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3 years ago

The mean of three number is 15. if 2 of the numbers are 18 and 16 what is the third number

Mathematics

1 answer:

MrMuchimi3 years ago

3 0

Answer:

Step-by-step explanation:

The mean is calculated as

mean = $\frac{sum}{count}$

let the third number be x , then

$\frac{18+16+x}{3}$ = 15 ( multiply both sides by 3 to clear the fraction )

34 + x = 45 ( subtract 34 from both sides )

x = 11 ← third number

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2 years ago

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3 years ago

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberr

Veseljchak [2.6K]

Answer:

The calculated value |t| = 2.375 > 2.1009 at 0.05 level of significance

Null hypothesis is rejected 

Alternative hypothesis is accepted

The extra carbonation of cola results in a higher average compression strength

Step-by-step explanation:

Step(i):-

Given data

First sample size (n₁) = 10

mean of the first sample(x₁⁻) = 537

standard deviation of the first sample (S₁) = 22

second sample size (n₂) = 10

mean of the second sample (x₂⁻) = 559

standard deviation of the second sample (S₂) = 17

Step(ii):-

Null hypothesis : H₀:- The extra carbonation of cola results in a lower average compression strength

Alternative Hypothesis :H₁

The extra carbonation of cola results in a higher average compression strength

Step(iii):-

By using student's t -test for difference of means

Test statistic

  $t = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } } )}$ 

 where 

  $S^{2} = \frac{n_{1}S^{2} _{1} + n_{2} S_{2} ^{2} }{n_{1}+n_{2} -2 }$ 

  $S^{2} = \frac{10(22)^{2} + 10 (17) ^{2} }{10+10 -2 } = \frac{ 7730}{18} = 429.4$ 

  $t = \frac{537-559 }{\sqrt{429.4 (\frac{1}{10 }+\frac{1}{10 } } )}$ 

 t = -2.375

|t| = |-2.375| = 2.375

Degrees of freedom

γ = n₁+n₂ -2 = 10+10-2 =18

 $t_{\frac{\alpha }{2} ,n-1}=t_{(\frac{0.05}{2} ,18)} = t_{(0.025,18)}}=2.1009$ 

The calculated value |t| = 2.375 > 2.1009 at 0.05 level of significance

Null hypothesis is rejected 

Alternative hypothesis is accepted

Final answer:-

The extra carbonation of cola results in a higher average compression strength

 

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2 years ago

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Step-by-step explanation:

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3 years ago

Evaluate the function at the indicated values. f(x)= 6x^2+ 5x -12

seropon [69]

Step-by-step explanation:

We need to find the value of the function at the indicated value.

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Hence, this is the required solution.

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3 years ago

The mean of three number is 15. if 2 of the numbers are 18 and 16 what is the third number​

The mean of three number is 15. if 2 of the numbers are 18 and 16 what is the third number