If the position of a moving object at a time t the curvature of the earth would be 1/4t.
A curved path having various radii of curvature is known as a variable-curvature path. from: 2020 Control Systems Design of Bio-Robotics and Bio-mechatronics with Advanced Applications.
A straight line has zero curvature. In contrast to the tangent, which is a vector quantity, the curvature at a point is often a scalar quantity or one that can be described by a single real integer.
|| r (t) || = 3[tex]t^{2}[/tex], || r' (t) || = 2t, || T (t) || = 1
|| T' || = 1/2
Curvature K = || T' (t) || / || r' (t) || = (1/2) / 2t
K = 1/4t
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Prior to the current period, Sol Berenson had earnings subject to FICA tax of $138,600. This week, Sol has gross earnings of $4,900, so he will have $ withheld in FICA tax for this period.
The amount withheld in FICA Tax for Sol Berenson's weekly earnings is given as follows:
$749.7.
How much will be withheld by the FICA Tax?To calculate the amount withheld by Berenson's employer in FICA tax, we apply the proportion of the FICA tax to his total earnings.
Researching on a web search, the FICA tax rate is given as follows:
15.3% = 0.153.
As the FICA tax is a combination of the Medicare tax with the Social Security tax.
Sol Berenson's gross weekly earnings are given as follows:
$4,900.
(as stated in the problem).
The amount withheld is 15.3% of that, which is found applying the proportion, which is the multiplication of 0.153 by 4900 as follows:
Amount Withheld = 0.153 x 4900 = $749.7.
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Can someone solve this please
Answer: B
Step-by-step explanation:
The two equations have the same slope, but different points. This means that the lines are parallel to one another and will not intersect.
The answer is B: No solution
Answer: No solution.
Step-by-step explanation: I graphed the two given functions below. It looks like there is no solution to the given functions.
Hope this helps! :)
Find the vertex of the graph of f(x) = |0.25x − 0.75|. vertex ?
The vertex of the graph (3, 0)
What is Vertex of graph?
A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.
According to question
when f(x) = 0
that's the minimum point, the vertex, or the intersection of two lines, g(x) = 0.25x − 0.75 and h(x) = 0.75 - 0.25x
Therefore
find the intersection of Two line which are
⇒ y = x/4 - 3/4
⇒ 4y = x - 3 → First line
⇒ y = 3/4 - x/4
⇒ 4y = 3 - x → Second line
So x - 3 = 3 - x
2x = 6 ,
x = 3
And y = 0
hence the vertex of f(x) = (3, 0)
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The sum of an infinite geometric series with first term a and common ratio r < 1 is given by The sum of a given a/1-r infinite geometric series is 300, and the common
ratio is 0.1. What is the second term of this series?
The second term of the series will be 27.
What is a Geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
Sum to infinity = a/1-r
where s = 300
r = 0.1
a = 300 (1 - 0.1)
a = 300 (0.9)
a = 270
The second term of the progression will be = ar
Second term = 270 x 0.1
Second term = 27
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I need help with this please help me
Which step shows the result of applying the subtraction property of equality?
Step
1
2
3
4
Step 1
Step 2
Step 3
O Step 4
(12x+8) +4=3
Solution
3x+2+4=3
3x+6=3
3x=-3
X=-1
Step 3 shows the result of applying the subtraction property of equality
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 1/4(12x+8)+4=3.
We need to find which step has the property of substitution.
The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount.
Given step 1 is 3x+2+4=3
Opened the brackets on left side and multiplied with 1/4.
Step 2: 3x + 6 = 3.
Added the numbers on the left.
Step 3: 3x = -3
Equal value subtracted or removed from two equal items will result in a new equal amount. So Subtracted both sides by 6.Step 3 shows the result of applying the subtraction property of equality
Step 4: x = -1
Divided both sides by 3.
Hence, in step 3 we have used the property of subtraction.
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Consider the function f (same as in the previous problem) defined on the interval [0, 4) as follows, F(x) = { 2/2 x. x € [0,2]. 2, x € [2, 4]Find the coefficients Cn of the eigenfunction expansion of function ff(x) = Σ[infinity], n=1 cnyn(x), where y... for n = 1,2,3,... are the unit eigenfunctions of the Regular Sturm-Liouville system - y^n = ꟾλy, y’(O) = 0, y(4) = 0Note: Label your eigenfunctions so the eigenfunction for the lowest eigenvalue corresponds ton = 1. Therefore, use 2n – 1 instead of 2n +1.C= ___
Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by
f(x) = Σ[∞], n=1 cnyn(x)
To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).
cn = (f,yn) = ∫[0,4]f(x)yn(x)dx
Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by
cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx
Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.
cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx
= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx
= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx
= 1/2 ∫[0,2] (x+2)yn(x) dx
Therefore, the coefficient Cn is given by
Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
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Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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data were collected on the number of days per week that members visit a certain fitness center. the values varied from 0 to 7, and a distribution of relative frequencies for the values was created. let the random variable x represent the number of days per week that a member visits. the mean of x is 3.12. which of the following statements is the best interpretation of the mean? responses each member visits the fitness center 3 or 4 days per week. each member visits the fitness center 3 or 4 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. for a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.
The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
The data of the number of days members visited a certain fitness center varied from 0 to 7.
The mean of the random variable x = 3.12
The mean of the random variable is also known as the long-run average value of a random variable.
Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
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PLEASE ANSWER QUICK!!
Consider the functions and f(x)=|x|-2 and g(x)=2f(x).
a. Complete the table.
b. Describe the graph of f. How does each point on the graph of f map to the corresponding point on g?
The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = |x| - 2 and g(x) = 2 f(x)
The function g(x) is rewritten as,
g(x) = 2 (|x| - 2)
g(x) = 2|x| - 4
The function f(x) is an absolute function and the function g(x) will be twice the function f(x).
x f(x) = |x| - 2 g(x) = 2f(x)
-2 0 0
-1 -1 -2
0 -2 -4
1 -1 -2
2 0 0
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Calculate two-thirds of three-quaters of one half
Answer:
0.25
Step-by-step explanation:
Step 1: Convert all fractions to decimals
Two-thirds = 0.6666
Three-quarters = 0.75
One-half = 0.5
Step 2: Multiply all fractions
0.6666 * 0.75 * 0.5 = 0.25
Step 3: The answer is 0.25
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Three-quarters of one half:
[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]
Two-thirds of "Three-quarters of one half":
[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]
Subtract 7x-9 from 2x² - 11.
O 2x²-7x-20
02x²-7x-2
O 2x²+7x-20
O 2x²+7x-2
The required, subtraction of 7x-9 from 2x² - 11 is 2x²-7x-2. Option B is correct.
What is arithmetic?Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To subtract 7x-9 from 2x² - 11, we need to distribute the negative sign across 7x and 9, and then combine like terms.
=2x² - 11 - (7x - 9)
= 2x² - 11 - 7x + 9
= 2x² - 7x - 2
Therefore, the answer is 2x²-7x-2.
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How to calculate rate of change of y=4x-3
Answer:
4
Step-by-step explanation:
Answer:
The rate of change is 4
Step-by-step explanation:
The rate of change is the slope.
Since the equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
The slope is 4 and the y intercept is -3
Denominator is 3 more than numerator. If both are increased by 2, the result is 2/3.
Eqn 1:
Eqn 2:
Answer:
Step-by-step explanation:
let numerator=x
denominator=x+3
again
[tex]\frac{x+2}{x+3+2} =\frac{2}{3} \\3(x+2)=2(x+5)\\3x+6=2x+10\\3x-2x=10-6\\x=?[/tex]
x=4
number is
[tex]\frac{4}{4+3} \\=\frac{4}{7}[/tex]
I need a little bit of help with this one
Step-by-step explanation:
boy come ladies yer wait for you
hvb-amor-jon
The linear regression equation for the data set is...
Answer: C
Step-by-step explanation: Because
find the most general antiderivative or indefinite integral. check your answers by differentiation cos2x-sec^2x
The general anti derivative or indefinite integral of the function
cos2x - sec²x is 1/2 sin2x + tan x + C .
The given function is of the form : cos2x - sec²x
Now we will use the indefinite integral on the above expression:
∫cos2x - sec²x
This can be broken into :
∫cos2x - ∫sec²x
Now we will integrate them separately:
∫cos2x, we will use u-substitution.
Let 2x = u
Differentiation both sides we get:
2 dx = du
or, dx = 1/2 du
Hence we will use this value:
∫cos2x
= ∫cos u · 1/2du
= 1/2 ∫ cos u du
=1/2 sin u + C , where C is a constant.
Again we will do the second part of the integral:
∫sec²x
= tan x + C
Hence the required integral will be:
1/2 sin2x + tan x + C .
Now we will use differentiation to check the integral
d/dx (1/2 sin2x + tan x + C )
= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)
= cos 2x + sec² x
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to specify that x1 must be at most 75% of the blend of x1 , x2 , and x3 , we must have a constraint of the form
The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)
The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,
Abd here we must have to find the linear constraint of the form of the variables.
While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.
And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.
Here the term of blend refers the sum of the terms,
Then the linear constraint form of the variables is written as,
=> X1 =< 0.75 (X1 + X2 + X3)
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What’s 7 1/3 - 5 1/6 ?
Pls hurry !!!
Consider a set of cards that has four cards labeled 1, 3, 5, and 7. Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set. Which of the following tables shows the sampling distribution? a.) Sample (n = 2) x̄ S1 = {1, 1} 1 S2 = {1,This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.Consider a set of cards that has four cards labeled 1, 3, 5, and 7.Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set
Answer:
one 2
one 3
two 4's
one 5
one 6
Step-by-step explanation:
We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.
[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:
[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]
[tex]_4C_2=\dfrac{24}{2(2)}[/tex]
[tex]_4C_2 = 6[/tex]
So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:
(1, 3) (3, 5) (5, 7)
(1, 5) (3, 7)
(1, 7)
Then, we can calculate the mean, or average, of each.
2 4 6
3 5
4
Finally, we can conclude that the distribution of the means for each possible set of number pairs is:
one 2
one 3
two 4's
one 5
one 6
Advanced Algebra - please help
Answer:
Below
Step-by-step explanation:
Only the middle three are tri -nomials ( three terms)
the third one reduces to (x+ 2)^2
Answer:
3
Step-by-step explanation:
(x+2)^2
6. If g(x)=-3x²-2 , find g(-2).
Answer:
g(-2) = -14
Step-by-step explanation:
We just need to substitute -2 for x
g(-2) = -3 * (-2)^2 - 2 = -3 * 4 - 2 = -12 - 2 = -14
Two different meal combinations at a chicken restaurant have the same number of total calories.
- The first meal has 8 chicken nuggets and a large order of fries.
- The second meal has 12 chicken nuggets and a small order of fries.
- The larger order of fries contains 288.5 calories.
- The small order of fries contains 193.5 calories.
Which equation and solution can be used to determine n, the number of calories in each chicken nugget?
A 12 n-288.5=8 n-193.5 ; n=24.1
B 8 n+193.5=12 n+288.5 ; n=23.75
C 193.5+12 n=288.5+8 n ; n=24.1
D 8 n+288.5=12 n+193.5 ; n=23.75
The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n
And n = 24.1
Option (C) is correct.
What is a linear equation?
A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.
To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:
8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories
We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:
193.5 + 12 n = 288.5 + 8 n
Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:
n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75
Therefore, the number of calories in each chicken nugget is 24.1 calories.
Hence, option (C) is correct.
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PLEASE HELP IM GOING TO FAIL
5. A student spends no more than two hours on his math and English homework. If math takes
about twice as long as English, what is the maximum time that the student can spend on
English?
O1/3
hour
O1/2 hour
O 1 hour
O 2/3 hour
(1 point)
Answer:
2/3 hour
Step-by-step explanation:
lets say English takes x hour to complete such that Math will take twice as long which is 2x hour. It takes 2 hours to complete both English and Math. So we can write the following equation:-
x+2x=2
or, 3x=2
or, x=2/3
Therefore, English takes 2/3 hour to complete (which is 40 minutes)
And Math takes 4/3 hour to complete (which is 80 minutes)
Solve. Write answers as an imaginary number. 3x^2=-12
80 POINTS
Answer:
Step-by-step explanation:
3x^2 = -12
divide both side by 3x^2 = -4
Solve the square root.x = ±√-4
this equation has no real solutions
Answer:
x = {- 2i; 2i}-------------------------------
GivenEquation 3x² = 12Solve as below3x² = - 12x² = - 4x = √-4x = ± 2√-1x = ± 2iA checkerboard is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Estimate the perimeter of the checkerboard.
The perimeter of the checker board 118.4 cm
Area of each square = 14 sq. cm.
What is the length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.
The square root of area is the length of one side
[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]
[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]
[tex]P=4 a[/tex]
[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]
[tex]\text { Perimeterofthecheckerboard }[/tex]
Therefor we get the perimeter of the checker board 118.4 cm
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Sketch the space curve represented by the intersection of the surfaces. Surfaces Parameter x2 + y2 + z2 = 4,x+z=2 x=1+sin t Represent the curve by a vector-valued function r(t) using the given parameter. r(t) = (1+sin t)1+Y2cos(t)1+ (1-sin)k (positive y portion) r(t) =| (1 + sin t)i+(-V2cos t)j+ (1-sin)k 、(negative y portion)
As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.
1. First, we need to find the vector-valued function r(t) using the given parameter.
2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:
y = √(4 − (1+sin t)2 − (1 − sin t)2).
3. We can now substitute this expression into the vector-valued function to obtain:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k
4. The space curve represented by the intersection of the surfaces is a helix in a graph.
The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.
The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.
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Find the range of the relation
Answer:
1st {-6, -3, 0, 3, 6}
Step-by-step explanation:
range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}
A researcher needs to assign 10 subjects, numbered 0 to
9, to one of two treatment groups: A and B. Use the table
of random digits, starting with the first row and first
column, to carry out the random assignment.
Table of Random Digits
1 07581 34728 65182 58648 53252 83952
2 23290 98227 30144 83191 12167 90414
3 79486 99776 71793 95330 58256 71156
4 46354 09077 98202 03946 07455 39303
5 00472 20787 54571 73719 04368 41032
Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1
A: 0, 2, 4, 6, 8
B: 3, 4, 7, 2, 8
B: 1, 3, 5, 7, 9
B: 2, 9, 1, 7, 4
OA: 0, 3, 6, 5, 8
A: 0, 7, 5, 8, 1
B: 3, 4, 2, 6, 9
In response to the question, we may say that As a result, the right answer expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To carry out the random assignment, we may utilise the following table of random digits:
Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.
Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.
We can get the following random assignment using this method:
A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9
As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
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Answer:
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
Step-by-step explanation:
THE ANSWER IS D
in 2001, progressive insurance asked cus- tomers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.
We get the following answers;
(a) The necessary histogram has been created and is supplied below.
(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.
Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.
Step 2:
Table :
Miles from home % of accidents Cumulative
Less than 1 23 23
1 to 5 29 52
6 to 10 17 69
11 to 15 8 77
16 to 20 6 83
over 20 17 100
(a) the required histogram is made and attached below.
(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.
Hence we get the required answers.
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