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liberstina [14]
3 years ago
5

What is the scale factor of XYZ to UVW

Mathematics
2 answers:
Varvara68 [4.7K]3 years ago
8 0
Answer: 
\boxed {\frac{1}{5}}
<span>
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>
Solution-
60 *  \frac{1}{5}  = 12

90 * \frac{1}{5} = 18

75 * \frac{1}{5} = 15
<span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━<span>━━
</span></span>Hence, the answer would be \boxed {\frac{1}{5}}
solong [7]3 years ago
7 0

Answer:

\frac{1}{5}

Step-by-step explanation:

We want to find the scale factor of the dilation from ΔXYZ to ΔUVW.


The scale factor is given by the formula;

k=\frac{Image\:Length}{Corresponding\:Object\:Length}


Since the dilation is from ΔXYZ to ΔUVW, our image triangle is ΔUVW.


We can now use any of the corresponding sides to determine the scale factor.


k=\frac{|UV|}{|XY|}


\Rightarrow k=\frac{12}{60}


We simplify to get;

\Rightarrow k=\frac{12}{12\times5}


We cancel the common factors to get;

\Rightarrow k=\frac{1}{5}


Therefore the scale factor is \frac{1}{5}



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A random sample of 25 ACME employees showed the average number of vacation days taken during the year is 18.3 days with a standa
Norma-Jean [14]

Answer:

a) Null hypothesis:\mu \leq 15  

Alternative hypothesis:\mu > 15  

b) df=n-1=25-1=24  

For this case the p value is given p_v = 0.0392

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 5% of signficance.  

c) Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.

So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.

Step-by-step explanation:

Data given and notation  

\bar X=18.3 represent the sample mean

s=3.72 represent the sample standard deviation

n=25 sample size  

\mu_o =15 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Part a: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean for vacation days is higher than 15, the system of hypothesis would be:  

Null hypothesis:\mu \leq 15  

Alternative hypothesis:\mu > 15  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part b: P-value  and conclusion

The first step is calculate the degrees of freedom, on this case:  

df=n-1=25-1=24  

For this case the p value is given p_v = 0.0392

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 5% of signficance.  

Part c

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.

So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.

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Answer:

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Sorry if this is wrong.

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Answer:

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cos A = adjacent / hyptenuse       ( the adjacent side is the one the angle 'sits' on)

tan A = opposite / adjacent   (  the opposite side is the one opposite the angle)

So to find the length of segment x in the first problem use

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cos 61 = y / 50
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The other questions can be solved in a similar way.

7 0
3 years ago
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