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3 years ago

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(20points + brainlesest) Tom has $10 that he wants to use to buy pens and pencils. however, he does not want to buy more pens an

d pencils a pen cost $3 and a pencil cost $1. witchcraft represents the scenario (X represents the number of times and why the numbers of pencil.)

1 answer:

Nitella [24]3 years ago

7 0

Answer:

Step-by-step explanation:

X<Y

10=3x+Y

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How does the graph of g(x) = 3X – 2 compare to the graph of f(x) = 3X?

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2 years ago

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Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given t

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Answer:

The minimum sample size required is 207.

Step-by-step explanation:

The (1 - <em>α</em>) % confidence interval for population mean <em>μ</em> is:

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

The margin of error of this confidence interval is:

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

Given:

$MOE=3\\\sigma=29\\z_{\alpha /2}=z_{0.01/2}=z_{0.05}=2.576$

*Use a <em>z</em>-table for the critical value.

Compute the value of <em>n</em> as follows:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207$

Thus, the minimum sample size required is 207.

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2 years ago

Mack wrote the equation x² + 7x + 84 = x² + 13x + 30 to show that the area of a changed rectangle is 84 ft² greater than the are

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2 years ago

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I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

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2 years ago