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Juliette [100K]
3 years ago
7

Graph the data in the table below. Which kind of function best models the data? write an equation to model the data.

Mathematics
1 answer:
harina [27]3 years ago
7 0

Answer:

A quadratic function.

y=2.5x^{2}

Step-by-step explanation:

If you plot the points given in the table, you obtain the graph shown in the figure attached.

As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.

By definition, the parent function of a quadratic function is:

y=x^{2}

You can compress or stretch it in the y-direction by multiplying the function by a constant C:

 y=Cx^{2}

If 0, then the function is compressed.

If C>1, then the function is stretched.

You can find the constant of the function asked as following:

- Substitute x=1 into the parent function to obtain the y-coordinate:

y=(1)^{2}=1

Then the point is (1,1)

- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:

C=2.5

Then the function is:

y=2.5x^{2}

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The answer should be $ 19.25. All you have to do is $7.70 * 2.5 which = $19.25
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Groups of four for the group of 288 and groups of five for the group of 360

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3 years ago
Angle P measures 112 degrees, what are the measures of angle N and O?
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3 years ago
Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $7.00 per pound w
Tcecarenko [31]

Answer:

The number of pounds of City Roast Columbian coffee they should buy is 1 and the number of pounds of French Roast Columbian coffee they should buy is 11.

Step-by-step explanation:

Let

x ----> the number of pounds of a City Roast Columbian coffee

y ---> the number of pounds of a French Roast Columbian coffee

we know that

x+y=12 -----> equation A

7x+8.20y=8.10(12) ----> equation B

Solve the system of equations by graphing

The solution is the intersection point both graphs

The solution is the point (1,11)

therefore

The number of pounds of City Roast Columbian coffee they should buy is 1 and the number of pounds of French Roast Columbian coffee they should buy is 11.

3 0
3 years ago
Find the mean of each distribution.
Vanyuwa [196]

Answer:

a) 23 °C

b) 5.81 m² (2 dp)

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

This set of data is presented as a <u>Dot Plot</u>.

The frequency (how often a data value occurs) is represented by the number of dots above each data value.

For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.

To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.

\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}

<h3><u>Part (b)</u></h3>

This set of data is presented as a <u>stem and leaf diagram</u>, where the units and tenths are split.  The units column is the 'stem' and the tenths become the 'leaf'.

Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8

To find the mean, sum the data values, then divide by the total frequency.

To find the total frequency, simply count the number of values in the leaf part of the diagram.

Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

Total frequency = 11

\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}

4 0
2 years ago
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