A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.
A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).
The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).
In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.
To learn more about confidence interval visit:
https://brainly.com/question/24131141
#SPJ4
When designing a study to determine a population proportion, what minimum number would you need to survey, e. G. , n, to be 90% confident that the population proportion is estimated to be within 0. 03?.
The minimum number would you need to survey sample Size N = 752.
A population proportion is the percentage of a population that falls into a specific category. Population proportions are estimated using confidence intervals.
Given,
A margin of error of 0.03
Z = 1.645 at a 90% confidence level
We use P=0.5 because there is no prior information about the population proportion.
To find the minimum number of subjects n= (Z*/M.E.)2 x P (1-P)
Solving by entering the given values into a formula: -
n = (1.645/0.03)2 × 0.5(1-0.5)
n = 3006.70 X 0.25
n= 751.67
Sample Size N = 752
To know more about Population proportions:
https://brainly.com/question/30053702
#SPJ4
Please help me!
I need to deliver it tomorrow.
Step-by-step explanation:
10.
-2 < 6x - 2 < 46
0 < 6x < 48
0 < x < 8
so the line goes (with empty dots because of "<") from 0 to 8.
11.
4 + 9r <= 58 or 7r - 3 >= 46
9r <= 54 or 7r >= 49
r <= 6 or r >= 7
the line goes (with filled dots because of ">=" and "<=") from 6 all the way to the left, and from 7 all the way to the right.
12.
filled dot at -4, empty dot at +3.
connecting line between both dots.
-4 <= x < 3
13.
filled dots at -1 and at +6.
lines going away left and right.
x <= -1 or x >= 6
14.
empty dots at +3 and +4.
lines going away left and right.
x < 3 or x > 4
15.
filled dot at +6, empty dot at +8.
connecting line between both dots.
6 <= x < 8
three less than twice an integer is greater than 1
please help put this in an equation
Answer:
2x-3>1
Step-by-step explanation:
lets say x is the interger
so twice an interger would be 2*x or 2x
and three less than 2x would be 2x-3
and 2x-3 is greater than 1
so 2x-3>1
When an investor considers putting their money into a potentially high rate of return investment, they should understand there will be
risk involved with the investment. Higher potential returns often come with a higher level of risk, as the investor is taking on the possibility of losing some or all of their investment in exchange for the chance to earn a higher return. It's important for investors to carefully consider the level of risk they are comfortable with and to do their due diligence before making any investment decisions. This may include researching the company or investment, reviewing financial statements, and consulting with financial professionals. Investors should also consider the potential tax implications of any investment, as well as how it fits into their overall financial plan.
Find a formula for RN for the function f(x) = (5x)2 on [1, 5] in terms of N.
Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.
The formula for R(N) for the function f(x) = (5x)2 on [1, 5] in terms of N is R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex] and area is 767(approx).
In the given question, we have to find a formula for R(N) for the function f(x) = (5x)^2 on [1, 5] in terms of N.
The given function is f(x) = (5x)^2 on [1, 5].
∆x = (5-1)/N
∆x = 4/N
X = 1+i∆x
X = 1+i4/N
f(x) = 25X^2
f(x) = 25(1+i4/N)^2
f(x) = 25(1+i8/N+16/N^2 i^{2})
R(N) = [tex]\sum_{i=1}^{N}f(X)\Delta x[/tex]
Now putting the value of f(x) and ∆x
R(N) = [tex]\sum_{i=1}^{N}\frac{4}{N}\left[25\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)\right][/tex]
R(N) = [tex]\frac{100}{N}\sum_{i=1}^{N}\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(\sum_{i=1}^{N}1+\sum_{i=1}^{N}\frac{8}{N}i+\sum_{i=1}^{N}\frac{16}{N^2}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\sum_{i=1}^{N}i+\frac{16}{N^3}\sum_{i=1}^{N}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\frac{N(N+1)}{2}+\frac{16}{N^3}\frac{N(N+1)(2N+1)}{6}\right)[/tex]
R(N) = [tex]\frac{100}{N}\times N+\frac{100}{N}\times\frac{8}{N^2}\times\frac{N(N+1)}{2}+\frac{100}{N}\times\frac{16}{N^3}\times\frac{N(N+1)(2N+1)}{6}[/tex]
R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex]
Now finding the area
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = [tex]\text{lim}_{N\rightarrow \infty}\left[100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}\right][/tex]
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 100 + 400 + 800/3
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 766.67
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 767(approx)
To learn more about finding the area of function link is here
brainly.com/question/17095700
#SPJ4
The zeros for this function are -7, 2, and -3. Verify the zeros. Show all working
(-3)^(3) + 8(-3)^(2) + (-3) - 42
The polynomial p(x) = x³ + 8 · x² + x - 42 contains the zeros - 7, 2 and - 3.
How to derive a polynomial that contains a given set of real roots
Polynomials are algebraic expressions, whose standard form is shown below:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m}
Where:
cₙ - n-th Coefficientm - Grade of the polynomialAnd whose factor form is:
p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m}
Where:
a - Lead coefficientrₙ - n-th ZeroIn this problem we need to find a polynomial whose zeros are only real and represented by r₁ = - 7, r₂ = 2 and r₃ = - 3, respectively. If we know that a = 1, r₁ = - 7, r₂ = 2 and r₃ = - 3, then the factor form of the polynomial is:
p(x) = 1 · (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x² + x - 6)
p(x) = x³ + x² - 6 · x + 7 · x² + 7 · x - 42
p(x) = x³ + 8 · x² + x - 42
To learn more on polynomials: https://brainly.com/question/20121808
#SPJ1
the security system in a house has two units that set off an alarm when motion is detected. neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. suppose that for motion in a certain location, the probability that detector a goes off and detector b does not go off is 0.25, and the probability that a does not go off is 0.35. what is the probability that b goes off?
The probability that detector B goes off is 0.75
In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.
Here, the probability that detector A will not go off is 0.35
And the probability that A will go off and B will not go off is 0.25
We need to find the probability that B goes off
The probability that detector A will go off would be,
1 - P( detector A will not go off )
= 1 - 0.35
= 0.65
And the probability that both A and B will go off would be,
= P(A will go off) - P( A will go off and B will not go)
= 0.65 - 0.25
= 0.40
Now we find the required probability.
P(B goes off) = P(both A and B will go off) + P(detector A will not go off)
= 0.40 + 0.35
= 0.75
Therefore, the required probability is 0.75
Learn more about the probability here:
https://brainly.com/question/30034780
#SPJ4
Please Help!!
\What additional information is needed to prove ΔTUX ≅ ΔDEO by HL?
The information required for ΔTUX to be congruent with ΔDEO by Hl is the corresponding legs of the right triangle. i.e. option a. TX ≅ DO
How to find congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.
Congruent triangles are triangles that have the same size and shape.
Therefore, ΔTUX is congruent to ΔDEO.
Triangle can be congruent base of HL(hypotenuse and leg).
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
Therefore, the additional information needed to prove ΔTUX ≅ ΔDEO by HL is TX ≅ DO.
TX and DO are the corresponding legs which are suppose to be equal.
learn more on congruent triangle here: brainly.com/question/28598083
#SPJ1
x (2x - 4) = (2x + 1) (x - 2) solve
Answer:
2
Step-by-step explanation:
First distribute the first x into the first parenthesis: x (2x - 4) = (2x + 1) (x - 2)
x times 2x is [tex]2x^{2}[/tex] and x times -4 is -4x
This changes the equation to: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Now multiply the other parentheses: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Do this by using the Foil method (I attached a picture of the method if you don't know it)
First: (2x + 1) (x - 2)
Do 2x times x which = [tex]2x^{2}[/tex]
Then 2x times -2 which = -4x
Then 1 times x which = x
Lastly, 1 times -2 which = -2
The order you do this is the order that the foil method says.
Now the equation is:
[tex]2x^{2}[/tex]-4x =[tex]2x^{2}[/tex]-4x+x-2 (I just added all the numbers we just got)
Next cancel out the equal terms. To combine like terms you'd usually move the right [tex]2x^{2}[/tex] over to the left one and subtract it. But since they are the same number, subtracting it would leave you with 0. So you can just get rid of both.
You can also do this with both -4x
This leaves you with:
0=x-2
Now you move the variable to the left
you also make it negative since it is going to the other side of the =
this leaves: -x=-2
You can't have a negative x so now you have to change the signs for both. Make them both positive.
Now you have x=2
so your answer is 2
Please help me respond this question. I am struggling!
Viktor is in the 60th percentile, which is 85, while the percentile for 71 is 26.666.
What is percentile?Percentile is defined as the value below which a given percentage falls under. Ben, for instance, is the fourth tallest child in a group of 20, and eighty percent of the kids are shorter than you. As a result, Ben is in the 80th percentile.
We have the data
Sort the data as follows: 58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
employing the percentile formula,
Percentile is calculated as follows: 71 Percentile
(4 / 15)*100 Percentile
26.666 Percentile = (Number of Values Below "x" / Total Number of Values) 100
Consequently, 71's percentile is equal to 26.666.
Identifying the rank
Thus, the ranking is 0.6.
To find the rank for viktor
Find the percentile using the formula,
Percentile = Rank × Total number of the data set
Percentile = 0.6 × 15
Percentile = 9
Now, counting 9 values from left to right we reach 85, and we can say that all the values below 85 will come under the 60th percentile. In other words, 60% of the values are below 85.
The 60th percentile is 85
Thus viktor is in 60th percentile is 85
To know more about Percentile click the link:
brainly.com/question/1561673
#SPJ1
a sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called:
A sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called: sequential sampling.
What is sequential sampling?
Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary.
An auditor develops a set of three groups of sampling units, where each successive group contains the same number of units to be sampled. The sampling plan is to continue to the next group of sampling units if the preceding group contains at least one deviation
Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are examples of probability sampling techniques.
To learn more about sequential sampling visit:
https://brainly.com/question/29203562
#SPJ4
if a chicken and a half can lay an egg and a half in a day and a half, how long would it take a pair of chickens to lay three dozen eggs? show your work.
It would take about 18 days for a pair of chickens to lay three dozen of eggs.
The unitary method is a method for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of just one unit is the key to answering such questions.
Given that 1.5 chickens can lay 1.5 eggs in a day.
The number of eggs 1 chicken can lay in a day = (1.5/1.5) eggs = 1 egg.
Then, two chickens can lay about 2 eggs in a day.
The number of days it takes for two chickens to lay 3 dozen (3×12=36) eggs is given by
[tex]\frac{\text{total number of eggs}}{\text{number of chicken}}=\frac{36}{2}=18\;\text{days}[/tex]
The answer is 18 days.
To know more about the unitary method:
https://brainly.com/question/22056199
#SPJ4
are required to complete the work in ays! 12 workers can complete a piece of work in 20 days. How many workers are needed to complete the work in 16
days?
Answer:
The answer is 15 workers are needed to complete the work in 16 days.
Step-by-step explanation:
To this incomplete sentence. ill try to answer it
Multiply. –4x(7 – 3x)
–28x – 3x^2
7 + 12x^2
–3x – 7x^2
–28x + 12x^2
Croissants cost 85p each and pain au chocolate cost 95p each. Didier buys 22 pastries and spends a total of £20. How many croissants and how many pain au chocolat did he buy?
Answer:
croissants: 10 pain au chocolat: 12
Step-by-step explanation:
85c + 95p = 2000
c + p = 22
85c + 95p = 2000
-
85c + 85p = 1870
10p = 120
p = 12
c + p = 22
c + 12 = 22
c = 10
Answer:
Step-by-step explanation: Let C be the number of croissants and P be the number of pain au chocolat that Didier buys. We know that C + P = 22 and 0.85C + 0.95P = 20.
We can solve this system of equations using substitution. First, we solve the first equation for P: P = 22 - C. Then, we substitute this expression for P into the second equation: 0.85C + 0.95(22 - C) = 20. Expanding the expression inside the parentheses and combining like terms, we get: 0.85C + 21.1 - 0.95C = 20.
Then, we can solve for C by moving all the terms to one side of the equation: -0.1C = -1.1. Dividing both sides by -0.1, we get: C = 11.
Substituting this value for C back into the equation P = 22 - C, we get: P = 22 - 11 = 11.
Therefore, Didier buys 11 croissants and 11 pain au chocolat.
a coin has two sides: heads and tails. a die has six sides, numbered through . if you flip the coin and roll the die, what is the probability that you flip ''heads'' and roll a number less than
The probability that you flip 'heads' and roll a number less than 5 is 1/3.
The probability of flipping heads is 1/2, and the probability of rolling a number less than 5 is 4/6.
The probability of both occurring is the product of the two probabilities, or 1/2 multiplied by 4/6, which is equal to 1/3.
This means that the probability of flipping heads and rolling a number less than 5 is 1/3.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
What are the domain and range of the function shown on this graph?
Domain is z>0, and range is y ≥ 0.
O Domain is 0 ≤z ≤0, and range is 0 ≤ y ≤ 200.
O Domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
O Domain is all real numbers, and range is all real numbers.
and range is y ≥ 0.
Distance
300
275
250
200
175
150
125
100
75
50
2
The domain and range of the function shown on the graph are (a) Domain is x ≥ 0, and range is y ≥ 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the line is a straight line
This means that the graph is a linear function
However, the function only covers the positive axes
This means that
Domain is x ≥ 0, and range is y ≥ 0
Read more about domain and range at
https://brainly.com/question/2264373
#SPJ1
6 The bottled water industry is currently worth over $200 billion annually. The average
cost of a bottle of water in the United States is 50 cents.
a Determine the equation that represents the cost (v) of buying x bottles of water.
What does the gradient represent in this equation?
b What is the total cost of buying one bottle of water a day for a year (not a leap year)?
c A high-quality, refillable water bottle costs approximately $40. How many bottles of
water would you have to drink in order for this option to be more cost effective?
Id What other factors, apart from cost, might inflence someone's decision whether to
carry their own water bottle or to buy bottles of water?
Answer:
a) The cost of buying x bottles of water is represented by the equation v = 0.50x, where v is the cost in dollars and x is the number of bottles of water. The gradient of this equation, which is 0.50, represents the cost per bottle of water.
b) The total cost of buying one bottle of water per day for a year (365 days) is 365 * 0.50 = $182.50.
c) If a refillable water bottle costs $40, then a person would have to drink 40 / 0.50 = 80 bottles of water in order for the refillable water bottle to be more cost effective.
d) Some factors that might influence someone's decision to carry their own water bottle or to buy bottled water include convenience, availability of clean drinking water, personal preference, and environmental impact.
Graph the following equation y-2=1/2(x+5)
Answer: I could be wrong, but I tried my best.
Slope: 1/2
Y-intercept: (0, 6)
Step-by-step explanation:
19) Which two integer values is 17 between?
C) 3 and 4
A) 13 and 14
B) 5 and 6
D) 2 and 3
Answer: D
Step-by-step explanation:
The exact answer is 2.571281591, which is between:
D) 2 and 3
consider the following birthday problem. if we randomly selected 3 people born in 2001, what's the probability that they all have different birthdays?
Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);
What is the probability that 3 people have different birthdays?
Since there are 363 days still “unused” out of 365, we have p = 363÷365 = about 0.9945. Multiply that by the 0.9973 for two people and you have about 0.9918, the probability that three randomly selected people will have different birthdays.
Poisson Way. The probability of same-birthdays triplet is 1 / (365 * 365), which is very small, and there are C(n, 3) triplets, which is a big number for the moderately high values of n (~>20).
Calculating the likelihood of three events
Probability that at least one of the three events occurs: Probability that each of the three occurrences will occur: P(A, B, C);
Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);
P() is the likelihood that none of the events will occur.
To learn more about different birthdays visit:
https://brainly.com/question/928420
#SPJ1
. Which list shows the numbers in descending order?
a
-19/2, -3 1/4, -1.2, 38/6, 7
b
7, 38/6, -19/2, -3 1/4, -1.2
c
-19/2, 7, 38/6, -3 1/4, -1.2
d
7, 38/6, -1.2, -3 1/4, -19/2
Answer:
d: 7, 38/6, -1.2, -3 1/4, -19/2.
Step-by-step explanation:
First, divide the fractions to get decimals, this is an easier approach to compare all the numbers.
-19/2 = -9.5
-3 1/4 = 4 x -3 = -12 + 1 = -3.25
38/6= 6.3333 (terminal 3)
The greatest numbers for this list is 6.33, -3.25, and -9.5. The rest of the numbers include -1.2 and 7.
With the entire order, we observe which lists are descending, starting with a positive or a negative number.
1. order can be: 7, 6.33, -1.2, -3.25, and -9.5 or 7, 38/6, -1.2, -3 1/4, -19/2.
2. order commonly confused can be: -9.5, -3.25, -1.2, 6.33, and 7 or -19/2, -3 1/4, -1.2, 38/6, 7.
The only order showing this is d: 7, 38/6, -1.2, -3 1/4, -19/2.
The reason why its not the second order starting with -19/2 is because descending typically refers to a positive number going down to a negative number. However, both orders can be right. For the sake of this problem, the best option is d.
The vertices of ABC are A(2,-1), B(0, 4), and C-3,5). Find the coordinates of the vertices of the image after the translation (x, y)-(x-1, y + 3).
Answer:
A(1,2), B(-1,7) C(-4,8)
Step-by-step explanation:
I think that is the answer.
8. You have an investment of $20,000 with
4.2% simple interest and weekly payments.
How much money (to the nearest dollar)
will you have after three years?
[A] $23,030
[B] $19,730
IC] $21,200
[D] $24,250
[E] $20,048
Answer:
[D] $ 24,250
Step-by-step explanation:
$24,250 dollar will I have after three years.
in writing a report, the researcher produced a single histogram of the combined data for region i and region ii. describe the shape of the histogram for the combined data.
Between $80,000 and $85,000, there is an outlier. Means are not immune to outliers, but medians are.
How do you define medians?
The middle number in a sorted series of numbers is referred to as the median in mathematics. Ordering the numerals reveals the center one. In descending sequence, the numbers are listed. The middle number, when the numbers are arranged, is referred to as the data set's median.
Why is median significant?
A useful way to determine where a dataset is in the middle is to use the median. You may gain a sense of a dataset's distribution by comparing both median and mean. The dataset is almost uniformly scattered from the mean if both mean and median are equal.
To know more about Median visit:
brainly.com/question/21396105
#SPJ4
Which of the following are possible side lengths
for a triangle?
A. 8, 16,4
B. 3, 6, 9
C. 3, 12, 10
Answer:
C. 3, 12, 10---------------------------
According triangle inequality theorem the sum of any two sides of a triangle is greater than the third side.
Apply this to our options, add up the two shortest sides and compare with the longest side.
Option A8 + 4 < 16, no, it is impossible to build a triangle.Option B3 + 6 = 9, no, it is impossible to build a triangle.Option C3 + 10 > 12, yes, possible triangle.I need help on this Math. It was due so long ago.
Answer:
y-intercept: (0,4)
y-intercept in the coordinate form: (0,4)
The equation in slope-intercept form: y=7x+4
Step-by-step explanation:
The slope is rise/run
We see that the y increase by 28 and the x increase by 4, so the slope is 28/4 = 7
m = 7
We know that the y-intercept is at (0,4)
So the slope-intercept equation will be
y = 7x + 4
Answer:
y- intercept = 0.4
y- intercept in the coordinate = 0.4
so the equation is : y=7x+4
I need help please….
The slope of the line as per the given points will be equal to 7/10.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope.
Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information in the question,
The given points are (25, 24) and (15, 17)
Use the formula to find the slope,
m = (y₂ - y₁)/(x₂ - x₁)
Substitute the values in the above formula,
m = (17 - 24)/(15 - 25)
m = -7/-10
m = 7/10
To know more about Slope:
https://brainly.com/question/3605446
#SPJ1
The scores for assessments are displayed in the box-and-whiskers plot below. What is the range of the middle 50% of the data of scores on the assessment?
The range of the middle 50% of the data of scores on the assessment is 10.
Option A is the correct answer.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
Median = 80
First quartile = 70
Third quartile = 90
The Middle 50% is from the Median to the First quartile.
Range.
= 80 - 70
= 10
Thus,
The range is 10.
Learn more about the range here:
https://brainly.com/question/15953457
#SPJ1
Find values of p, q, r and s such that (2x + 3) (px^3 + qx^2+rx+ s) = 2x^4+ 13x^3 + 7x^2 + 18
Answer:
p = 1q = 5r = -4s = 6Step-by-step explanation:
You want values of p, q, r and s such that (2x + 3) (px^3 +qx^2 +rx +s) ≡ 2x^4 +13x^3 +7x^2 +18.
Find coefficientsMultiplying out the left side of the equation, we have ...
2px^4 +(3p+2q)x^3 +(2r +3q)x^2 +(2s +3r)x +3s
Match coefficientsWhen we match coefficients between the two polynomials, this gives rise to 5 equations in the four unknown values:
2p = 23p +2q = 132r +3q = 72s +3r = 03s = 18The first and last equations tell us ...
p = 2/2 = 1
s = 18/3 = 6
Using these values in the 2nd and 4th equations makes them be ...
3 +2q = 13 ⇒ q = 10/2 = 5
12 +3r = 0 ⇒ r = -12/3 = -4
The values of p, q, r, s are ...
p = 1q = 5r = -4s = 6__
Check
We can use the 3rd equation to check these results:
2r +3q = 7
2(-4) +3(5) = 7
-8 +15 = 7 . . . . . . . true