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ELEN [110]
3 years ago
13

Solve the system of equations: 2x + 9y = 0 and 3x + 5y = 17.

Mathematics
1 answer:
choli [55]3 years ago
7 0
<span>2x + 9y = 0 (1st)
</span><span>3x + 5y = 17 (2nd)

multiply (st) by 3 and (2nd) by 2

</span>6x + 27y = 0 (1st)
6x + 10y = 34 (2nd)
----------------------------subtract
17y = -34
    y = -2

2x + 9y = 0
2x +9(-2) = 0
2x = 18
x = 9

answer
(9, -2)
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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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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}}

25\sqrt{n} = 400

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

\sqrt{n} = 16

(\sqrt{n})^2 = 16^2[tex][tex]n = 256

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

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

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