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Scrat [10]
3 years ago
5

(07.03)

Mathematics
2 answers:
Sloan [31]3 years ago
8 0
The answer would be log base 2 of 6 over log base 2 of 3

julia-pushkina [17]3 years ago
5 0

Answer:

Log base 2 of 6 over log base 2 of 3

Step-by-step explanation:

In order to make a change of base of a logarithm, we apply this principle:

log_{a}b = \frac{log_{c}b}{log_{c}a}

Where:

a: current base of the logarithm [in this case a = 3]

b: argument of the logarithm [in this case b = 6]

c: new base of the logarithm [in this case c = 2]

Applying this principle in this exercise, we have:

log_{3}6 = \frac{log_{2}6}{log_{2}3}

This quotient of logarithms can be expressed as:

Log base 2 of 3 over log base 2 of 6

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How many pies are there if someone eats 2 and then someone else eats 4 then I eat 13? We started with 200 pies.
Leno4ka [110]

Answer:

183

Step-by-step explanation: 13+4=17    200-17=183

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If it takes Katie 4 hours to make 20 cupcakes that at that rate how many cupcakes could made in 12 hours answer
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The answer is 60 cupcakes

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Factor 2y^2+7y-14=0<br> How do I solve this by factoring ?
Gre4nikov [31]

Answer:

y=−7−(√161/4), −7+(√161)/4

Decimal form- y=1.42214438, -4.92214438

Step-by-step explanation:

3 0
3 years ago
7
marta [7]

Option c is correct formula

6 0
2 years ago
In the university library elevator there is a sign indicating a 16-person limit as well as a weight limit of 2750 pounds. Suppos
Alona [7]

Answer:

0.039 = 3.9% probability that the random sample of 16 people in the elevator will exceed the weight limit

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

If n variables are added, the mean is n\mu and the standard deviation is s = \sqrt{n}\sigma

In this problem:

n = 16, \mu = 160*16 = 2560, s = \sqrt{16}*27 = 108

What is the probability that the random sample of 16 people in the elevator will exceed the weight limit?

This is 1 subtracted by the pvalue of Z when X = 2750. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{2750 - 2560}{108}

Z = 1.76

Z = 1.76 has a pvalue of 0.961

1 - 0.961 = 0.039

0.039 = 3.9% probability that the random sample of 16 people in the elevator will exceed the weight limit

7 0
2 years ago
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