The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.
Polynomial equation: what is it?Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.
Our equation is [tex]x^{3} - 8[/tex]
and we know that: [tex]x^{3} = 8[/tex]
then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]
And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]
where a = x and b = 2, then our equation is:
them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.
[tex]x^{2} + 2x +2^{2}[/tex] = 0
Here we need to use.
a[tex]x^{2}[/tex] + bx + c = 0 if for a, b and c constants, then:
x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]
in our problem we have:
x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2
x = -1 +-[tex]\sqrt{-3}[/tex]
x = -1 +-[tex]\sqrt{3}[/tex] i
So here we have two complex solutions: -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
So the value of x are 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
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I think you mean
What are the real and complex solutions of the polynomial equation? (1 point)
[tex]x^{3} - 8[/tex] = 0
( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)
The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
Answer:
(a) The value 550 represents the initial balance in the account, which means the account started with $550.
Step-by-step explanation:
You want the meaning of 550 in the simple interest expression 687.5 = 550(1 + 0.05t).
Simple interestThe formula for computing the amount A of an account earning simple interest at annual rate r on its initial balance P for t years is ...
A = P(1 +rt)
Comparing this formula to the given equation, we see ...
687.5 = 550(1 +0.05t)
A = 687.5P = 550 . . . . the initial balancer = 0.05The initial balance (starting amount) was 550.
Hello please solve this with steps
Identify the number of solutions Or zeros of
F(x)=12x-32x^2+40-x^3
Answer:
3 solutions
Step-by-step explanation:
You want to know the number of solutions (zeros) of the cubic function ...
f(x) = -x³ -32x² +12x +40
Cubic functionAny 3rd-degree polynomial function has 3 zeros. (This is the fundamental theorem of algebra.)
Signs of rootsDescartes' rule of signs says the one sign change in the coefficients (--++) means there is one positive real root. On its face, this means there will be 0 or 2 negative real roots.
Values of rootsThe value of f(0) is positive (40), and the value of f(-1) is negative (-3), so there must be two negative real roots. (F(x) is positive for very large negative x, so there must be two x-intercepts for x < 0.)
A graph shows the roots to be irrational. The three real roots are approximately ...
−32.3328769399−0.9582093098981.29108624985__
Additional comment
The "steps" are to find the degree of the polynomial. It is 3, so there are 3 zeros. It is not complicated.
What is more complicated is finding their values. The checks we described above can tell whether there are 1 or 3 real roots. (An odd-degree polynomial always has at least 1 real root.) A graph is helpful for finding whether the roots are real or complex, rational or irrational.
Here, any rational roots must be integer divisors of the constant term, 40. We know the root between 0 and -1 is irrational, so all of them are.
The above root values were obtained by Newton's Method iteration, starting from the approximate values shown on the graph.
find the distance from point (-3,7) to the line y=1/3x-2. round your answer to the nearest 10th if necessary
The distance between the point (-3,7) and the line y=1/3x-2 is 11.0 units
How to determine the distance?Distance shows how long it is between a point and another
We can do this by drawing a segment that is perpendicular to the line
the given equation is 1/3x-2
The slope here is 1/3 That is slope =3
From the equation of slope=intercept form = y=mx+c
put m=3 to have
y=3x+c
From the given coordinates (-3,7)
7=3(-3)+c
7+9=c
c=16
This implies that y=3x+16
Find the line where the equation intersect the line
⇒3x+16=1/3x-2
Rearrange the equation
8x/3=-18
Make x the subject. x=6.75
Recall that y=1/3(6.75)-2
y=2.25
The second coordinates are (6.75,2.25) and first (-3,7)
The distance is given by
d=[tex]\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }[/tex]
d= √(6.75+3)²+(2.25-7)²
d=√9.75²+(-4.75)²
d=√95.0625+22.5625
d=√117.625
d=10.8455059817
Therefore the distance is 11 units
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There are about 34 million gallon of water in Reervoir A and about 38 million gallon in Reervoir B. During a drought, Reervoir A loe about 0. 8 million gallon per month and Reervoir B loe about 1. 1 million gallon per month. After how many month will the reervoir contain the ame amount of water?
The water levels in reservoirs A and B, which initially had 34 million gallon and 38 million gallon water, respectively, will be equal after 13.3 months.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. No, a mathematical equation cannot be solved since it lacks the "equal to" sign $(=)$, but it can be simplified. Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Here,
Let the number of months be x.
34-0.8x=38-1.1x
1.1x-0.8x=38-34
0.3x=4
x=40/3
x=13.33 months
After 13.3 months, The reservoir A and reservoir B will have same amount of water when initially they have 34 million gallon water and 38 million gallon water respectively.
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What is the percent of increase from 25 to 49?
In right the hypotenuse, 117 cm and tan P= 0.51 Calculate
side lengths p and q to the nearest centimetre and all three interior angles to
the nearest degree.
For the given right triangle the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
Given that,
In a right triangle tan(P) = 0.051
And, hypotenuse = 117 cm.
The given data can be shown in the diagram as follows,
From the diagram it can be written as,
tan(P) = 0.051
=> P = 2.9°
Then, ∠Q = 180° - (90° + 2.9°)
= 87.1°
Now, Sin(P) = p/117
=> Sin(2.9°) = p/117
=> p = 117 × Sin(2.9°)
= 5.9
Similarly, Cos(P) = q/117
=> Cos(2.9°) = q/117
=> q = 117 × Cos(2.9°)
= 116.85
Hence, the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.
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Which equation represents this statement?
3 times the sum of 4 and a number is 18.
3 + 4n = 18
3⋅4+n=18
3n + 4 = 18
3(n+4)=18
Answer:
3(n+4)=18
Step-by-step explanation:
Answer:3(n+4)=18
Step-by-step explanation:
The sum of 4 and a number is 4+n
Three times the sum of 4 and a number is 3(4+n)
is means equal sign
3(n+4)=18
Quick loans will loan you $250 with the understanding that you will repay them $295 in two weeks. What is the APR for this loan?
The APR for this loan is equal to 468%.
What is APR?In Mathematics, APR is an abbreviation for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.
Mathematically, the annual percentage rate (APR) of a loan can be calculated by using this formula:
APR = [((simple interest/principal)/n) × 365] × 100
Where:
n represents the number of days.
Note: n is equal to 14 days (2 weeks).
Next, we would determine the FC for this loan as follows;
FC = $295 - $250
FC = $45.
For the two-week period, we have;
Interest = 45/250
Interest = 0.18.
Therefore, the annual percentage rate (APR) of this loan is given by;
APR = 0.18 × 52/2
APR = 468%.
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Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute how many gallons would be in the tub after 3 minutes?
If Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute, 3.375 gallons would be in the tub after 3 minutes.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute.
We have to find gallons that would be in the tub after 3 minutes
We can utilize multiplication for the given task,
2/3 minutes = 3/4 gallons
1 minute = 3/4 × 3/2
1 minute =1.125
3 minutes = 3 × 1.125
3 minutes =3.375 gallons
Thus, if Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute, 3.375 gallons would be in the tub after 3 minutes.
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Amy ued her firt 2 token at gimmer arcade to play a game of roll and core then he played her favorite game balloon bouncer over and over until he ran out of token balloon bouncer cot 3 toke per game and amyl tart with a bucket of 35 token game token. Which equation can Amy ue to find how many game of balloon bouncer, g, he player?
The Number of Ballon bouncer games played is 11.
What is number ?
A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words can be used to represent numbers in language.
The expression for the number of ballon bouncer games played at the arcade is : 2 + 3b = 35
Let :
Glimmer arcade, g = $2 per game
Ballon bouncer, b = $3 per game
Total game tokens = 35
Her spending could be represented using the expression :
2 + 3b = 35 ; b = number of ballon bouncer games played
2 + 3b = 35
3b = 35 - 2
3b = 33
b = 33/3
b = 11
Therefore, the Number of Ballon bouncer games played is 11.
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The area A if rectangle is represented by the formula A = lw where l is the length and w is width. The length of the rectangle is 5. What is the equation to that?
Answer:
black and white striped bass
A fraction and a whole number with a product greater than 1
Answer: 1/2 * 6 = 3
Step-by-step explanation:
A rectangle is shown on the coordinate plane below
Select all of the transformations that carry the rectangle back onto itself.
a reflection across the line x=32
a reflection across the line y=23x
a clockwise rotation of 360 degrees about the origin
a reflection across the x-axis followed by a reflection across the y-axis
a clockwise rotation of 180 degrees about the point (6,−2), followed by
a translation of 9 units in a negative x-direction
Answer:
Step-by-step explanation:
Looks like the clockwise rotation of 180 degrees about the point (6,−2), followed by a translation of 9 units in a negative x-direction. That is because once it's rotated it will be at x=15 and then if you subtract -9x you will land exactly where you started
f(x) = -x²
Find f(-10)
plug in -10 for x in -x^2
-1(-10)^2 =
10^2 = 100
Plot the graph of y = 3x -
to x = 3
-2
-1
y-8
-6-
-4
2-
0
--2-
-4
--6-
-8
Submit Answer
1
2 from x = -1
2
3
X
4
Plot only the portion between x of -2 to 3. See the attached graph.
function rule to find f(3)
Answer:
f(3)=25
Step-by-step explanation:
f(3)=11(3)-8
f(3)=33-8
f(3)=25
Answer:
f(3)=25
Step-by-step explanation:
substitute 3 into the equation for x.
f(3)=11(3)-8
11×3=33 so,
33-8=25
f(3)=25
−3.5(8.5+5.5y)=−15.5
Answer: y= -14.25/19.25
Step-by-step explanation:
−3.5(8.5+5.5y)=−15.5 can be write as
-29.75 - 19.25y= -15.5
-19.25y = 14.25
y= -14.25/19.25
ALL questions are for this situation:
You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
1. How many seconds does it take to reach the highest point (vertex)?
It takes 1 second for the ball to reach its highest point.
What is acceleration of gravity?Acceleration of gravity is the acceleration by which earth pulls
objects towards itself. Acceleration is the rate of change of speed.
Given,
The initial velocity of the ball = 16 feet/second
The initial height of the ball = 10 feet
The ball will first travel upward with an initial velocity of 16 feet/second
and the ball will reach a height of x feet from the point of release. After
that the ball will travel a total downward distance of (10+16) = 26 feet.
At highest point, velocity=0.
Applying, v = u + at
0 = 16 + (-16)t
t = 16/16
t = 1 second
Hence, the ball will take 1 second to reach the highest point.
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Cookies baked 375 degrees for 12 minutes. Find the gas unit, g, used if t = time in minutes:
375 - 15t
g = t
To find the gas unit used in baking of cookies, we plug the values into the given equation: g = t, g = 12. Thus, the gas unit used is 12.
What is gas unit?Organic gas usage or production is measured in "gas units." It is frequently employed to estimate the price of natural gas for a predetermined time period, such as a month or a year.
British thermal units (BTUs), a measure of the energy content of natural gas, are the industry standard for quantifying this fuel. One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree Fahrenheit.
To compute the gas unit for a given time period, the total amount of natural gas used or generated is first converted into BTUs.
How to solve?
To find the gas unit used, we plug the values into the given equation:
g = t, g = 12. Thus, the gas unit used is 12.
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PLEASEE HELP
At a local college, only 60% of students live off campus. Of those who live off campus, 58% of those students get a part-time job. Of those who live on campus, 67% work part-time. The tree diagram shows how the college students are divided into subgroups.
The tree diagram shows college students branching off into two categories, off campus and on campus students. Off campus students branches off into two sub-categories, work part-time and do not work. On campus branches off into two subcategories, work part-time and do not work.
What is the percentage of students who live off campus and do not have a part-time job?
42.6%
34.8%
25.2%
24.3%
The percentage of students who live off campus and do not have a part-time job will be 25.2%. Then the correct option is C.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
At a neighborhood school, just 60% of understudies live off the grounds. Of the people who live off-grounds, 58% of those understudies find a part-time line of work. Of the people who live nearby, 67% work part-time. The tree chart shows how the undergrads are separated into subgroups.
The number of students who live off campus and do not have a part-time job is given as,
⇒ 0.60 x (1 - 0.58) x 100
⇒ 0.252 x 100
⇒ 25.2%
The percentage of students who live off campus and do not have a part-time job will be 25.2%. Then the correct option is C.
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To make a cake, Roe needed 2 cup of ugar. Thi i 3 cup le than the amount of flour, f , he needed for the cake. Write a ubtraction equation that could be ued to find the amount of flour he needed for the cake
He might use the equation y = (3/2) x to determine how much flour he required for the cake.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
Accordingly, we require 2.3 cups of sugar for every cup of flour.
It also means that you need 3 1/2 cups of flour for every cup of sugar.
Therefore, if x cups of sugar and y cups of flour, respectively, are used:
y = (3/2) x.
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miguel has 30,000 in his savings account. sam has 40,000 in hissavings account. whatis the ratio of miguel savings to sam saving? what is the ratio of sam savings to miguel savings? what fraction of miguel savings is sam savings? what fraction of sam savings to miguel saving?
Match each system of equations with the number of solutions the system has.
A. y = - (4/3)x + 4.
y = - (4/3)x - 1.
No solution.
B. y = 4x - 5.
y = - 2x + 7.
one solution.
C. 2x + 3y = 8
4x + 6y = 17.
No solution.
D. y = 5x - 15.
y = 5(x - 3).
Infinitely many solutions.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.
y = - (4/3)x + 4.
y = - (4/3)x - 1.
These are parallel lines no solution.
y = 4x - 5.
y = - 2x + 7.
These lines intersect at (2, 3) one solution.
2x + 3y = 8
4x + 6y = 17.
They are parallel to each other.
y = 5x - 15.
y = 5(x - 3).
These are coinciding lines if we distribute the terms hence infinitely many solutions.
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The buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. How many dollars should be bought and sold to have the profit of $ 10? Find it.
The number of dollars that should be bought and sold to have the profit of $10 is 8.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. Let the dollars bought be illustrated as x.
This will be:
116.5x - 115.25x = 10
1.25x = 10
Divide
x = 10 / 1.25
x = 8
The number is 8.
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is 7x a linear expression
Answer: Yes, it is linear expression
Step-by-step explanation:
The equation is y=mx + b
Here we have 7x, which we have the slope
We don't see the y-intercept, so it is 0
Three numbers are in automatic sequence and there sum is 15 if 1,3,9 be added to them respectively they forms geometric sequence find the three numbers.
Answer:
There is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.
Step-by-step explanation:
To find the three numbers in the arithmetic sequence, let's call the first number in the sequence "a," the second number "a + d," and the third number "a + 2d," where "d" is the common difference between the numbers. The sum of these three numbers is:
a + (a + d) + (a + 2d) = 15
This simplifies to:
3a + 3d = 15
To find the three numbers in the geometric sequence, let's call the first number in the sequence "b," the second number "r * b," and the third number "r^2 * b," where "r" is the common ratio between the numbers. The sum of these three numbers is:
b + (r * b) + (r^2 * b) = 15 + b + (r * b) + (r^2 * b)
This simplifies to:
b(1 + r + r^2) = 15 + b + br + br^2
We are told that if 1, 3, and 9 are added to the three numbers in the arithmetic sequence, we get the three numbers in the geometric sequence. Therefore, we can set up the following system of equations:
3a + 3d = 15
b(1 + r + r^2) = 15 + b + br + br^2
Subtracting b from both sides of the second equation gives:
b(1 + r + r^2) - b = 15 + br + br^2
This simplifies to:
b(r^2 + r - 1) = 15 + br + br^2
Subtracting br and br^2 from both sides gives:
b(r^2 + r - 1) - br - br^2 = 15
This simplifies to:
b(r^2 + r - 1 - r - r^2) = 15
This simplifies to:
b(r - 1)(r + 1) = 15
Dividing both sides by (r - 1)(r + 1) gives:
b = 15 / (r - 1)(r + 1)
We are told that the three numbers in the arithmetic sequence add up to 15, so we can substitute 3a + 3d = 15 into the equation above to solve for "b":
3a + 3d = 15
b = 15 / (r - 1)(r + 1)
Substituting 3a + 3d = 15 into the equation above gives:
b = 15 / (r - 1)(r + 1)
Substituting b = 15 / (r - 1)(r + 1) into the second equation gives:
15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15 / (r - 1)(r + 1) + 15 / (r - 1)(r + 1)*r + 15 / (r - 1)(r + 1)*r^2
This simplifies to:
15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15r + 15r^2
Multiplying both sides by (r - 1)(r + 1) gives:
15 = 15 + 15r + 15r^2
Subtracting 15 from both sides gives:
0 = 15r + 15r^2
Subtracting 15r^2 from both sides gives:
0 - 15r^2 = 15r
This simplifies to:
-15r^2 = 15r
Dividing both sides by -15 gives:
r^2 = r
Solving for "r" gives:
r = 1 or r = 0
If "r" is equal to 1, then the common ratio between the numbers in the geometric sequence is 1, which means that the three numbers in the geometric sequence are the same. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution.
If "r" is equal to 0, then the common ratio between the numbers in the geometric sequence is 0, which means that the three numbers in the geometric sequence are all 0. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution as well.
Therefore, there is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.
What is the greatest common factor of the terms in the polynomial 12x4 + 27x3 + 6x2?3x3x26x26x4.
The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.
What is polynomial?Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial=12x⁴+27x³+6x²
On simplifying,
=3x²(4x²+9x+2)
With a degree of 2 and a coefficient larger than 1, 3x² has the highest common factor of the three components.
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A certain statistic dˆ is being used to estimate a population parameter d. The expected value of dˆ is not equal to d. What property does dˆ exhibit?.
The correct option for the given problem is the statistic is biased which is (e) option.
What is Central Limit Theorem?The central limit theorem states that in the event that you have a populace with mean μ and standard deviation σ and take adequately enormous irregular examples from the populace with substitution , then, at that point, the conveyance of the example means will be roughly regularly circulated.
According to question:By using above central limit theorem establishes that for a proportion p in a sample of size n.
The expected value is μ = p
The standard error is s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Now, in this problem the expected d value is different from the expected of μ = p.
Thus, the statistic is biased, and the correct option is E.
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Correct question:
A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?
A. The sampling distribution of d hat is normal.
B. The sampling distribution of d hat is binomial.
C. The sampling distribution of d hat is uniform.
D. d hat is unbiased.
E. d hat is biased.
Maya wants to put fencing around her
rectangular backyard. The width of the yard
is 55 feet and the length is 75 feet. How
many feet of fencing does Maya need?
3) 260
7) 130
6) 3,905
9) 4,125
Answer:
3) 260 ft
Step-by-step explanation:
You want the perimeter of a rectangle 55 ft by 75 ft.
PerimeterThe equation for the perimeter of a rectangle is ...
P = 2(L +W)
ApplicationFor the given rectangle, the perimeter is ...
P = 2(75 ft +55 ft) = 2(130 ft) = 260 ft
Maya needs 260 feet of fencing to put fence around her rectangular yard.
identities included in Venn diagram
Answer:
Step-by-step explanation:
Aub, probability, set theory and discrete math?