=p(-1)q(-1) + p(070) +p(3)q(3) defines an inner product in P3- Use this inner product to find
||P||||9||, and the angle between p(x) and (x) for p(x) = 2x2 + 6 and 7(x) = 4x2 - 4x. < p, >= ||pl= ||ql| = A = radians.
If p(x) and q(x) are arbitrary polynomials of degree at most 2 then
||p||||q|| = 26([tex]\sqrt{640}[/tex]) and angle between p(x) and q(x) is 0.233.
Given that
<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)
and p(x) = 2x²+ 6 , q(x)= 4x²-4x
then the values of p and q at x = -1,0,3 are given as;
x = -1,
p(-1) = 2(-1)² + 6 = 8 , q(-1) = 4(-1)² - 4(-1) = 8
x = 0,
p(0) = 2(0)² + 6 = 6 , q(0) = 4(0)² - 4(0) = 0
x = 3,
p(3) = 2(3)² + 6 = 24 , q(3) = 4(3)²- 4(3) = 24.
<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)
= (8)(8) + (6)(0) + 24(24)
= 64 + 0 + 576
<p,q> = 640
Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||
||p|| = [tex]\sqrt{ < p,p > }[/tex]
= [tex]\sqrt{8(8) + 6(6) + 24(24)}[/tex]
= [tex]\sqrt{676}[/tex]
||p|| = 26
and
||q|| = [tex]\sqrt{ < q,q > }[/tex]
=[tex]\sqrt{8(8) + 0(0) + 24(24)}[/tex]
||q|| =[tex]\sqrt{640}[/tex]
∴||p||||q|| = 26([tex]\sqrt{640\\[/tex])
Now we have to find angle between p(x) and q(x),
∴ α = cos⁻¹[tex]\frac{ < p,q > }{||p||||q||}[/tex]
= cos ⁻¹ [tex]\frac{640}{26(\sqrt{640}) }[/tex]
= cos ⁻¹ [tex]\frac{4\sqrt{10} }{13}[/tex]
α = 13.34°
In radian
α = 0.233.
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question content area top part 1 find the arc length of the following curve on the given interval. x
The arc length of the curve is L= π^2/8
In order to get the length of the arc's curved line, an arc length formula is used (a segment of a circle). The arc length is the length of the circle's curved line, which can be expressed as a distance through the curve.
To find arc length of the curve on the given interval
X= sin t-cos t y= cos t +t sin t
0≤ t ≤ π/2
On differentiating x and y w.r.t t
dx/dt = cos t - [cos t+t (-sin t)]= cos t – cost + t sin t
dy/dt = sin t + [t cos t+sin t]= sin t+ sin t+ t cos t
So we have
dy/dt = t cost and dx/dt= t sin t
Arc length for parametric equation is given by
L= ∫_0^(π/2)▒〖√((〖dx/dt)〗^2+(〖dy/dt)〗^2 ) 〗 dt
L= ∫_0^(π/2)▒〖√((t^2 〖cos〗^2 t+t^2 〖sin〗^2 t) ) 〗 dt
L= ∫_0^(π/2)▒t dt
L= [t^2/2] (π/2)¦0 = π^2/4*1/2
L= π^2/8
Therefore the arc length of the curve is L= π^2/8
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if we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is
Z test and the X² test (Chi squared) will be used to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2.
What is Z-test?Any statistical test for which the test statistic's distribution under the null hypothesis may be roughly represented by a normal distribution is known as a Z-test. Z-tests examine a distribution's mean. To determine if a discovery or relationship is statistically significant or not, hypothesis testing uses a z-test. It specifically checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more can a z-test be applied.
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Samuel and Jaon pent 3/4 of their combined earning from 100 by gift. How much do they pend? I there enough left over from Wedneday’ earning to buy a card that cot $3. 25
There is not enough money left to buy a card for $3.25 but they spend $ 5.88 to buy a gift.
What are combined earnings?
The term "Combined Earnings" refers to the total (without repetition) of (a) the aggregate (without repetition) Dividend Capacity of the Regulated Subsidiaries, (b) EBITDA, and (c) the aggregate (without repetition) tax provision, created in accordance with GAAP, for the Regulated Subsidiaries.
Here, we have
The earnings from Wednesday of Samuel and Jason are:
Samuel earnings = 12.5 x 0.40 = $5
Jason earnings = 7.1 x 0.40 = $2.84
The combined earnings from Wednesday are as follows:
Combined earnings = Samuel's earnings + Jason's earnings
Combined earnings = $5 + $ 2.84 = $ 7.84
The spended earnings are:
Spended earnings = combined earnings x ¾
Spended earnings = 7.84 x ¾ = $ 5.88
The leftover is:
Leftover = combined earnings – spended earnings
Leftover = 7.84 – 5.88 = $ 1.96
Hence, they spend $ 5.88 to buy a gift but not enough money to buy a card for $3.25.
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which of the following binary operations are commutative? a. substraction of integers b. division of nonzero real numbers c. function composition of polynomials
None of the options are commutative for the given binary operations.
Define the term commutative property?According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. With addition and multiplication, the principle is true, but not for division or subtraction.commutative property:
a*b = b*a
* is any binary operation.
Consider option a: subtraction of integers
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Option b: . division of nonzero real numbers
Let a = 2, b = 3
a/b = b/ a (commutative property)
But
2/3 ≠ 3/2 not commutative
Option c. function composition of polynomials.
Let polynomial be a - b
Let a = 2, b = 3
a - b = b - a (commutative property)
But
2 - 3 ≠ 3 - 2
-1 ≠ 1 not commutative
Thus, none of the options are commutative for the given binary operations.
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instructor number of failures prof. a 13 prof. b 0 prof. c 11 prof. d 16 what are the .95 (5 percent risk of type i error) upper and lower control limits for the p-chart?
The Average proportional failure of the instructors is 0.10
From the question we are told that
Sample size 100
Instructor Number of Failures
Prof. A 13
Prof. B 0
Prof. C 11
Prof. D 16
Confidence level= 0.95
From Z table
Z=1.96
Generally proportion for failure is mathematically given as
proportion of failure = number of failure/ sample size
Prof A
Pa = 13/100
Pa = 0.13
Prof B
Pb = 0/100 = 0
Prof c
Pc = 11/100 = 0.11
Prof D
Pd = 16/100 = 0.16
Average proportional failure = (0.13 + 0.16 + 0.11 +0)/4 = 0.10
Therefore the Range is 0.0412 to 0.1588
Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options
Therefore, the Average proportional failure of the instructors is 0.10
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Why do we use graphing?.
A factor is a number
that is ___.
with another number
to get a ___
Answer:
A Factor is a number that is multiplied. With another number to get a Product.
Step-by-step explanation:
Example 7 * 5 = 35
7 and 5 are factors of 35 that when multiplied give a product of 35
Given a collection of paired sample data, the between the two variables, x and y. y = bo + b1x algebraically describes the relationship between x and y. Given a collection of paired sample data, the between the two variables, x and y. ỹ = bo+bqx algebraically describes the relationship between x and y.
The answer is regression equation.
What is regression equation?
The regression of y on x is that the algebraic expression of the regression lines. it's accustomed predict the values of the variable quantity from the given values of freelance variables.
Main Body:
When there is a relation between 2 variables , regression equation is used to describe the relation .
Hence regression equation is the result.
The actual question is like:
Given a collection of paired sample data, the ____________________ y with caret=b0+b1x algebraically describes the relationship between the two variables, x and y.
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Given that D( x ) = 2 x , select all of the following that are true statements.
D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3
The true statements are:
D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).D(x) is a direct variation.x is the dependent variable.D(x) is a function.How to determine the true statements?The function is given as D(x) = 2x
The function D(x) is a linear function, and it is also a proportional function
Proportional functions represent direct variation
This means that (b) and (e) are true
Also set x = 5, 6 and -2
D(5) = 2 x 5 = 10
D(6) = 2 x 6 = 12
D(-2) = 2 x -2 = -4
This means that (a) is true
Lastly, the function D(x) is dependent on x for its value
This means that x is the dependent variable.
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How many of an acute triangle's angles are less than 90 degrees?.
In an acute triangle, all the three angles are less than 90°.
How do triangles work?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to a total of 180 degrees.The definition of an acute triangle?
When all three of the triangle's internal angles are acute, the triangle is said to be acute. Triangles with sharp angles are also known as acute triangles. Acute triangles can have different side lengths, but their interior angles can never exceed 90 degrees.Learn more about acute triangle
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Factor completly
(x-5)^2-16
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" 4y sec(2z). a. Find the most general solution to the associated homogeneous differential equation. Use c and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2 b. Find a particular solution to the nonhomogeneous differential equation y" +4y sec(2). c. Find the most general solution to the original nonhomogeneous differential equation. Use ci and c2 in your answer to denote arbitrary constants.
The general solution of equation y''+4y=sec(2z) is
y = c₁cos2z + c₂sin2z + [tex]\frac{cos2z}{4}[/tex] ln(cos2z) + [tex]\frac{z sin2z}{2}[/tex].
Given differential equation is,
y'' + 4y = sec(2z)
Characteristic equation of this equation is
(D²+4)=0
⇒ D² = -4
D = ±2i
Therefore the roots are imaginary.
D₁=2i ⇒ y₁ = e⁰cos2z = cos2z
D₂=-2I⇒ y₂ = e⁰sin2z = sin2z
yn= c₁cos2z + c₂sin2z
Noe to solve yp, first we need to solve Wronskian
y₁= cos2z , y₂=sin2z
y₁'= -2sin2z , y₂'=2cos2z
⇒ W = [tex]\left[\begin{array}{ccc}y1&y2\\y1'&y2'\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}cos2z&sin2z\\-2sin2z&2cos2z\\\end{array}\right][/tex]
= (cos2z)(2cos2z)-(-2sin2z)(sin2z)
= 2cos²2z + 2sin²2z
=2 (cos²2z + sin²2z)
= 2 ≠ 0
yp = - y₁[tex]\int\ {\frac{y2 g(z)}{W} } \, dz[/tex] + y₂[tex]\int\ {\frac{y1 g(z)}{W} } \, dz[/tex]
= -(cos2z)[tex]\int\ {\frac{(sin2z)(sec2z)}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{(cos2z)(sec2z)}{2} } \, dz[/tex]
= - (cos2z)[tex]\int\ {\frac{sin2z/cos2z}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{cos2z/cos2z}{2} } \, dz[/tex]
= - [tex]\frac{cos2z}{2}[/tex][tex]\int\ {tan2z} \, dz[/tex] + [tex]\frac{sin2z}{2}[/tex][tex]\int\ \,dz[/tex]
= - [tex]\frac{cos2z}{2}[/tex](-[tex]\frac{1}{2}[/tex] ln (cos2z)) + [tex]\frac{sin2z}{2}[/tex] (z)
= [tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]
Now the general equation will become
y = yn + yp
y = c₁cos2z + c₂sin2z +[tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex] .
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount of money that Erica owes at the end of 6 years is $8,551.56.
What is the amount owed?The amount of money that has in his account would increase at a compound rate each month. Compound growth is when both the amount that was invested and the interest that has already been earned increases at each compounding time.
The formula that can be used to determine the future value with monthly compounding is:
A = P(1 + r/n)^nt
Where:
P = amount invested r = yearly interest rate = 8% / 12 = 0.67%n = number of compounding in a year t = number of yearsA = $5300 x (1 + 0.0067)^(6 x 12)
A = $5300 x 1.0067^72 = $8,551.56
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Approximately what percentage of the almost 1,500 highway deaths in pennsylvania each year are attributed to aggressive driving?.
5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.
What is aggressive driving?Aggressive driving is defined as any behind-the-wheel exertion that, without regard for safety, puts another person( or people) and/ or property in peril.
Aggressive driving can vary from potentially dangerous conduct to serious assault.
From the data attained the percentage of the nearly 1500 highway deaths in Pennsylvania each year attributed to aggressive driving will be 50%
5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.
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a 20,000 m3 waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river. the inflow to the pond has a flow rate of q
Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L
What is unitary method?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.Consider your square as being composed of smaller unit squares.The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.According to our question-
Qin = 4 000m3/day
Cin = 25mg/L
V = 20 000m3
k = 0.25/day
Find: Count = ?
outStarting from the mass balance equation for steady state 0 = QCin - QCount - kCountV
manipulate the equation to get:
\(Count=Cin(Q/Q+kV)\)
Then simple plug in your givens:
Count = (25mg/L)((4000m3/day)/(4000m3/day + 0.25/day(20000m3))
Count = 11mg/L
Hence, Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L.
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The cot of 2 kg muhroom and 2. 5 kg of turnip i £8. 55. The cot of 3 kg of muhroom and 4 kg of turnip i £13. 10. Work out the cot of a) 1 kg of turnip. B) 1 kg of muhroom
One kilogram of mushrooms costs $2.90, whereas one kilogram of turnips costs $1.10.
An expression that describes the relationship between two or more numbers and variables is called an equation.
Dependent and independent variables are the two different categories. A dependent variable depends on another variable, whereas an independent variable does not depend on other variables.
Let x stand in for the price per kilogram of mushrooms, and y for the price per kilogram of turnips.
2 kg of mushrooms and 2.5 kg of turnips are priced at £8.55.
2x + 2.5y = 8.55 ________(1)
3 kg of mushrooms and 4 kg of turnips are priced at £13.10.
3x + 4y = 13.10 ________(2)
From both equations:
x = 2.9, y = 1.1
A kg of mushrooms costs $2.90, whereas a kg of turnips costs $1.10.
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Computing a one-sample t test is appropriate when
-Participants are assigned to only one group
-The population variance is unknown
-Participants are observed one time
-All of the above
Computing a one-sample t-test is appropriate when d) all of the above
A statistical hypothesis test called the one-sample t-test is used to examine whether an unknown population mean differs from a given value. The test is applicable to continuous data. When doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.
When performing a one-sample t-test, the data should be collected at random from a population that is generally healthy. When each participant is put into a single group and is present on time, it is suitable. Additionally, it is suitable when the population variance is unknown.
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What is the role of auditor in accounting?.
the role of auditor is in management skill.
What is accounting?
Accounting, conjointly referred to as business, is that the activity, processing, and communication monetary|of monetary|of economic} and non financial data concerning economic entities like businesses and companies.
Main body:
The role of the auditor or reviewer is to relinquish knowledgeable and freelance on these monetary statements. The review or audit of associate association’s monetary report will guarantee larger responsible to the members and supply associate assurance that every one funds received by the organisation are properly accounted for.
therefore the role of auditor is in management skill.
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sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 if he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
The service life that appear to be out of control is 0.0456 as per the given sample service life.
What is meant by sample standard deviation?The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.
The sample standard deviation (s) is the square root of the sample variance and a measure of the deviation from expected values.
It is given that,
Rationale:
UCL=520
LCL=480
Mean [tex]\bar{x}[/tex]=500
The standard deviation of sample([tex]S_{n}[/tex])=11.55
Z(for UCL)=(UCL-Mean)/[tex]S_{n}[/tex]
=(520-500)/10
=2
Similarly, Z(for LCL)=(LCL-Mean)/[tex]S_{n}[/tex]
==(480=500)/10
=-2
Now, by using the z table for finding the confidence level between the Z value of -2 and 2.
Therefore, confidence level=0.4772+0.4772
=0.9544
Risk(alpha)=1-confidence level
=1-0.9544
=0.0456
The service life that appear to be out of control is 0.0456 as per the given sample service life.
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the monthly utility bills in a city are normally distributed with a mean of $70 and a standard deviation of $8. find the monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75. do not round and do not include the $ sign.
The monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75 is 64
Z-score gives you an idea of how far from the mean a data point is.
it’s a measure of how many standard deviations below or above the population mean a raw score is. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).
The basic z score formula for a sample is:
z = (x – μ) / σ
According of the question,
Monthly utility bills in a city follows normal distribution
Mean of the monthly utility bills in a city : μ = $70
A standard deviation of monthly utility bills in a city : σ = $8
Z-score of utility bill = -0.75
z - score = x - μ / σ
=> - 0.75 = x - 70 / 8
=> -6 = x - 70
=> x = 70 - 6
=> x = 64
Hence , the x-value is 64
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).
If W(t) denotes the sumo wrestler's weight then the Function's formula will be w(t) = 5.5t + 79.5
Function formula: This relationship is often represented as y = f(x), or "f of x," and y and x are related in such a way that there is a unique value of y for every x; consequently, f(x) cannot have multiple values for the same x.
if we take y = mx + b,
the slope, m = 5.5, we need to find b,
at x = 11 and y = 14
14 = (5.5) (11) + b
b = 79.5
We plug in the qualities for x, y, and m. Then, we rearrange and deduct 60.5 from the two sides.
This makes the equation,
y = 5.5x + 79.5
or we can write as
w(t) = 5.5t + 79.5
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(complete question)
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).
Write the function's formula.
W(t)=?
Which western trail stretched 1,300 miles from illinois to utah territory? the mormon trail the santa fe trail the california trail the oregon trail
The Oregon Trail is a western route that runs 1,000 miles from Illinois to Utah Territory.
In American history, the Oregon Trail, also known as the Oregon-California Trail, was an overland route that connected Independence, Missouri, with Oregon City, which is located close to Portland, Oregon, today, in the Willamette River valley. In the nineteenth century, it was one of two major emigration routes to the American West, the other being the southerly Santa Fe Trail from Independence to Santa Fe (now in New Mexico). A spur of the northerly Oregon route, which was a component of the Oregon Trail, headed to the Great Salt Lake region of what is now northern Utah. Additionally, branches from each main trail provided links to places in California.
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Answer:
I can "Confirm" The answer is not Oregon Trail, I believe the answer is "The Mormon Trail "
Step-by-step explanation:
Or "A"
Have a Joyous Day
Present age of nick is 8 years and Jonas age is 14 years. What fraction of Jonas age represent the age of nick after 6 years? (Complete solution with data)
The fraction of Jonas age represent the age of nick after 6 years is 7/10.
Given that, present age of nick is 8 years and Jonas age is 14 years.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
After 6 years
Nick's age =14 years and Joan's age =20 years
So, the fraction =14/20
= 7/10
Therefore, the fraction of Jonas age represent the age of nick after 6 years is 7/10.
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What’s the answer?? Please HELPP!!!
David is trying to solve the following. If 24 people have the flu out of 360 people, how many would have the flu out of 900? choose every proportion that david could use to solve this problem.
After choosing every proportion, if 24 people have the flu out of 360 people, then 60 people would have the flu out of 900.
We know very well that if any relation of one quantity is given with the second quantity at any instant of time and same relation question is asking at another instant of time, then always use unitary methods.
The unitary method is defined as a technique for solving a problem by first finding the value of a single unit, and then with the help of found value the necessary value can be find by multiplying the single unit value.
Here, In 360 people number of people would have flu=24
∴In 900 people number of people would have flu=(24×900)/360
=21600/360
=60people.
Hence, number of people would have flu is 60.
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you are given the following total market values for an index over a five-year period. assuming the index starts at 1,000, calculate the index value each year.
The index value for 5 years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, Year 5: 1,414.74 as it starts at 1000 index points.
What is percent?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Here,
Market value of the stocks:
Year 1: 2,645 million
Year 2: 2,957 million
Year 3: 3,318 million
Year 4: 3,193 million
Year 5: 3,742 million
Value of Index in 5 years:
Year 1: 1,000
Year 2: 1,117.96
Year 3: 1,254.44
Year 4: 1,207.18
Year 5: 1,414.74
Calculations:
Year 1: 2,645 million / 2,645 million × 1,000 = 1,000.00
Year 2: 2,957 million / 2,645 million × 1,000 = 1,117.96
Year 3: 3,318 million / 2,645 million × 1,000 = 1,254.44
Year 4: 3,193 million / 2,645 million × 1,000 = 1,207.18
Year 2: 3,742 million / 2,645 million × 1,000 = 1,414.74
Since the index starts at 1,000 points, the values for the subsequent years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, and Year 5: 1,414.74.
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at 95% confidence, how large a sample should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion? assume that past data are not available for developing a planning value for
For a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.
It is given to us that -
There is 95% confidence
The margin of error is 0.04
We have to do the estimation of the population proportion.
We know that in case of unknown population proportion, we can assume that the value of population proportion can be regarded as 0.5.
It is known that the formula of sample size is given by -
[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }[/tex] ----- (1)
where,
n = sample size
Z = critical value of Z-value
p = population proportion
E = margin of error
Also, we know that for a 95% confidence interval, Z = 1.960
From the given information, we have
p = 0.5
and E = 0.04
Substituting the values in equation (1), we have
[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }\\= > n = \frac{(1.960)^{2}*0.5(1-0.5) }{(0.04)^{2} }\\= > n = \frac{3.8416*0.25}{0.0016}\\ = > n = 600.25[/tex]
Since this is the value of minimum sample size, rounding up, we have the sample size as 601.
Therefore, for a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.
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Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Round your answer to four decimal places.)
1/3x^3+1/2x^2+8=0 x1=-3
what is x3= ?
(PLEASE SHOW YOUR WORK)
The third approximation is x3 = 19.6
The Newton's method allow to approximate the root of a function as:
Newton's method, commonly referred to as the Newton-Raphson method after Isaac Newton and Joseph Raphson, is a root-finding algorithm that generates progressively improved approximations to the roots (or zeroes) of a real-valued function. The most fundamental form begins with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial point x0 for the root of f.
xₙ = xₙ₊₁ + f(xₙ)/f'(xₙ)
For this function, it is:
f(x) = 1/3x³+1/2x²+8
f'(x) = 2/3x²+x
For x1=-3,
f(x1) = 1/3x³+1/2x²+8 = -9 + 4.5 + 8 =3.5
f'(x1) = 2/3x²+x = 3
x2 = x1 + f(x1)/f'(x1) = -1.8
Therefore, x2 = -1.8
Then, the third approximation is x_3 is
x3 = x2 + f(x2)/f'(x2) = -1.8+ (7.72/0.36)
x3 = 19.6
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a bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles. you randomly select one marble from the bag. what is the probability that you select a gold marble? write your answer as a reduced fraction. p (gold marble)
After solving, the probability that we select a gold marble is 2/31.
In the given question,
A bag contains 2 gold marbles, 8 silver marbles, and 21 black marbles.
So, Total marbles = 2+8+21
Total marbles = 31
As we know that, probability refers to the likelihood that an event will occur. If we don't know how such an event will end out, we can analyze the probability or likelihood of various outcomes. Statistic is the analysis of events that follow a probability distribution.
We have to randomly select one marble from the bag then we have to find the probability that we select a gold marble is
P(G) = Total number of gold marble/Total marbles
P(G) = 2/31
Hence, the probability that we select a gold marble is 2/31.
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area of a rectangle, measured in cm^2, is numberically equal to 4 times its perimeter, measured in cm. ratio of the rectangle's length to its width is 5:2
A rectangle's area of 28cm2 (measured in cm2) is numerically equal to 4 times the rectangle's circumference (measured in cm). The rectangle's length to width ratio is 5:2.
Given,
l/b = 5/2
l = 5b/2
area = 4 times the rectangle's perimeter,
which equals 4*2(l+b)
= 8(l+b)
= 8(5b/2 + b)
= 28b cm2.
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