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Rasek [7]
3 years ago
15

2. X-5 = 13 1. x + 7 = 21 4. x/7= 15 3. 4x = 48

Mathematics
1 answer:
mylen [45]3 years ago
8 0
1. X+7=21
-7 -7
X=14
2. X-5=13
+5 +5
X=18
3. 4x=48
— —
4 4
X=12
4. 7(X/7)=(15)7
X=105
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Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline
yawa3891 [41]

Answer:

B) 4.07

Step-by-step explanation:

First we need to calculate the mean of all the data, which is the same as the mean of the means of each grade of gasoline:

Regular    BelowRegular   Premium   SuperPremium

39.31             36.69                38.99             40.04

39.87            40.00                40.02             39.89

39.87            41.01                  39.99             39.93

X1⁻=39.68    X2⁻= 39.23       X3⁻= 39.66    X4⁻=  39.95

Xgrand⁻ = (39.68+39.23+39.66+39.95)/4 = 39.63

Next we need to calculate the sum of squares within the group (SSW) and the sum of squares between the groups (SSB), and the respective degrees of freedom):

SSW = [ (39.31-39.68)² + (39.87-39.68)² + (39.87-39.68)² ] + [ (36.69-39.23)² + (40.00-39.23)² + (41.01-39.23)² ] + [ (38.99-39.66)² + (40.02-39.66)² + (39.99-39.66)² ] + [ (40.04-39.95)² + (39.89-39.95)² + (39.93-39.95)² ] = [0.2091] + [10.2129] + [0.6874] + [0.0121] = 11.12

SSW =  11.12

Degrees of freedom in this case is calculated by m(n-1), with m being the number of grades of gasoline (4) and n being the number of trial results for each one (3), so we would have 4(3-1) = 8 degrees of freedom

SSB = [ (39.68-39.63)² + (39.68-39.63)² + (39.68-39.63)²] + [ (39.23-39.63)² + (39.23-39.63)² + (39.23-39.63)² ] + [ (39.66-39.63)² + (39.66-39.63)² + (39.66-39.63)² ] + [ (39.95-39.63)² + (39.95-39.63)² +(39.95-39.63)² ] = [0.0075] + [0.48] + [0.0027] + [0.3072] = 0.7974

SSB =  0.80

For this case, the degrees of freedom are m-1, so we would have 4-1 = 3 degrees of freedom

Now we can establish the hypothesis for the test:

H0: μ1 = μ2 = μ3 = μ4

The null hypothesis states that the means of miles per gallon for each fuel are the same, indicating that the drade of gasoline does not make a difference, therefore our alternative hypothesis will be:

H1: the grade of gasoline does makes a difference

We will use the F statistic to test the hypothesis, which is calculated like follows:

F - statistic = (SSB/m-1) / (SSW/m(n-1)) = (0.80/3) / (11.12/8) = 0.19

We know that the level of significance we are using is α = 0.05, so to find the critical value F we need to look at some table of critical values for the F distribution for the 0.05 significance level (like the attached image). Then we just need to look fot the value that is located in the intersection between the degrees of freedom we have in the numerator (horizontal) and the denominator (vertical) of the statistic (3 and 8). That critical value is:

Fc = 4.07

3 0
3 years ago
Please find for y thank you
Vlad1618 [11]
Since the triangles are congruent your equation would be 2y+8=19

Solve for y

y=5.5
4 0
3 years ago
Pls help me I reallyyyyy don't understand
mash [69]

Answer:

9

Step-by-step explanation:

range is the range from the lowest # through the biggest # in other words subtract the smaller number from the bigger number

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3 years ago
What is the probability that no more than 5 of the next 100 skiers who attempt this run will injure themselves
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