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Alecsey [184]
3 years ago
14

Leonardo makes the following purchases at the store: 1 backpack for $16.89 5 spiral notebooks for $1.19 each 1 pack of mechanica

l pencils for $3.68 2 packs of lead refills for $1.88 each Leonardo has 2 coupons, each for 45 cents off on the purchase of a pack of lead refills. The coupons are applied after tax and the sales tax is 5% of the purchase. If Leonardo paid $30.89 , then he _____ for his purchase. a. did not pay enough b. paid the correct amount c. paid $0.04 too much d. paid $0.57 too much
Mathematics
2 answers:
Alex787 [66]3 years ago
6 0
I believe the correct answer is he paid the right amount

vovikov84 [41]3 years ago
3 0

Answer:

Option B is correct choice.

Step-by-step explanation:

1 backpack for $16.89

5 spiral notebooks for $1.19 each so total cost = 5*1.19=5.95

1 pack of mechanical pencils for $3.68

2 packs of lead refills for $1.88 each so total becomes =2*1.88=3.76

Total becomes : 16.89+5.95+3.68+3.76=$30.28

Sales tax on the purchase = 5 % the value is 0.05*30.28=1.514

Now total cost becomes = 30.28+1.514 = $31.794

Leonardo has 2 coupons, each for 45 cents off on the purchase of a pack of lead refills. That means he got 90 cents off on both packs. So, new total Leo has to pay is : 31.794-0.90 = $30.894

Hence, Leo paid $30.89 in total. So, he paid the correct amount.

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You were shopping for a Christmas present. You found the item on sale for 20% off. Tax is 8%. If the original price was $450, ho
klio [65]

Answer:

Cost\ of\ gift=\$ 388.8

Step-by-step explanation:

Original Price=\$450

Discount:

Discount=20\%

20\%\ of\ 450=\frac{20}{100}\times 450=90\\\\Discounted\ Price=450-90=\$360

Tax:

Tax=8\%

8\%\ of\ 360=\frac{8}{100}\times 360=28.8\\\\Final\ cost=360+28.8=\$388.8

4 0
3 years ago
3. A new process has been developed for applying pho­ toresist to 125-mm silicon wafers used in manufac­ turing integrated circu
dlinn [17]

Answer:

a

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

The null hypothesis is rejected

b

The  99% confidence level is   13.3930  < \mu  < 13.3994

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  10

   The  population mean is  \mu =  13.4 000 \  angstroms

   The level of significance is  \alpha =  0.05

   The  sample data is  

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

        \= x =  \frac{13.3987+ 13.3957\cdots +13.4002 }{10}

=>     \= x = 13.3962

Generally the sample standard deviation  is mathematically represented as

    \sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }

=> \sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 +  (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2  }{10} }

=>  \sigma =0.0039

The null hypothesis is  H_o : \mu  =  13.4000

The alternative hypothesis is  H_a :  \mu \ne  13.4000

Generally the test statistics is mathematically represented as

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

=>    z  =  \frac{13.3962 -  13.4000}{\frac{0.0039}{\sqrt{10} } }

=>   z =  3.08

Generally the p-value is mathematically represented as

       p-value  = 2P( z   >  3.08)

From the z-table  P(z >  3.08)= 0.001035

So

       p-value  = 2* 0.001035

      p-value  = 0.00207

So from the obtained value we see that

     p-value  < \alpha

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is  99%  then the level of significance is

    \alpha =  (100 -99)\%

=> \alpha =  0.01

Generally from the normal distribution table critical value  of  \frac{\alpha }{2} is  

    Z_{\frac{\alpha }{2} } =  2.58

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>   E = 2.58  *  \frac{0.0039}{\sqrt{10} }

=>    E = 0.00318

Generally the 99% confidence interval is mathematically represented as

     13.3962   - 0.00318  < \mu  < 13.3962   +  0.00318

=>   13.3930  < \mu  < 13.3994

 

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