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3 years ago

What is the factorization of the trinomial below -x^2 + 2x + 48

Mathematics

1 answer:

OlgaM077 [116]3 years ago

4 0

For this case we must factor the following expression:

$-x ^ 2 + 2x + 48$

We take the sign "-" as a common factor of the expression, taking into account that:

$- * - = +\\- (x ^ 2-2x-48)$

To factor, we must find two numbers that, when multiplied, result in -48 and when added, result in -2. These numbers are -8 and +6.

$-8 + 6 = -2\\(-8) * (+ 6) = - 48$

Then, we factor the expression within the parenthesis as:

$- ((x-8) (x + 6))$

Answer:

$- (x-8) (x + 6)$

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Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 45

krok68 [10]

Answer:

The 95% confidence interval is $1003 < \mu$

Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 1000$

The sample size is $n = 453$

The sample mean is $\= x = 1013$

The standard deviation is $s = 108$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

=> $\alpha = 5\%$

=> $\alpha = 0.05$

The critical value for $\frac{\alpha }{2}$ obtained from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }$

=> $E = 1.96 * \frac{108}{\sqrt{453} }$

=> $E = 9.946$

Generally the 95% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

=> $1013 - 9.946 < \mu < 1013 + 9.946$

=> $1003 < \mu$

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

4 0

3 years ago

Given right triangle MNL what is the value of cos(M)?

FromTheMoon [43]

Step $1$