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3 years ago

Explain why the equation (x-6)^-13=12 has two solutions. Then solve the equation to find the solutions. Show your work.

Mathematics

1 answer:

Gala2k [10]3 years ago

4 0

Answer:

x = 10 and x = (-2) are the solutions.

Step-by-step explanation:

In the given equation (x - 4)² - 28 = 8

we will first find the zero factors which will further decide the number of solutions.

(x -4)² - 28 = 8

(x - 4)² -28 - 8 = 8 - 8 (By subtracting 8 on both the sides of the equation)

(x - 4)² - 36 = 0

(x - 4)²- 6² = 0

(x - 4 - 6)(x - 4 + 6) = 0

(x - 10)(x + 2) = 0

Now the equation only two zero factors or two solutions.

x = 10 and x = -2

Answer is two solutions only x = 10 and x = (-2)

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3 years ago

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Read 2 more answers

Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of

maksim [4K]

Answer:

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Out of 100 people sampled, 42 had kids.

This means that $n = 100, \pi = \frac{42}{100} = 0.42$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.293$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.547$

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

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3 years ago

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3 years ago

You are making a new type of deodorant from two different mixtures the first mixture is 30% smell proof and the second mixture i

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Answer:

600 L of 30% proof and 400 L of 80% proof is needed

Step-by-step explanation:

Let the amount of 30% smell proof be x while that of 80% smell proof is y

Then;

x + y = 1000 •••••(i)

Also;

30% of x + 80% of y = 50% of 1000

0.3x + 0.8y = 500 •••••(ii)

From i, x = 1000 - y

Put this into ii

0.3(1000-y) + 0.8y = 500

300 - 0.3y + 0.8y = 500

0.5y = 500-300

0.5y = 200

y = 200/0.5

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3 years ago