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3 years ago

Please help..If you know the correct answer

Mathematics

1 answer:

never [62]3 years ago

3 0

Answer:

AC is the longest side

AB is the shortest side

Step-by-step explanation:

We can find the third angle

A+B+C = 180

55+80+C = 180

135+C = 180

C = 180-135

C =45

The longest side is opposite the largest angle

B is the largest angle so AC is the longest side

C is the the smallest angle so AB is the shortest side

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Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true

IgorLugansk [536]

Answer:

(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

Step-by-step explanation:

We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Also, the average porosity for 20 specimens from the seam was 4.85.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average porosity = 4.85

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 20

$\mu$ = true average porosity

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $4.85-1.96 \times {\frac{0.75}{\sqrt{20} } }$ , $4.85+1.96 \times {\frac{0.75}{\sqrt{20} } }$ ]

= [4.52 , 5.18]

Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.

The pivotal quantity for 98% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average porosity = 4.56

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 16

$\mu$ = true average porosity

Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 98% confidence interval for the true mean, $\mu$ is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98 {As the critical value of z at 1% level

of significance are -2.3263 & 2.3263}

P(-2.3263 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.3263) = 0.98

P( $-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.3263$ ) = 0.98

P( $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $4.56-2.3263 \times {\frac{0.75}{\sqrt{16} } }$ , $4.56+2.3263 \times {\frac{0.75}{\sqrt{16} } }$ ]

= [4.12 , 4.99]

Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

7 0

3 years ago

Anyone know how to do this?

suter [353]

Answer:

Step-by-step explanation:

Because A isn' at all right and B, and C equal the same but D = 36 So the sides are 18 each side.

7 0

3 years ago

3/4√5-√3 + 2/4√5+√3 =b√3+a√5 find the value of b and a

Zielflug [23.3K]

Answer:

a = 5 / 4

b = 0

Step-by-step explanation:

3/4√5 - √3 + 2/4√5 + √3 = b√3 + a√5

3/4√5 + 2/4√5 + √3 - √3 = b√3 + a√5

5/4√5 + 0 = b√3 + a√5

0 + 5/4√5 = b√3 + a√5

b√3 = 0

b = 0 / √3

b = 0

a√5 = 5/4√5

a = 5/4√5 / √5

a = 5 / 4

3 0

3 years ago

6.7z = 5.2z + 12.3 z=

vladimir1956 [14]

Answer:

z = 8.2

Step-by-step explanation:

6.7z = 5.2z + 12.3

combine like terms by subtracting 5.2z from both sides

1.5z = 12.3

divide by 1.5

z = 8.2

7 0

3 years ago

Read 2 more answers

Simplify.

Softa [21]

Answer:

√12-2/5×√75

2√2-2/5×5√3

2√2-2√3

2(√(2×3)

2√6

3 0

2 years ago

Read 2 more answers

Please help..If you know the correct answer​

Please help..If you know the correct answer