A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts.
Is it possible for a parabola to have more than one x-intercept?Image search results for The x-intercepts of two parabolas are the same (one positive and one negative). The maximum or minimum of the first is twice the maximum or minimum of the other. Draw these parabolas using the same coordinate grid (with at least 3 points) “-15” “-10” “-10” “-15” 10
The x-intercepts are the spots where the parabola contacts the x-axis. A parabola can have two, one, or no real x intercepts. A parabola might have two x-intercepts, one x-intercept, or none at all.
X-intercepts, or zeros, are the places where a parabola (or any curve) crosses/touches the x-axis. As we’ll see later, the amount that determined
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help me please I really don't get this and I have sooo many questions about this stuff >_
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{7}{8})^4}[/tex]
[tex]\mathsf{= \dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}}[/tex]
[tex]\mathsf{= \dfrac{7\times7\times7\times7}{8\times8\times8\times8}}[/tex]
[tex]\mathsf{= \dfrac{49\times49}{64\times64}}[/tex]
[tex]\mathsf{= \dfrac{2,401}{4,096}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{2,401}{4,096}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The number of households in the U.S. that own homes is 79.4 million, or 63.5% of all households. Find the total number of households to the nearest hundredth of a million.
Answer:
125 million
Step-by-step explanation:
[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]
Which decimal is greatest, .54, .504, or .45?
Answer:
The correct solution is .54
Step-by-step explanation:
Think about this like counting change.
0.54 is the largest amount. Next would be 0.504 (which in change would be close to 0.50 rounded down), lowest amount would be 0.45
Suppose I want to find an inverse to the function |cos x|. I intend to restrict the domain of the function to an interval whose left endpoint is x = 0 On which of the following intervals is |cos x| one-to one? Select one [0, pi/4] [0, pi/2] [0, pi] [0, 2 pi]
In the interval [0, π/2], the function is one-to-one or injective.
The functions which have one-to-one behaviour are called injective functions. An injective function is a function in which every horizontal line in the plane intersects the graph of f at most one point or we can say if f(x) = f(y) then x = y.
First, we need to draw the graph of y = |cos x|. The graph of y = |cos x| is attached.
We can see from the graph that the value of the function is 1 when x = 0 and the value of the function decreases till it takes 0 at x = π/2 and then the value of the function increases again.
In the option [0, π] and [0, 2π] the behaviour of the function is not injective.
In [0, π/4], the function is injective but [0, π/2] is the correct answer as it represents the largest interval starting from 0 on which this function is one-to-one.
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he radius of a circle is tripled. Which of the following describes the effect of this change on the area? The area is multiplied by 1/9 . The area is multiplied by 9. The area is multiplied by 3. The area is multiplied by 1/3.
Tripling the radius of a circle results in a nine-fold increase in its area.
The radius of a circle is a critical component in determining its size. Tripling the radius of a circle means that the size of the circle has increased three times its original size.
The area of a circle can be calculated using the formula
=> A = πr²,
where A represents the area of the circle, π is Pi, and r is the radius. When the radius of a circle is tripled, the value of r becomes 3 times its original value, meaning the formula becomes
=> A = π(3r)² = π * 9r² = 9πr².
Therefore, the new area of the circle is nine times the original area of the circle.
Complete Question:
The radius of a circle is tripled. Which of the following describes the effect of this change on the area?
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During the time interval 4 St ≤ 8, the rate at which the number of wolves in a forest is changing, in wolves per week, can be modeled by the function
E(t) = 31 cos(0.11t?), where t is measured in weeks.
What is the rate at which the number of wolves in the
forest is changing at timet = 7? You may use a
calculator and round to the nearest thousandth. Indicate units of measure.
For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)
Here t is the time measured in weeks.
The time value is given as t = 7
Substitute the value of t in the equation -
E(t) = 31 cos (0.11t)
Apply the arithmetic operation of multiplication -
E(7) = 31 cos (0.11 × 7)
E(7) = 31 cos (0.77)
E(7) = 31 × 0.7179
E(7) = 22.2549
Therefore, the rate value is obtained as 22.2549.
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In 1976, a certain model of car cost $5,000. What would be the cost of that car in 1983 dollars? Express your answer rounded to the nearest cent.
The cost of car in the year 1983 is 2845
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The CPI (consumer price index) is a measure of the overall change in prices of goods and services over a certain period of time. It is given by:
CPI = (cost of market basket in a given year / cost of market basket in base year) * 100
Given that:
CPI = 56.9 in 1976, cost of market basket in a given year = x, cost of market basket in base year = $5000
Hence:
56.9 = (x/ 5000) * 100
x = 2845
The cost of car is 2845
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investigate whether the set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations. drag and drop yes or no into each box to show whether the set of polynomials in one variable is closed under the four basic operations. then complete the statement that explains whether polynomials are like whole numbers, integers, or rational numbers with respect to closure.
The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.
Whole numbers:
Addition: Yes
Subtraction: No (e.g. 5 - 7 = -2)
Multiplication: Yes
Division: No (e.g. 4 ÷ 2/3 is not a whole number)
Integers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (e.g. 4 ÷ 1/2 is not an integer)
Rational numbers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: Yes (provided the denominator is non-zero)
Polynomials:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (in general, polynomials cannot be divided by other polynomials)
Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.
However, they are not closed under division like rational numbers.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
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If f(x) = 2x³ + x² - 3x + 4 , what is f'(2) ?
Answer:
f'(2) = 25
Step-by-step explanation:
differentiate f(x) using the power rule
[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant) = 0
f(x) = 2x³ + x² - 3x + 4
f'(x) = 3× 2x² + 2x - 3 = 6x² + 2x - 3 , then
f'(2) = 6(2)² + 2(2) - 3
= 6(4) + 4 - 3
= 24 + 1
= 25
Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
A= -2,2
B=6,2
C=0,6
Step-by-step explanation:
we need to calculate the distances between the points as the side lengths of the triangle.
these side lengths must satisfy the Pythagoras principle :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.
the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.
this is then caked the distance formula, but it is all Pythagoras again.
AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =
= 8² + 0² = 8²
AB = 8
AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20
AC = sqrt(20)
BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52
BC = sqrt(52)
as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.
if this is a right-angled triangle, then
8² = sqrt(20)² + sqrt(52)²
must be true.
but
64 = 20 + 52 = 72
is wrong.
so, the segments do not form a right-angled triangle.
A B C Total
Male 5 15 20 40
Female 2 14 16 32
Total 7 29 36 72
If one student is chosen at random from those who took the test,
Find the probability that the student was female GIVEN they got a 'B'.
Round answer 4 places after the decimal if needed.
The probability that the student was female GIVEN they got a 'B' is 0.194.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
A B C Total
Male 5 15 20 40
Female 2 14 16 32
Total 7 29 36 72
We have to find the probability that the student was female GIVEN they got a 'B'
P(Female ∩ B) = 14/72 = 0.1944
Hence, the probability that the student was female GIVEN they got a 'B' is 0.194.
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determine if ST is parallel to PR
Answer:
Step-by-step explanation:
Picture?
You didn’t give enough info. Are you able to provide more information? Or a picture?
solve 10 + x ≥ 14. then graph the solution.
Answer:
x ≥ 4
Step-by-step explanation:
Just treat the equation like you would a regular algebraic equation.
10 + x ≥ 14
10 + x - 10 ≥ 14 - 10
x ≥ 4
As for graphing it, I'm not really sure if you want a proper graph or a number line.
For a number line, put a closed dot on a 4
En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor
The Percentage of bags with correct weight will be 84%
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, the following can be gotten:
Total number of bags = 2500
Bags with correct weight = 2100
Bags with lower weight = 275
Bags with higher rate = 125
Percentage of bags with correct weight will be:
= 2100 / 2500 × 100
= 84%
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phil bikes a distance of x miles at a rate of 15 miles per hour. how many hours did the trip take?
Answer:
Below
Step-by-step explanation:
The equation you need to remember is:
rate X time = distance re-arrange to
time = distance / rate sub in the numbers given to get
time = x / 15 hours
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 18 m, and d = 3 m.)
W = __________ J
Answer:
Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.
Step-by-step explanation:
Two cyclists leave towns 255 kilometers apart at the same time and travel toward each other. One cyclist travels 7 kmh slower than the other. If they meet in 5 hours, what is the rate of each cyclist?
Check the picture below.
r = rate of the faster cyclist
r - 7 = rate of the slower cyclist
we know they both met 5 hours later, so the time each one has been cycling has been 5 hours for each.
let's say the faster cyclist on those 5 hours covered "k" kilometers, that means the slower one cover the slack, namely "255 - k" kilometers.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km s}{distance}&\stackrel{km/h}{rate}&\stackrel{hour}{time}\\ \cline{2-4}&\\ \textit{faster cyclist}&k&r&5\\ \textit{slower cyclist}&255-k&r-7&5 \end{array}\hspace{5em} \begin{cases} k=(r)(5)\\\\ 255-k=(r-7)(5) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{k=5r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{255-(5r) = (r-7)(5)} \\\\\\ 255-5r=5r-35\implies 255=10r-35\implies 290=10r \\\\\\ \cfrac{290}{10}=r\implies 29=r\hspace{5em}\stackrel{\textit{faster cyclist}}{\text{\LARGE 29}~\frac{km}{h}}\hspace{5em}\stackrel{\textit{slower cyclist}}{\text{\LARGE 22}~\frac{km}{h}}[/tex]
Scale Factor: 2; Center: (-2, 1)
Answer:
Brhaaliarwoiagsajaidgsiuaaidywlx
Graph the piecewise function. You must graph on your own and not use a web-based program to graph. f(x)={(1/3 x-1 if " x≤0 -1/2 x+6 if 0
The graph for the piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6 is attached in the solution.
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals.
Given is a piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
Plotting the graph for:
f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
From the graph, we conclude that:
The graph of the given piecewise function is a straight line with two segments.
The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6.
The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.
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The doctor orders 1000 mL D5RL to run at 100 ml/hr. How long will this IV infusion run?
This IV infusion will run for ____ hours.
(Round your answer to the nearest whole number.)
Answer: The IV infusion will run for 10 hours.
To find out, you divide the total volume of fluid (1000 mL) by the rate of infusion (100 mL/hr):
1000 mL / 100 mL/hr = 10 hours.
Rounding to the nearest whole number, the IV infusion will run for 10 hours.
Step-by-step explanation:
Answer:
The doctor orders 1000 mL of fluid to run at a rate of 100 mL per hour. To find out how long this IV infusion will run, divide the total volume of fluid by the flow rate:
1000 mL / 100 mL/hr = 10 hours
So, the IV infusion will run for 10 hours.
[100 points] A force of 6 lb is required to hold a spring stretched 2 in. beyond its natural length. How much work W is done in stretching it from its natural length to 4 in. beyond its natural length?
W = ___________ ft-lb
Answer:
its 48 lb·in.
I'll give you an example and plug in the numbers:
Given:
6 lb is needed to stretch 4 inches beyond natural length.
Need work done to stretch same string from natural length to 8 inches.
Solution:
string stiffness, K
= Force / stretched distance
= 6 lb / 4 inches
= 1.5 lb/inch
Work done on a string of stiffness K
= (Kx^2)/2 lb-in
= 1.5 lb/in *(8 in)^2)/2
= 48 lb-in.
May someone please help me on this question? Thank you so much <33
Answer:
3 hours
Step-by-step explanation:
According to the Anxiety and Depression Association of America (ADAA), approximately 8.7% of all adults suffer from a specific phobia, such as high bridges or old elevators. An experiment consists of selecting adults at random and asking them if they suffer from any kind of phobia. Is there any evidence to suggest the ADAA claim is false? Justify your answer. Because the probability that 35 people are selected before the first person with a phobia is chosen is 0.0453, there _____ evidence that the claim about the probability of people having a phobia being 8.7% is false.
The probability of 35 people being selected before the first person with a phobia being chosen does not provide sufficient evidence to suggest that the ADAA claim is false. To determine if the ADAA claim is false, we would need to perform a statistical hypothesis test to compare the sample proportion of adults with phobias to the ADAA estimate of 8.7%. This would involve collecting data on a random sample of adults, calculating the sample proportion of adults with phobias, and comparing it to the ADAA estimate of 8.7%.
If the sample proportion is significantly different from 8.7%, we can conclude that there is evidence to suggest that the ADAA claim is false. However, without performing a statistical hypothesis test, we cannot make a conclusion about the validity of the ADAA claim based solely on the probability of 35 people being selected before the first person with a phobia is chosen.
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Please help me I don't know
the answer be quick
Answer:
5:2 is the answer of that question.
The population of 6 different states is shown below. Order the populations from the source to the target in order of GREATEST to LEAST value.
Florida: 1.98 x 10^7
Arizona: 6,730,000
Washington: 7.06 x 10^6
New York: 19,700,000
California: 3.88 x 10^7
Massachusetts: 6.74 x 10^6
Ordering the populations of the 6 different states, written in scientific notations, in order of the greatest to the least value is as follows:
California: 3.88 x 10^7Florida: 1.98 x 10^7New York: 19,700,000Washington: 7.06 x 10^6Massachusetts: 6.74 x 10^6Arizona: 6,730,000.What is scientific notation?Scientific notation is the standard way of writing very long or short numbers in their shorthand forms.
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10, with the following parts: coefficient, base, and exponent.
For instance, New York's population is 19,700,000 and can be written in scientific notation as 1.97^7.
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The market for cast iron marble urns has the supply and demand functions below.
Supply: p = 15 + 0.1q
Demand: p= √650- 5q
(a) Find the point of equilibrium for this market.
(b) Find the Consumers' surplus for this market.
(c) Find the Producers' surplus for this market.
By applying supply and demand concept, it can be concluded that:
a. Point of equilibrium for this market will be reached when p = 20 and q = 50
b. Consumers' surplus for this market when -150 < q < 50
c. Producers' surplus for this market when 50 < q < 130
Demand is the number of goods purchased or requested in the market at a certain price and time, while supply is the number of goods sold or offered in the market at a certain price and time.
Point of equilibrium will be reached when supply and demand are in balance.
We have the following supply and demand functions:
Supply: p = 15 + 0.1q
Demand: p= √(650- 5q)
A. The point of equilibrium occurs when supply and demand are in balance:
15 + 0.1q = √(650- 5q)
(15 + 0.1q)² = 650 - 5q
225 + 3q + 0.01q² = 650 - 5q
0.01q² + 3q + 5q + 225 - 650 = 0
0.01q² + 8q - 425 = 0
q² + 800q - 42500 = 0
q² + 800q + 160000 - 202500 = 0
(q + 400)² - 202500 = 0
(q + 400)² = 202500
q + 400 = 450
q = 50
As we know q, we can calculate the p:
p = 15 + 0.1q
= 15 + 0.1 * 50
= 20
B. The Consumers' surplus when demand > supply:
√(650- 5q) > 15 + 0.1q ⇔ q < 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Consumers' surplus for this market when -150 < q < 50
C. The Producers' surplus when supply > demand:
15 + 0.1q > √(650- 5q) ⇔ q > 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Producers' surplus for this market when 50 < q < 130
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At an amusement park, the straight water slide is 42m long and drops 20m. What angle does the slide ma with the horizontal?
The angle formed 28.42 degree between the slide and the drop.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
length of water slide is 42m. (Hypotenuse)
and length of drop = 20 m (Perpendicular)
Using Trigonometry
sin [tex]\theta[/tex] = P/ H
sin [tex]\theta[/tex] = 20 / 42
sin [tex]\theta[/tex] = 10 /21
sin [tex]\theta[/tex] = 0.476
[tex]\theta[/tex] = [tex]sin ^{-1[/tex] (0.476)
[tex]\theta[/tex] = 28.42 degree.
Hence, the angle is 28.42 degree.
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Please help me with this question.
The value of the given indefinite integral is[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
What are indefinite integrals?An integral which is not having any upper and lower limit is known as an indefinite integral. Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted, ∫f(x) dx = F(x) + C.
Given is an indefinite integral, [tex]\int \frac{x-6}{\left(x+3\right)^2+36}dx[/tex]
Solving,
Applying u-subsituition,
[tex]=\int \frac{u-9}{u^2+36}du[/tex]
Expanding,
[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex]
Since, [tex]\int \frac{u}{u^2+36}du = \frac{1}{2} ln|u^2+36|[/tex]
And,
[tex]\int \frac{9}{u^2+36}du = \frac{3}{2} tan^-^1(\frac{u}{6} )[/tex]
Therefore,
[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex] [tex]=\frac{1}{2}\ln \left|u^2+36\right|-\frac{3}{2}\arctan \left(\frac{u}{6}\right)[/tex]
Substitute u = x+3
[tex]=\frac{1}{2}\ln \left|\left(x+3\right)^2+36\right|-\frac{3}{2}\arctan \left(\frac{x+3}{6}\right)[/tex]
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)[/tex]
Add constant c,
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
Hence, the value of the given indefinite integral is
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
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a square has an perimeter of 56 ft what is the length of each side?
Answer:
14ft
Step-by-step explanation:
Perimeter of a square = 4s where s = side length
Here, we are given the perimeter, and we want to find the side length. To do so we plug in the perimeter and solve for s
Perimeter = 56
So 56 = 4s
==> divide both sides by 4
14 = s
A square with a perimeter of 56 feet has a side length of 14 feet
Is the following statement true or false? the mean of a random sample equals the mean of the population from which it was drawn.
The claim that the average of a random sample is the same as the average of the population from which it was taken is False.
Is the sample mean the same as the population mean?The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.
Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.
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