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Reil [10]
3 years ago
15

What is the simplified base of the function f(x) = 1/4 3/108*x?

Mathematics
2 answers:
frozen [14]3 years ago
5 0

Answer:

The Option A. 3 is correct.

Step-by-step explanation:

The function is given to be :

f(x)=\frac{1}{4}(\sqrt[3]{108} )^x

Now, we need to simplify the above function in order to obtain the base simplified form of the given function f(x)

\implies f(x)=\frac{1}{4}\cdot (108)^{\frac{x}{3}}\\\\\implies f(x)=(27)^\frac{x}{3}\\\\\implies f(x)=(3^3)^\frac{x}{3}\\\\\implies f(x)=(3)^{3\times \frac{x}{3}}\\\\\implies f(x)=3^x

Hence, the base simplified form of the given function f(x) is 3

Therefore, The Option A. 3 is correct.

Zinaida [17]3 years ago
4 0
The Answer is B. 3 x 3/4
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1 (66 divided by 6)+31"
Juliette [100K]

Answer:

1. 42

2. 6

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Step-by-step explanation:

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6 0
3 years ago
Bottles of sparkling water usually cost $1.69. The grocer changed the price to 4 for $5. You bought one bottle last week for $1.
sleet_krkn [62]

Given :

Cost of single bottle, C = $1.69 .

Cost of 4 bottles, B = $5 .

You bought one bottle last week for $1.69 and one bottle this week at the 4 for $5 price.

To Find :

Did you pay more or less for the bottle this week at 4 for $5? How much more or less?

Solution :

Effective price per bottle if we purchase 4 is, E = 5/4 = $1.25 .

Regular price, R = $1.69 .

Change in price, C = $( 1.69 - 1.25 ) = $0.44 .

Therefore, we are paying $0.44 less than the actual price.

Hence, this is the required solution.

8 0
3 years ago
Read 2 more answers
the sum of four consecutive integers is 2174. what are the integers? (continuation) the smallest of four consecutive integers is
timofeeve [1]
The smallest of the four numbers is x.
Since the four numbers are consecutive, this means that each number is one more than the previous.
Therefore, the four numbers are:
x
x + 1
x+1 + 1 = x+2
x+2 + 1 = x+3

Now, we are given that the sum (s) of the four numbers is 2174
This means that:
s = x+x+1+x+2+x+3
s = 4x + 6

We are given that s = 2174. Substitute with s in the above equation and solve for x as follows:
2174 = 4x + 6
4x = 2174 - 6
4x = 2168
x = 2168 / 4
x = 542

Based on the above calculations, the four numbers are:
542, 543, 544 and 555

7 0
3 years ago
Read 2 more answers
Polly's Polls asked 1850 second-year college students if they still had their original major. According to the colleges, 65% of
suter [353]

Answer:

The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424

Step-by-step explanation:

The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.

Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.

The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.

We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words

W = \frac{X-\lambda}{\sigma} = \frac{X-1202.5}{20.5152}

The values of the cummulative function of the standard normal variable W, which we will denote \phi are tabulated and they can be found in the attached file.

Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.

P(1184 < X < 1221) = P(\frac{1184-1202.5}{20.5152} < \frac{X-1202.5}{20.5152} < \frac{1221-1202.5}{20.5152})\\ = P(-0.9018 < W < 0.9018) = \phi(0.9018) - \phi(-0.9018) = \phi(0.9018)-(1-\phi(0.9018))\\ = 2\phi(0.9018)-1 = 2*0.8212-1 = 0.6424

Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.

Download pdf
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