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3 years ago

I Need help on this.

Mathematics

1 answer:

AlekseyPX3 years ago

6 0

To solve this question you would set 3x+3 and 6x-57 to equal each other, giving you 3x+3=6x-57. You would then add 57 to both sides, getting you 3x+60=6x, then you would subtract 3x from both sides, getting you 60=3x. Finally, you would divide both sides by 3, getting x=20.

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What’s 8x8 This is to test how the app works not serious

lisov135 [29]

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Step-by-step explanation:

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4 years ago

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Snezhnost [94]

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3 years ago

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

4 years ago

PLEASSSEEE HELLPPP

Sidana [21]

Answer:

D: 14q + 21√qr

Step-by-step explanation:

We want to find the product of;

(2√q + 3√r) and 7√q.

Where p and q are integers.

Using distributive property, we have;

(2√q × 7√q) + (3√r × 7√q)

>> 14q + 21√qr

Correct option is D

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3 years ago

ANSWER THIS PLEASE IT IS A MATH QUESTION

MaRussiya [10]

Answer:

Step-by-step explanation:

Least to largest:

First compare the whole parts of the decimal number. The whole part with greater number will be the greatest number.

2) Then compare the decimal parts. Compare tenth place. The decimal number that has greater number in the tenth place will be greater.

3) If the number in tenth place is equal, then compare 100th place and so on

A) 15.99 ; 16 ; 16.02 ; 16.2

B) 4.45 ; 4.9945 ; 5.545 ; 5.56

c) 44.11 ; 44.5 ; 45 ; 45.01

D) 8.995 ; 9.0599 ; 9.27 ; 9.6

Greatest to least

A) 2.111 ; 2.11 ; 2.1 ; 2.01

B) 32.32 ; 32.302 ; 32.032 ; 3.99

c) 7.666 ; 7.66 ; 7.6 ; 7.06

D) 57.68 ; 57.57 ; 57.057 ; 5.75

5 0

3 years ago