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Elena L [17]
3 years ago
9

The city of Madison regularly checks the quality of water at swimming beaches located on area lakes. Fifteen times the concentra

tion of fecal coliforms, in number of colony forming units (CFU) per 100ml of water, was measured during the summer at one beach. 180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80. What is the sample standard deviation?
Mathematics
1 answer:
Maksim231197 [3]3 years ago
3 0

Answer:

The sample standard deviation is 393.99

Step-by-step explanation:

The standard deviation of a sample can be calculated using the following formula:

s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }

Where:

s= Sample standart deviation

N= Number of observations in the sample

{\displaystyle \textstyle {\bar {x}}}= Mean value of the sample

and \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} } simbolizes the addition of the square of the difference between each observation and the mean value of the sample.

Let's start calculating the mean value:

\bar {x}=\frac{1}{N}  \sum_{i=1}^{N}x_{i}

\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)

\bar {x}=\frac{1}{15}*(3810)

\bar {x}=254

Now, let's calculate the summation:

\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2

\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160

So, now we can calculate the standart deviation:

s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }

s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}

s=\sqrt[ ]{\frac{2173160}{14}}

s=393.99

The sample standard deviation is 393.99

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e-lub [12.9K]

Answer:

Option D 3/16

Step-by-step explanation:

Carol is cross-country skiing.

With the help of the given table we have to calculate the rate of change.

If we draw a graph for distance traveled on y-axis and tins at x-axis we find two points, ( 2, 1/6) and (3, 17/48).

Then slope of the line connecting these points will be the rate of change.

Rate of change = Slope = \frac{y-y'}{x-x'}

= \frac{\frac{17}{48}-\frac{1}{6}}{3-2}

= \frac{17-8}{48}

= \frac{9}{48}=\frac{3}{16}

Option D 3/16 is the answer.

3 0
3 years ago
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Romashka [77]
I think Mason could use a calculator
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3 years ago
Fracciones contesta lo siguiente
IgorLugansk [536]

Answer:

Tienes que dividir las fracciones en el dibujo por las fracciones de los números y luego obtendrás las respuestas correctas.

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2 years ago
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snow_tiger [21]

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C

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3 years ago
77. the volume of a cube is increasing at a rate of <img src="https://tex.z-dn.net/?f=10%20%5Cmathrm%7B~cm%7D%5E%7B3%7D%20%2F%20
Colt1911 [192]

Answer:

\displaystyle \frac{4}{3}\text{cm}^2/\text{min}

Step-by-step explanation:

<u>Given</u>

<u />\displaystyle \frac{dV}{dt}=10\:\text{cm}^3/\text{min}\\ \\V=s^3\\\\SA=6s^2\\\\\frac{d(SA)}{dt}=?}\:;s=30\text{cm}

<u>Solution</u>

(1) Find the rate of the cube's edge length with respect to time at s=30:

\displaystyle V=s^3\\\\\frac{dV}{dt}=3s^2\frac{ds}{dt}\\ \\10=3(30)^2\frac{ds}{dt}\\ \\10=3(900)\frac{ds}{dt}\\\\10=2700\frac{ds}{dt}\\\\\frac{10}{2700}=\frac{ds}{dt}\\\\\frac{ds}{dt}=\frac{1}{270}\text{cm}/\text{min}

(2) Find the rate of the cube's surface area with respect to time at s=30:

\displaystyle SA=6s^2\\\\\frac{d(SA)}{dt}=12s\frac{ds}{dt}\\ \\\frac{d(SA)}{dt}=12(30)\biggr(\frac{1}{270}\biggr)\\\\\frac{d(SA)}{dt}=\frac{360}{270}\biggr\\\\\frac{d(SA)}{dt}=\frac{4}{3}\text{cm}^2/\text{min}

Therefore, the surface area increases when the length of an edge is 30 cm at a rate of \displaystyle \frac{4}{3}\text{cm}^2/\text{min}.

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