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xeze [42]
3 years ago
5

Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She

decides to use the scale 1 in. = 4 in. Is this a reasonable scale?
Please show all work thank you.
Mathematics
2 answers:
romanna [79]3 years ago
8 0

Answer:

The scale is not reasonable .

Step-by-step explanation:

We are given that Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high.

Her paper is 12 in. wide and 24 in. tall.

Scale :  1 in. = 4 in.

Since 1 inch = 4 inch

So, 12 inch = 12\times 4 = 48 inches

24 inch = 24\times 4 =96 inches

The given scale is not reasonable because the scale is true for the width but false for the height

Since the actual height is 120 inches and we are getting 96 inches using the given scale .

Hence the scale is not reasonable .

noname [10]3 years ago
3 0
48 / 12 = 4
120 / 24 = 5

This is not a reasonable scale because ratios of tall and wide are not proportional.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 P(X = 8) =  0.0037

b

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I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is p = 0.267

Generally data collected from this study follows  binomial  distribution because the number of trials is  finite , there are only two outcomes, (covering  , and  not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable  X we have that  

   X \ \ \~ \ \ { B ( p , n )}

The probability distribution function for binomial  distribution is  

    P(X = x ) =  ^nC_x *  p^x *  (1 -p) ^{n-x}

Considering question a

Generally the  the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing is mathematically represented as

     P(X = 8) =  ^{12} C_8 *  (0.267)^8 *  (1- 0.267)^{12-8}

Here C denotes  combination

So

     P(X = 8) =  495  *  0.000025828 * 0.28867947

    P(X = 8) =  0.0037

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when​ sneezing is mathematically represented as

     P(X <  5 ) =[P(X = 0 ) + \cdots + P(X = 4)]

=>   P(X <  5 ) =[ ^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0} + \cdots +  ^{12} C_4 *  (0.267)^4 *  (1- 0.267)^{12-4} ]

=> P(X <  5 )  =  0.02406 +  0.10516 + 0.21067 + 0.25580 + 0.20964

=>  P(X <  5) =  0.805

Considering question c

Generally the probability that fewer than half(6) covered their mouth when​ sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

      P(X > 6) =  1 - p(X \le  6)

=>    P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]

=>    P(X > 6)=1 - [^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 *  (0.267)^6 *  (1- 0.267)^{12-6} ]

=>    P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]  

=>    P(X > 6) =  0.0206

I would be surprised because the value is very small , less the 0.05

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