_s)}{P(S_s)}=0.4\\P(S_b|S_p) =\frac{P(S_b\bigcap S_p)}{P(S_p)}=0.2

From these relations you can compute the probabilities of the intersections colored in the image:

pink\;set:\;P(S_b \bigcap S_s) =0.6*0.4=0.24\\blue\;set\;:P(S_b \bigcap S_p)=(1-0.6)*0.2 =0.08

You are asked about the conditional probability:

P(S_s|S_b) = \frac{P(S_s \bigcap S_b)}{P(S_b)}

To calculate this, you need  P(S_b) . In the image you can see that the set S_b is the union of the two disjoint pink and blue sets. Then:

P(S_b)=P((S_b \bigcap S_s)\bigcup(S_b \bigcap S_p)) = 0.24 + 0.08 = 0.32

Finally:

P(S_s|S_b) = \frac{0.24}{0.32}=0.75

4 0
2 years ago
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standa
Lunna [17]

Answer:

P = 0.0215 = 2.15%

Step-by-step explanation:

First we need to convert the values of 900 and 975 to standard scores using the equation:

z = \frac{x - \mu}{\sigma}

Where z is the standard value, x is the original value, \mu is the mean and \sigma is the standard deviation. So we have that:

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z = 2 -> p_2 = 0.9772

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We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:

P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215

So the probability is 0.0215 = 2.15%

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Answer:

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Step-by-step explanation:

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