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lisov135 [29]
3 years ago
10

What is the standard deviation of the data set given below? 4, 7, 8, 9, 12

Mathematics
2 answers:
astraxan [27]3 years ago
4 0

Answer:

sqrt 8.5

Step-by-step explanation:

apex

Sergeeva-Olga [200]3 years ago
3 0

Answer:

SQRT 8.5

Step-by-step explanation:

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For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write a
Ulleksa [173]

I am going to graph the situation on an external graphing utility and show you the answer, it will take a

minute, stay with me.

m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3y\text{ = mx+b}\rightarrow\text{ b =-1}

So the equation of the line is.

y\text{ =3x -1}y\text{ -1 = m(3-0)}

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1 year ago
At the same time a 32-foot water tower casts a 14-foot shadow , a nearby light posts a casts a 7-foot shadow. How tall is the li
Serhud [2]
To solve this problem you can use proportions. The shadow of the water tower and light post are a match, and the height of the water tower and light post are a match. Since we are finding the height of the light post we can replace it with x. The proportion can be set up like this: x/32=7/14. First, multiply 32 and 7 which equals 224. Then take 224 and divide it by the leftover number, 14, and you get 16. So, the answer is c).
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4 years ago
The sum of the first n terms of an arithmetic series is n/2(3n-5). If the second and fourth terms of the arithmetic series are t
sergiy2304 [10]

Let <em>a</em> be the first term in the arithmetic sequence. Since it's arithmetic, consecutive terms in the sequence differ by a constant <em>d</em>, so the sequence is

<em>a</em>, <em>a</em> + <em>d</em>, <em>a</em> + 2<em>d</em>, <em>a</em> + 3<em>d</em>, …

with the <em>n</em>-th term, <em>a</em> + (<em>n</em> - 1)<em>d</em>.

The sum of the first <em>n</em> terms of this sequence is given:

a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n(3n-5)}2

We can simplify the left side as

\displaystyle \sum_{i=1}^n (a+(i-1)d) = (a-d)\sum_{i=1}^n1 + d\sum_{i=1}^ni = an+\dfrac{dn(n-1)}2

so that

an+\dfrac{dn(n-1)}2 = \dfrac{n(3n-5)}2

or

a+\dfrac{d(n-1)}2 = \dfrac{3n-5}2

Let <em>b</em> be the first term in the geometric sequence. Consecutive terms in this sequence are scaled by a fixed factor <em>r</em>, so the sequence is

<em>b</em>, <em>br</em>, <em>br</em> ², <em>br</em> ³, …

with <em>n</em>-th term <em>br</em> ⁿ⁻¹.

The second arithmetic term is equal to the second geometric term, and the fourth arithmetic term is equal to the third geometric term, so

\begin{cases}a+d = br \\\\ a+3d = br^2\end{cases}

and it follows that

\dfrac{br^2}{br} = r = \dfrac{a+3d}{a+d}

From the earlier result, we then have

n=7 \implies a+\dfrac{d(7-1)}2 = a+3d = \dfrac{3\cdot7-5}2 = 8

and

n=2 \implies a+\dfrac{d(2-1)}2 = a+d = \dfrac{3\cdot2-5}2 = \dfrac12

so that

r = \dfrac8{\frac12} = 16

and since the second arithmetic and geometric terms are both 1/2, this means that

br=16b=\dfrac12 \implies b = \dfrac1{32}

The sum of the first 11 terms of the geometric sequence is

<em>S</em> = <em>b</em> + <em>br</em> + <em>br</em> ² + … + <em>br</em> ¹⁰

Multiply both sides by <em>r</em> :

<em>rS</em> = <em>br</em> + <em>br</em> ² + <em>br</em> ³ + … + <em>br</em> ¹¹

Subtract this from <em>S</em>, then solve for <em>S</em> :

<em>S</em> - <em>rS</em> = <em>b</em> - <em>br</em> ¹¹

(1 - <em>r</em> ) <em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹)

<em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹) / (1 - <em>r</em> )

Plug in <em>b</em> = 1/32 and <em>r</em> = 1/2 to get the sum :

S = \dfrac1{32}\cdot\dfrac{1-\dfrac1{2^{11}}}{1-\dfrac12} = \boxed{\dfrac{2047}{32768}}

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3 years ago
How do you write 100, in an exponential form
Allushta [10]

1. 10^2

2. 10^5

3. 10^4

Hope this helped!

Nate

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3 years ago
a scale drawing of valarie's garden uses a scale of 2 inches = 5 feet. If the garden's width on the scale drawing measures 3 inc
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Valarie's garden is 7.5 feet in width
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