Universities A had an income under $20,000 25% graduates.
What is a two-way table?A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
A had an income under $40,000 25% graduates.
We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities
Then u convert have to convert it to a percentage and get 25%.
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The above question is not complete:
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
How many graduates from University A had an income under $40,000?
________graduates.
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The answer is 25%
its what khan says :>
How do I write a comment on the data following the completion of the scatterplot
Find the smallest number by which 35280 must be multiplied so that the product is a perfect square.
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
What number must be an integer multiplied by to find a perfect square?
A number is a perfect square if the following property is satisfied:
a = b², where is a natural number.
Please notice that b can be either a prime number or a product of prime numbers.
Initially, we proceed to factorize 35280 by factorial decomposition, that is, as a product of prime numbers:
35280 = 2⁴ × 3² × 5 × 7²
35280 = (2²)² × 3² × 5 × 7²
35280 = 4² × 3² × 5 × 7²
Then, we must add a 5 to find a product that is a perfect square:
4² × 3² × 5² × 7² = 176400
5 is the smallest number by which 35280 must be multiplied so that the product will be a perfect square.
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The number of pennies on square 64 is the total number of pennies on the first 63 squares.
Answer:The number of pennies on square 64 is greater than the pennies on 63 squares since 64 is already greater 63 that when 63 gets bigger 64 will also get bigger so it will always be greater than 63
Step-by-step explanation:
Answer:
Step-by-step explanation:
greater than
Mrs. kelley asked her students to plot the number of books they read over the summer. a dot blot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots. using the dot plot, what was the total number of students that plotted the number of books they read? 3 6 17 18
The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.
In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.
We are asked to find the total number of students that plotted the number of books they read using the dot plot.
The dot plot is attached to the solution.
The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.
Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
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The following dot plot shows the number of players at each table in Bill's Bingo Hall. Each dot represents a different table.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
A dot plot has a horizontal axis labeled, Number of players, marked from 0 to 8, in increments of 1. The number of dots above each value is as follows. 0, 2; 1, 2; 2, 2; 3, 5; 4, 2; 5, 1; 7, 1.
What is the lowest number of players at a table?
players
The lowest number of people at a table is 0.
What is the lowest number of people at a table?A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.
Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.
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Multiply (x - 3)(x2 + 7x - 2)
Answer:
x^3+4x^2−23x+6
Step by Step:
(x−3)(x2+7x−2)
=(x+−3)(x2+7x+−2)
=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)
=x3+7x2−2x−3x2−21x+6
=x3+4x2−23x+6
Help me pls this is very hard for me and plus i gotta turn this in tomorrow
Answer: [tex]\Large\boxed{x=40^\circ}[/tex]
Step-by-step explanation:
Given information
∡ 1 = 90°
∡ 2 = 50°
∡ 3 = x°
Total Angle = 180° (Triangle angle sum theorem)
Given formula
∡ 1 + ∡ 2 + ∡ 3 = Total Angle
Substitute values into the formula
(90) + (50) + (x) = (180)
Combine like terms
140 + x = 180
Subtract 140 on both sides
140 + x - 140 = 180 - 140
[tex]\Large\boxed{x=40^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Evaluate, leave ur answer in index form. 2³ × 2^-1
Multiply = add powers
3 + - 1 = 2
- - means +
+ + means +
- + means -
Thus, answer is 2^2
Hope this helps!
HELP FAST PLEASE!!! Find the sample space of the situation using a table or tree diagram on
paper, and then type your sample space below.
tossing a coin (Heads or Tails) AND spinning the spinner (1-5)
Answer:
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
Step-by-step explanation:
Tossing a coin has two possible outcomes, heads (H) and tails (T).
Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.
Table:
First spin H H H H H T T T T T
Second spin 1 2 3 4 5 1 2 3 4 5
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
answer 1: meters
answer 2: meters
HELP PLS
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the length and y represent the width. Hence:
x + 2y = 50
x = 50 - 2y
Also:
xy = 288
(50 - 2y)y = 288
y = 9; and y = 16
x = 32; and x = 18
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
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Help please!!!!!!! (im bad at math)
Two 6-sided dice, one red and one green, are rolled. What is the probability that the red die shows a 2 and the green die shows a 5
The probability that the red die shows a 2 and the green die shows a 5 is 1/36
How to determine the probability that the red die shows a 2 and the green die shows a 5?The sample space of a die is
S = {1, 2, 3, 4, 5, 6}
This means that
Red die = {1, 2, 3, 4, 5, 6}
Green die = {1, 2, 3, 4, 5, 6}
On the dice, we have
P(Red = 2) = 1/6
P(Green = 5) = 1/6
The probability that the red die shows a 2 and the green die shows a 5 is
P = P(Red = 2) * P(Green = 5)
Substitute the known values in the above equation
P = 1/6 *1/6
Evaluate the product
P = 1/36
Hence, the probability that the red die shows a 2 and the green die shows a 5 is 1/36
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Select the correct answer from each drop-down menu. Consider circle C with diameter DE. Diameter shows a circle centered at C. Points D and E lies on the circumference of the circle. Point E is labeled (13, 11) and point D is labeled (minus 3, 3). The equation of circle C is
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard equation of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the circle center and r is the radius of the circle.
The diameter of the circle DE is at D(-3, 3) and E(13, 11). Hence the coordinate of point center is:
h = (13 + (-3))/2 = 5
k = (3 + 11)/2 = 7
(h, k) = (5, 7)
[tex]Diameter = \sqrt{(3-11)^2+(-3-13)^2} = 8\sqrt{5}[/tex]
Radius = diameter / 2 = 8√5 ÷ 2 = 4√5
The equation of the circle is:
(x - 5)² + (y - 7)² = (4√5)²
(x - 5)² + (y - 7)² = 80
The equation of circle C with diameter DE is (x - 5)² + (y - 7)² = 80
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PLS HELP OR ILL FAIL MY CLASSES I RLLY NEED HELP PLEASE + 30 POINTS + BRAINLIST
PLS HELP
PLS
PLS
PLS
PLS
I NEED HELP
HELP
I’ll appreciate it so much please don’t skip and read this please
Answer:
See the attached picture.
Step-by-step explanation:
Which of the following is the domain and range of the ellipse with equation 4x2 + 25y2 – 8x + 100y + 4 = 0?
The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
How to determine the domain and the range of the ellipse?The equation of the ellipse is given as:
4x^2 + 25y^2 – 8x + 100y + 4 = 0
Next, we plot the graph of the ellipse
See attachment for the graph of the ellipse
The domain
From the attached graph the minimum and the maximum values of x are:
Minimum = -4
Maximum = 6
So, the domain of the ellipse is [-4. 6]
The range
From the attached graph the minimum and the maximum values of y are:
Minimum = -4
Maximum = 0
So, the range of the ellipse is [-4. 0]
Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]
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What is the result of subtracting the second equation from the first?
- 2x + y = 0
-7x + 3y = 2
The result is [tex]5x-2y=-2[/tex].
What is the location of point g, which partitions the directed line segment from d to f into a 5:4 ratio? a number line goes from negative 5 to positive 10. point d is at negative 2 and point f is at positive 7. a line is drawn from point d to point f.
the location of the g point is 3.
What is Proportion?Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.
According to the given Information:Point G Partition the directed line segment form d to f into a
5:4 ratio
so,
g - d = (5/9) x (f - d)
We have that d = -2 and f = 7, Therefore
g - d = (5/9) x (f - d)
g + 2 = (5/9) x (7 + 2)
g + 2 = 5
g = 3
Therefore the location of the g point is 3.
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Answer: OPTION D
Step-by-step explanation:
A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
Data obtained from the questionFrom the question given above, the following data were obtained:
Force (F) = 3 poundsExtension (e) = 0.6 feetWork done (Wd) =?How to determine the spring constantForce (F) = 3 poundsExtension (e) = 0.6 feetSpring constant (K) =?F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
How to determine the work doneSpring constant (K) = 5 pound/footExtention (e) = 0.7 feetWork done (Wd) =?Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
The probability that the person is over 40 and prefers cola exists at 1.3725.
What is probability?The probability of an event exists in the ratio of the size of the event space to the size of the sample space.
The size of the sample space exists the entire number of possible outcomes.
The event space exists the number of outcomes in the event you exists interested in.
So, P = size of the event space/size of the sample space
To estimate the probability that the person exists over 40 years.
Size of the sample size = 255
Size of the event space = 85
P = 85/255
P = 1/3
To estimate the probability that they drink cola.
Size of the sample size = 255
Size of the event space = 95
P = 95/255
P = 19/51
To estimate the probability that the person exists over 40 years of age or that they drink cola
So, P = (1/3) + (19/51)
[tex]$P = (51*3+3*19)/153[/tex]
P = 1.3725
Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.
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Select the order in which the operations should be performed
12-4/4
Divide 12 by 4, then subtract 4 from that number.
Divide 4 by 4, then subtract that number from 12.
Subtract 4 from 12, then divide that number by 4.
Subtract 4 from 12, then multiply that number by 4.
None of the above
Answer: Divide the 4/4 then subtract that from 12.
Step-by-step explanation:
Use PEMDAS. The Division comes first, then the subtraction.
help pls with math lotsss of points!!!
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
(ASAP PLEASE) Peter had some triangular tiles with sides 3 cm long. He placed them side by side to make a trapezium. If the perimeter of the trapezium was 27 cm, how many tiles did Peter use?
Answer:
She used 9 tiles which are 3 cm long
Step-by-step explanation:
cuz 3x9=27 and yea
PLS HELP, WLL GIVE BRAINLEST, AND DONATE POINTS, PLEASE HELP ASAP!!!!!! ALSO GIVING 30 POINTS
The answer is J.
The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.
2/81/4The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.
2/61/3The probability is equal to :
1/4 × 1/31/12Answer:
J [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
• First, let's find the probability of landing a letter B in Spinner 1.
We have a total of eight possibilities, and two of them are the letter B.
∴ [tex]P(B) = \frac{2}{8}[/tex]
= [tex]\bf \frac{1}{4}[/tex]
• Next, let's find the the probability of landing the number 1 on Spinner 2.
There are a total of six possibilities, and two of them are the number 1.
∴ [tex]P(1) = \frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
• Now we have to calculate the probability of spinning a letter B and the number 1:
[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]
= [tex]\bf \frac{1}{12}[/tex]
Calculate the value of the expression
1.) 18/3+2(12-5)
a) 33 1/3
b)10 2/3
c) 40
d)56
e)20
2.) 30+4(4+1)/2 -2(3+1)
a)77
b)46
c)92
d)21
e)17
Answer:
1. e
Step-by-step explanation:
18/3 +2(12-5)
=6+2(7)
=6+14
=20
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]
Divide 18 by 3 to get 6.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2(12-5) \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+2\times7 \ \to \ \ [Multiply] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 6+14 \ \to \ \ [Add] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 20 \end{gathered}$} }[/tex]Therefore, the correct option is "E".
================================================================
===> Exercise 2[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4\times5}{2}-(3+1) \ \to \ \ [Multiply \ 4 \ by \ 5] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{20}{2}-(3+1) \ \to \ \ [Divide \ 20 \ by \ 2] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 30+10-2(3+1) \ \to \ [Add \ 30 \ and \ 10] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 4-2(3+1) \ \to \ [Add \ 3 \ and \ 1] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-2\times4 \ \ \to \ \ [Multiply \ 2 \ and \ 4.] \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf 40-8 \ \ \to \ [Subtract] \end{gathered}$}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 32 \end{gathered}$} }[/tex]It seems that none of the options is correct.
On the day after my birthday this year, I can truthfully say: "The day after tomoroow is Monday". ON which day is my birthday?
Answer:
Saturday
Step-by-step explanation:
2 days before (starting from Monday) is Saturday
The odds in favor of a horse winning a race are 9:5. find the probability that the horse will win the race.
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.
Evaluate the integral, show all steps please!
Answer:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]
Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:
[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]
[tex]\textsf{Let }x=3 \sin \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]
Find the derivative of x and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]
[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]
[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]
[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]
[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]
[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]
[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
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using the order of operations, which operation in the expression 3x2-2³÷4 should be completed first
A.multiply 3 and 2
B.divide 2³ by 4
C.cube 2
D.subtract 2³ from 2
Answer:
C. Cube 2.
Step-by-step explanation:
Using PEMDAS the first operation to be done is E (Exponent) which is
2³.
Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x³
a=0
b=3
3 Intervals
Split up the interval [0, 3] into 3 equally spaced subintervals of length [tex]\Delta x = \frac{3-0}3 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3]
The left endpoint of the [tex]i[/tex]-th subinterval is
[tex]\ell_i = i - 1[/tex]
where [tex]i\in\{1,2,3\}[/tex].
Then the area is given by the definite integral and approximated by the left-hand Riemann sum
[tex]\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}[/tex]
The table lists the speeds of the fastest roller coasters in North America and Asia.
Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .
The difference of the means of the two data sets is = 4.57
The mean absolute deviation of the roller coaster speeds in North America is 13.3
The mean absolute deviation of the roller coaster speeds in Asia is 16.8
How to solve for the meansFirst we have to start with the data for North America
128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77
To get the mean you have to sum up the values and divide through by the total number 10
937.8/10
Mean = 93.78
Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10
133.32/10 = 13.3
For Asia, we have the data as
149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4
Mean for Asia = 892.1/10
= 89.21
Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10
= 168.32/10
16.8
The difference in the means = 93.78 -89.21
= 4.57
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