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3 years ago

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A hotel elevator starts on the 5th floor. It went up 7 floors, down 3 floors, and then down 6 floors. On what floor did the elev

ator finally stop?

1 answer:

ch4aika [34]3 years ago

7 0

5+ 7 = 12th floor

12-3 = = 9th floor

9- 6 = 3rd floor

The answer is the 3rd floor

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The degree of the polynomial function f(x) is 3. The roots of the equation f(x)=0 are −4 , 0, and 2. Which graph could be the gr

KATRIN_1 [288]

We know that the polynomial function is of degree 3, and that its roots are -4, 0, 2.

With this data we can write a generic equation for the function:

f (x) = bx (x + 4) (x-2)

Since the function is of degree 3 and cuts the axis at x = 0, then it has rotational symmetry with respect to the origin.

The graph of the function can be of two main forms, based on the value of the coefficient b.

If b is positive then the function grows from y = -infinite and cuts the x-axis for the first time in -4. Then it decreases, cuts at x = 0 and begins to grow again cutting the x-axis for the third time at x = 2. and continues to grow until y = infnit

If b is negative, then the function decreases from y = infinity and cuts the x-axis for the first time in -4. Then it grows, cuts at x = 0 and begins to decrease again by cutting the x-axis for the third time at x = 2, and continues to decrease until y = -infnit.

In the attached images the graphs of the function f (x) are shown assuming b = -1 and b = 1

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3 years ago

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Reflect shape a in the line y=1

Hatshy [7]

The coordinates of the reflected figure are:

(1,1), (1,2), (0,2), (-1,1), (0,4), (-1,4)

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3 years ago

The swimming instructor has a list of 152 students who have signed up for swimming lessons. The swimming instructor can register

mezya [45]

Answer:

13 classes

Step-by-step explanation:

152 divided by 12 is 12.6666666667 so the remaining number of stundents would not be in a class.

But, we can make a class for that remaining students.

So the answer is 13.

I hope this helped ;)

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3 years ago

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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

A rectangle has an area of 81 square centimeters. Which of the following would be the rectangle's length and width? (Area = equa

mestny [16]

Answer:

length: 9cm

width: 9cm

Step-by-step explanation:

9×9=81

3 0

3 years ago

Read 2 more answers