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2 years ago

Find five rational numbers between 2/3and4/5

Mathematics

2 answers:

daser333 [38]2 years ago

8 0

Answer:

31/45, 32/45, 11/15, 34/35, 7/9.

Step-by-step explanation:

The LCM of 3 and 5 is 15 so we can write 2/3 and 4/5 as:

10/15 and 12/15 so one rational number between these is 11/15.

Now 11/15 = 33/45 and 4/5 = 36/45

So 2 rationals between these are 34/45 and 35/45 = 7/9

2/3 = 30 /45 and 11/15 = 33/45

so 2 rationals between these are 31/45 and 32/45.

alexdok [17]2 years ago

7 0

Answer:

61 / 90, 62 /90, 63 /90, 64/90, 65/90

Explanation:

2/3 = 2 x 5 / 3 x 5

= 10 / 15

4/5 = 4 x 3 / 5 x 3

12 / 15

we can find 5 rational numbers betwen 2/3 and 4/5 by multiplying them with 5 + 1 = 6

10 / 15 X 6 /6

= 60 / 90

12/ 15 X 6 /6

= 72 / 90

the rational numbers = 61 / 90 62 /90 63 /90 64/90 65/90

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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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Find five rational numbers between 2/3and4/5​

Find five rational numbers between 2/3and4/5