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Umnica [9.8K]
3 years ago
13

Listed below are the amounts​ (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the​ range,

variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any​ outliers, and are they likely to have much of an effect on the measures of​ variation?7 50 50 55 65 75 80 110 190 211 255 350 500 2000 3000 The range of the sample data is _____
Mathematics
1 answer:
velikii [3]3 years ago
5 0

Answer:

Range = Max -Min= 3000-7 = 2993 dollars

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

And after replace we got s^2=734983.55 dollars^2

s =\sqrt{734983.55}=857.312 dollas

For this case we can consider as an outilers values that are very far away from the others. And for example 2000 and 3000 could be considered outliers since are too high values compared to the remain and the same for 7 since is a value too low compared with the rest.

Step-by-step explanation:

The data given : 7 50 50 55 65 75 80 110 190 211 255 350 500 2000 3000

The range is defined as:

Range = Max -Min= 3000-7 = 2993 dollars

In order to find the variance and deviation we need to find first the mean given by:

\bar X = \frac{\sum_{i=1}^n X_i}{n}= \frac{7+50+50+55+65+75+80+110+190+211+255+350+500+2000+3000}{15}=466.53 dollars

Now we can calculate the sample variance with the following formula:

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

And after replace we got s^2=734983.55 dollars^2

And the standard deviation for the sample would be just the square root of the sample variance:

s =\sqrt{734983.55}=857.312 dollas

For this case we can consider as an outilers values that are very far away from the others. And for example 2000 and 3000 could be considered outliers since are too high values compared to the remain and the same for 7 since is a value too low compared with the rest.

You might be interested in
(**15 POINTS**)
bonufazy [111]

Answer:

0.6x = 87

Step-by-step explanation:

Hi, to answer this question we have to write en equation:

We have to multiply the variable x by the percentage given (60%) in decimal form (divided by 100). That expression must be equal to 87.

Mathematically speaking:

x (60/100) = 87

0.6x = 87

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
I am having trouble with this relative minimum of this equation.<br>​
Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach.  You have to let me know if you want this done another way.

Here are some rules I'm going to use:

(f+g)'=f'+g'       (Sum rule)

(cf)'=c(f)'          (Constant multiple rule)

(x^n)'=nx^{n-1} (Power rule)

(c)'=0               (Constant rule)

(x)'=1                (Slope of y=x is 1)

y=4x^3+13x^2-12x-56

y'=(4x^3+13x^2-12x-56)'

y'=(4x^3)'+(13x^2)'-(12x)'-(56)'

y'=4(x^3)'+13(x^2)'-12(x)'-0

y'=4(3x^2)+13(2x^1)-12(1)

y'=12x^2+26x-12

Now we set y' equal to 0 and solve for the critical numbers.

12x^2+26x-12=0

Divide both sides by 2:

6x^2+13x-6=0

Compaer 6x^2+13x-6=0 to ax^2+bx+c=0 to determine the values for a=6,b=13,c=-6.

a=6

b=13

c=-6

We are going to use the quadratic formula to solve for our critical numbers, x.

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}

x=\frac{-13 \pm \sqrt{169+144}}{12}

x=\frac{-13 \pm \sqrt{313}}{12}

Let's separate the choices:

x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}

Let's approximate both of these:

x=0.3909838 \text{ or } -2.5576505.

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

f(x)=4x^3+13x^2-12x-56

f'(x)=12x^2+26x-12

f''(x)=24x+26

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here:  x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

24(-2.6)+25

-37.5  

So we have a maximum at x=-2.6.

24(.4)+25

9.6+25

34.6

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56

I'm shoving this into a calculator:

y=-58.4654411

So the approximate relative minimum is (0.4,-58.5).

If you graph y=4x^3+13x^2-12x-56 you should see the graph taking a dip at this point.

3 0
3 years ago
A company has fixed operating costs of $2,137.00 per month with a production cost of $15.15 per unit. If each unit brings $33.09
vampirchik [111]
Y=2,137.00-(15.15*X)+(33.09*X)

Its simple arithmetic when you get down to it. The $2,137 won't change because it is the base rate per month, meaning even if they don't make any units they will still earn that much in the month. You subtract from that the cost to make a unit, in this case it is $15.15 per unit, so you multiply the cost by number of units to get the month's total costs. Then add the total month's profits by multiplying the number of units by the profits of one unit.
8 0
3 years ago
What is −2/5 + 4/5
igor_vitrenko [27]

Answer:

5/2 or 0.4

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
On the coordinate plane, Kyle graphs a line that represents a proportional relationship between x and y
goldenfox [79]

Option D) (0, 0)

<h2>Explanation:</h2>

The complete question is:

_______________________________________

On the coordinate plane, Kyle graphs a line that represents a proportional relationship between x and y. Which point MUST be on the line?

A) (0, 1)

B) (1, 0)

C) (1, 1)

D) (0, 0)

_______________________________________

A proportional relationship between x and y can be written in a mathematical language as follows:

y=kx

For any non-constan k-value. As you can see, this k-value represents the slope of a line. Remember that the Slope-intercept form of a line is given by:

y=mx+b \\ \\ m:Slope \\ \\ b:y-intercept

In the case of y=kx the y-intercept is zero, so the line passes through.

In conclusion, <em>Kyle's graph is a line that represents a proportional relationship between x and passes through point (0, 0)</em>

<h2>Learn more:</h2>

Direct variation: brainly.com/question/13881905

#LearnWithBrainly

7 0
3 years ago
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