By how many factors of 10 did you multiply 0.008? Why?

Find the correlation coefficient of the line of best fit for the points (-3,-40), (1,12), (5,72), (7,137). Explain how you guy y

vodka [1.7K]

Answer:

r = 0.9825; good correlation.

Step-by-step explanation:

One formula for the correlation coefficient is

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

The calculation is not difficult, but it is tedious.

1. Calculate the intermediate numbers

We can display them in a table.

x y xy x² y²

-3 -40 120 9 1600

1 12 12 1 144

5 72 360 25 5184

7 137 959 49 18769

Σ = 10 181 1451 84 25697

2. Calculate the correlation coefficient

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}$

The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.

3 0

2 years ago

g A sailing ship stopped at several islands, releasing one mating pair of goats onto each one. On the large island, the goats' g

PSYCHO15rus [73]

Answer:

The goat population reaches 1000 in 12.4 years

Step-by-step explanation:

After t years, the number of goats is given by

$N = N_0e^{bt}$

where $N_0$ is the initial number of goats and b is the per capita growth rate.

From the question,

$N_0 = 2$
b = 0.5
N = 1000

$1000 = 2e^{0.5t}$

$e^{0.5t} = 500$

$0.5t = \ln 500 = 6.214$

$t = \dfrac{6.2}{0.5} = 12.4$

5 0

2 years ago

Read 2 more answers

A person died leaving property worth rs.4000.40. His widow get 0.125 of the property and his son got 0.4 of the remainder. What

belka [17]

Answer:

Widow's Share = Rs 500.05

Son's share = Rs 1400.14

Step-by-step explanation:

Property = 4000.40

Widow get share = 0.125

So, Share of Widow = 0.125 * 4000.40

Widow's Share = Rs 500.05

Remaining Property = 4000.40 - 500.05

Remaining Property = 3500.35

Son's share = 0.4 * 3500.35

Son's share = Rs 1400.14

6 0

2 years ago

Wang Hao wants to spend at most $15 on dairy products. Each liter of goat milk costs $2.40 and each liter of cow's milk costs $1

Mashutka [201]

Answer:

2.40g + 1.20c ≤15

Step-by-step explanation:

Each liter of goat milk costs $2.40 and each liter of cow's milk costs $1.20

Let g = liters of goats milk

c = liters of cows milk

What we are buying is the liters times the cost

2.40g + 1.20c

This must be less than or equal to 15 dollars

2.40g + 1.20c ≤15

8 0

2 years ago

Read 2 more answers

A dolphin is 42 feet underwater and ascends at a constant rate for 14 seconds until it reaches the surface. Identify and interpr

Cloud [144]

Ok so, based on the graph lets say that x = seconds and y = depth of dolphin. the interception in both points is when they are at 0 i.e when x is equals 0 and y equals 0. So At 0 seconds, the dolphin is 42 feet below the surface. So we say that x = 0, y = -42 and then the y intercepts = -42 so the point of interception is(0 (seconds),-42(depth of the dolphin)) When the clock says it's 14 seconds, the dolphin is even with the surface (0 below the surface this time). So we say that x = 14, y = 0. In this case The x intercept = 14 (14,0). But we need to calculate The slope with the formula= (y2 - y1)/(x2 - x1) = 42/14 = 3. Therefore, the formula for this line is y = 3x - 42.

3 0

2 years ago