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3 years ago

Explain which properties you would use to fully expand (the problem in the screenshot)

Mathematics

1 answer:

Sholpan [36]3 years ago

5 0

Answer:

Firs property used : Quotient Property

$log_b(\frac{X}{Y} ) = log_bX -log_bY$

$log_b(\frac{\sqrt[3]{x} }{36y^2} ) = log_b(\sqrt[3]{x}) - log_b(36y^2)$

Second property used : Product Property

$log_b(XY) = log_bX + log_b Y$

$log_b(\sqrt[3]{x}) - log_b(36y^2) = (log_b(\sqrt[3]{x}) - [log_b36 + log_by^2)$

Third property used : Power Property

$log_b \sqrt[n]{X} = log_b(X)^{\frac{1}{n}} = \frac{1}{n} log_b X$

$(log_b(\sqrt[3]{x}) - [log_b6^2 + log_by^2) = \frac{1}{3} log_bx - 2log_b 6 - 2log_by$

Fully expanded form:

$log_b(\frac{\sqrt[3]{x} }{36y^2} ) = \frac{1}{3} log_b x-2log_b6-2log_by$

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Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and

balu736 [363]

Answer:

(a) The sample size required is 43.

(b) The sample size required is 62.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

$CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

(a)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 72 seconds = 1.2 minutes

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1.2}]^{2}\\\\=42.684\\\\\approx 43$

Thus, the sample size required is 43.

(b)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 1 minute

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1}]^{2}\\\\=61.4656\\\\\approx 62$

Thus, the sample size required is 62.

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3 years ago

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 12 each week for a number of

Gre4nikov [31]

Answer:

what the answer

Step-by-step explanation:

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3 years ago

-0.5,1.25,-1/3,0.5,-5/3 ordered from least to greatest

vampirchik [111]

Answer:

Step-by-step explanation:

-5/3,-0.5,-1/3,0.5,1.25

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3 years ago

the local Swim Center is making a special offer they regular charge is $7 per day to swim at the pool the special offer would ha

algol [13]

To fill in the first column =
Every day is 7 dollars, which you have already answered.
The second one would be =
day 0 = 30 dollars. And then it would be 4$ for days 1 through 10.
Hope this helps!

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3 years ago

What is the sum of the difference?

Alona [7]

Answer:

A. 9x^4 and 3x^5y

Step-by-step explanation:

there are two ways to solve this:

first way:

You can solve this my substituting numbers for x and y in this case i used 2 for x and 3 for y and see which one is equal to the original equations

the second way is the regular way

when you add or subtract numbers with variables and exponents you want to add the constants and add the exponents in this case $5x^{4} +4x^2$ is the same as $(5x+4x)^(4+4)$ = $9x^4$ and you can do the same process for subtraction

$12x^{5}y-9x^5 y\\(12x-9x)^(5+5)*y$ = $3x^5y$

8 0

3 years ago