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Free_Kalibri [48]
2 years ago
9

Rewrite the following expression as a single logarithm 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

Mathematics
1 answer:
mixer [17]2 years ago
5 0

The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).

<h3>What is the rewritten form of the expression?</h3>

The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;

2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)

= log {(x+3)²(x-2)^5}/(x-7)³(x²)

Read more on logarithm;

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A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Ke
yaroslaw [1]

Answer:

a. 0.563 = 56.3% probability that for the next 60 minutes (two time periods) the system will be in the delay state.

b. 0.625 = 62.5% probability that in the long run the traffic will not be in the delay state

Step-by-step explanation:

Question a:

The probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75.

The system currently is in traffic delay, so for the next time period, 0.75 probability of a traffic delay. If the next period is in a traffic delay, the following period will also have a 0.75 probability of a traffic delay. So

0.75*0.75 = 0.563

0.563 = 56.3% probability that for the next 60 minutes (two time periods) the system will be in the delay state.

b. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places.

If it doesn't have a delay, 85% probability of continuing without a delay.

If it has a delay, 75% probability of continuing with a delay.

So, for the long run:

x: current state

85% probability of no delay if x is in no delay, 100 - 75 = 25% if x is in delay(1-x). So

0.85x + 0.25(1 - x) = x

0.6x + 0.25 = x

0.4x = 0.25

x = \frac{0.25}{0.4}

x = 0.625

0.625 = 62.5% probability that in the long run the traffic will not be in the delay state

5 0
3 years ago
A store can buy 8 cartons of milk for $24 dollars or 7 cartons of milk for $28.
Anettt [7]

Answer:

C

Step-by-step explanation:

Divide 24 by 8 equals 3..

7 0
2 years ago
Can somone please help me with this
Vitek1552 [10]

Answer:

I hope this helps!

6 0
3 years ago
A shipping company is creating their own shipping boxes. They have created a box with a volume of 800in^3 , a height of 8 inches
Firdavs [7]

Answer:

Length = 10 inches

Width = 10 inches

Step-by-step explanation:

The perimeter of the base is 40 inches, so we can write the following equation:

2*Length + 2*Width = 40

Length + Width = 20 (eq1)

The volume of the box is 800 in3, so we have:

800 = Length*Width*8

Length*Width = 100 (eq2)

From the (eq1), we have:

Length = 20 - Width

Using this value of Length in (eq2), we have:

(20 - Width)*Width = 100

20*Width - Width^2 - 100 = 0

Using Bhaskara's formula, we have:

Delta = b^2 - 4ac = 400 - 400 = 0

Width = -b/2a = -20/(-2) = 10 inches

Length = 20 - Width = 20 - 10 = 10 inches

So the length is 10 inches and the width is 10 inches

3 0
3 years ago
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What is the answer?​
romanna [79]

Answer:

x = 5

Step-by-step explanation:

3 0
3 years ago
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