Measures of dispersion are used to indicate the spread or variability of the data.
What is measure of dispersion?Measures of dispersion are crucial for representing the spread of the data, or its fluctuation around a central value, whereas measures of central tendency are used to assess a dataset's "normal" values.
The four main measure of dispersion include
Range Standard deviationInterquartile rangeVarianceThe range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.
The standard deviation deals with how much the data is away from the mean
The variance is standard deviation squared
These measures the spread, variability or distribution of data
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the rectangular coordinates of a point are s2, 2, 21d. find the cylindrical and spherical coordinates of the point
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Rectangular coordinates of a point is written like (x, y, z)
Cylindrical coordinates of a point is written like (r, θ, z)
Spherical coordinates of a point is written like (p, θ, φ)
First talk about Rectangular vs Cylindrical.
x = rcosθ
y = rsinθ.
z = z
x^2 + y^2 = r^2
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
r^2 = 4+4 = 8.
r = [tex]\sqrt{8}[/tex]
r = 2[tex]\sqrt{2}[/tex]
θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .
z = -1.
So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).
Now let's us talk about Rectangular vs Spherical Coordinates.
x = pcosθsinφ.
y= psinθsinφ.
z = pcosφ.
p^2 = x^2+y^2+z^2.
tanθ = y/x
cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].
given rectangular coordinates as (2,2,-1)
x=2, y=2, z=-1.
p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3
θ = [tex]tan -1[/tex](y/x) = 0.78rad .
φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad
So Spherical coordinates is (3, 0.78rad, 1.91rad).
The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.
Given Question is incomplete, Complete Question here
The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,
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Magic number puzzle. Help asap
Answer:
Step-by-step explanation:
1. 0
2. 3
3. 18
4. 33
5. 48
6. 198
find the distance between the two points rounding to the nearest tenth (if necessary). (5,5) (-1,-3)
The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.
Given that,
The points area (5,5) and (-1,-3)
We have to find the distance between the two points.
We know that,
What is distance formula?The distance between two points is the length of the line segment spanning those two points on the plane.
d=√((x₂ - x₁)² + (y₂ - y₁)²) is a common formula to calculate the distance between two points.
Any two points on an x-y plane or coordinate plane can have their separation between them determined using this equation.
We get,
(5,5) and (-1,-3)
Distance= [tex]\sqrt{(-1-5)^{2}+(-3-5)^{2} }[/tex]
Distance= √(-6)²+((-8)²
Distance= √36+64
Distance= √100
Distance =10
Therefore, The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.
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Marco has 2 peices of rope that are each 8 yards long.how many feet of rope does m arco have
Answer:
48 feet
Step-by-step explanation:
Marco has 2 pieces of rope that are each 8 yards long.
2 x 8 = 16 yards.
Marco has a total of 16 yards of rope.
Note that for converting yard to feet, that: 1 yard = 3 feet.
Marco, in this case, has 16 yards. Multiply 16 yards with 3 feet to obtain your answer:
16 yards x (3 feet/1 yard) = 48 feet/16 yards.
Marco has 48 feet worth of rope.
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what is the equation in slope intercept form of the line that passes through the point (-0.5,7) and is parallel to the graph of y=-8x-2 please help
Answer:
y = -8x + 3
Step-by-step explanation:
Pre-SolvingWe are given that a line passes through the point (-0.5,7), and is parallel to y = -8x - 2
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
Parallel lines have the same slopes.
Therefore, we can start by finding the slope of y = -8x - 2.
It is also written in slope-intercept form. -8 is where m (slope) should be; therefore, the slope of the line is -8.
SolvingWe can plug in -8 for m in y=mx+b.
y = -8x + b
Now we need to find b.
As the equation passes through the point (-0.5,7), we can use its values to help solve for b.
Substitute -0.5 as x and 7 as y.
7 = -8(-0.5) + b
Multiply
7 = 4 + b
Subtract 4 from both sides
3 = b
Substitute 3 as b in the equation.
y = -8x + 3
Topic: parallel and perpendicular lines
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. If g = -4 and h = -5 find the value of
a) 4gh
b) g²h
c) 5h - g²
Answer:
a) 80
b) -80
c) -41
Step-by-step explanation:
For g = -4 and h = -5, you want the values of ...
4ghg²h5h -g²To evaluate these expressions, put the value of the variable where the variable is, and do the arithmetic. A calculator can help.
a) 4gh= 4(-4)(-5) = 80
b) g²h= (-4)²(-5) = -80
c) 5h -g²= 5(-5) -(-4)² = -25 -16 = -41
A credit card has an APR of 32.47%, and its billing cycle is 30 days long. What is the credit card's periodic interest rate?
If a credit card has an APR of 32.47%, and its billing cycle is 30 days long. The credit card's periodic interest rate is 2.67%.
What is credit card periodic interest rate?A credit card periodic rate can be defined as the interest amount that a person pays on the balance of their credit card.
Given data:
Billing cycle = 30 days long
APR = 32.47%
Using this formula to find the credit card periodic interest rate
Credit card periodic interest rate = APR / (Number of days in a year /Billing cycle)
Where:
Credit card periodic interest rate =?
Annual percentage rate (APR) = 32.47%
Number of days in a year =365 days
Billing cycle = 30 days
Now let find the credit card periodic interest rate
There is 365 days in a year.
Credit card periodic interest rate = 32.47% ÷ (365 days / 30 days)
Credit card periodic interest rate =32.47% / 12.17
Credit card periodic interest rate = 2.67%
Therefore the periodic interest rate is 2.67%
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if i have a b and then i get a 72% on a test that is 30% of my grade, what will my grade be?
Answer:
if you have about an 85 now than you shouldn’t go below a b
Step-by-step explanation:
4. Here is a diagram of the track King'sis thinking of adding around the new field. It
consists of two parallel lines and a semicircle at each end. The track is 10 meters wide. -
100-
СР
64m
a) If someone runs one lap on the inside of the track, how far will they have run?
b) If someone runs one lap on the outside of the track, how far will they have run?
c) Find the difference between the distances of running on the inside or outside of the
track.
Answer:
Step-by-step explanation:
Find the equation of a line that passes through the point (0,-1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answer:
Step-by-step explanation:
y = 2x - 1
when you sub in 0 in x and -1 in y, the y-intercept is -1.
If 50% of a number is 120 and 80% of the same number is 192, find 30% of that
number.
Answer: the answer is 72
Step-by-step explanation:
if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240
Now we need to determine 30% of 240 and the procedure explaining it as such
Step 1: In the given case Output Value is 240.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 240 = 100%.
Step 4: In the Same way, x = 30%.
Step 5: On dividing the pair of simple equations we got the equation as under
240 = 100% (1).
x = 30% (2).
(240%)/(x%) = 100/30
Step 6: Reciprocal of both the sides results in the following equation
x%/240% = 30/100
Step 7: Simplifying the above obtained equation further will tell what is 30% of 240
x = 72%
Therefore, 30% of 240 is 72
I hope this helps
Answer:
72
Step-by-step explanation:
You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.
SolutionThe 30% you want will be the difference between 80% and 50%:
80% -50% = 30%
192 -120 = 72
30% of the same number is 72.
what is 10 to the 10th power rounded to the nearest 10th?
Answer:
10,000,000,000
Step-by-step explanation:
[tex]10^{10}[/tex]= 10,000,000,000
rounded to the nearest 10th = 10,000,000,000
in a technique called _____, the programmer simulates each program outcome or result and displays a message to indicate whether or not the program executed successfully.
In a technique called stub testing, the programmer simulates each program outcome or result and displays a message to indicate whether or not the program executed successfully.
What is stub testing?Test stubs are programs that imitate the behaviors of software components that a module undergoing tests rely on in advanced polymorphism computer science. Test stubs react to calls with pre-programmed prefabricated responses; they typically don't respond at all to calls that aren't part of the test. A stub is a brief piece of code used in testing to replace another component. Using a stub has the advantage of returning consistent results, which makes the test easier to write. And tests can be performed even if the other components are not yet operational.
The programmer simulates each program outcome or result and displays a message to show whether or not the program executed successfully. This process is known as stub testing.
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Suppose K⊆Rn is compact, f:K→R is continuous, and ϵ>0. Show that there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
By using the concept of compact set, it can be proved that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
What is compact set?
A set K is said to be compact if every open cover of K has a finite subcover.
Let K⊆Rn is compact f:K→R is continuous, and ϵ>0
Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,
Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.
So, |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,
Since f is continuous,
We can write
|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,
This is true for infinite many [tex]n_k[/tex]
So ||x - y|| = 0
|f(x) - f(y)| > ϵ, a contradiction since f is continuous
So, there is a number A>0 such that
|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.
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What is the solution to the inequality 2n-5 > 1
Answer:
n > 3
Step-by-step explanation:
2n - 5 > 1
Add 5 on both sides
2n > 6
Divide by two on both sides to isolate n
n > 3
three less than the product of nine and number is eight as a word equation
Answer:9x-3=8
Step-by-step explanation:
3 less means minus 3 from a number
product of 9 and a number is 9 times x
9x-3=8
is eight means = sign
alexis likes to go for boat rides along a river with her family. in still water, the boat travels about 7 kilometers per hour. in the river, it takes them the same amount of time t to go upstream 4 kilometers as it does to travel downstream 8 kilometers. if the speed of the river is r, which of the following expressions represents the time it takes to travel 4 kilometers upstream?
It takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?
it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.
speed of boat = 7 km/hr
speed of river = r km/hr
speed upstream = 7-r km/hr
speed downstream = 7+r km/hr
time taken to go upstream 4 km = 4/(7-r)
time taken to go downstream 8 km = 8/(7+r)
as time taken is equal in both scenario:
4/(7-r) = 8/(7+r)
on solving we get:
r = 7/3 km/hr
put this value in time taken for upstream
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
What is relative velocity?Think about two trains that are traveling in the same direction and at the same pace.
Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.
The other train seems to be moving at a constant speed.
So, we know that:
Speed of boat = 7 km/hr
Speed of river = r km/hr
Now,
Speed upstream = 7-r km/hr
Speed downstream = 7+r km/hr
Time taken to go upstream 4 km = 4/(7-r)
Time taken to go downstream 8 km = 8/(7+r)
As the time taken is equal in both scenarios:
4/(7-r) = 8/(7+r)
On solving we get:
r = 7/3 km/hr
Put this value in time taken for upstream as follows:
4/(7-(7/3)) = 6/7 km/hr or 51.33 min
Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.
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estimate using compatibl numbers.
241 divided by 34
help meeeee please i do not understand this
Answer:
10.4 g/cm³
Step-by-step explanation:
Find the volume with formula, l x b x h
Then the formula gram / volume to find density.
A company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction. What percent of the people had a mild
allergic reaction?
The percent of the people had a mild that has an allergic reaction is 0.6%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Given that the company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction.
It should be noted the percentage will be:
= Allergic people / Total people × 100
= 12/2000 × 100
= 0.6%
The percentage is 0.6%.
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The heights, in feet, of the trees for sale at two nurseries are shown below.
Yard Works: 7, 9, 7, 12, 5
The Grow Station: 9, 11, 6, 12, 7
Which statements are true regarding the measures of center and variability of these data sets? Select three choices.
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
THIS IS URGENT NEED NOW
The correct option regarding the heights of the trees include:
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow StationHow to calculate the value?The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:
(12 - 5) > (12 - 7)
7 > 5
The mean of tree heights at Yard Works is 8 feet.
The mean of tree height at The Grow Station is 9 feet.
The mean absolute deviation of the tree heights at both yards is 2.
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simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
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A line has a slope of 1/2 and includes the points (-4,-7) and (w,-3) What is the value of w?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
I need help with this question, I don't understand how we get the x value in the equation.
I'm not trying to cheat, I just need steps to see how we get to the end of it.
y=x-1
y=-x+3
Step-by-step explanation:
the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.
recursively define the set of binary strings with more 0s than 1s.
0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.
What do binary strings mean?A series of bytes make up a binary string. A binary string is used to store non-traditional data, including images, as opposed to a character string, which typically holds text data. The quantity of bytes in a binary string determines its length. The CCSID for a binary string is 65535.Binary refers to this system of 1s and 0s. Because of the way they are made, computers only speak in binary. A computer is nothing more than a sizable number of switches. On those curiously engraved boards inside the computer, there are millions of microscopic electronic switches.If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y. A procedure P is defined recursively if its action, P(x), is defined in terms of another action, P(y), where x>y.Explanation:
0>1.
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Simplify -1(15+4-27) over 16
Answer:
1/2
Step-by-step explanation:
-1(15+4-27)/16
Add 15 and 4 to get 19.
Now you have -1(19-27)/16
Subtract 27 from 19 to get −8.
-1(-8)/16
Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.
-(-1/2)
Simplify
1/2
Answer:
1/2
Step-by-step explanation:
⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆
Calculate:
-(15 + 4 - 27) / 16
-(19-27)/16
-(-8) / 16
= 8/16
Simplify:
= 1/2
3k/2 - k+3/3=8- k+2/4
answer is 6
pls help and explain
Answer:
3k/2 - k+3/3=8- k+2/4
(3k/2)x3 - (k+3/3)x2=(8)x4 - k+2/4
9k-2k-6/6 = 32-k-2/4
7k-6/6 = 30-k/4
(7k-6)x4 = (30-k)x6
28k - 24 = 180 - 6k
34k = 204
k = 204/34
k=6
Step-by-step explanation:
First, you multiply both sides by the numbers there to both the numerator and denominator, to get the same denominator. Then, simplify the answers in the second step. Next, cross multiply by multiplying the numerator of the left side to the denominator of the right side; and multiplying the numerator of the right side of the denominator of the left side. When you reach the fifth step, move -6k to the left side it will turn to +6k and add with 28k to get 34k. Move -24 to the right side it will turn +24 and add with 180 to get 204. Lastly, divide 204 by 34 to get k = 6.
Identify the solution set of the following quadratic inequality:
-a^2+4a+7>2
options
(-1,5)
(-∞,-1)∪(5,∞)
(-∞,-1]∪[5,∞)
(-∞,-3]∪[0,∞)
The solution set of the quadratic inequality is (-1,5)
What is Quadratic inequality?
Inequalities can take many various forms, just like equations, one of which is the quadratic inequality.
A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign.
The two roots are always provided in the answers to quadratic inequality. Different types of roots may exist, and discriminating between them is possible (b2 – 4ac).
The following are the quadratic inequalities' generic forms:
ax2 + bx + c < 0
ax2 + bx + c ≤ 0
ax2 + bx + c > 0
ax2 + bx + c >= 0
According to the given question
-a^2 + 4a + 7 > 2
-a^2 + 4a + 5 >0
multiplying with - 1
a^2 -4a -5 < 0
a^2 - 5a + a - 5 < 0
a(a-5) + 1(a-5) < 0
(a+1)(a-5) < 0
a<-1 & a< 5
a is in between -1 and 5
(-1,5)
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[tex]3({\frac{7}{5} x+4)-2(\frac{3}{2} -\frac{5}{4}x)[/tex]
Answer: -1.34328358
Step-by-step-explanation;
3(7/5x + 4) - 2(3/2-5/4x) = 0
3·(7/5·x + 4) - 2·(3/2-5/4·x) = 0
134x = -180
x = -180/134 = -1.34328358
