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Ksenya-84 [330]
3 years ago
7

Automobile mechanics conduct diagnostic tests on 150 new cars of a particular make and model to determine the extent to which th

ey are affected by a recent recall due to faulty catalytic converters. They find that 42 of the new cars tested do have faulty catalytic converters. The​ 99% confidence interval for the true proportion of new cars with faulty catalytic converters is​ _______.
Mathematics
1 answer:
Aleks04 [339]3 years ago
8 0

Answer:

99% Confidence interval: (0.185,0.375)                                                  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 150

Number of cars that have faulty catalytic converters, x = 42

\hat{p} = \dfrac{x}{n} = \dfrac{42}{150} = 0.28

99% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58

Putting the values, we get:

0.28\pm 2.58(\sqrt{\frac{0.28(1-0.28)}{150}}) = 0.28\pm 0.095\\\\=(0.185,0.375)

The​ 99% confidence interval for the true proportion of new cars with faulty catalytic converters is​ (0.185,0.375)

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Vinil7 [7]

Answer:

The factors of  2(x+y)^2-9(x+y)-5 is ((x+y)-5)(2x+2y+1)

Step-by-step explanation:

Given polynomial

=>2(x+y)^2-9(x+y)-5

To Find:

The factors of the polynomial =?

Solution:

Lets assume  k = (x+y)

Then 2(x+y)^2-9(x+y)-5 can be written as 2k^2-9k-5

Now by using quadratic formula

k =\frac{-b\pm\sqrt{(b^2-4ac}}{2a}

where

a= 2

b= -9

c= -5

Substituting the values, we get

k =\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}

k =\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}

k =\frac{-(-9) \pm \sqrt{(81+40)}}{4}

k =\frac{-(-9) \pm \sqrt{(121)}}{4}

k =\frac{-(-9) \pm 11}}{4}

k= \frac{ 9 \pm 11}{4}

k =  \frac{20}{4}                         k =  \frac{-2}{4}    

k_1 =5                                      k_2 = -\frac{1}{2}

2k^2-9k-5= 2(k-5)(k+\frac{1}{2})

Solving the RHS we get

\frac{2}{2}(k-5)(2k+1)

(k-5)(2k+1)

Substituting k = x+y

((x+y)-5)(2(x+y+1)

((x+y)-5)(2x+2y+1)

5 0
3 years ago
Sarah and Bridget have played 45 tennis matches.
Ainat [17]

Answer:

P(Sarah wins)= 1/3

P(Bridget wins)= 2/3

Step-by-step explanation:

15/45 = 1/3

1 - 1/3 = 2/3

8 0
2 years ago
In the diagram below, the area of $\triangle BCD$ is 60. What is the length of side $\overline{BC}$?
Phantasy [73]

Area of triangle = 1/2 bh

60 = 1/2 (15) h

8 = h

Quadrilateral area = h x (b1 + b2)/2 = 8 x (15+9)/2 = 96 sq units

96 -60 = triangle BAD area = 36 sq units

8 0
3 years ago
Is my answer right? the other options are <br><br> A.0.33<br> B.0.42<br> C.0.58<br> D.0.67
Fittoniya [83]
Yes 0.42 is correct!!
4 0
3 years ago
1
kvv77 [185]

Answer:

so the right answer is of option D

Step-by-step explanation:

Have a great day and hope this helps!!!

7 0
2 years ago
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