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3 years ago

Select all expressions that are equivalent to 4(y + 2).

Mathematics

1 answer:

hram777 [196]3 years ago

3 0

Answer:

Step-by-step explanation:

× A = 4y + 2 = 2(4y/2 + 2/2) = 2(2y + 1) ≠ 4(y + 2)

✓ B = 4y + 8 = 4(4y/4 + 8/4) = 4(y + 2) = 4(y + 2)

× C = y + y + y + y + 2 =

y (1 + 1 + 1 + 1) + 2 = 4y + 2 = A ≠ 4(y + 2)

✓ D = 5(y + 2) – (y + 2) = 5(y + 2) – 1(y + 2) =

(5 – 1)(y + 2) = 4(y + 2)

✓ E = y + y + y + y + 2 + 2 + 2 + 2 =

y (1 + 1 + 1 + 1) + (2 + 2 + 2 + 2) =

4y + 8 = B = 4(y + 2)

× F = 5(y + 2) – (y – 2) =

(5y + 10) + (-y + 2) =

(5y – y) + (10 + 2) =

4y + 12 = 4(y + 3) ≠ 4(y + 2)

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4 years ago

A survey is conducted to find out whether people in metropolitan areas obtain their news from television (Event T), an newspaper

MrMuchimi

Answer:

e) P ( R' | T ) = 0.62857

f) P ( T' | N ) = 0.32258

g) P ( R' | N ) = 0.70968

h) P ( T' | N&R ) = 5/6

Step-by-step explanation:

Given:

- The probability of Television as news source P ( T ) = 0.7

- The probability of Newspaper as news source P ( N ) = 0.62

- The probability of Radio as news source P ( R ) = 0.46

- The probability of Television & Newspaper as news source P (T&N) = 0.42

- The probability of Television & Radio as news source P (T&R) = 0.26

- The probability of Radio & Newspaper as news source P (R&N) = 0.18

- The probability of all 3 as news source P ( T & R & N ) = 0.03

Find:

Given that TV is a news source, what is the probability that radio is not a news source?

Given that newspaper is a news source, what is the probability that TV is not a news source?

Given that newspaper is a news source, what is the probability that radio is not a news source?

Given that both newspaper and radio are news sources, what is the probability that TV is not a news source?

Solution:

- We will first compute the individual probability of each event occurring alone.

P (Television is the only news source) = P(T) - P(T&R) - P(T&N) + P(T&N&R)

P ( Only Television ) = P ( only T ) = 0.7 - 0.42 - 0.26 + 0.03 = 0.05

P (Newspaper is the only news source) = P(N)-P(N&R)-P(T&N)+P(T&N&R)

P ( Only Newspaper ) = P ( only N ) = 0.62 - 0.18 - 0.42 + 0.03 = 0.05

P (Radio is the only news source) = P(R) - P(T&R) - P(N&R) + P(T&N&R)

P ( Only Radio ) = P ( only R ) = 0.46 - 0.26 - 0.18 + 0.03 = 0.05

- Now for part e)

We are asked for a conditional probability of the form as follows:

P ( R' | T ) = P ( R' & T ) / P ( T )

First compute the probability that next news source is not Radio provided it is already a source of TV.

P ( R' & T ) = P( only T ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | T ) = 0.44 / 0.7

P ( R' | T ) = 0.62857

- Now for part f)

We are asked for a conditional probability of the form as follows:

P ( T' | N ) = P ( T' & N ) / P ( N )

First compute the probability that next news source is not TV provided it is already a source of Newspaper.

P ( T' & N ) = P( only N ) + P ( only R & N ) = 0.05 + 0.18 - 0.03 = 0.2

Hence,

P ( T' | N ) = 0.2 / 0.62

P ( T' | N ) = 0.32258

- Now for part g)

We are asked for a conditional probability of the form as follows:

P ( R' | N ) = P ( R' & N ) / P ( N )

First compute the probability that next news source is not Radio provided it is already a source of Newspaper.

P ( R' & N ) = P( only N ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | N ) = 0.44 / 0.62

P ( R' | N ) = 0.70968

- Now for part h)

We are asked for a conditional probability of the form as follows:

P ( T' | N&R ) = P ( T' & N & R) / P ( N & R )

First compute the probability that next news source is not TV provided it is already a source of both radio and Newspaper.

P ( T' & N & R) = P ( only N & R ) = 0.18 - 0.03 = 0.15

Hence,

P ( T' | N&R ) = 0.15 / 0.18

P ( T' | N&R ) = 5/6

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3 years ago

Item 20 A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles

Digiron [165]

Answer:

A) total distance covered = 60miles

B) total time taken = 4hrs 30 mins

Step-by-step explanation:

Detailed explanation and calculation is shown in the image below

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3 years ago

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