What is the image of the point (5,-6) after a rotation of 90 counterclockwise about the origin.

Mathematics

1 answer:

WITCHER [35]3 years ago

4 0

Answer:

(-6,5)

Step-by-step explanation:

ignore this part

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A simple random sample was taken of 44 water bottles from a bottling plant’s warehouse. The dissolvedoxygen content (in mg/L) wa

AleksAgata [21]

Answer:

a) $9.14-2.33\frac{2}{\sqrt{44}}=8.44$

$9.14+2.33\frac{2}{\sqrt{44}}=9.84$

b) The 98% confidence interval would be given by (8.44;9.84)

For this case we can conclude that we have 98% of confidence that the true mean for the oxygen content is between 8.44 and 9.84 mg/L

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=9.14$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=2$ represent the population standard deviation

n=44 represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=18-1=17$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.01$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.33$