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Ira Lisetskai [31]
3 years ago
10

Find the distance between the points (2, 7) and (-6, -2).

Mathematics
1 answer:
maw [93]3 years ago
7 0

Answer:

Approximately 12.04 units.

Step-by-step explanation:

The find the distance between any two points, we can use the distance formula, which is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

We have the points (2,7) and (-6,-2). Let's let (2,7) be (x₁, y₁) and let's let (-6, -2) be (x₂, y₂). Substitute:

d=\sqrt{(-6-2)^2+(-2-7)^2

Subtract:

d=\sqrt{(-8)^2+(-9)^2

Square:

d=\sqrt{64+81}

Add:

d=\sqrt{145}

Approximate

d=\sqrt{145}\approx12.04

So, the distance between (2,7) and (-6,-2) is approximately 12.04 units.

And we're done!

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If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these
igomit [66]

Answer:

64

Step-by-step explanation:

If the mean is 15, the sum of 5 numbers is:

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Minimum value for the first four numbers would be:

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Then the fifth number is:

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So the maximum difference is:

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The prior probabilities for events A1 and A2 are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A1 ∩ A2) = 0. Suppose P(
san4es73 [151]

Answer:

Check Explanation

Step-by-step explanation:

a) Yes, the two events are mutually exclusive. The true meaning of mutually exclusive is that both A1 and A2 have no sample points in common and cannot both occur at the same time.

The only sure mathematical way to tell is from P(A1 n A2) = 0.

Note that this is different from when two events are independent. Two events are independent when the chances of one occurring does not depend on the chances of the other event occurring at all. Independent events can both occur at the same time. Mathematically, independent events are described as P(A1|A2) = P(A1) and P(A2|A1) = P(A2)

b) To solve for P(B)

We use the mathematical definition of the conditional statement

P(B|A1) = P(B n A1)/P(A1)

P(B n A1) = P(B|A1) × P(A1) = 0.2 × 0.4 = 0.08

P(B|A2) = P(B n A2)/P(A2)

P(B n A2) = P(B|A2) × P(A2) = 0.05 × 0.6 = 0.03

P(B) = P(B n A1) + P(B n A2) (especially because A1 and A2 are mutually exclusive)

P(B) = 0.08 + 0.03 = 0.11

Hope this helps!!

5 0
3 years ago
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