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Zielflug [23.3K]
4 years ago
10

Solve the equation, if possible. (If all real numbers are solutions, enter REALS. If there is no solution, enter NO SOLUTION.) x

2 = (x + 3)(x − 3) + 9
Mathematics
1 answer:
UkoKoshka [18]4 years ago
6 0

Answer:

REALS. all real numbers are solution for the equation

Step-by-step explanation:

for the equation

x² = (x + 3)*(x − 3) + 9

distributing the terms in the parenthesis

x² = (x + 3)*(x − 3) + 9  = [x² - 3*x + 3*x - 3*3 ] + 9

x² = x² - 9 + 9

0 = 0

since this statement will be true regardless of the value of x , then the equation has solution for all real numbers .

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Answer:

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Step-by-step explanation:

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3 years ago
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In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat
Dvinal [7]

Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

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}.

427 had paid for coaching courses and the remaining 2733 had not.

This means that n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

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3 years ago
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Hope that helps.
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Answer:

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Step-by-step explanation:

Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.

And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.

Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527

We will find the HCF of 391, 425 and 527 by prime factorization method.

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So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.

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