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4 years ago

What is the solution to the equation below? Round your answer to two

Mathematics

1 answer:

adoni [48]4 years ago

4 0

Answer:

The Solution to the equation 4ˣ = 9.2 is the option D ) x = 1.60

Step-by-step explanation:

Given:

$4^{x}=9.2$

To Find:

x = ?

Solution:

We know Logarithmic identity as

$\log (A)^{B}= B\log A\\$

$4^{x}=9.2$ .............Given

Taking Log on both the side we have

$\log 4^{x}=\log 9.2\\\textrm{using the above identity we get}\\\\x\log 4 = \log 9.2\\\\x=\frac{\log 9.2}{\log 4} \\\\\therefore x =\frac{0.9637}{0.6020} \\\\\therefore x =1.6008\\\\\therefore x = 1.60$

The Solution to the equation 4ˣ = 9.2 is the option D ) x = 1.60

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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

6 0

3 years ago

Which line is perpendicular to the line 3y=5x-1

Ainat [17]

For lines to be perpendicular their slopes have to be negative reciprocals of one another, mathematically...

m1*m2=-1...in this case:

y=5x/3=1/3 so the slope of the lines is 5/3 so any line that has a slope of:

5m/3=-1,

m=-3/5 is perpendicular to the original line...

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3 years ago

A cylindrical glass is 3 inches in diameter and 6.5 inches tall. How much water can the glass hold when full? Round your answer

Vitek1552 [10]

3 inches diameter mean 1,5 in the radius
the height is 6,5 in.

volume of a cylinder = area of base time height

V= pir^2 *h

V = 3,14*1,5^2 *6,5

V = 45,92 in^3

hope helped

3 0

4 years ago

Your parents charge a family ski trip of $3000 on a credit card, the simple interest rate is 20%. The charges are paid after 6 m

torisob [31]

Answer:

$300

Step-by-step explanation:

In this question, we are simply asked to calculate the simple interest on $3000, at a rate of 20% paid after 6 months.

We can do this as follows. Mathematically, it should be remembered that:

S.I = PRT/100

In this case, we lost out the individual values as follows:

P = $3000, R = 20% and T = 6 months = 0.5years, S.I = ?

We substitute the parameters into the equation:

S.I = (3000 * 20 * 0.5)/100 = $300

7 0

3 years ago

Complete the sentence.

ss7ja [257]

Answer:

size of the dog

Step-by-step explanation:

Hope this helps

8 0

3 years ago

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