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balu736 [363]
2 years ago
13

Is it possible to place 158 books on three shelves so that the first shelf has 8 less books than the second and 5 more books tha

n the third shelf?
Mathematics
1 answer:
Lisa [10]2 years ago
5 0
Let
x-----------------> books in <span>the first shelf
</span>y-----------------> books in the second shelf
z-----------------> books in the third shelf
we know that
x+y+z=158-------------> equation (1)
x=y-8---------> y=x+8 ------->  equation (2)
x=z+5--------> z=x-5  --------> equation (3)
<span>
 substitute (2) and (3) in (1)
</span>x+(x+8)+(x-5)=158--------> 3x=155----------> x=51.7


<span>the number of books in the first shelf (x=51.7) is not a whole number
therefore

the answer is
Is not possible to place the amount of 158 books in the amounts indicated in the problem</span>



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ycow [4]

Step-by-step explanation:

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Hannah and Leah are running around a circular track. Hannah takes 5 minutes to complete one lap, and Leah takes 6 minutes to com
Dima020 [189]
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4 0
1 year ago
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In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were
AnnZ [28]

Answer:

F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32

So then the best option is:

a. 7.32

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have 3 groups and on each group from j=1,\dots,10 we have 10 individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}

Where SST represent the total sum of squares.  

The degrees of freedom for the numerator on this case is given by df_{num}=k-1=3-1=2 where k =3 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=30-3=27.  

And the total degrees of freedom would be df=N-1=30 -1 =29  

From the info given we know that MSR=\frac{SSR}{2}=45.89

And MSE=\frac{SSE}{27}=6.27

From definition the F statisitc is defined as:

F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32

So then the best option is:

a. 7.32

3 0
2 years ago
Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an init
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Answer: the hourly fee for the rototiller is $3

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Let h represent the hourly fee for renting the rototiller.

The rental company charged an initial fee of $43 with an additional fee per hour. Assuming that they rented the rototiller for x hours. This means that if they rented the rototiller for x hours, the total amount that they would pay is

43 + hx

If they paid $64 after renting the rototiller for 7 hours, the equation that models this problem would be

43 + 7h = 64

7h = 64 - 43 = 21

h = 21/7 = $3

8 0
2 years ago
Read 2 more answers
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