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Veseljchak [2.6K]
3 years ago
8

Suppose ABCD is a convex quadrilateral. Points M and N are midpoints of sides BC and AD, respectively. The area of the quadrilat

eral AMCN is equal to 6 square units. Find the area of quadrilateral ABCD.

Mathematics
1 answer:
Katena32 [7]3 years ago
7 0

Answer:

12 unit²

Step-by-step explanation:

area ΔAMC = 1/2 CM x AH' = 1/4 BC x AH'

area ΔABM = 1/2 BM x AH' = 1/4 BC x AH'

area ΔAMC = area ΔABM

for the same calculation, we can prove

area ΔACN = area ΔDCN

area ΔAMC + area ΔACN = 6

area ΔABM + area ΔDCN = 6

ABCD = area ΔAMC + area ΔACN + area ΔABM + area ΔDCN = 6 = 6 = 12

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A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the i
Lana71 [14]

Answer:

a

The  null hypothesis is H_o :  \  \sigma^2 =  1.9

The alternative hypothesis is  H_a :  \  \sigma^2 \ne 1.9  

b

 X^2 =  13.74

c

The decision rule is  

Reject the null hypothesis

d

The conclusion is  

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Step-by-step explanation:

From the question we are are told that

   The variance is \sigma ^2 =  1.9

    The sample size is  n =  30  

    The  sample variance  is  s^2 = 0.9

    The level of significance is  \alpha  =  0.05

   

The  null hypothesis is H_o :  \  \sigma^2 =  1.9

The alternative hypothesis is  H_a :  \  \sigma^2 \ne 1.9  

Generally the test statistics  is mathematically represented as

          X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }

=>       X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9  }

=>       X^2 =  13.74

Generally  from the degree of freedom is mathematically represented as

         df =  n- 1

=>      df =   30 - 1

=>      df =   29

Generally from the chi distribution table the critical value of  \frac{\alpha}{2}  \   and  \   1 - \frac{ \alpha }{2} at a degree of freedom  of  df =   29 is  

       X^2 _{ \frac{\alpha }{2} ,  df } =  X^2 _{ \frac{0.05 }{2}  , 29 }  =  45.7

=>     X^2 _{ 1 - \frac{\alpha }{2} ,  df } =  X^2 _{1 -  \frac{0.05 }{2}  , 29 }  =  16.0 5

Gnerally from the values obtained we see that

         X^2 <  X^2 _{ 1 - \frac{\alpha }{2}  ,  df } hence

The decision rule is  

Reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

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3 years ago
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Answer:

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b. x-4

Step-by-step explanation:

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4 0
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Answer:

1/25

Step-by-step explanation:

f(x) = 5^x

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Aleks04 [339]
Left side goes up 5 right side goes up 7

The rate of change between 5,15 is 10
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what is the difference between multiplying fractions and adding/subtracting fractions? complete sentances pleaseo
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Answer:

See explaination for answer! Hope this helps!

Step-by-step explanation:

When multiplying and deviding, you are raising them or lowering them by a certain degree, but <u>adding or subtractions</u> is just <u>combining two fractions. </u>

<u />

Just to quickly explain the "combining" aspect, during subraction, you are combining a positive with a negative.

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