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3 years ago

5

The following list gives the number of public libraries in each of 11 cities. 12, 3, 5, 4, 7, 8, 11, 13, 10, 6, 2 Find the modes

of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."

1 answer:

svetoff [14.1K]3 years ago

6 0

2,3,4,5,6,7,8,10,11,12,14

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3 years ago

Which points are coplanar and noncollinear

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3 years ago

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3 years ago

Determine f(x-1) f(x)=√x+6-8

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3 years ago

Can someone please help me with my Question #29 of The Quadratic Relations for me please?

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Answer:

Calculate the <u>first differences</u> between the y-values:

$\sf 3 \underset{+1}{\longrightarrow} 4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19$

As the first differences are <u>not the same</u>, we need to calculate the <u>second differences</u>:

$\sf 1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7$

As the second differences are the <u>same</u>, the relationship between the variable is quadratic and will contain an $x^2$ term.

--------------------------------------------------------------------------------------------------

<u>To determine the quadratic equation</u>

The coefficient of $x^2$ is always <u>half</u> of the <u>second difference</u>.

As the second difference is 2, and half of 2 is 1, the coefficient of $x^2$ is 1.

The standard form of a quadratic equation is: $y=ax^2+bx+c$

(where a, b and c are constants to be found).

We have already determined that the coefficient of $x^2$ is 1.

Therefore, a = 1

From the given table, when $x=0$ , $y=12$ .

$\implies a(0)^2+b(0)+c=12$

$\implies c=12$

Finally, to find b, substitute the found values of a and c into the equation, then substitute one of the ordered pairs from the given table:

$\begin{aligned}\implies x^2+bx+12 & = y\\ \textsf{at }(1,19) \implies (1)^2+b(1)+12 & = 19\\ 1+b+12 & = 19\\b+13 & =19\\b&=6\end{aligned}$

Therefore, the quadratic equation for the given ordered pairs is:

$y=x^2+6x+12$

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2 years ago