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Annette [7]
3 years ago
12

Leah has a 20% off coupon for a sports store. There is a tennis racket that is available at a discount of 10%. The store applies

the coupon after the 10% is taken. She buys the racket for $34. Approximately, what was the orginal price of the tennis racket
Mathematics
1 answer:
Art [367]3 years ago
3 0

Answer:the orginal price of the tennis racket is $47

Step-by-step explanation:

Let x represent the original price of the tennis racket at the sports store.

Leah has a 20% off coupon for the sports store. The tennis racket is available at a discount of 10%.

The store applies the coupon after the 10% is taken. The value of the discount on the original price of the tennis racket would be

10/100 × x = 0.1 × x = $0.1x

The discounted price of the racket would be

x - 0.1x = 0.9x

The value of the coupon would be

20/100 × 0.9x = 0.2 × 0.9x = 0.18x

The selling price after the coupon was applied would be

0.9x - 0.18x = 0.72x

She buys the racket for $34. This means that

0.72x = 34

x = 34/0.72 = $47

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Complete Question

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks with a sample standard deviation of the time unemployed is 6.7 weeks.

1 Which of the following statements is the correct alternative hypothesis?

2 The test statistic for testing the hypothesis is

a. -2.64

b. -2.32

c. -2.11

d. -1.28

e. none of these are correct

Answer:

1  

 The  alternative hypothesis  H_a  :  \mu < 15.9

2

The  test statistics z =  -2.64  

Step-by-step explanation:

From the question we are told that

     The population  mean value for time  citizens remain unemployed is  \mu  =  15.9 \  weeks

     The  sample size is  n =  50

     The  sample standard deviation is  6.7 weeks.

      The  sample mean value for time  citizens remain unemployed is  \mu  =  15.9 \  weeks

       

     The  null hypothesis is  H_o  :  \mu \ge 15.9

      The  alternative hypothesis  H_a  :  \mu < 15.9

Generally test statistics is mathematically represented as

       z =  \frac{ \= x  - \mu }{ \frac{s}{\sqrt{n} } }  

=>    z =  \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}

=>     z =  -2.64  

   

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