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Lemur [1.5K]
3 years ago
15

Which of the following is a solution to the following system of inequalities let the green region represents the answer region

Mathematics
1 answer:
Fofino [41]3 years ago
8 0

The given inequalities are

x+2y≤4, 3x-y>2

To plot the graph first convert it into slope intercept form in two coordinate system i.e To convert equation of the type Ax + By= C in Slope intercept form

x/C÷A + y/C÷B =1

So,the equation becomes

x/4 + y/2≤ 1,

x/2÷3 + y/-2>1,

We have to also consider x>0 and y>0.

Now The shaded area in green is shown in the graph.

x=8/7 and y=20/7 is the point of intersection of lines

A triangular region is formed having vertices (0,0) (4,0) and (8/7,20/7) is the required solution.

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Answer:

The 95% confidence interval of the proportion of Americans who believe in the conspiracy is  0.551<  p <  0.610

Step-by-step explanation:

From the question we are told that

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Generally the sample proportion is mathematically represented as

      \^ p =  \frac{614}{1057 }

=>   \^ p = 0.5809

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

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

   Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }

=>   E = 1.96 * \sqrt{\frac{0.5809 (1- 0.5809)}{1057} }    

=>   E = 0.02975  

Generally 95% confidence interval is mathematically represented as  

      \^ p -E <  p <  \^ p +E

=>    0.5809 - 0.02975<  p <  0.5809 + 0.02975

=>    0.551<  p <  0.610

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3 years ago
A triangle's height is 10 feet more than its base. If the area of the triangle is 100 square feet, use factoring to find its dim
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The base length of the triangle is 10 ft. and the height of the triangle is 20ft.

Step-by-step explanation:

Height = base + 10

Area = 100 square ft

Area of a triangle= (1/2) (b) (h)

100 = (1/2) (b) (b + 10)

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b(b) + 20b - 10b - 200 = 0

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(b-10) (b+20) =0

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Here b is the length and cannot be negative.

So, b = 10ft

h = b + 10

h = 10 + 10

h = 20 ft.

The base length of the triangle is 10 ft. and the height of the triangle is 20ft.

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Mika read a 405- page book in 6 hours, how many pages per minute did she read?
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