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3 years ago

The two top questions

Mathematics

1 answer:

il63 [147K]3 years ago

8 0

Answer:

1a. x=1/2 1b. x= 4

Step-by-step explanation:

1a. 30x= 16- 2x

(add 2x to both sides)

32x= 16

(divide both sides by 16)

x= 1/2

1b. 2(3x-5)=2x+6

(distribute the 2)

6x-10=2x+6

(add 10 to both sides)

6x=2x + 16

(subtract 2x from both sides)

4x= 16

(divide both sides by 4)

x=4

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The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

b) $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

4 0

3 years ago

Colossal canyon was formed in the shape of a parabola.The graph below shows the shape of the canyon.What interval is the functio

Roman55 [17]

Answer:

The function increasing ⇒ 3 ≤ x ≤ 6 answer C

Step-by-step explanation:

∵ The vertex of the parabola is (3 , -6)

∴ The minimum value = -6 at x = 3

∵ The left part of the parabola is decreasing because the value of y decreased from 3 to -6 when 0 ≤ x ≤ 3

∵ The right part of the parabola is increasing because the value of y increased from -6 to 3 when 3 ≤ x ≤ 6

∴ The function is increasing at interval 3 ≤ x ≤ 6

8 0

3 years ago

Which or the following is not a possible value for the correlation coefficient (r)?

Reil [10]

The correct answer is 2– it is NOT a possible value for correlation coefficient (r) because the value of “r” must always be between +1 and –1.

6 0

3 years ago

Read 2 more answers

Increase £36.00 by 10%

OLEGan [10]

Answer:

3.6

Step-by-step explanation:

10% = .10

36 * .10 = 3.6

4 0

4 years ago

Please helpppppp!!!! D:

zloy xaker [14]

Answer:

Its -1 have a great day!

Step-by-step explanation:

6 0

3 years ago