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damaskus [11]
3 years ago
6

What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? 5xy 15x3y 45x3y5 75x5y7

Mathematics
2 answers:
Rasek [7]3 years ago
8 0

Answer: 15x3y

Step-by-step explanation:

We rewrite the expressions by using factorisation method of their primes. This will give:

60x4y7= 2×2×3×5×x×x3×y×y6

45x5y5= 3×3×5×x×x4×y×y4

75x3y= 3×5×5×x×x2×y

Common factors= 3 × 5 × x3 × y

= 15x3y

Pepsi [2]3 years ago
6 0
I believe it’s 5xy since all the numbers are factors of five and since each number contains the variables xy.
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Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years.
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Answer:

a) Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=\pm 1.64

b) \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})

And the standard error is given by:

SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1

c) \bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And the margin of error is:

ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64

And then the confidence interval is be given by:

200-1.64 = 198.36

200+1.64 = 201.64

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= 200 represent the sample mean

\mu population mean (variable of interest)

\sigma=3 represent the population standard deviation

n=9 represent the sample size  

Part a

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=\pm 1.64

Part b

The distribution for the sample mean is given by:

\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})

And the standard error is given by:

SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1

Part c

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And the margin of error is:

ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64

And then the confidence interval is be given by:

200-1.64 = 198.36

200+1.64 = 201.64

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