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Oksanka [162]
3 years ago
12

A toy company manufactures a certain toy at a cost of $300 per day plus $25 per toy. The company sells the toy for $35. How many

toys must the company sell in one day.
Mathematics
1 answer:
Leto [7]3 years ago
6 0

Answer:

30 toys to break-even in one day

Step-by-step explanation:

Let "x" be the number of toys the company makes in a day. The cost of the company is $ 300 per day + $ 25 per toy

Since, the cost is $25 for one toy, the cost for x toys would be $ 25x.

The cost $300 is the fixed cost and does not depend on how many toys are made in a day. Therefore, the total cost the company pays to make x toys in a day would be:

Total Cost = 300 + 25x

The company sells toy for $ 35 each. So x toys would be sold in $ 35x. Hence, total revenue/sales would be:

Total Sales = $ 35x

In order to break-even, the total cost in one day must be equal to total sales of the day i.e.

Total Cost = Total Sales

300 + 25x = 35x

300 = 10x

x = 30

This means, if the company makes and sells 30 toys it would break-even i.e. no loss no profit. For getting profit, the company had to sale more than 30 toys in a day.

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g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha
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Answer:

Null hypothesis:p_{1} = p_{2}    

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

z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502    

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Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.    

Step-by-step explanation:

Data given and notation    

X_{1}=410 represent the number of people indicating that their financial security was more than fair for the recent year

X_{2}=245 represent the number of people indicating that their financial security was more than fair for the year before

n_{1}=1000 sample 1 selected  

n_{2}=700 sample 2 selected  

p_{1}=\frac{410}{1000}=0.410 represent the proportion estimated of indicating that their financial security was more than fair this year

p_{2}=\frac{245}{700}=0.35 represent the proportion estimated of indicating that their financial security was more than fair the year before

\hat p represent the pooled estimate of p

z would represent the statistic (variable of interest)    

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

\alpha significance level given  

Concepts and formulas to use    

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, 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{410+245}{1000+700}=0.385  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.    

Calculate the statistic  

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

z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502    

Statistical decision  

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p_v =2*P(Z>2.502)= 0.0123    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.    

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