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jeyben [28]
3 years ago
11

Write an expression that can be used to multiply 6x198 mentally.

Mathematics
2 answers:
mel-nik [20]3 years ago
7 0
Assuming you meant 6x198 do a mental sum for 6x200 (1200) then subtract 6x2(12)to give you 1188
Mkey [24]3 years ago
7 0
In this problem, we are asked to give an expression that can be used to mentally multiply 6 and 198. In order not to go through the rigorous multiplication, we can estimate 198 to 200, that is 6 *200 equal to 1200. Since there is a 2*6 excess or 12 then we subtract: 1200 -12 equal to 1188.  
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The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1700 vot
lara [203]

Answer:

z=\frac{0.66 -0.63}{\sqrt{\frac{0.63(1-0.63)}{1700}}}=2.562  

p_v =P(z>2.562)=0.0052  

So the p value obtained was a very low value and using the significance level given \alpha=0.02 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.

Step-by-step explanation:

Data given and notation

n=1700 represent the random sample taken

\hat p=0.66 estimated proportion of voters that favored construction

p_o=0.63 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)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that percentage of residents who favor construction is more than 63%.:  

Null hypothesis:p \leq 0.63  

Alternative hypothesis:p > 0.63  

When we conduct a proportion test we need to use the z statisitc, 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.

Calculate the statistic  

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

z=\frac{0.66 -0.63}{\sqrt{\frac{0.63(1-0.63)}{1700}}}=2.562  

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>2.562)=0.0052  

So the p value obtained was a very low value and using the significance level given \alpha=0.02 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.

7 0
3 years ago
Can y'all solve and show me the steps on how you got it
Tju [1.3M]
The x-coordinate of the right-most point of S' is 4. In the original, it is 6. The dilation multiplier is 4/6 = 2/3.

Selection B matches that.
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