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babymother [125]
3 years ago
5

Find the distance between (-4,-3) and (-8,7)​

Mathematics
1 answer:
wariber [46]3 years ago
8 0

Answer:

√116  (or 10.77)

Step-by-step explanation:

(refer to attached )

in this case the points given are (-4,-3) and (-8,7)

hence x1 = -4, y1 = -3, x2 = -8, y2 = 7

D = √[ (x2-x1)² + (y2-y1)²  ]

= √[ (  -8 - (-4) )² + (  7 - (-3)  )²  ]

= √[ (  -8 +4 )² + (  7 + 3  )²  ]

= √[ (  -4 )² + (  10  )²  ]

= √[ (  16 ) + (  100  )  ]

= √116

= 10.77

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A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per we
Katen [24]

Answer:

Step-by-step explanation:

Hello!

For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:

Group 1: Single long exercise period five days per week

Group 2: Several 10' exercise periods five days per week

Group 3: Several 10' exercise periods five days per week using a home treadmill

All subjects were weighed before and after 6 months of training and their weight loss was determined.

The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.

To test this you have to conduct an ANOVA, with the hypothesis:

H₀: μ₁= μ₂= μ₃

H₁: At least one μi differs from the others. ∀ i=1, 2, 3

α: 0.05

The statistic is:

F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}

Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.

As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.

Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df

So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.

Treatments:

> The degrees of freedom between treatments are k-1 (k represents the number of treatments):

DfTr: 3-1= 2

>The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean is the mean that results of all the groups together.

So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9

SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54

> The Means Squares is:

MSTr= SSTr/DFTr= 0.54/2= 0.27

Errors

>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.

DfEr= N-k= 30-3= 27

>The mean square error (MSEr) is the estimation of the variance error (σ_{e}^2 → S_{e}^2), you have to use the following formula:

S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643

Finally you calculate the statistic:

F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012

This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:

F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35

Using the critical value approach, the decision rule is:

If F_{H_0} ≥ 3.35, reject the null hypothesis.

If F_{H_0} < 3.35, do not reject the null hypothesis.

The calculated value is less than the critical value, the decision is to not reject the null hypothesis.

So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"

I hope this helps!

5 0
3 years ago
Find all the zeros of the polynomial x^4+x^3-34x^2-4x+120 if two of its zeros are 2,-2
miskamm [114]

Answer:

The zeroes are 2, -2, -6, 5.

Step-by-step explanation:

If 2 of the zeroes are 2 and -2 then (x - 2)(x + 2) is factor of the polynomial.

We can now do long division.

Note (x - 2)(x + 2) = x^2 - 4, so we have:

x^2 - 4 ( x^4 + x^3 - 34x^2 - 4x + 120 ( x^2 +   x  - 30 <--- Quotient

             x^4            - 4x^4

                      x^3 -  30x^2 - 4x

                      x^3                -4x

                                  -30x^2   + 120  

                                  -30x^2   + 120

                                           

x^2 +   x  - 30 = 0        

(x + 6)(x - 5) = 0

x = -6, 5.              

7 0
2 years ago
Read 2 more answers
Write each fraction as a decimal. Use bar notation if necessary<br> 3/11
LenKa [72]

Answer:

0.27272727 repeated

Step-by-step explanation:

the fraction 3/11 just means 3 divided by 11

and the answer is

3/11=0.2727272727272727272727272727 repeating

6 0
3 years ago
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If DF = 61 and EF = 18, find DE
vova2212 [387]

Answer:

43 i jus subtracted

Step-by-step explanation:

5 0
3 years ago
X + 5 &gt; 7<br> it’s inequalities
Hatshy [7]

Answer:

X>2

Step-by-step explanation:

X+5>7

X>2

7 0
3 years ago
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