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Anna11 [10]
3 years ago
13

A baker bought 4 gallons oficing to decorate cakes. He uses 4 % cups

Mathematics
1 answer:
sergejj [24]3 years ago
5 0

25 cakes can be completely decorated using 4 gallons of icing.

<u>Step-by-step explanation:</u>

Given:

4 gallons of icing

16 cups =1 gallon

No. of icing cups = 4\times16 cups

       =64 cups

No. of cups required to decorate and frost a cake= 4% of total no. of icing cups

          = \frac{(4\times64)}{100}

          = 2.56

2.56 cups of icing is required to decorate each cake.

Maximum no. of cakes decorated = \frac{ (64\times1)}{2.56}

                    = 25

25 cakes can be completely decorated using 4 gallons of icing.

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If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal
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Answer:

a

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            P(x_1 <  X <  x_2 ) =   51.1 \%

b

   The probability is  P(Z >  2.5 ) =  0.0062097

Step-by-step explanation:

From the question we are told that

        The  population mean is  \mu =  800

        The  variance is  var(x) =  1600 \ kg

        The  range consider is  x_1 =  778 \ kg  \  x_2 =  834 \ kg

         The  value consider in second question is  x =  900 \ kg

Generally the standard deviation is mathematically represented as

        \sigma =  \sqrt{var (x)}

substituting value

        \sigma =  \sqrt{1600}

       \sigma = 40

The percentage of a cucumber give the crop amount between 778 and 834 kg  is mathematically represented as

       P(x_1 <  X <  x_2 ) =  P( \frac{x_1 -  \mu }{\sigma} <  \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma }   )

    Generally  \frac{X - \mu }{ \sigma } = Z (standardized \  value  \  of  \  X)

So

      P(x_1 <  X <  x_2 ) =  P( \frac{778 -  800 }{40} < Z< \frac{834 - 800 }{40 }   )

      P(x_1 <  X <  x_2 ) =  P(z_2 < 0.85) -  P(z_1 <  -0.55)

From the z-table  the value for  P(z_1 <  0.85) =  0.80234

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So

             P(x_1 <  X <  x_2 ) =   0.80234 - 0.29116

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            P(x_1 <  X <  x_2 ) =   51.1 \%

The probability of cucumber give the crop exceed 900 kg is mathematically represented as

             P(X > x ) =  P(\frac{X - \mu }{\sigma }  > \frac{x - \mu }{\sigma } )

substituting values

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From the z-table  the value for  P(Z >  2.5 ) =  0.0062097

 

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Step-by-step explanation:

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Which of the following illustrates how to find the difference of 4h^5k and -7hk^5

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