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Ipatiy [6.2K]
2 years ago
9

Given that 3y = x + 6 and y = kx + 12 are perpendicular, find the value of k

Mathematics
1 answer:
fenix001 [56]2 years ago
6 0

k = -3

Step-by-step explanation:

Let's rewrite the equations in their slope-intercept forms:

y = \frac{1}{3}x + 2\:\:\:\:\:\:\:(1)

y = kx + 12\:\:\:\:\:(2)

In order for Eqn(2) to be perpendicular to Eqn(1), the slope of Eqn(2) must be the negative reciprocal of that of Eqn(1). Therefore, k = -3.

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ducational Television In a random sample of people, said that they watched educational television. Find the confidence interval
SIZIF [17.4K]

Complete Question

Educational Television In a random sample of 200 people, 159 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. Round the answers to at least three decimal places.

Answer:

The 90% confidence interval is   0.748  <  p <  0.842      

Step-by-step explanation:

From the question we are told that

     The sample size is  n = 200

     The number of people that watched the educational television is k =  159

Generally the sample proportion is mathematically represented as

               \^ p =  \frac{159}{200}

=>               \^ p =  0.795

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90) \%

=>   \alpha = 0.10

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

   Z_{\frac{\alpha }{2} } =  1.645

Generally the margin of error is mathematically represented as  

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

=>     E =  1.645  * \sqrt{\frac{0.795 (1- 0.795)}{200} }

=>     E = 0.04696

Generally 95% confidence interval is mathematically represented as  

      \^ p -E <  p <  \^ p +E

=>    0.795  -0.04696  <  p <  0.795 + 0.04696

=>    0.748  <  p <  0.842      

3 0
3 years ago
Here is my question i need help answering it
ollegr [7]
Ur answer will be C… basically u make the equation equal to zero and then use the quadratic formula to find ur answers…. x = -3 and 9
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2 years ago
What is 41687 rounded to the nearest Highest Place
erik [133]

Answer:

40,000

Step-by-step explanation:

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At a football stadium, 20% of the fans in attendance were teenagers. If there
valina [46]

Answer:cgffffffffh

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
I have several other questions
Licemer1 [7]

Answer:

81 m²

Step-by-step explanation:

A = 6*10 + 7*6/2

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= 60 + 21

= 81 m²

6 0
3 years ago
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