What is the area and why?

Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = -3 and x

trasher [3.6K]

This can occur through a parabola that has zeroes at x = 3 and x = -3. There is no rate of change because the y values do not change at those points because they are both 0. Karly can be correct because that turning point can be a vertex of a parabola. The parabola's function would increase until it reaches it's highest point and then go back down again. In this way, Karly and Tucker can both be correct.

Hope this helps :)

3 0

3 years ago

A large grandfather clock strikes its bell once at 1:00, twice at 2:00, three times at 3:00, etcetera. what is the total number

erastovalidia [21]

There is a formula for adding consecutive integers.
sum = (n * (n+1)) / 2
for summing 1 through 12 it is
sum = (12 * 13) / 2 = 156/2 = 78
The clock goes through two "12-hour cycles" in a day, so the answer is 2 * 78 or 156 times.

8 0

4 years ago

Read 2 more answers

Which of the following are square roots of the number below? check all that apply.

IceJOKER [234]

D. 20 because 20 x 20=400

4 0

3 years ago

Josiah is playing a computer game that lets him customize a story There are 5 different eras and 2 location to choose from. How

pychu [463]

Answer:

10

Step-by-step explanation:

GIVEN: Josiah is playing a computer game that lets him customize a story There are $5$ different eras and $2$ location to choose from.

TO FIND: How many different stories can Josiah construct.

SOLUTION:

Total different eras $=5$

Total different locations $=2$

He can choose one era and one location.

Total different stories that Josiah can construct $=^5C_1\times^2C_1$

$=10$

Hence Josiah can construct 10 different stories.

4 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Alex Ar [27]

Answer:

$y=-2.86 x +228.84$

Step-by-step explanation:

We assume that the data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 53, 22, 35, 38, 166, 13, 185, 25

Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

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

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

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

So we can find the sums like this:

$\sum_{i=1}^n x_i = 50+ 55+ 50+ 79+ 44+ 37 +70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152 + 53 + 22 + 35 + 38 + 166 + 13 + 185 + 25=689$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 53^2 + 22^2 + 35^2 + 38^2 + 166^2 + 13^2 + 185^2 + 25^2=91641$

$\sum_{i=1}^n x_i y_i =50*152+ 55*53+ 50*22+ 79*35+ 44*38+ 37*166 +70*13+ 45*185+ 49*25=32654$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.56$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=32654-\frac{479*689}{9}=-4016.11$

And the slope would be:

$m=-\frac{4016.11}{1403.56}=-2.86$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.22$

$\bar y= \frac{\sum y_i}{n}=\frac{689}{9}=76.56$

And we can find the intercept using this:

$b=\bar y -m \bar x=76.56-(-2.86*53.22)=228.84$

So the line would be given by:

$y=-2.86 x +228.84$

8 0

4 years ago