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gayaneshka [121]
2 years ago
13

The image of the point (2, -9) under a translation is (4, -14). Find the coordinates of the image of the point (5,6) under the s

ame translation.​
Mathematics
2 answers:
inysia [295]2 years ago
6 0

Answer:

(7,1)

Step-by-step explanation:

I just did it the same way the other one went, but tbh don't just listen to me I'm not that smart I just believe it's the answer from my math.

Strike441 [17]2 years ago
4 0

Answer:

(7, 1)

Step-by-step explanation:

translation = \left[\begin{array}{c}2\\-5\end{array}\right]

(2 units to the right and 5 units down)

Therefore, x coordinate = 5 + 2 = 7

y coordinate = 6 - 5 = 1

So translated point is (7, 1)

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Answer:

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b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. How large was the sample used in this survey?

We have that s = 25, \sigma = 400. We want to find n, so:

s = \frac{\sigma}{\sqrt{n}}

25 = \frac{400}{\sqrt{n}}

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15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

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