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Sholpan [36]
3 years ago
6

Kelly tells you that when variables are in the denominator, the equation one over two plus three over x equals three over four b

ecomes unsolvable. Kelly explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Kelly how the equation is still solvable and explain your reasoning.
Mathematics
1 answer:
Gnom [1K]3 years ago
4 0
The equation is 1/2+3/x=3/4, it is still solvable
the equivalent of the equation is (1.x+2.3)/2.x = 3/4, or (x+ 6)/2.x=3/4, this last can be solved as follow: 4.(x+ 6) = 2x.3, 4x+ 24 = 6x, so 24=6x-4x=2x, and when 2x= 24 , it means x=24/2 =12, finally the equation is solvable because x=12 is a solution
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Let n1equals50​, Upper X 1equals30​, n2equals50​, and Upper X 2equals10. Complete parts​ (a) and​ (b) below. a. At the 0.05 leve
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Answer:

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082    

p_v =2*P(Z>4.082)=4.46x10^{-5}  

So the p value is a very low value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

Step-by-step explanation:

1) Data given and notation  

X_{1}=30 represent the number of people with a characteristic in 1

X_{2}=10 represent the number of people with a characteristic in 2

n_{1}=50 sample of 1 selected  

n_{2}=50 sample of 2 selected  

p_{1}=\frac{30}{50}=0.6 represent the proportion of people with a characteristic in 1

p_{2}=\frac{10}{50}=0.2 represent the proportion of people with a characteristic in 2

z would represent the statistic (variable of interest)  

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

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , the system of hypothesis would be:  

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{30+10}{50+50}=0.4  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082    

4) Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test.    

Since is a two sided test the p value would be:  

p_v =2*P(Z>4.082)=4.46x10^{-5}  

So the p value is a very low value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.  

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Step-by-step explanation:

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Step-by-step explanation:

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