The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.
Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.
The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.
Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.
Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).
Now,
a=1,b=4,Δx =(b-a)/n =3/6 =1/2
f(x)=4√(ln(x))
trapezoidal rule:
∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1)) +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]
∫4√(ln(x)) dx =10.365336
midpoint rule :
∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]
∫4√(ln(x)) dx =(1/2)[4√(ln(1.25)) +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]
∫4√(ln(x)) dx =10.724182
simpsons rule:
∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+ 2*f(3)+ 4*f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1)) +4*4√(ln(1.5)) + 2*4√(ln(2)) +4*4√(ln(2.5)) +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]
∫4√(ln(x)) dx =10.527905
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The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph of that data is shown:
A graph with Number of Owners on the x axis and Yearly Cost of Pets, in hundreds, on the y axis. The x axis has a scale from 1 to 10 with an increment of 1. The y axis has a scale of 5 to 15 with increments of 1. A curved line connecting 1, 15, approx 3, 7, and 10, 0 is drawn.
Would (3, 7.2) be a realistic solution for the function? Explain.
Group of answer choices
Yes, it is realistic to have 7.2 owners who spend $300 dollars on their pet(s).
No, it is not realistic to have 3 owners.
Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
No, it is not realistic that owners spend $720 a year on their pet(s).
It is realistic that 3 owners spend $720 a year on their graph
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).Given that
In the displayed graph, the y-axis shows the annual cost of pets in hundreds of dollars, while the x-axis shows the number of pet owners.The graph's path through the points(1,15),(3,7), and (10,0).To find
Would (3, 7.2) be a realistic solution for the function?So, according to the question
We can say that,
3 owners are present and,
A pet's annual cost is $720.
So, the option C (Yes, it is realistic that 3 owners spend $720 a year on their pet(s) ) is correct explanation of it.
Because no fractional value can represent the number of owners. Therefore, having 7.2 owners is not feasible and other options showing only one value. So A, B, and D are wrong answer.
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
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Consider this figure.
For A-C, select True or False for each statement about the sequences of transformation that can verify that traingle ABC is congruent to A'B'C'.
A. Triangle ABC is translated 1 unit to the left, followed by a reflection the x-axis. True/False
B. Triangle ABC is translated 1 unit to the right, followed by a reflection the x-axis. True/False
C. Triangle ABC is reflected across the x-axis, followed by a translation 1 unit to the right.
True/False
Answer is
A. False
B. True
C. False
According to the graph,
A (1, -2), B(b, - 2), C(1, -7), A'(-b , b), B'(-1 ,b), C'(-b , 1).
A. if ABC is reflected across x-axis. (x, y) reflected x-axis→ (x-y)
so A'(1,2), B' (b-2), C'(1-7) , it's no equal to title .
so A is false.
B. if ABC is translated 7 units to the left , up 8 units.
(x, y)→(x-7,y+8),
so A'(-b , b), B'(-1 ,b), C'(-b , 1)
it's equal to title. so B is true.
C. if ABC is translated 8 units down, 7 units to right
(x y)→(x+7, y-8),
so A' (8,-10),B'(13,-10), C'(8,-15)
it's not equal to title. so C is false.
A transformation is the movement of a figure. There are four types of transformations: reflection, rotation, translation, and dilation. Of these four types of transformations, a transformation can either be a congruent or similar shape to the original image. Congruent means that the shape or figure retains its size, shape, length, and angles of the original shape.
A rotation is a turn around a centre point. In a rotation, the distance from each point on the shape to the centre remains the same. A rotation is identified by a shape turning a specific amount degrees, usually 90, 180, or 270 degrees, around a point either clockwise or counter clockwise. This means with each rotation performed four things are given.
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Someone know this? The graph of g(x)is the graph of f(x)=x2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)?
The function g(x) is given as: g(x) = 3 ( x + 4 )^2 + 5
Given data
f(x)=x2
shifted 4 units left
stretched by a factor of 3
shifted 5 units up
How to find the function rule for g(x)The function g(x) is formed from the function f(x) by the following moves:
Shifting 4 units to left
To shift the graph 4 units to the left is given by
f(x) = x^2
f(x) = ( x + 4 )^2
Stretching by a factor of 3
to stretch by a factor of 3 means multiplying by 3
f(x) = 3 * ( x + 4 )^2
f(x) = 3 ( x + 4 )^2
Shifting 5 units up
This movement is shows in the y axis and is represented as follows
f(x) = 3 ( x + 4 )^2 + 5
At this stage the function rule for g(x) is completed hence
f(x) = 3 ( x + 4 )^2 + 5 = g(x)
and
g(x) = 3 ( x + 4 )^2 + 5
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Im stuck can someone help?
Answer:
- p / 2
Step-by-step explanation:
4 / -8 = - 1/2
p^3 / p^2 = p
- 1/2 * p = - p / 2
Student tickets to a theme park are $15 per person plus a travel fee of $50. The equation y = 50+ 15x represents the total cost, where x is the number of students. If there are at least 10 students but no more than 15 going on the trip, what is the domain of the situation?
Based on the given parameters, the domain of the situation is 10 <= x <= 15
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the domain of the situation?The equation of the function is given as:
y= 50 + 15x
Where
Travel fee = $50Theme park ticker = $15 per personFrom the question, we understand that:
At least 10 students but no more than 15 are going on the trip
When the above is represented as an inequality, we have
10 <= x <= 15
Where x is the number of students
Hence, the domain of the situation is 10 <= x <= 15
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Is the following sentence true?
Changing 3x + 6 into 3(x + 2) is
an
example of reverse distributing
Answer:
true
Step-by-step explanation:
what are the answers ?! help pls !!! this is a timed T-T
Answer:I would say c
Step-by-step explanation: because it is the only one that makes sense
Givien h(x)= 3x+1, solve for x when h(x) = 4
The value of x = 1 when the value of the function h(x) = 4.
What is a function?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Given that,
h(x)= 3x+1
The value of h(x) = 4:
4 = 3x + 1
4 - 1 = 3x
3x = 3
x = 1
Hence, the value of x = 1 when the value of the function h(x) = 4.
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The sum of three consecutive even integers (3 integers in a row) is 120.
Use the following setup and given equation to find your solution:
1st integer = x
2nd integer = x+2
3rd integer = x+4
Equation: x+(x+2)+(x+4)=120
Solve the equation above. What is the largest of the three integers?
Answer:
42
Step-by-step explanation:
x + x + 2 + x + 4 = 120
3x + 6 = 120
3x = 114
x = 114/3
x = 38
38, 40, 42
The three integers are 38, 40, and 42.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that the sum of three consecutive even integers (3 integers in a row) is 120. The value of integers will be calculated as below:-
x + x + 2 + x + 4 = 120
3x + 6 = 120
3x = 114
x = 114/3
x = 38
1st integer = x = 38
2nd integer = x+2 = 38 + 2 = 40
3rd integer = x+4 = 38 + 4 = 42
Therefore, the three integers are 38, 40, and 42.
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A line passes through the point(9,-8)
and has a slope of-2/3. Write an equation in slope-intercept form for this line.
.
KJSAnflkadfalkdmnfaldskjfnasd...
Please help meeeeeee I’m stressingggg out
Answer:
see attached for the tablelimit is 3Step-by-step explanation:
You want a table of values of the function sin(3x)/x as x nears zero, and an estimate of the limit of the function value as x → 0.
Table of valuesThe function f(x) = sin(3x)/x is an even function. That is ...
f(-x) = sin(-3x)/(-x) = -sin(3x)/-x = sin(3x)/x = f(x)
When f(-x) = f(x), the function is even. It is a reflection of itself across the y-axis. This means all of the function values for negative x-values are the same as for the corresponding positive x-values. We only need to fill in half the table to know what the other half looks like.
See the attachment for values calculated by a spreadsheet and rounded to 8 decimal places.
LimitThe table shows the difference from 3 gets smaller as x gets closer to 0. If we add more rows to the spreadsheet table (2nd attachment), we see that the value gets even closer to 3 as x nears zero. At x = 10^-7, we run up against the accuracy limits of the spreadsheet.
The limit of the expression is 3 as x approaches 0.
Kofi is 5years older than Ama now. Two years ago, Kofi was twice as old as Ama. Find their ages now.
Answer:
Ama is an elephant so she is 2 years old
Step-by-step explanation:
The test statistic value calculated by the statistical procedure selected is known as the?
The test statistic value calculated by the statistical procedure selected is known as the T-test.
What is a T-test?
The mean difference between two sets of observations is zero using the T-test, also known as the dependent sample t-test. When the population standard deviation is unknown, the student's t-test is a statistical tool for assessing assumptions about the mean of a small sample taken from a normally distributed population.
Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Therefore, the test statistic value calculated by the statistical procedure selected is known as the T-test.
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Quadrilateral B is a scaled copy of quadrilateral A.
Its shortest side is 5 units long.
What is the scale factor from A to B?
By using the concept of dilation, we find that scale factor from A to B is equal to l' / 5, where l' is the length of the shortest side of the quadrilateral B.
What is the scale factor between two quadrilaterals?
Scale factor is a key variable used to dilate lengths and distances by rigid transformations. Then, the length of the shortest side of the quadrilateral B is equal to the product of the scale factor and the length of the shortest side of the quadrilateral A. Mathematically speaking, this kind of rigid transformation is represented by the following formula:
r = l' / l
Where:
r - Scale factorl - Length of the shortest side of the quadrilateral A.l' - Length of the shortest side of the quadrilateral B.If we know that l = 5, then the length of the shortest side of the quadrilateral B is equal to the following linear equation:
l' = 5 · r
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If the sum of squares for a sample containing 51 items equals 400, what is the standard deviation? 8.00 7.84 4.47 2.83
The standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}[/tex]
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
∑(x(i) - X)² = 400
n = 51
SD = √(400/51-1)
SD = √8
SD = 2.828 ≈ 2.83
Thus, the standard deviation is 2.83 if the sum of squares for a sample containing 51 items equals 400 option (D) is correct.
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2x+15=25 find for x
Answer:
x= 5
Step-by-step explanation:
2x+ 15=25
-15 -15
2x= 10
/2 /2
x=5
Answer:
x = 5
Step-by-step explanation:
2x + 15 = 25
2x + 15 - 15 = 25 - 15 (subtract 15 from both sides)
2x = 10
2x/2 = 10/2 (divide by 2 on both sides)
x = 5
the of a vector is the which that vector makes with
The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
What do we mean by a vector?Vector is a colloquial term in mathematics and physics that refers to some quantities that cannot be expressed by a single number (a scalar) or to elements of some vector spaces.Vectors were first used in geometry and physics (typically in mechanics) to represent quantities with both a magnitude and a direction, such as displacements, forces, and velocity. In the same way that distances, masses, and time are represented by real numbers, such quantities are represented by geometric vectors.To find the angle of the given vector:
Given: [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]
So,
[tex]\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}[/tex]
Using the formula [tex]\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}[/tex], we obtain:
[tex]\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}[/tex]
Therefore, the angle that the vector [tex]\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
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The correct question is given below:
The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is:
(A) tan⁻¹ 3/2
(B) tan⁻¹ 2/3
(C) sin⁻¹ 2/3
(D) cos⁻¹ 3/2
-4x-3=-2x-2 solving for x
Answer:
x = 1/2
Step-by-step explanation:
4x -3 = 2x - 2 There are many ways to approach this problem. I am going to start by subtracting 2x from both sides of the equation.
2x -3 = -2 I am going to add 3 to both sides of the equation
2x = 1 Divide both sides of the equation by 2
x = 1/2
38. Автор, проверяя набранные на компьютере страницы будущей
книги, обнаружил опечатки, данные о которых приведены в
таблице:
Номер страницы
1 2 3 4 5 6 7 8
Число опечаток 0 1 0 2 1 2 4 3
Верно ли, что стандартное отклонение данных этой выборки
не больше 1?
Answer:
the answer is clear
Step-by-step explanation:
you have to get the answer by completing the answer
A formula for 6 gallons of light green paint uses 3/8 gallon of white paint. Liam has 9/16 gallon of white paint. Does Liam have enough white paint to make 8 gallons of light green paint?
Yes, 9/16 gallon of white paint is enough for Liam to make 8 gallons of light green paint.
How do you defined the term unitary method?It is a method for estimating the value of a single unit from of the value of multiple units, as well as the value of multiple units from of the value of a single unit. With in unitary method, we everytime count the value of a unit one or quantity first, and then calculate the values of more or lesser quantities.For the given conditions; use unitary method.
3/8 gallons white paints ------> 6 gallons of light green paint.
Thus, from 1 gallons of white paint.
1 gallons white paints ------> (6×8)/3 gallons of light green paint.
For preparing 8 gallons of light green paint, multiply both side of equation by 9/16.
9/16 gallons white paints ------> (6×8)/3 × (9/16) gallons of light green paint.
on solving.
9/16 gallons white paints ------> 9 gallons of light green paint.
The requires value for light green paint is 8 gallons, we have prepared more than that that is 9 gallons.
Thus, Liam has sufficient white paint to make 8 gallons of light green paint.
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In February 2003,
the Battlefords Chamber of
Commerce in Saskatchewan
placed a cage containing a
64-cubic foot ice cube along
Yellowhead Highway. Local
customers were asked
to predict when the ice cube
would melt enough for a ball
above the ice cube to fall through it. What was
the surface area of the cube?
The side length of the cube is 4 feet. Then the surface area of the cube will be 96 square feet.
What is a volume of a cube?Suppose that: The side length of the considered cube is L units. Then, we get:
The volume of that cube = L³ cubic units.
The surface area of that cube = 6L² square units.
In February 2003, the Battlefords Chamber of Commerce in Saskatchewan placed a cage containing a 64-cubic foot ice cube along Yellowhead Highway. Then the side length of a cube will be
64 = L³
L = ∛64
L = 4 feet
Then the surface area of the cube will be
SA = 6 x 4²
SA = 6 x 16
SA = 96 square feet
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What does it mean when a data set or distribution has more variability than another
Answer: Standard deviation
Step-by-step explanation: The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.
What can you conclude from the results of (a), (b), and (c)? a. when each entry is multiplied by a constant k, the sample mean and the sample standard deviation remain unaffected.
It is true that the sample mean and the sample standard deviation remain unaffected.
What is mean ?Mean is the average of the given data.
According to the given question when each entry is multiplied by a constant k each term will k times of the previous term.
Suppose we have 3 terms x, y, z.We know that their mean will the middle term as there are odd number of terms which is y.
Now if we multiply each term by a constant k the terms will be kx, ky, kz and the middle term is ky.
As each term is multiplied by k we have divide by k which is
= ky/k
= y.
So from both the results we can observe that the mean and the standard deviation remains same.
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Initial estimates of the probabilities of events are known as _____ probabilities.
Initial estimates of the probabilities of events are known as prior probabilities.
Prior probability, in Bayesian statistics, is the probability of an event before new data is collected. This is the best rational assessment of the probability of an outcome based on the current knowledge before an experiment is performed.
The prior probability of an event will be revised as new data or information becomes available, to produce a more accurate measure of a potential outcome. That revised probability becomes the posterior probability and is calculated using Bayes' theorem. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred.
The prior probability is the probability assigned to an event before the arrival of some information that makes it necessary to revise the assigned probability. The revision of the prior is carried out using Bayes' rule. The new probability assigned to the event after the revision is called posterior probability.
Initial estimates of the probabilities of events are known as prior probabilities.
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Which data set is the most spread from its mean?
14, 26, 24, 28
O22, 16, 18, 36
O22, 28, 20, 22
O 21, 19, 27, 25
Option B (22,16,18,36)
Mean- Mean is an average of the data collected in the data set. It can be found by dividing the sum of the values by the number of values. Median is the middle value of the data set when the values are placed in order from least to greatest.
It is easy to calculate: add up all the numbers, then divide by how many numbers there are.
Add all the numbers (22+16+18+36) = 92
Avarage = sum of the all given numbers/ total numbers
total numbers =4
so avarage= mean= 92/4 =23
(22,16,18,36) has the most spread because one number as low as 16 and one as high as 36. Our mean is 23, so that means that the spread is huge.
Hence the answer is (22,16,18,36).
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Evaluate the expression 3^5 five is small and on top
Answer:
243
Step-by-step explanation:
3 to the power of 5
3 x 3 x 3 x 3 x 3
3 x 3 = 9 x 3 = 27 x 3 = 81 x 3 = 243
The following are the amounts of radiation received at a greenhouse.
6.1 6.8 8.7 9.0 10.2 10.3 10.6 10.8 10.9 11.0 11.1 11.5 11.7 12.2 13.4
find the sample range.
The given data be 6.1, 6.8, 8.7, 9.0, 10.2, 10.3, 10.6, 10.8, 10.9, 11.0, 11.1, 11.5, 11.7, 12.2, 13.4 then the sample range is 7.3.
What is meant by sample range?A well-liked and straightforward method for comparing the variability of various data distributions is the sample range. The formula for the sample range is the greatest value minus the smallest value. It is based on two values in a data set: the maximum and minimum.
The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
Arrange all values in your information set from low to high.
Subtract the lowest value from the highest value.
Let the given data be 6.1, 6.8, 8.7, 9.0, 10.2, 10.3, 10.6, 10.8, 10.9, 11.0, 11.1, 11.5, 11.7, 12.2, 13.4
13.4 - 6.1 = 7.3
Therefore, the sample range is 7.3
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Open the cpt manual to the page that contains code 40490. what section of the cpt coding manual is this code listed in?
The section of the CPT coding manual is the code 40490 is listed in is "digestive system."
What is CPT codes?CPT is the language used by providers and payers when billing medical procedures and services for reimbursement.
Some key features regarding the CPT codes are-
CPT or Current Procedural Terminology, is a set of medical codes used to describe the procedures and services performed by physicians, allied health care professionals, provided by trained practitioners, healthcare facilities, outpatient facilities, and laboratories.CPT codes, in particular, are used to notify services and procedures to both federal and private payers for repayment of rendered healthcare services.CPT codes were developed by the American Medical Association (AMA) in 1966 to standardize reporting of medical, surgery, and diagnosis and treatment procedures and services performed in both inpatient and outpatient settings. Each CPT system defines a written description of a process or service, removing the need for the patient's subjective interpretation of what was provided.To know more about the CPT codes, here
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I CAN SOLVE PROBLEMS.
5. Create an equivalent expression using the
additive inverse property.
-17- (25)
-17-25
6. Divide
debelow and determine if it will
terminate or repeat
The equivalent expression using the additive inverse property is -17- 25
How to create an equivalent expression using the additive inverse property?The expression is given as:
-17- (25)
The additive inverse property states that:
-x + x = 0
This also states that
-(x) = -x
Using the above as a guide, we have the following equation
-17- (25) = -17- 25
Hence, the equivalent expression using the additive inverse property is -17- 25
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I really need help in this question
The height of the isosceles triangle is 8.08 cm.
Given the sides of the triangle are:
a = 9 cm (one side of the triangle)
b = 8 cm ( base of the triangle)
Therefore, height of the triangle =?
An isosceles triangle's height is determined by measuring perpendicularly from one vertex to the other's triangle base. A triangle's height is one of its crucial parameters since it enables us to determine the triangle's area.
we know that h = √a²₋ b²/4
substitute a and b values in the above formula, to find height:
h = √9² ₋ 8²/4
h = √81 ₋ 64/4
h = √(81 × 4) ₋ 64 / 4
h = √324 ₋ 64/4
h = √260/4
h = √65
h= 8.06 cm
Therefore the height of the isosceles triangle is 8.06 cm.
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