The appropriate measure of variability for this data is the IQR, and its value is 250.
We have,
The range is not the best measure of variability for this data since it only takes into account the maximum and minimum values and does not consider the other values in the dataset.
The IQR (interquartile range) is a better measure of variability since it gives a measure of the spread of the middle 50% of the data.
To find the IQR, we first need to find the median:
Arranging the data in order, we get:
200, 450, 600, 650, 700, 800
The median is the middle value, which is 650.
The first quartile (Q1) is the median of the lower half of the data:
Q1 = median(200, 450, 600) = 450
The third quartile (Q3) is the median of the upper half of the data:
Q3 = median(700, 800, 650) = 700
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
= 700 - 450
= 250
Therefore,
The appropriate measure of variability for this data is the IQR, and its value is 250.
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The volume of a gas was measured as the temperature was increased from 173 K to
423 K in 50 K intervals. The gas volumes recorded, starting at 173 K, were 16, 21, 26, 30, 36, and 40 cm . Determine whether the data is best described by an increasing or decreasing function, and whether it is linear or exponential. Find a regression equation.
The data is best described by an increasing function. The regression equation is y =0.0965x - 0.61.
Here is a table of the data:
Temperature (K) Gas Volume (cm³)
173 16
223 21
273 26
323 30
373 36
423 40
The data is best described by an increasing function, and it is likely to be linear since the volume of the gas increases uniformly with the temperature.
Let x be the temperature and y be the volume of the gas.
The slope is given by (nΣxy - ΣxΣy) / (nΣx² - (Σx)²),
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σx² is the sum of the squares of x.
The y-intercept is given by (Σy - bΣx) / n, where b is the slope.
Using the data, we have n = 6, Σx = 17788, Σy = 169, Σxy = 4225, and Σx² = 43750.
Substituting these values into the formulas gives the slope b = 0.09657 and the y-intercept a = -0.61.
Therefore, the regression equation is y =0.0965x - 0.61.
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If A and B are m × n matrices such that Ax = Bx for all x ∈ R n , then A = B. Please prove this.
From matrix property it can be showed that A=B.
Given,
If A,B and x are matrices with x≠0 and AX=BX
Now.
X must be non-singular matrix because
A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]
[tex]XX^{-1}[/tex] = I( identity matrix )
AI = BI
A = B
Hence Proved, A = B .
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What is this expression in simplified form?
✔-1, 728
O A. -12
OB. -36
O C.
-42
OD. -576
Benjamin is planning what to wear tomorrow evening.
• He has 3 shirts to choose from: red, white, and green.
• He has 2 pairs of pants to choose from: blue jeans and khaki pants.
• He has 3 pairs of shoes to choose from: sneakers, flip flops, and boots.
Benjamin randomly chooses one item from each group. What is the probability that he chooses
sneakers and the green shirt? Type in simplest form!!! Anything else will be considered correct, no exceptions
Answer:
1/9
Step-by-step explanation:
P =
[tex](no \: of \: favorable \: outcomes) \div (total \: numeber \: of \: outcomes \: )[/tex]
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A multiple choice question has five Anne’ answer options of which two options are correct what is the probability of randomly choosing the correct pair of answer options
Answer:
1/10
Step-by-step explanation:
2/5 * 1/4 = 2/20 = 1/10
2 right answers, 5 possible choices
Select one right choice = 2/5
After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4
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A rectangle measures 2 3/4 inches by 2 3/4 inches. What is its area?
The area of the given rectangle is 121/16 square inches.
As know that the area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
To find the area of the rectangle, we need to multiply the length by the width. We have:
Length = 2 3/4 inches = 11/4 inches
Width = 2 3/4 inches = 11/4 inches
Area = Length x Width
Area = (11/4) inches x (11/4) inches
Area = 121/16 square inches
Therefore, the area of the rectangle is 121/16 square inches.
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A certain car has a fuel efficiency of 28.1 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).
Answer:
the answer is 10.63km/L.
If sinx= 5/13 and x is in quadrant 1, then Tanx/2=
OA. -5
O B. - 1/5
OC. 5
O D. 1/5
Answer: D: 1/5
Step-by-step explanation:
sinx = 5/13
this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).
there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]
the + or - sign is decided by the quadrant the half angle is in;
since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.
so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:
One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.
tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]
tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]
tan(x/2)= [tex]\sqrt{1/25}[/tex]
tan(x/2) = 1/5
Option D is the answer :)
Please help I am struggling a lot thank you so much have a great day
Answer:
Step-by-step explanation:
To calculate the values of the given function, substitute the given values of x into the function f(x) = 7x^2 - 8x + 8:
f(-2) = 7(-2)^2 - 8(-2) + 8
= 7(4) + 16 + 8
= 28 + 16 + 8
= 52
f(-1) = 7(-1)^2 - 8(-1) + 8
= 7(1) + 8 + 8
= 7 + 8 + 8
= 23
f(0) = 7(0)^2 - 8(0) + 8
= 0 - 0 + 8
= 8
f(1) = 7(1)^2 - 8(1) + 8
= 7(1) - 8 + 8
= 7 - 8 + 8
= 7
f(2) = 7(2)^2 - 8(2) + 8
= 7(4) - 16 + 8
= 28 - 16 + 8
= 20
Therefore, the values of the function for the given inputs are:
f(-2) = 52
f(-1) = 23
f(0) = 8
f(1) = 7
f(2) = 20
There are 8 strawberry plants in each row. Each plant has 11 strawberries on it. What equation could you use to find how many strawberries there are in 7 rows?
8 + 11 x 7 = ___
8 x 11 + 7 = ___
8 x 11 x 7 = ___
8 x 11 ÷ 7 = ___
what is the difference between a linear functuon and nonlinear function
Answer:
In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.
For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.
On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.
For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.
In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.
The local high school is hosting an ice cream social for new students. They
record the ice cream choices of the students throughout the event.
What is the probability that a female student chose strawberry ice cream?
Male
Female
Total
Vanilla Strawberry
6
4
8
9
14
13
Chocolate Total
13
23
21
44
4
17
The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.
From the given information, we have the following breakdown:
Male Female Total
Vanilla 6 4 10
Strawberry 9 14 23
Chocolate 13 4 17
Total 28 22 50
To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:
Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)
Therefore, the probability of a female student choosing strawberry ice cream is:
Probability = 14 / 22
Simplifying the fraction, we have:
Probability = 7 / 11
Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
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Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of -4, -2, 4, and 2.
Step-by-step explanation:
Using the roots given in order given:
y= ( x+4)(x+2)(x-4)(x-2) would fit the bill.....
.
What is the x-coordinate of the solution to the following system of equations?
2x + y = -4
5x + 3y = -6
Ox=-6¹
Ox=6
Ox = -8
Ox=8.
Answer:
Option : A
Step-by-step explanation:
To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:
Equation 1: 2x + y = -4 (multiply by 3)
Equation 2: 5x + 3y = -6 (multiply by 1)
Multiplying equation 1 by 3 gives us:
6x + 3y = -12
Multiplying equation 2 by 1 gives us:
5x + 3y = -6
Now we can subtract equation 2 from equation 1 to eliminate y:
(6x + 3y) - (5x + 3y) = -12 - (-6)
6x + 3y - 5x - 3y = -12 + 6
x = -6
Therefore, the x-coordinate of the solution to the system of equations is x = -6.
The correct option is: Ox=-6.[tex][/tex]
which represents 10 times the value of the digit 8 in 308.19
Answer: 0
Step-by-step explanation:8th Place 100*10 1000th Place is 0
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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What time is shown on the clock?
Answer:
3:55
Step-by-step explanation:
3:55
Imagine a clock with the hour hand at 12 and the minute hand at 2. Does the angle formed by the two hands have a measure greater than, less than, or equal to 1/4 turn?
The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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Find the m angle DEG and angle DEF. H D 6x E 4x° G F
Based on the application of the complementary angles, the measures of the angles are: m<DEG = 54 degrees; mm<GEF = 36 degrees
What are Complementary Angles?When two angles make up a right angle, they are referred to as complementary angles because they add up to 90 degrees when summed.
6x and 4x make up a right angle, this means their sum will give us 90 degrees when we add them up. Therefore:
6x + 4x = 90
10x = 90
Divide both sides by 10
10x/10= 90/10
x = 9
measure of angle DEG = 6x = 6(9) = 54 degrees.
Measure of angle GEF = 4x = 4(9) = 36 degrees
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The bedroom, garage, office, and bathroom of a house will be painted, each with a different color. There are 15 colors to choose from. This means that there are ________ color arrangements possible.
Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.
Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.
Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:
P(n, r) = n! / (n - r)!
where n is the total number of options (15 colors) and r is the number of positions (4 rooms).
Using the formula, the number of color arrangements possible is:
P(15, 4) = 15! / (15 - 4)!
= 15! / 11!
= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
= 32,760
Which of the following reflective symmetries
apply to the hexagon below?
Symmetry
D
E
F
C
A
Reflective symmetry over AD
Reflective symmetry over CE
B
Applies to th
Yes/No
Yes/No
The table can be filled as Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No
We are given that;
The hexagon DEFCA
Now,
the hexagon has reflective symmetry over AD, because if we fold it along AD, the vertices B and F will match, as well as the vertices C and E. Therefore, the answer for reflective symmetry over AD is Yes.
However, the hexagon does not have reflective symmetry over CE, because if we fold it along CE, the vertices A and F will not match, nor will the vertices B and D. Therefore, the answer for reflective symmetry over CE is No.
Therefore, Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No.
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Find the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4).
The coordinates of the intersection of the diagonals are ( , )
If the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4). The coordinates of the intersection of the diagonals are (4/3, 0).
What is the coordinates?Using the two point form of the equation of a line to determine the The equation of the line that contains AC
y₋y₁ = (y₂-y₁)/(x₂-x₁) * (x₋x₁)
where:
(x₁, y₁) and (x₂, y₂)= two points on the line
y - 2 = (-4 - 2)/(4 - 0) * (x - 0)
Simplify
y - 2 = -3/2 * x
2y - 4 = -3x
3x + 2y = 4
Equation of the line that has BD
y - 2 = (-4 - 2)/(8 - (-4)) * (x - 8)
Simplify
y - 2 = -3/4 * x + 9/2
4y - 8 = -3x + 36
3x + 4y = 44
Now let find the point of intersection:
3x + 2y = 4
3x + 4y = 44
Multiplying the first equation by -2
-6x - 4y = -8
Eliminate x
0x + 0y = 36
So,
y = 0
3x + 2(0) = 4
3x = 4
x = 4/3
Therefore the coordinates is (4/3, 0).
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equivalent value of the equation is 18x-9=72 and x=4.5
Given data ,
Let the equation be represented as A
Now , the value of A is
(3/5)(30x-15)=72
On simplifying the equation , we get
3(6x-3)=72
On further simplification , we get
18x-9=72
x=81/18
x=4.5
Hence , the equation is 18x-9=72
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Can u find “V”
XXX* YV=••••+666=799Y
The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
How to simplify equations?The equation can be simplified to XXX × YV=1335.
If both sides of the equation are divided by 3, X × YV = 445.
If now all the X's is replaced with 5's, 5 × YV = 445.
This gives the following equation:
5 × YV = 445
Now multiply both sides of the equation by Y, to get 5Y = 445.
This gives us the following equation:
5Y = 445
Finally, divide both sides of the equation by 5, to get Y=89.
Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
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PLEASE HELP!! WIKL GIVE BRAINLIEST!!
Action. 2,150
Comedy. 1,271
Drama. 829
Romance. 300
The manager of the theater expects to sell 8,000 movie tickets next month. The theater earns $4.53 profit on each movie ticket sold. Based on last month's results, how much profit can the theater manager expect to earn from ticket sales to romance movies next month?
Answer:
$2174.40
Step-by-step explanation:
2150+1721+829+300=5000
They sold 5000 tickets last month.
300÷5000=0.06
So 6% of the tickets each month are romance.
They expect to sell 8000 next month.
8000x.06=480
They should sell 480 romance tickets next month.
480x4.53=2174.40
Which expression will complete the proof?
O cos(k0-0) + i sin(k0 - 0)
O cos(k0 - 0) + / sin(k0 + 0)
O cos(k0 + 0) + i sin(k0 – 0)
O cos(k0 + 0) + i sin(k0 + 0)
The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function [tex]e^(ik0)[/tex].
The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.
This expression represents the complex exponential function [tex]e^(ik0)[/tex], where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.
The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 ([tex]since cos^2 +[/tex] [tex]sin^2 = 1[/tex] for all angles).
Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.
Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.
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dentify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is units.
The center of the circle is at (, ).
Answer:
Step-by-step explanation:
General formula
(x-h)^2 + (y-k)^2 = r^2
where (h,k) center of circle whose radius r
applying the formula to our Q
(x – 5)² + y² = 81
(x – 5)² + (y-0)² = 9^2
---> center of circle (5,0)
---> radius is 9
The probability that a machine will produce
all bolts in a production run within
specification is 0.998. A sample of 8
machines is taken at random then the
probability that 7 or 8 machines is:
Select one:
O
a. 0.9999
b. 0.9841
c. 1
d. 0.8
The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.
Using the binomial distribution formula, we get:
P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081
P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003
Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.
Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.
It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.
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What is one value of x that could replace the missing value in the table
The value of x which could replace the missing value in the table so that y is not a function of x is; 7.
What is the missing value of x that could make y not a function?It follows from the task content that the value of x which could make y not a function of is required to be determined.
Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.
On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.
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