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3 years ago

The diameter of your new bicycle wheel is 22 inches. What is the radius of the bicycle wheel?

Mathematics

1 answer:

nata0808 [166]3 years ago

6 0

The radius is 11 inches

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On Monday, Byron spent $8.00 on lunch to purchase two tacos and one burrito. On Wednesday, he purchased one enchilada, one taco,

ad-work [718]

Answer:

2t+b=8

e+t+b=8.5

2e+2t=10

8 0

3 years ago

Can somebody plz help answer both the word problem question and number 24. (I can’t find the right answers) :(

vagabundo [1.1K]

Answer:

23:600

a12

b27

c36

d45

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

List six consecutive prime numbers

AnnZ [28]

Answer:

Step-by-step explanation:

In case someone is not sure what consecutive prime numbers are, here is an example: 17, 19, 23, 29, 31, and 37 are six consecutive prime numbers because they are ALL the prime numbers from 17 to 37 and they are listed in order.

6 0

3 years ago

Two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall. If a 24 foot wire is stretched bet

lianna [129]

Answer:

The distance between the posts is $3\sqrt{55}$ feet.

Step-by-step explanation:

In the attached figure, let DB and AC be the posts and let AD be the wire attached to the top of the posts.

BC is the distance between the posts and we need to find BC.

Note that BC = DE

Also, EC = DB = 8m and AE = AC - EC = 17 - 8 = 9 m.

Now, in the right triangle ADE,

$AD^{2} =AE^{2} +DE^{2}$

$24^{2} =9^{2} +DE^{2}$

$DE^{2} =24^{2} -9^{2}$

= (24+9) (24-9)

= 33(15)

= (3 × 11) × (3 × 5)

$DE=3\sqrt{55}$

Since DE = BC,

$BC=3\sqrt{55}$

Hence, the distance between the posts is $3\sqrt{55}$ feet.

7 0

3 years ago

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