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3 years ago

The midpoint of A (-4, 2) and B(8,5) is (2, 7/2) (-6, 3/2) (4, 7/2)

Mathematics

1 answer:

maria [59]3 years ago

6 0

Answer:

A. (2,7/2)

Step-by-step explanation:

The midpoint formula is (x1+x2/2 , y1+y2/2).

So just plug the numbers into that formula and you get the answer.

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Two bottles and their labels are mathematically similar.

Trava [24]

Answer:

The area of the larger label is 187.5 square centimeters.

Step-by-step explanation:

If the two bottles are mathematically similar, then the label area is directly proportional to the capacity of the bottle. If we know that a 0.512 L-bottle has a label area of 96 square centimeters, then the label area of a 1-L bottle is determined by this simple rule of three:

$x = 96\,cm^{2}\times \frac{1\,L}{0.512\,L}$

$x = 187.5\,cm^{2}$

The area of the larger label is 187.5 square centimeters.

3 0

3 years ago

Catalina and Morgan are finding the length of the third side of the right triangle. Who is correct? Explain your reasoning.

algol13

Answer:

Morgan

Step-by-step explanation:

because the pythagoras theorem is

${h1}^{2} = {b}^{2} + {h2}^{2}$

where h1=hypotenuse

h2=height

b=base

5 0

2 years ago

if a fish tank,8/11 of the fish have a red stripe on them.If 16 of the fish have red stripes,how many total fish are in there

Arisa [49]

8/11--------> 16

to find the total number of fish, divide 16 by 8 and multiply it by 11,

16÷8=2
2×11=22

total number of fish= 22

check,

22÷11×8=16

if you want to find the number of fish without the red stripes,

8/11--------> 16
11/11------->22
3/11--------->?

you can either subtract 16 by 22=6
or
22÷11×3=6

hope this helps......

3 0

4 years ago

The first step to solve for y in y 3 = 6 + x is

vodomira [7]

Divide both sides by 3

5 0

4 years ago

Read 2 more answers

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