A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.
In the given question,
The confidence level = 99%
Given width = 0.5
Standard deviation of resistance(σ)= 1.55
The formula to find the a big sample that should the experimenter take from the population is
Margin of error(ME) =[tex]z_{\alpha /2}\frac{\sigma}{\sqrt n}[/tex]
So n= [tex](z_{\alpha /2}\frac{\sigma}{ME})^2[/tex]
where n=sample size
We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].
Firstly finding the value of ME.
ME=Width/2
ME=0.5/2
ME=0.25
Now finding the value of [tex]z_{\alpha /2}[/tex].
The given interval is 99%=99/100=0.99
The value of [tex]\alpha[/tex] =1−0.99
The value of [tex]\alpha[/tex] =0.01
Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005
From the standard table of z
[tex]z_{0.005}[/tex] =2.58
Now putting in the value in formula of sample size.
n = [tex](2.58\times\frac{1.55}{0.25})^2[/tex]
Simplifying
n=(3.999/0.25)^2
n=(15.996)^2
n=255.87
n≈256
Hence, the sample that the experimenter take from the population is 256.
Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.
The new values,
Standard deviation of resistance(σ)= 2×1.55
Standard deviation of resistance(σ)= 3.1
width = 2×0.5
width = 1
Now the value of ME.
ME=1/2
ME=0.5
The z value is remain same.
Now putting in the value in formula of sample size.
n= [tex](2.58\times\frac{3.1}{0.5})^2[/tex]
Simplifying
n=(7.998/0.5)^2
n=(15.996)^2
n=255.87
n≈256
Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.
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On Friday, Carlos sold two and two-thirds pitchers of lemonade at his lemonade stand. On Saturday, he sold one and four-sixths times as much lemonade as he sold on Friday. How many pitchers of lemonade did he sell on Saturday?
A. two and six-ninths
B. three and eight-eighteenths
C. four and eight-eighteenths
D. eight and eight-ninths
Answer:
The correct answer is 1 pitcher.
Step-by-step explanation:
Oscar sold 2 pitchers of lemon are from his lemonade stand on Friday.
On Saturday, he sold as much lemonade as on Friday.
The number of pitchers of lemon from the lemonade stand which Oscar sold on Saturday is given by × 2 = 1 pitcher.
Thus Oscar sold 1 pitcher on Saturday which is half of the number of pitchers of lemon he could sell on Friday.
Answer:
c
Step-by-step explanation:
Pls help! i can get pt1 but not Pt2
Answer: 18/20
Step-by-step explanation:
100 points I Will Mark Brainliest Please Help ASAP i only have 30 min
jason bought 10 of the 30 raffle tickets for a drawing. Assuming that he chooses the winning ticket each time, what is the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize, the ticket is thrown away?
6/203
1/27
3/29
1/9
Answer:
the answer is 1/27
Step-by-step explanation:
so firstly
10/30 has 20 tickets left
3 tickets are winning so
1/27
three cards are dealt. what is the probability that the first is a king, the second a diamond and the third a diamond quizlrt
The probability that the first is a king, the second a diamond and the third a diamond quiz let is 1/13, 1/4 and 10/52 respectively.
Now, we know that there are 52 cards in the deck of cards, and there are 13 cards of each suits i.e. diamonds, spade, heart and clubs. Also there are 12 face cards in total of the deck.
So, the probability if getting the first card is king :
King is a face card and there are 4 kings in the deck so the probability will be :
P(getting 1st card as king) = 4/52 = 1/13.
The probability of getting the second card a diamond is :
we know that there are 13 cards of the diamond in the deck so the probability will be :
P(getting the diamond card) = 13/52 = 1/4.
Now, lastly the probability if getting the diamond quiz let is :
There are 10 flashcards of the diamonds in the deck, so the probability will be :
P(getting the diamond flashcard) = 10/52.
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Hercules had to clean out a stable for King Augeas. The king had 3,000 cattle. Hercules said he would clean the stable in one day if the king paid him by giving him 1/10 of the cattle. How many cattle did Hercules want for his work?
Hercules got 300 cattle from the King for cleaning out his stable
FractionsMultiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.
To find how many cattle Hercules got for his work, we can simply multiply 3000 by 1/10 and get the value.
3000 * 1/10 = 300.
He got 300 cattle for his work.
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using a loan calculator,find the total cost to repay a one year long credit loan with principal of 6,000 and an interest rate of 12% APR,
The total cost to repay a one year long credit loan is 6720.
Given,
In the question;
Principal is = 6,000
Interest rate = 12%
To find the total cost to repay a one year long credit loan .
Now According to the question;
Based on the given condition:
Principal is = 6,000
Interest rate = 12%
Formulate:
6000 x (1 + 12%)
6000 x ( 1 + 0.12)
Calculate the sum or difference:
6000 x 1.12
= 6720
Hence, The total cost to repay a one year long credit loan is 6720.
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Ryan will drive hi car in Spain. The peedometer in the car how the peed in mile per hour only. He will be driving on a road with a peed limit of 100 kilometre per hour. Ryan ue thi rule to find thi peed in mile per hour
Ryan will use the multiplication with 0.621 to find the speed in mile per hour.
To find the speed in mile per hour we will convert the unit from mentioned unit to desired unit. As per the known fact, 1 kilometre is 0.621 mile.
Keeping the value of mile in the place of kilometres, we will calculate the speed in miles per hour.
Speed = (100 × 0.621)/1
Performing multiplication in numerator on Right Hand Side of the equation to find the value of speed in miles per hour
Speed = 62.1 miles per hour
Thus, Ryan should multiply the value with 0.621 miles per hour and hence, the value of speed in miles per hour is 62.1.
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Unit 6 Sample Work: Do all questions. Show your work!
Sketch a graph of the quadratic function with the given vertex and through the given point. Then write the
equation of the parabola in vertex form and describe how the function was transformed from the parent
function y = ².
1. vertex (0, 0), point (-2.3)
The graph of the quadratic function y = 0.75x² is given by the image at the end of the answer.
The notation y = 0.75x² is already in vertex form, meaning that the function was vertically compressed by a factor of 3/4 from the original graph.
How to define the quadratic equation?The definition of a quadratic equation with vertex (h,k) is given as follows:
y = a(x - h)² + k.
In which a represents the leading coefficient of the quadratic function.
In this problem the coordinates of the vertex are:
(0,0).
Hence the parameters are:
h = 0, k = 0.
Thus the equation is:
y = ax².
When x = -2, y = 3, hence the leading coefficient is given as follows:
3 = a(-2)²
4a = 3
a = 3/4
a = 0.75.
Hence the equation is:
y = 0.75x².
The multiplication by 0.75 means that the parent function y = x² is vertically compressed by a factor of 0.75.
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The 10 numbers from 1 to 10 are split into two groups. The sum of the numbers in one group is N, and the product of the numbers in the other group is eggs. What is the largest possible value of 10
The largest possible value of 10 can be calculated using factorials and the largest value would be = 3628800
What are factorials?Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 5, then it's factorial would be =5×4×3×2×1 = 120.
Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.
The total numbers of the two groups = 10
The factorials of 10 = 10×9×8×7×6×5×4×3×2×1
= 3,628,800.
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Jacob reduced the size of a painting to a width of 3 in. What is the new height if it was originally 8 in tall and 6 in wide?
The original width is 6 inches, and was reduced to 3 inches, which is half. Keeping this in mind, the new height should be half the original 8 inch height, being halved to 4 inches.
Activity 6: What Property does 1 Exhibit? Directions: Complete the table by determining the property of operations on integers that justifies each statement. (Note: a xb can also be written as ab.)
Given:
1. 0 + (-3) = = -3
2. 2(3-5) = 2(3)3) - 2(5)
3. (-6) + (-7) = (-7) + (-6)
4. 1(-9) = = -9
5.(-4) [tex]( - \frac{1}{4} )[/tex] = 1
6. 2 (3 x 7) = (2 X 3) x 7
7. 10 + (-10) = 0
8. 2(5) 5(2)
9. 1 [tex]( - \frac{1}{4}) [/tex] = = [tex] - \frac{1}{4} [/tex]
10. (-3)(4 + 9) = (-3)(4) + (-3)(9)
1). 0 + (-3) = = -3 is Additive Inverse
2).2(3-5) = 2(3)3) - 2(5) is Associative Property
3). (-6) + (-7) = (-7) + (-6) is Commutative Property
4).1(-9) = = -9 is Multiplicative Identity
5).(-4) (-1/4) = 1 is Commutative Property
6). 2 (3 x 7) = (2 X 3) x 7 is Associative Property
7). 10 + (-10) = 0 is Additive Inverse
8). 2(5) 5(2) is Commutative Property
9).1(-1/4)= -1/4 is Multiplicative Identity
10). (-3)(4 + 9) = (-3)(4) + (-3)(9) is Distributive Property
What is Additive inverse ?
To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
What is Commutative Property ?
This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.
A+B=B+A
What is Multiplicative Identity ?
An element of a set that remains intact after being multiplied by any other element of the set. In the set of real numbers, 1 is a multiplicative identity.
What is Distributive Property?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
What is Associative Property?
A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.
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Find the whole. Explain your method. 30% of what is 15
Answer: 50
Step-by-step explanation:
30% as a decimal is 0.3.
Let's say "what" is a variable, x.
0.3x=15
Divide both sides by 0.3 and you get x=50
Answer:50
Step-by-step explanation:30/100×x=15
x=15×100/30
x=50
A line's slope is 6,and its y -intercept is–4 . What is its equation in slope -intercept form?
Answer:
slope: 6
y-intercept: -4
easy: y = 6x -4
Why is 27/22 as a decimal rounded to the nearest hundredth?
The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.
How to divide fractions using long divisionTo divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.
27/22 = 1 whole number and a remainder of 5
1 × 22 = 22
27 - 22 = 5
drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}
50/22 = 2 whole number and a remainder of 6
2 × 22 = 44
50 - 44 = 6
drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}
60/22 = 2 whole number and a remainder of 16
2 × 22 = 44
69 - 44 = 16
we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.
Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.
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Rectangle QPRS i dilated about the origin by a cale factor of 12, then tranlated 2 unit up to form rectangle Q′P′R′S′. What are the coordinate of S′?
Repone
(1,1)
( 1 , 1 )
(1,3)
( 1 , 3 )
(5,2)
( 5 , 2 )
(7,2)
The new coordinates for point S are (84,24), for a dilation centered around the origin,
Dk (x,y) = (kx, ky) ,
K is the dilated scale factor that is multiplied by points vertices of a rectangle,
then rectangle QPRS where vertices were,
P = (1,1)
Q = (1,3)
R = (5,2)
S = (7,2)
To get the dilation of this QPRS to Q'P'R'S' with a scale factor of 12 you have to multiply each and every coordinate of its vertices by 12.
Q' = (12,12)
P' = (12,36)
R' = (60,24)
S' = (84,24)
Hence, The new coordinates for point S are (84,24)
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factorise 16-(5y-2)^2
The factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)
The expression is
16 - [tex](5y-2)^2[/tex]
The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators
The expression is
The expression is
16 - [tex](5y-2)^2[/tex]
We know the identity
[tex](a+b)^2= a^2+2ab+b^2[/tex]
Apply this identity on the expression
= 16 -( [tex]25y^2[/tex]- 20y + 4)
Apply the distributive property
= 16 - [tex]25y^2[/tex]+ 20y - 4
Subtract the like terms
= - [tex]25y^2[/tex]+ 20y + 12
Take common term outside
= -1([tex]25y^2[/tex]- 20y - 12)
Split the middle term and apply factorization
= -1 ([tex]25y^2[/tex]+ 10y -30y - 12)
Take common term outside
= -1 ( 5y(5y+ 2) -6(5y +2)
Take common term outside
= -1(5y+2)(5y-6)
Hence, the factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)
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In triangle EFG, m∠E = 95.2° and m∠F = 43.7°. Determine the measure of the exterior angle to ∠G.
138.9°
84.8°
51.5°
41.1°
The measure of the exterior angle to ∠G is 138.9°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.
We know the sum of all the interior angles in a triangle is 180°.
We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.
∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.
= 95.2° + 43.7°.
= 138.9°.
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Which two points should the line of best fit go through to best represent the data in the scatterplot?
A graph with points (1, 3), (2, 7), (3, 8), (4, 11), (5, 12), (6, 13).
(1, 3) and (2, 7)
(1, 3) and (6, 13)
(3, 8) and (5, 12)
(5, 12) and (6, 13)
The best line fit go through to represent the data is (3,8) and (5,12)
The correct option is Option c)
What is best fit line?
A straight line that minimises the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
We are given some points we will plot the graph on the points
From that if we plot the line through the point (3,8) and (5,12)
That will leave 2 points above the line and 2 point below the line
Hence it is the best fit line
The correct option is option C)
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Please help
Identify the proportional relationship
There is no proportional relationship between the given equations.
What is proportional relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".
The given equations are,
7x - 2 = y
y = 2x + 4
y = 5x
y + 1 = 3x
These equations can be written as,
y = 7x - 2
y = 2x + 4
y = 5x
y = 3x - 1
Now consider the following table,
x y y/x
7 1 1/7
2 1 1/2
5 1 1/5
3 1 1/3
From above we can see that none of the ratio are equal, all ratios are different.
Hence, none of the given equations having proportional relationship.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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Matthew's curtain company is making curtains for a local hotel. he wants each curtain to be 36 inches long. at the fabric store, fabric is sold by the foot. if matthew's curtain company wants to make 74 curtains, how many feet of fabric will he need?
Matthew will need 222 feet of fabric to make 74 curtains.
According to the question,
We have the following information:
Required length of each curtain = 36 inches
Total number of curtains to be made = 74
Now, the total length of the fabric needed to make 4 curtains can be found by multiplying length of one curtain by total number of curtains.
So, we have the following expression:
36*74
2664 inches
Now, we will convert this into feet:
1 inch = 1/12 foot
2664 inches = 2664/12 feet
2664 inches = 222 feet
Hence, Matthew will need 222 feet of fabric to make 74 curtains.
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Determine which set of statements is inductive reasoning.
O
Given: Everyone dressed casually on Friday
Conjecture: All Fridays are casual days
Given: 3a²
48
Conjecture: a = 6
-
Given: WXYZ is a rectangle.
Conjecture: WX = YZ and WZ = XY
Given: All donuts are unhealthy
Conjecture: This chocolate donut is unhealthy.
From the given set of statements, the conjecture which represent the inductive reasoning are given by :
a. Given : Everyone dressed casually on Friday
Conjecture : All Fridays are casual days.
c. Given : WXYZ is a rectangle.
Conjecture : WX = YZ and WZ = XY
d. All donuts are unhealthy.
Conjecture : This chocolate donut is unhealthy.
As given in the question,
Inductive reasoning is the conclusion which is based on the process of observed pattern.
Given set of statements represents the inductive reasoning or not:
a. Given : Everyone dressed casually on Friday
Conjecture : All Fridays are casual days.
From observing pattern based on Friday dressing we conclude all Fridays are casual days.
Represent inductive reasoning.
b. Given : 3a² = 48
Conjecture : a = 6
Here we cannot observe the process , we have to show the calculation.
Not representing inductive reasoning.
c. Given : WXYZ is a rectangle.
Conjecture : WX = YZ and WZ = XY
From observing pattern based on property of rectangle it is concluded that WX = YZ and WZ = XY.
Represent inductive reasoning.
d. All donuts are unhealthy.
Conjecture : This chocolate donut is unhealthy.
From observing pattern based on all donuts property it is concluded that chocolate donuts is also unhealthy.
Represent inductive reasoning.
Therefore, from the given set of statements, the conjecture which represent the inductive reasoning are given by :
a. Given : Everyone dressed casually on Friday
Conjecture : All Fridays are casual days.
c. Given : WXYZ is a rectangle.
Conjecture : WX = YZ and WZ = XY
d. All donuts are unhealthy.
Conjecture : This chocolate donut is unhealthy.
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What are the repeating digits in the smallest group of repeating digits in the decimal equivalent of 2811?
Answer:
54
Step-by-step explanation:
We can divide 28 by 11 to get...
11 ÷ 28 = 2.545454
22
60
55
50
44
60
55
50
44
60
55
50
44
60
The division quotient reveals that the numbers 5 and 4 repeat themselves frequently. It is a situation of a repeating decimal that does not end.
This means that in the decimal equivalent of [tex]\frac{28}{11}[/tex], the smallest group of repeating digits is composed of 54 repeating digits.
Hope this helps! :)
which characteristic allows a gas to be compressed
Answer:
"Gases are compressible because most of the volume of a gas is composed of the large amounts of empty space between the gas particles. At room temperature and standard pressure, the average distance between gas molecules is about ten times the diameter of the molecules themselves."
Step-by-step explanation:
Found information on Compressibility | CK-12 Foundation website
Type the missing number to complete the proportion.
94 kilometers in 6 hours = 47 kilometers in _
hours
Using proportion, if 94 kilometres is 6 hours, 47 kilometres is 3 hours.
How to solve proportion?Proportion is a mathematical comparison between two numbers
Proportion says that two ratios (or fractions) are equal.
Therefore, let's solve the proportion.
94 kilometres = 6 hours
47 kilometres = ?
cross multiply
time = 47 × 6 / 94
time = 282 / 94
time = 3 hours
Therefore, if 94 km is 6 hours, 47 km is 3 hours.
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the average height of students at uh from an srs of 14 students gave a standard deviation of 2.5 feet. construct a 95% confidence interval for the standard deviation of the height of students at uh. assume normality for the data. a) (2.812, 10.028) b) (1.812, 4.028) c) (1.312, 8.028) d) (0.812, 6.028) e) (3.812, 8.028) f) none of the above
The following is the 95% confidence interval for the standard deviation of UH students' height: CI = (1.81, 4.028) that is option B is correct.
What is standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful.
Here,
The formula for the standard deviation's confidence interval is given as CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
Number of participants; n = 14 D F = n - 1 = 14 - 1 = 13
Deviation from the mean; s = 2.5
Significant level; = 1 - 0.95 = 0.05
Confidence level; CL = 95% = 0.95
As a result, using an online Chi-square distribution table, we have:
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]
CI = (1.81, 4.03) (1.81, 4.03)
The range with a 95% confidence level for the height standard deviation of UH students is as follows: CI = (1.81, 4.028), so option B is the proper one.
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Jack works after school. each day he is paid a set amount, plus an hourly wage. Which is the reasonable domain for the function f(x)=10x+8
Answer:
x>-⅘ OR x<-⅘ (Can I have brainliest ;-;)
Step-by-step explanation:
1) Find x-int:
0=10x+8
-8=10x (÷10)
-⅘=x
x(-⅘;0)
2) Domain:
x>-⅘x<-⅘3) Choose 1 of those, since i cant see the graph i cant say which domain would fit the graph
Please help me it’s due today!!
Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.
Define PEMDAS.Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are referred to as PEMDAS in this context. Teachers in the United States constantly remind their students about the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction. BODMAS, which stands for brackets, ordering, division and multiplication, and addition and subtraction, is another acronym used by educators. A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
Given,
Expression:
5²- 9 ÷ 3
Using PEDMAS,
Squaring,
25 - 9 ÷3
Dividing,
25 - 3
22
Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.
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I can’t understand the question please I need this done asap
The equation of circle can be written as (x-4)^2+ (y+2)^2 = 6^2. The center of the circle is (4,-2) and radius is 6.
What is a circle?
A circle is locus of points which have same distance from a point known as center. Circle is a 2 dimensional figure.
We are given a equation
x^2+y^2-8x+4y-16 = 0
Using completing square method
x^2-8x+ 16+y^2+4y+4-36=0
(x-4)^2 + (y+2)^2 = 6^2
Comparing with standard equation
The center of circle is (4,-2) and and radius of the circle is 6.
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Find the 3rd degree equation that is divisible by x, (x − 3), (x+1)
The 3rd degree equation that is divisible by x, (x − 3), (x+1) is x³ - 2x² - 3x.
Define cubic polynomial.A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3. An algebraic statement having variables, constants, and exponents that are whole integers is called a polynomial.
The given factors are x, (x - 3), (x + 1)
To find the 3rd-degree polynomial divisible by x, (x - 3), (x + 1) multiply the three expressions.
First multiply x, (x - 3)
x × (x - 3)
= x × x - 3 × x
= x² - 3x
Now multiply x² - 3x and (x +1)
(x² - 3x) × (x + 1)
= x²(x) - 3x(x) + x²(1) - 3x(1)
= x³ - 3x² + x² - 3x
= x³ - 2x² - 3x
So, this is the 3rd-degree equation that is divisible by x, (x − 3), (x+1).
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