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raketka [301]
2 years ago
8

The sum of three numbers is 54. The third number is 2 times the second. The second number is 10 more than the first. What are th

e numbers?
Mathematics
1 answer:
Svetllana [295]2 years ago
6 0

Answer:

8, 18 and 36 respectively.

<h2>explanation</h2>

sum=54

1st number=x

2nd number=x+10

3rd number =2(x+10)=2x+20

x+x+10+2x+20=54

put the liketerms together

x+x+2x=54-10-20

4x=24

divide both sides by 4 to get

x=8

Input the other values

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An article reported on the results of an experiment in which half of the individuals in a group of 60 postmenopausal overweight
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Answer:

Step-by-step explanation:

From the given information:

Let's first compute the null and alternative hypothesis

Null hypothesis:

\mathbf{H_o: \mu_1-\mu_2=1}

Alternative hypothesis:

H_a :\mu_1 -\mu_2 > 1

The number of samples is half in a group of 60

i.e

n_1=n_2 = 30

the sample mean for sample 1 \overline x_1 = 5.7

the standard deviation for sample 1 s_1 = 3.1

the sample mean for sample 2 \overline x_2 = 3.9

the standard  deviation for sample 2 s_2 = 2.7

degree of freedom  for this test can be computed by using the formula:

df = \dfrac{\begin {pmatrix} \dfrac{s_1^2}{n_1} + \dfrac{s^2_2}{n_2}   \end {pmatrix}^2  }  {\dfrac{ (\dfrac{s_1^2}{n_1}^2)}{ n_1-1}  + \dfrac{ (\dfrac{s_2^2}{n_2}^2)}{ n_2-1}  }

df = \dfrac{\begin {pmatrix} \dfrac{3.1^2}{30} + \dfrac{2.7^2}{30}   \end {pmatrix}^2  }  {\dfrac{ \begin {pmatrix} \dfrac{3.1^2}{30} \end {pmatrix}^2}{ 30-1}  + \dfrac{ \begin {pmatrix} \dfrac{2.7^2}{30} \end {pmatrix}^2}{ 30-1}  }}

df = 114.68

The test statistics can be computed as follows:

t = \dfrac{ \overline x_1 -\overline x_2- (\mu_1 -\mu_2)}{\sqrt{ \dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} }}

t = \dfrac{ 5.7-3.9- (1)}{\sqrt{ \dfrac{3.1^2}{30} +\dfrac{2.7^2}{30} }}

t = 1.07

Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:

P-value = 0.143

Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.

Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.

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What is the area, in square inches, of the trapezoid with th
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A pair of pants that regularly costs $55 are on sale for 35% off the regular price. What is the sale price of the pants?​
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How can I solve this equation 5x^2-2x-6=-2x^2+9x
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Add 2x^2 to both sides
7x^2-2x-6=9x

Subtract 9x from both sides
7x^2-11x-6=0

Factor by using slip and slide
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Then use the Zero Product Property to find roots
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Final answer: x=-3/7, x=2
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