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vodka [1.7K]
3 years ago
14

Suppose a package delivery company purchased 17 trucks at the same time. Six trucks were purchased from manufacturer A, five fro

m manufacturer B, and six from manufacturer C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom must be in the denominator?
17

4

3

14
Mathematics
1 answer:
yaroslaw [1]3 years ago
4 0

Answer:

df_{den}=df_{between}=N-K=17-3=14.

Step-by-step explanation:

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 (A,B,C) and on each group we have sample of size (6,5,6) respectively , 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}=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}  

The degrees of freedom for the numerator on this case is given by df_{num}=df_{within}=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=17-3=14.

And the total degrees of freedom would be df=N-1=17 -1 =16

On this case the correct answer would be 2 for the numerator and 14 for the denominator.  

Best answer

14

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IgorC [24]

Answer:

Interest rate, R = 244%

Step-by-step explanation:

Given the following data;

Principal = $270

Simple interest = future amount - principal = 309.60 - 270 = $39.60

Time = 22/360 = 0.06 years

To find the interest rate?

Mathematically, simple interest is calculated using this formula;

S.I = \frac {PRT}{100}

Where;

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Substituting into the equation, we have;

39.60 = \frac {270*R*0.06}{100}

Cross-multiplying, we have;

39.6 * 100 = 16.2*R

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R = \frac {3960}{16.2}

<em>Interest rate, R = 244.44 ≈ 244%</em>

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+6y       + 6y

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katrin [286]
<h2>Hello!</h2>

The answer is: The first graphic representation.

<h2>Why?</h2>

We are given a quadratic equation, meaning that it could be two possible solutions for the exercise, however, we are talking about time, so we have to consider only the obtained positive values.

Let's make the equation equal to 0 in order to find the values of "t"

h(t)=-16.1t^2 + 150\\0=-16.1t^2 + 150\\16.1t^2=150\\t^2=\frac{150}{16.1}=9.32\\t=+-\sqrt{9.32}=+-3.05\\t1=3.05\\t2=-305

So, discarding the negative value, we can use the possitive value to find the correct graphic representation.

To find the correct graphic representation we must take into consideration the following:

- We must remember that the sign of the coefficient of the quadratic term (t^2) will define if the parabola opens downward or upward.

From the given quadratic (or parabola) equation we have:

a=-1\\b=0\\c=150

So, since the coefficient of the quadratic term is negative, the parabola opens downward.

- Since we are looking for a graphic that represents the change in height over time, we need to look for a graphic that shows only positive values for the x-axis (time)

- We are looking for a parabola which y-axis intercept is equal to 150.

Therefore, the graphic representation of the quadratic function that models a ball's height over time is the first graphic representation.

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