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3 years ago

Arun has captured many yellow-spotted salamanders. He weights each and then counts the number of yellow spots on its back

Mathematics

2 answers:

vichka [17]3 years ago

7 0

Answer:

Step-by-step explanation:

This is a positive anotation.

Hope this helps have a good day!

Mashutka [201]3 years ago

4 0

Answer:

Its c

Step-by-step explanation:

i took the quiz and i got it right don’t believe the person abov me

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Given the point (1, 3) and a slope of 2, write an equation in point-slope form.

Sunny_sXe [5.5K]

Answer:

y=2x+1

Step-by-step explanation:

Since we are given a point and a slope, we can use the point slope formula

$y-y_{1} =m(x-x_{1})$

m is the slope. In this case, m is 2.

y1 is the y coordinate of the point given. y1 is 3.

x1 is the x coordinate of the point given. x1 is 1

y-3=2(x-1)

Now, we need to get the equation into point slope form: y=mx+b

To do this, we need to get y by itself

First, distribute the 2 on the right

y-3=2*x+ 2*-1

y-3=2x-2

Add 3 to both sides

y-3+3=2x-2+3

y=2x+1

The equation is in y=mx+b form, so our final equation is:

y=2x+1

6 0

2 years ago

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