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deff fn [24]
3 years ago
8

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variab

les represent positive real numbers.
7log x + 2log y

log(14xy)

log(x7 + y2)

log(x7y2)

log(7x + 2y)
Mathematics
1 answer:
Viefleur [7K]3 years ago
5 0

Answer:

log(x^7·y^2)

Step-by-step explanation:

The applicable rules are ...

... log(a^b) = b·log(a)

... log(ab) = log(a) +log(b)

_____

The first term, 7log(x) can be rewritten as log(x^7). Note that an exponentiation operator is needed when this is written as text.

The second term 2log(y) can be rewritten as log(y^2). These two rewrites make use of the first rule above.

Now, you have the sum ...

... log(x^7) +log(y^2)

The second rule tells you this can be rewritten as ...

... log(x^7·y^2) . . . . . seems to match the intent of the 3rd selection

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Describe a model that represents 3/3 x 4/4??
Oduvanchick [21]
They are both fractions, but 3/3 is 1 whole and 4/4 is 1 whole also.
so 1 whole times 1 whole equals 1
number form of my explanation:
3/3=1
4/4=1
1x1=1
Describe complete!
4 0
3 years ago
Karl is making a pot of chili. The recipe calls for StartFraction 3 Over 8 EndFraction cup of chili powder, but Karl only wants
mina [271]

Given:

The recipe calls for \dfrac{3}{8} cup of chili powder.

Karl only wants to use half as much so it won’t be so spicy.

To find:

How much chili powder should Karl use?

Solution:

We have,

Chill power for recipe = \dfrac{3}{8} cup

Chill power used by Karl is half  of chill power for recipe.

\text{Chill power used by Karl}=\dfrac{1}{2}\times \dfrac{3}{8} cup\text{Chill power used by Karl}=\dfrac{3}{16} cup

Therefore, \dfrac{3}{16} cup of chili powder should Karl use.

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3 years ago
Read 2 more answers
Describe how you could use algebraic operations to solve the equation 1 = -3x + 4
Anna11 [10]

Answer:

x=1

Step-by-step explanation:

3x=4-1

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3 0
3 years ago
You are given the information that P(A) = 0.30 and P(B) = 0.40.
Ad libitum [116K]

Answer:

1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).

Step-by-step explanation:

We can solve this question considering the following:

For two mutually exclusive events:

\\ A_{1}\;and\;A_{2}

\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) (1)

An extension of the former expression is:

\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2}) (2)

In <em>mutually exclusive events,</em> P(A and B) = 0, that is, the events are <em>independent </em>one of the other, and we know the probability that <em>both events happen</em> <em>at the same time is zero</em> (P(A <em>and</em> B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A <em>and</em> B) is some number different from zero. Notice the difference between <em>OR</em> and <em>AND. The latter implies that both events happen at the same time.</em>

In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not <em>mutually exclusive</em>, that is, there are some cases in which the events share the same probabilities in a way that these probabilities <em>must be subtracted</em> from the total, so those probabilities in common do not "inflate" the actual probability.

For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.

The number 0.07 represents the probability that <em>both events occur at the same time</em>, so the probability that this person ask for checking a tire or the lube oil of his/her car is:

P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.

That is why we cannot simply add some given probabilities <em>without acknowledging if the events are or not mutually exclusive</em>, whereas we can certainly add the probabilities in question when we know that both probabilities are <em>mutually exclusive</em> since P(A and B) = 0.

In conclusion, knowing the events are mutually exclusive <em>does</em> provide <em>extra information</em> and we can proceed to simply add the probabilities of either event; thus, the answers are those in which <em>we need to previously know the value of P(A and B)</em>.  

7 0
3 years ago
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