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Juliette [100K]
3 years ago
10

Write log(x^2-9)-log(x+3) as a single logarithm.

Mathematics
2 answers:
AfilCa [17]3 years ago
5 0
One way: log(A)-log(B) = log(A/B) right?

So, log( x^2-9/(x+3))

Now x^2-9 = (x+3)*(x-3), and x^2-9/(x+3) = x-3,

so log(x^2-9)-log(x+3) = log(x-3),

Indeed for all x but for x = -3, but probably no one asks you about that detail?
Tresset [83]3 years ago
5 0

Answer:

b edge

Step-by-step explanation:

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The expression can be represented as 16 3/4 divided by 3 7/8
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The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and a standard
Anarel [89]

Answer:

a) 266 tubes ,  TC_r = $53.2

b) 266 tubes ,  T.Loss = $13.30

Step-by-step explanation:

Given:

- The sample size of tubes n = 1,000 tubes

- The mean of the sample u = 6.5 oz

- The standard deviation of the sample s.d = 0.8 oz

- Cost of manufacturing a tube C_t = 50 cents

- Cost of refilling a tube C_r = 20 cents

- Profit loss per tube Loss = 5 cents

Find:

a). How many tubes will be found to contain less than 6 ounces? In that case, what will be the total cost of the  refill?

b) How many tubes will be found to contain more than 7 ounces? In that case, what will be the amount of  profit lost?

Solution:

- First we will compute the probability of tube containing less than 6 oz.

- Declaring X : The amount of toothpaste.

Where,                         X ~ N ( 6.5 , 0.8 )

- We need to compute P ( X < 6 oz )?

Compute the Z-score value:

                  P ( X < 6 oz ) =  P ( Z < (6 - 6.5) / 0.8 ) = P ( Z < -0.625 )

Use the Z table to find the probability:

                               P ( X < 6 oz ) = P ( Z < -0.625 ) = 0.266

- The probability that it lies below 6 ounces. The total sample size is n = 1000.

       The number of tubes with X < 6 ounces = 1000* P ( X < 6 oz )

                                                                           = 1000*0.266 = 266 tubes.

- The total cost of refill:

                            TC_r = C_f*(number of tubes with X < 6)

                            TC_r = 20*266 = 5320 cents = $53.2

- We need to compute P ( X > 7 oz )?

Compute the Z-score value:

                  P ( X > 7 oz ) =  P ( Z > (7 - 6.5) / 0.8 ) = P ( Z < 0.625 )

Use the Z table to find the probability:

                               P ( X > 7 oz ) = P ( Z > 0.625 ) = 0.266

- The probability that it lies above 7 ounces. The total sample size is n = 1000.

       The number of tubes with X > 7 ounces = 1000* P ( X > 7 oz )

                                                                           = 1000*0.266 = 266 tubes.

- The total cost of refill:

                            T.Loss = Loss*(number of tubes with X > 7)

                            T.Loss = 5*266 = 1330 cents = $13.30

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Step-by-step explanation:

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Answer:

the answer is below

Step-by-step explanation:

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