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Gekata [30.6K]
1 year ago
8

What is the answer to the question down below

Mathematics
1 answer:
ratelena [41]1 year ago
5 0

We conclude that the measure of that angle is 150 degrees.

<h3>How to get the measure of angle BFE?</h3>

Notice that  the measure of angle ∠BFE will be equal to:

∠BFE = ∠BFC + ∠CFD + ∠DFE

Where:

∠CFD = 90°

∠DFE = 30°

And we will have that:

∠AFC = 180° - 90° - 30° = 60°

And we know that BF bisects that angle, then:

∠BFC = 30°

So we conclude that:

∠BFE = ∠BFC + ∠CFD + ∠DFE = 30° + 90° + 30° = 150°

We conclude that the measure of that angle is 150 degrees.

If you want to learn more about angles:

brainly.com/question/17972372

#SPJ1

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Six inches.

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A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
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Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

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