MATHEMATICS COLLEGE

A study is given in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in millimeters per year) over a several-year period at different locations. Here are the data: Sea Surface Temperature 29.69 29.87 30.16 30.22 30.48 30.65 30.80
Growth 2.63 2.57 2.67 2.50 2.47 2.38 2.25

Required:
a. Find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y.
b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)
c. Say in words what the numerical value of the slope tells you.

Answers

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Sea Surface Temperature (x) : 29.69 29.87 30.16 30.22 30.48 30.65 30.80

Growth : (y) 2.63 2.57 2.67 2.50 2.47 2.38 2.25

Mean (x) :

Σ(X) / n

n = number of observations

Mean (m1) = Σ(X) / n = 211.87 / 7 = 30.27

Standard deviation(sx) = 0.3742 (using calculator)

Mean (m2) :

Σ(y) / n = 17.47 / 7 = 2.50

Standard deviation(sy) = 0.1354 ( using calculator)

Correlation (r) :

(1/n)Σ[(x - m1) / sx] × [(y - m2) /sy]

Using calculator to save computing time :

r = - 0.8642

b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)

The least square line using the regression calculator :

y = -0.31 + 11.96x

Comparing to the regression equation format :

y = mx + c

Where ;

-0.31 = intercept ; 11.96 = slope ; x = independent variable ; y = dependent variable

c. Say in words what the numerical value of the slope tells you.

For every 1° degree rise in surface temperature, growth increases by 11.96

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Difficult Math. Up to the challenge?

For his long distance phone service, Bill pays a $3 monthly fee plus 11 cents per minute. Last month, Bill's long distance bill was $16.09. For how many minutes was Bill billed?

Answers

Answer:

1.19 minutes

Step-by-step explanation:

First, subtract the $3 monthly fee:

16.09 - 3

= 13.09

Then, divide this by 11:

13.09/11

= 1.19

So, he was billed for 1.19 minutes

An experiment consists of drawing 1 card from a standard 52 card deck? What is the probability of drawing a queen?

Answers

4/52, or 1/13, or 8 percent(not very accurate or precise). You take the number of queens in a deck(4) and put it over the total number of cards in a deck(52). This gives you a probability of 1 in 13 or about 8 percent

4 out of 52 which is equal to 1/13

Find the measure of AB *

14 cm
24 cm
10 cm
140 cm

Answers

Answer:

10 cm

Step-by-step explanation:

Because it is a parrallogram and by its property it will be 10

During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 3 hours, at a rate of 3 inches per hour for the next 5 hours, and at a rate of 0.75 inch per hour for the final hour.How many inches of snow accumulated from the storm?

Answers

Answer:

use f(x)=y=mx+b

let snow = S, time = t instead of y and x

S(t)=mt+b

The rate of inches per hour represents the slope of the graph, m.

The y-variable would be the amount of snow, S.

The x-variable would be the time, t, in hours.

The function has three pieces:

i) S(t)= 2t (slope = 2)

ii) S(t) = 3t (slope = 3)

iii) S(t) = 0.75t (slope = 0.75)

For the first piece, i), t=3, so the amount of snow is 6 inches.

For the second piece, ii) t=5, so the amount of snow is 15 inches.

For the third piece, iii) t=1, so the amount of snow is 0.75 inch.

In total, it snowed 21.75 inches.

total snow

Final answer:

To find the total accumulation of snow during the nine-hour snowstorm, we calculate the snow accumulation for each hour and then sum them up. The total accumulation of snow from the storm is 21.75 inches.

Explanation:

To find the total accumulation of snow during the nine-hour snowstorm, we need to calculate the amount of snow that fell during each hour and then sum them up. First, we calculate the snow accumulation for each hour:

For the first 3 hours, it snowed at a rate of 2 inches per hour, so the accumulation is 3 * 2 = 6 inches.
For the next 5 hours, it snowed at a rate of 3 inches per hour, so the accumulation is 5 * 3 = 15 inches.
For the final hour, it snowed at a rate of 0.75 inch per hour, so the accumulation is 1 * 0.75 = 0.75 inches.

Finally, we sum up the accumulations for each hour: 6 + 15 + 0.75 = 21.75 inches. Therefore, the total accumulation of snow from the storm is 21.75 inches.