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3 years ago

Explain what each of the following correlations means:

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

Answer:

a. The number of crude oil imports from Norway and the number of drivers killed in a collision with a train, have a very strong positive relationship. This means that an increase in the number of crude oil imports from Norway will strongly influence and lead to an increase in the number of drivers killed in a collision with a train and vice versa.

b. There is a moderately strong negative relationship between how much precipitation Texas gets and how much revenue online retailers bring in on Thanksgiving. An increase in how much precipitation Texas gets will moderately influence and lead to a decrease in how much revenue online retailers bring in on Thanksgiving and vice versa.

c. The amount of coffee consumed by the average American and how many iPhones were sold have a very strong negative relationship. An increase in one will strongly lead to a decrease in the other.

d. There is an extremely strong (near perfect) positive relationship between the divorce rate in Maine and the per capita consumption of margarine.

e. There is no relationship between how many males in Wisconsin died due to slipping or tripping and how many farms there are in the US. They are completely independent of one another.

Step-by-step explanation:

Correlation measures the degree of association between 2 variables.

The Correlation coefficient (r) can assume values that lie between -1 and +1

If r is between 0.1 to 0.5 or -0.1 and -0.5, then the 2 variables in the relationship are said to be weakly related.

If the value of r is between 0.9 and 1 or -0.9 and -1, then the variables are said to be strongly related.

r = 0 means that there is no correlation between the variables and r = ±1 means a perfect positive of perfect negative relationship between the variables.

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Explain the distance formula. Then use it to calculate the

Alex777 [14]

Answer:

$dAB=10\ units$

Step-by-step explanation:

we know that

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(1, 1) and B(7, −7)

Let

(x1,y1)=A(1, 1)

(x2,y2)=B(7, −7)

substitute the given values in the formula

$dAB=\sqrt{(-7-1)^{2}+(7-1)^{2}}$

$dAB=\sqrt{(-8)^{2}+(6)^{2}}$

$dAB=\sqrt{64+36}$

$dAB=\sqrt{100}$

$dAB=10\ units$

6 0

3 years ago

Read 2 more answers

At 6:00 A.M. the temperature was 33°F. By noon the temperature had increased by 10°F and by 3:00 P.M. it had increased another 1

sergij07 [2.7K]

Answer:

The temperature needs to decrease by 7°F to return to the original temperature.

Step-by-step explanation:

The temperature starts at 33 degrees then increases by 10 then 12 then decreases by 15 which will equal 40.

33 + 10 = 43

43 + 12 = 55

55 - 15 = 40

40 - 33 = 7

The temperature needs to decrease by 7 degrees.

5 0

3 years ago

What is 43.043 in expanded form

nordsb [41]

40+3+.04+.003

expanded form is showing what you have to add together

3 0

3 years ago

What is the product,in square of the width (x = 18x) and the height (y) of the prism??

a_sh-v [17]

I think the answer to (Y) may be 40 cubic units

6 0

3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

3 0

3 years ago