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miss Akunina [59]
3 years ago
7

A clock is constructed using a regular polygon with 60 sides. The polygon rotates every minute. How much has the polygon

Mathematics
1 answer:
beks73 [17]3 years ago
8 0

In 7 minutes, the clock has rotated 42 degrees

<u>Solution:</u>

Given, A clock is constructed using a regular polygon with 60 sides.  

The polygon rotates every minute.  

As there will be 60 minutes in clock, and this clock has 60 sides, each minute represents a side.  

Now we know that, in a clock, 1 hour = 60 minutes

60 minutes = 360 degrees

Then, 7 minutes = “n” degrees

So, by criss cross multiplication,

\begin{array}{l}{n \times 60=360 \times 7} \\\\ {\rightarrow n=6 \times 7} \\\\ {\rightarrow n=42}\end{array}

Hence, in 7 minutes, the clock has rotated 42 degrees

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the second option

Step-by-step explanation:

5+(1+3)= (5+1) +3

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Solve the system by substitution.<br> 3x + y = 20<br> -7y=x<br><br> Please help
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  (x, y) = (7, -1)

Step-by-step explanation:

The expression for x makes it easy to use that for substitution.

  3(-7y) +y = 20

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2 years ago
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1000 voters in th
garri49 [273]

Answer:

z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945  

p_v =P(Z>1.945)=0.0259  

If we compare the p value obtained with the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 2% of significance the proportion of residents who favored annexation is not significantly higher than 0.39.  

Step-by-step explanation:

1) Data given and notation  

n=1000 represent the random sample taken

\hat p=0.42 estimated proportion of residents who favored annexation

p_o=0.39 is the value that we want to test

\alpha=0.02 represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is higher than 0.39:  

Null hypothesis:p\leq 0.39  

Alternative hypothesis:p > 0.39  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.42 -0.39}{\sqrt{\frac{0.39(1-0.39)}{1000}}}=1.945  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.02. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(Z>1.945)=0.0259  

If we compare the p value obtained with the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 2% of significance the proportion of residents who favored annexation is not significantly higher than 0.39.  

4 0
3 years ago
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