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3 years ago

Which exponential equation correctly rewrites this logarithmic equation? log6 18=x

Mathematics

1 answer:

Zanzabum3 years ago

3 0

Given:

The logarithmic equation is:

$\log_618=x$

To find:

The exponential equation of this logarithmic equation.

Solution:

According to the properties of logarithm:

$\log_bm=x\Leftrightarrow m=b^x$

We have,

$\log_618=x$

Here, $b=6, m=18$ . Using the above property of logarithm, we get

$18=6^x$

Therefore, the required exponential equation is $18=6^x$ .

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Assume the sample variances to be continuous measurements. Find the probability that a random sample of 25observations, from a n

konstantin123 [22]

Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

$T = \frac{(n-1) S^2}{\sigma^2}$

And the distribution for this statistic is $T \sim \chi^2_{n-1}$

For this case we know that n =25 and $\sigma^2 = 6$ so then our statistic would be given by:

$\chi^2 = \frac{(n-1)S^2}{\sigma^2}=\frac{24 S^2}{6}= 4S^2$

With 25-1 =24 degrees of freedom.

Solution to the problem

Part a

For this case we want this probability:

$P(S^2 > 9.1)$

And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

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2 years ago

Freddy is helping buy ingredients for salads for the school spaghetti dinner. He bought 10 pounds of onions at $0.69 per pound,

dezoksy [38]

Hey there,

Answer: Tomatoes

If you multiply 10 x 0.69 (for onions) it would be 6.9
If you multiply 100 x 0.99 (for tomatoes) it would be 99
Lastly, if you multiply 100 x 0.69 (for lettuce) if would be 69

Which are the most? Tomatoes.

~ Hope this helps, and if you have any questions or concerns, feel free to pm me or comment down below :)

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2 years ago

4 students is ____% of 20 students

Rudiy27

Answer:

20%

Step-by-step explanation:

20 * 20% = 4

or you can change it to a decimal

20 * .2 = 4

hope this helped! :)

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2 years ago

Find the distance between each pair of point. Round to the nearest hundredth(-8, -2) and (6, -1)

Murljashka [212]

Answer:

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Step-by-step explanation:

delta x=14

delta y=1

therefore with the Pythagorean theorem, the hypotenuse/distance is the square root of 197

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ikadub [295]

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