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dsp73
2 years ago
15

Calculate a and b if

Mathematics
1 answer:
const2013 [10]2 years ago
4 0

Notice that

7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}

12=2^2\times3, so

\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}

Then taking the positive square root gives

\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}

so \boxed{a=2} and \boxed{b=1006}.

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3 years ago
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A random sample of 8 recent college graduates found that starting salaries for architects in New York City had a mean of $42,653
ycow [4]

Answer:

C. (36337.32, 48968.68)

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{9114}{\sqrt{8}} = 6315.68

The lower end of the interval is the sample mean subtracted by M. So it is 42653 - 6315.68 = 36337.32.

The upper end of the interval is the sample mean added to M. So it is 42653 + 6315.68 = 48968.68.

So the correct answer is:

C. (36337.32, 48968.68)

3 0
3 years ago
Solve<br>-6x^2 + 6 - 2x =x​
Tanzania [10]

Answer:

x1= -1-√17/4

x2= -1+√17/4

3 0
3 years ago
1 tree makes approximately 230 newspapers. Estimate (by rounding each number to 1 S.F.) how many newspapers 56 trees will make.
andriy [413]

Answer:

56 trees will make 10000 newspapers.

Step-by-step explanation:

Given:

One tree makes approximately 230 newspapers.

Now, for estimating how many newspapers will be made with 56 trees.

By multiplying 56 trees with 230 newspapers we get,

56\times230=12880.

And, rounding 12880 to one significant number (1 S.F.) is 10000.

Therefore, 56 trees will make 10000 newspapers.

7 0
3 years ago
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Simplify this: log√24+ log6​
Kitty [74]

simplifying log\sqrt{24}+log6 we get log(12\sqrt{6})

Step-by-step explanation:

We need to simplify: log\sqrt{24}+log6

Solving:

Applying the rule:

log a + log b = log(ab)

log\sqrt{24}+log6\\=log(6\sqrt{24})\\\sqrt{24} = \sqrt{2*2*2*3} =\sqrt{2^2*6} =\sqrt{2^2} \sqrt{6}=2\sqrt{6}\\  Putting\,\,value:\\=log(6*2\sqrt{6})\\=log(12\sqrt{6})

So, simplifying log\sqrt{24}+log6 we get log(12\sqrt{6})

Keywords: Simplifying Logarithms

Learn more about Simplifying Logarithms at:

  • brainly.com/question/11921476
  • brainly.com/question/10633485
  • brainly.com/question/5758530

#learnwithBrainly

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3 years ago
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