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Rudik [331]
3 years ago
5

Please help me answer thanks.

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³  ← k is the constant of proportion

To find k use the condition when r = 4, M = 160, thus

160 = k × 4³ = 64k ( divide both sides by 64 )

2.5 = k

M = 2.5r³ ← equation of variation

(a)

When r = 2, then

M = 2.5 × 2³ = 2.5 × 8 = 20

(b)

When M = 540, then

540 = 2.5r³ ( divide both sides by 2.5 )_

216 = r³ ( take the cube root of both sides )

r = \sqrt[3]{216} = 6

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Natalija [7]

The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively

<h3>The value of P(A)</h3>

The event A is given as:

A : Sum greater than 6

In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes

This means that:

P(A) = 21/36

Simplify

P(A) = 7/12

<h3>The value of P(B)</h3>

The event B is given as:

B : Sum is divisible by 2

In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes

This means that:

P(B) = 18/36

Simplify

P(B) = 1/2

Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively

Read more about probability at:

brainly.com/question/251701

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2 years ago
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Step-by-step explanation:

Verticle angles are formed when two lines intersect. The angles opposite each other are congruent, those angles are called vertical angles.

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