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3 years ago

Help ASAP! Can someone explain how?

Mathematics

1 answer:

Kay [80]3 years ago

3 0

Answer:

Step-by-step explanation:

cos theta is 5/13

so, adjacent=5 ,hypotenuse=13 and opposite=?

hypotenuse^2=adjacent^2+opposite^2

13^2=5^2+opposite^2

169-25=opposite^2

$\sqrt{144}$ =opposite

12=opposite

sin theta=opposite/hypotenuse

=12/13

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A study is given in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (

Natalka [10]

Answer:

a) $\bar x= \frac{\sum x_i}{n}=\frac{211.81}{7}=30.26$

$\bar y= \frac{\sum y_i}{n}=\frac{17.63}{7}=2.52$

$r=\frac{7(533.1304)-(211.81)(17.63)}{\sqrt{[7(6410.063) -(211.81)^2][7(44.5511) -(17.63)^2]}}=-0.85$

$b = \frac{S_{xy}}{S_{xx}}$

Where:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6410.063-\frac{211.81^2}{7}=0.9950$

$S_{yy}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=44.5511-\frac{17.63^2}{7}=0.1487$

$b = \frac{S_{xy}}{S_{xx}}$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=533.1304-\frac{211.81*17.63}{7}=-0.3282$

And the slope would be:

$m=\frac{-0.3282}{0.9950}=-0.330$

And we can find the intercept using this:

$b=\bar y -m \bar x=2.52-(-0.3299*30.26)=12.502$

So then the linear model would be:

$y =-0.330 x + 12.502$

b) > x<-c(29.67, 29.87, 30.15, 30.21, 30.47, 30.64, 30.80)

> y<-c(2.64,2.59, 2.69, 2.60, 2.48, 2.38, 2.25)

> lm<- lm(y~x)

> lm

Call:

lm(formula = y ~ x)

Coefficients:

(Intercept) x

12.5009 -0.3299

And the model is given by:

$y= -0.330 x +12.501$

c) Every increase of one degree Celsius means about -0.330 fewer mean millimeters of coral growth per year.

Step-by-step explanation:

For this case we have the following data:

X: 29.67 29.87 30.15 30.21 30.47 30.64 30.80

Y: 2.64 2.59 2.69 2.60 2.48 2.38 2.25

Part a

$\bar x= \frac{\sum x_i}{n}=\frac{211.81}{7}=30.26$

$\bar y= \frac{\sum y_i}{n}=\frac{17.63}{7}=2.52$

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.

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=7 $\sum x = 211.81, \sum y = 17.63, \sum xy = 533.1304, \sum x^2 =6410.063, \sum y^2 =44.5511$

$r=\frac{7(533.1304)-(211.81)(17.63)}{\sqrt{[7(6410.063) -(211.81)^2][7(44.5511) -(17.63)^2]}}=-0.85$

We can calculate the slope for the regression model with this formula:

$b = \frac{S_{xy}}{S_{xx}}$

Where:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6410.063-\frac{211.81^2}{7}=0.9950$

$S_{yy}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=44.5511-\frac{17.63^2}{7}=0.1487$

And if we replace we got:

$b = \frac{S_{xy}}{S_{xx}}$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=533.1304-\frac{211.81*17.63}{7}=-0.3282$

And the slope would be:

$m=\frac{-0.3282}{0.9950}=-0.330$

And we can find the intercept using this:

$b=\bar y -m \bar x=2.52-(-0.3299*30.26)=12.502$

So then the linear model would be:

$y =-0.330 x + 12.502$

Part b

For this case we use the following R code:

> x<-c(29.67, 29.87, 30.15, 30.21, 30.47, 30.64, 30.80)

> y<-c(2.64,2.59, 2.69, 2.60, 2.48, 2.38, 2.25)

> lm<- lm(y~x)

> lm

Call:

lm(formula = y ~ x)

Coefficients:

(Intercept) x

12.5009 -0.3299

And the model is given by:

$y= -0.330 x +12.501$

Part c

For this case the best interpretation is:

Every increase of one degree Celsius means about -0.330 fewer mean millimeters of coral growth per year.

8 0

3 years ago

(20 points)

likoan [24]

A = a + b over 2

First multiply both sides by 2:

2A = a+b

Now subtract a from both sides:

b = 2A - a

6 0

3 years ago

One positive integer is 3 greater than 4 times another positive integer. If the product of the two integers is 76, then what is

andrew11 [14]

Answer:

The sum of the two integers is 23

Step-by-step explanation:

Let one integer be x and the other integer be y

Then according to the statement "One positive integer is 3 greater than 4 times another positive integer.."

x be the integer that is One positive integer is 3 greater than 4 times another positive integer.

Then

x= 3+4y----------------------------------(1)

Product of the two integer is 76, this can written as

$x \times y =76$

substituting the values of x from eq(1)

$( 3+4y) \times y =76$

$3y + 4y^2 = 76$

$3y + 4y^2-76= 0$

$4y^2 + 3y -76= 0$

Solving the quadratic equation equation we get

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

here

a = 4

b= 3

c = -76

susbtituting the above values in the formula

$y=\frac{-3 \pm \sqrt{3^2-4(4)(-76)}}{2(4)}$

$y=\frac{-3 \pm \sqrt{9- 4(4)(-76)}}{8}$

$y=\frac{-3 \pm \sqrt{9- (16)(-76)}}{8}$

$y=\frac{-3 \pm \sqrt{9- (-1216)}}{8}$

$y=\frac{-3 \pm \sqrt{9 + 1216}}{8}$

$y=\frac{-3 \pm \sqrt{1225}}{8}$

$y=\frac{-3 \pm 35}{8}$

$y=\frac{-3 +35}{8}$ $y=\frac{-3 -35}{8}$

$y=\frac{32}{8}$ $y=\frac{-38}{8}$

y= 4 y = −4.75

Since in the question it is given that it is a positive integer

so y = 4

substituting y=4 in eq (1) we get,

x= 3+4(4)

x= 3+16

x= 19

The sum of the two integers

=> x + y

=> 19+4

=>23

8 0

4 years ago

Angle r° = 2w°. What is the measure of angle r°? 120° 240° 143° 286°

Tanya [424]

Answer:

D = 286°

Step-by-step explanation:

Find both the angles of each right triangle.

Triangle A : 53°, 37°, 90°

180° - 127° = 53°

53° + 90° = 143°

180° - 143° = 37°

Triangle B: 90°, 53°, 37°

180° - 127° = 53°

53° + 90° = 143°

180° - 143° = 37°

Now, we find w.

w = 180° - 37° = 143°

r = 2w = 143 × 2

r = 286°

4 0

2 years ago

The difference between 42 and 19

Vladimir [108]

Like 42-19??????????????

cause the answer for that is 23

3 0

4 years ago