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Leto [7]
3 years ago
10

How do I simplify this? With steps please :)

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

{ \tt{ =  \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\  \\  = { \tt{  \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)}  }} \\  \\  = { \tt{ \frac{(x + 4)}{(x - 4)} }}

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= -6(x-7) – 9 =what will the equal to ​
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5 0
2 years ago
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

Z = \frac{X - \mu}{s}

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
PLZ HELP!!! 10 POINTS!!!Which relationship describes angles 1 and 2?
kkurt [141]

Answer:

The answer is C: Vertical angles I'm pretty sure

Step-by-step explanation:


7 0
3 years ago
Out of 30 problems on the test jose got 4 wrong. What percentage did jose get correct?
dedylja [7]
Jose got 80% correct 
8 0
3 years ago
Read 2 more answers
Last Tuesday was silly hat day at Molly's school. 90 students wore a silly hat and 810
Elan Coil [88]
There are a total of 900 students at Molly’s school. 810 is 90% of 900. 90% of students did not wear a silly hat.
5 0
2 years ago
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