Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
As given,
Total members in the committee=14
Number of members serve as chairman and ranking member=2
Total number of ways to assigned new position
=¹⁴P₂
=(14!) / (14-2)!
=(14 × 13 × 12!) / 12!
=14 ×13
=182
Each member is equally likely to serve in any of positions.
Each position there is only one way to reassign position.
Probability of randomly selecting two members = 1 /182
Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
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Solve for x. Enter the solutions from least to greatest.
x²+x-42=0
lesser x =
greater x =
Find the sum of 8.6 x10 ^6and 3.7x 10^5
Answer:
8.97 x 10^6
Step-by-step explanation:
To add in scientific notation, the exponents need to be the same for the bases of 10. You can either make them both to the exponent of 6 or 5. It does not matter. I made them both to the power of 5
(8.6 x10^6 ) + (3.7 x10^5 )
(86 x 10^5) + (3.7x10^5)
(86 x 3.7) x 10^5
89.7 x 10^5 Rewrite in scientific notation
8.97 x 10^6
Precalculus transformation review
The original function and its expression derived from rigid transformations are defined below:
Original: f(x) = |x|; Image: g(x) = |x - 3| + 2Original: f(x) = |x|; Image: g(x) = |x + 4| - 2Original: f(x) = |x|; Image: g(x) = - |x| - 3Original: f(x) = x²; Image: g(x) = (x - 3)² - 2Original: f(x) = √x; Image: g(x) = √(- x) + 5How to use rigid transformations to modify functions
In this problem we must use rigid transformations to change the definition of a series of functions. Rigid transformations are transformations applied on functions such that its form is not altered. There are the following transformations, which are used in the five cases:
Horizontal translation
g(x) = f(x - k), translation is to the right for k > 0.
Vertical translation
g(x) = f(x) + k, translation is upward for k > 0
Reflection over the x-axis
g(x) = - f(x)
Reflection over the y-axis
g(x) = f(- x)
Now we proceed to present the image of each function after using a sequence of rigid transformations:
f(x) = |x|; g(x) = |x - 3| + 2f(x) = |x|; g(x) = |x + 4| - 2f(x) = |x|; g(x) = - |x| - 3f(x) = x²; g(x) = (x - 3)² - 2f(x) = √x; g(x) = √(- x) + 5To learn more on rigid transformations: https://brainly.com/question/1761538
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Qube learning
Summative Test - Formulae N/L1..
REVISION AVAILABLE
V
2019 FS L1 Word Formulae Summative
Ella wants to put a wire fence around her property. What is the length of the fence she would need to buy to cover her property?
Consider the function [tex]p(x)=\frac{cos^{2}x }{sin2x}[/tex]. Which of the following accurately describes the limit as x approaches 0 of the function?
a. as x approaches 0, the limit of p(x) approaches a large negative y-value
b. As x approaches 0, the limit of p(x) does not exist
c. As x approaches 0, the limit of p(x) approaches 0
d. As x approaches 0, the limit of p(x) approaches a large positive y-value
The function, [tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex] has a limit that is undefined (does not exist) as x approaches 0. The correct option therefore option b;
b. As x approaches 0, the limit of p(x) does not exist
What is a function in mathematics?The given function is presented as follows;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex]
Required;
The limit of the function as x approaches (zero) 0
Solution;
The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.
Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.
cos²(0) = 1
sin(2×0) = sin(0) = 0
Therefore;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}0 }{sin(2 \times 0)} = \frac{ 1 }{0} = \infty}[/tex]
Therefore, the limit of the function does not exist as x approaches 0
The correct option is therefore, option b
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HELP
In this unit, you will investigate some real-world scenarios which can be modeled through logarithmic functions. In particular, we'll investigate three phenomena using logarithmic models: magnitude of earthquakes, intensity of sound, and pH (or acidity) of substances. Research online and find an additional scenario not mentioned above that uses logarithmic functions, and explain why it is beneficial to your everyday life. Be sure to cite any sources you used in your response.
One example of real-world situation that uses logarithms is for amount of substance that are decaying over time.
Logarithms and amount of substancesAn amount of a decaying substance after t years is modeled by the following exponential equation:
[tex]P(t) = P(0)e^{-kt}[/tex]
In which:
P(0) is the initial amount.k is the exponential decay rate, as a decimal.The simplest example of the use of logarithms is to find the half-life of the substance, that is, the year t for which P(t) = 0.5P(0).
Then:
[tex]0.5P(0) = P(0)e^{-kt}[/tex]
[tex]e^{-kt} = 0.5[/tex]
The natural logarithm is used to find the half life, as it is the inverse of the exponential.
[tex]\ln{e^{-kt}} = \ln{0.5}[/tex]
[tex]-kt = \ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{k}[/tex]
Hence we showed another application of logarithms in a real-word model.
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Snow plowing plan , In the relationship between the amount of snowfall and the number of trucks proportional explain
Based on the number of trucks needed and the snowfall per inch, the relationship between snowfall and trucks is proportional.
When is a relationship proportional?A relationship is said to be proportional when the two variables increase at a set rate. In other words, proportional relationships will see variables increasing at the same rate.
The rate of snowfall per trucks for 6 inches of snowfall is:
= 15 / 6
= 2.5 trucks per inch of snowfall
The rate of snowfall per trucks for 12 inches of snowfall is:
= 30 / 12
= 2.5 trucks per inch of snowfall
The rate is therefore the same across the table so the relationship between snowfall and the number of trucks is proportional.
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HELP PLEASEEEEE!!!!
( -4)¹⁹ = - 274877906944 is standard form of 4 to power -19.
What are power and exponent?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. There is a claim of power throughout the entire sentence 34.a) ( -8 )⁰ = 1 ( positive )
b) ( -4 )⁶ = - 4× -4 × -4 × -4 × -4 × -4 = 4096 ( Positive )
c) ( -5 )¹² = 244,1406,25 ( positive )
d) ( -4)¹⁹ = - 274877906944 ( Negative)
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Please help me I have had help with the 3 one but I can not reproduce it. Thank you to who helps me.
Note that:
[tex]\int f(x) \text{ } dx=-e^{-x/5}+C[/tex]
Part (b)
[tex]\int^{1}_{0} f(x) \text{ } dx =-e^{-1/5}+e^{0} \approx 0.1813[/tex]
Part (c)
[tex]\int^{\infty}_{0} f(x) \text{ } dx =1.0000[/tex]
Part (e)
[tex]\int^{6}_{1} f(x) \text{ } dx \approx 0.5175[/tex]
The coldest recorded temperature in the United States is
–
80°F, in Alaska. The warmest recorded temperature in the United States is 134°F, in California.
How much higher is the warmest recorded temperature than the coldest recorded temperature?
The warmest recorded temperature than the coldest recorded temperature is 54oF
How to determine the amount of temperature difference?The given parameters are:
Coldest recorded temperature = 80°F, in Alaska
Warmest recorded temperature = 134°F, in California
Next, we calculate the difference between these temperatures
Difference = Warmest recorded temperature - Coldest recorded temperature
Substitute the known values in the above equation
Difference = 134 - 80
Evaluate
Difference = 54
Hence, the amount of temperature difference is 54oF
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A jet travels 1324 miles against a jetstream in 2 hours and 1584 miles with the jetstream in the same amount of time. what is the rate of the jet in still air and what is the rate of the jetstream rate of the jet in still air ___mi/hrate of the jetstream___ mi/h
In still air, the rate of the jet is Distance traveled/ time taken
[tex]\frac{1324}{2}=662\text{ mi/h}[/tex]With the jetstream, the rate of jetstream is
[tex]\frac{1584}{2}=792\text{ mi/h}[/tex]Solve For X the picture of the problem will be provided
Answer:
x = 37
Step-by-step explanation:
∡CAE = 180°
Then:
∡ABC = 180° - (10+8X)
∡ABC = 180 - 10 -8X
∡ABC = 170 -8X
The sum of the internal angles of a triangle results im 180°:
70 + (6x+14) + (170-8x) = 180
70 + 14 + 170 + 6x - 8x = 180
254 - 2x = 180
254 - 180 = 2x
74 = 2x
x = 74/2
x = 37
The squared pictured below has side lengths of 4 units. Questions are in the picture below-
A.
The length of the diagonal is given by the Pythagorean theorem therefore
[tex]d=\sqrt[]{4^2+4^2}=\sqrt[]{16+16}=\sqrt[]{32}[/tex]The length of the diagonal is ) units
B.
The area of the square is given by the next formula
[tex]A=s^2[/tex]where s is the side
s=4
[tex]A=(4)^2=16units^2[/tex]The area of the square is 16 units^2
C.
For the area of the triangle we will use the next formula
[tex]A=\frac{1}{2}b\times h[/tex]where b is the base and h is the height
b=4 units
h=4units
[tex]A=\frac{1}{2}(4)(4)=\frac{1}{2}(16)=8units^2[/tex]The area of the triangle formed by a diagonal and two of the sides is 8 units^2
D.
For the area of this triangle, we will use the same formula that we use in C. but in this case
b=sqrt(32)/2
h=sqrt(32)/2
We substitute the values
[tex]A=\frac{1}{2}(\frac{\sqrt[]{32}}{2})(\frac{\sqrt[]{32}}{2}))=4units^2[/tex]The area of one of these triangles is 4 units^2
ANSWER
A. sqrt(32) units
B.16 units^2
C. 8 units^2
D. 4 units^2
How to find the percent of a number
Explanation:
y% of some value, x:
Convert y to a decimal by dividing y by 100.
Then multiply that decimal value to x.
Given (12, 8) and (X, -4 ) find all X such that the distance between these two points is 13separate multiple answers with a comma
Given:
(12, 8) and (X, -4 )
Required:
To calculate the value of x
Explanation:
Determine the parameter through distance formula
Required answer:
x=7 or x=17
Use what you know about domain to select all of the following functions that could be the one graphed.
Using transformations, more specifically a translation, the functions that could represent the one graphed are given as follows:
y = sqrt(x) - 3.y = sqrt(x) - 1.Why is the transformation in this problem a translation?We first consider the parent square root function, defined as follows:
y = sqrt(x).
It's domain, that is, the possible values that the input x can assume, is given as follows:
x ≥ 0.
The graphed function has the same domain as the parent square root function, just with a different range, as it was shifted down, assuming the following format:
y = sqrt(x) - a.
In a translation, the function keeps the same format and orientation, just changing it's position, which is what happened in this case.
The possible translations are:
1 unit down, hence a = 1 and y = sqrt(x) - 1.3 units down, hence a = 3 and y = sqrt(x) - 3.The other functions would change the domain of the function, hence they are not possible.
What is the missing information?The information to solve this problem is given by the image at the end of the answer.
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(LO11) The weight of adult male beagles is normally distributed with a mean of 25.0pounds and a standard deviation of 2.9 pounds. Find the probability that a randomlyselected beagle weighs more than 21.8 pounds.0.1280O 0.13490.86510.8720
A randomly chosen beagle has a 0.86508 probability of weighing more than 21.8 pounds.
How can probability be explained?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be represented as percentage with values between 0 and 1.
What does the term "z-score" mean?The relationship between a value and the mean of a group of values is quantified by a Z-score.
Adult male beagle weight is normally distributed, with a mean of 25.0 pounds and a standard deviation of 2.9 pounds.
Given values are:
Mean(μ) = 25 pounds
Standard deviation(σ) = 2.9 pounds
Sample mean(x') = 21.8
We need to calculate z-score:
z = (x' - μ)/σ
z = (21.8 - 25)/2.9
z = 1.25
P-value from Z-Table:
P(x>21.8) = 1 - P(x<21.8) = 0.86508
As a result, the probability of a randomly selected beagle weighing more than 21.8 pounds is 0.86508.
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4. Identify all possible proper subset relationships that occur among the following sets.
Show work please.
The proper subset relationship of the given set A, B and C are in option;
Option A; C ⊂ AOption C: C ⊂ BOption D: B ⊂ AWhat is meant by the term proper subset?A subset is a subset of a larger set (someother set or same set). A B is the set notation used to symbolize a set A as a subset of a larger set B.A proper subset would be any subset of a set that is not the set itself. Every set, we know, is a subset of itself, but it is not a proper subset of it's own.The correct subset symbol is ⊂ . In other words, if A is a proper subset of B, after which:A ⊂ B andA ≠ BFor the given question;
The set are given as;
A = { x | x = 2n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
A = {1, 5, 7, 9 , 11 ..}
B = { x | x = 4n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
B = {1, 5, 9, ....}
C = { x | x = 8n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
C = {1, 9, 17...}
Thus, it is clear from the above relation that,
C contain B and A while B contain some element of A.
Thus, C ⊂ A, C ⊂ B and B ⊂ A are the correct relationship of the proper subset.
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Deepak wants to tile his bathroom using 1 m square tiles.
His bathroom measures 7 m x 7 m.
How many tiles will he need?
The bathroom must be tiled with 49 tiles, each of which has a surface area of 1 square meter and measures 7 meters by 7 meters.
How can I figure out how many tiles I need to tile the bathroom?
The bathroom's area is,
A= 7m x 7m
A= 49m^2
likewise the area of each tile = 1 square meter
The total amount of tiles needed to tile the bathroom is thus,
49/1 = 49
Therefore, the bathroom must be tiled with 49 tiles.
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1) 65x12-92+13 =
2) 4/2+19-5x11 =
1.
[tex] = (65 \times 12) - 92 + 13 \\ =780 - 92 + 13 \\ = (780 - 92) + 13 \\ = 688 + 13 \\ = 701 [/tex]
2.
[tex] = \frac{4}{2} + 19 -(5 \times 11) \\ = (2 + 19 )- 55 \\ = 21 - 55 \\ = - 34[/tex]
ATTACHED ARE THE SOLUTIONS
divide r by 8, then double the result
The expression divide r by 8 when doubled is r/4
What is an algebraic expression?An algebraic expression can be seen or described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.
These expressions are also known to be composed of mathematical operations, such as;
SubtractionAdditionMultiplicationBracketDivision, etcFrom the information given, we have;
divide r by 8
This is expressed as;
r/8
In doubling the expression, we get;
2(r/8)
expand the bracket
2r/8
Simplify further
r/4
Hence, the expression is r/4
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Guests staying at Marada Inn were asked to rate the quality of their accommodations
as being excellent (E), above average (AA), average (A), below average (BA), or poor
(P). The ratings provided by a sample of 20 guests are shown below. Give the
frequencies, in order, for the frequency distribution shown.
Α ΒΑ ΑΑ E E
AA P ΒΑ ΑΑ Α
A P A BA A A E A PA
If guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent (E), above average (AA), average (A), below average (BA), or poor (P). The frequency is : 1, 8, 6, 3, 2.
FrequencyAnalysis
E = E =1
AA= AA +AA + AA + AA + AA+ AA + AA +AA = 8
A= A + A+ A+ A+ A+ A = 6
BA = BA + BA + BA =3
P = P + P =2
Hence,
Class frequency
E 1
AA 8
A 6
BA 3
P 2
Total 20
Therefore 1, 8, 6, 3, 2 is the frequency .
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X =
(5x - 7)
(8x-55)
Answer:
The triangle shown is an isosceles triangle. It has two equal sides and the base angels are equal.
5x - 7 = 8x - 55
3x = 48
x = 16
The table below shows a runner's time t, in mintues, and distance traveled d, in miles.
Write an equation that shows a relationships between t and d.
The equation that shows a relationship between t (time in minutes) and d (distance in miles) is d = 0.075t
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
Let d represent the runners distance after t minutes.
From the table, using the points (12, 0.9) and (16, 1.20):
d - 0.9 = [(1.2 - 0.9)/(16 - 12)](t - 12)
d - 0.9 = 0.075(t - 12)
d = 0.075t
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The state department of transportation recorded the number of vehicles that passed through a toll booth between midnight and 5 am over a period of several months, and found that the average number of vehicles per night was 27. Find the probability that a randomly selected night has exactly 25 vehicles passing through the toll booth. Use Excel to find the probability.
Round your answer to three decimal places.
Provide your answer below:
$$
The probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes
Let X be the number of vehicles passing through the toll booth per night
X~Poisson(27)
The probability that exactly 25 vehicles passing through the toll booth is
⇒ P(X = 25) = (e⁻²⁷ × 27²⁵) / 25!
⇒ P(X = 25) = 0.074
Thus, Excel Command = POISSON.DIST(25,27,FALSE)
Therefore, the probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.
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Combine like terms and simplify please
Simplifying the given term
What is Like Terms?
In algebra, equal terms are terms that have the same variables and powers. Coefficients do not have to match. Dissimilar terms are two or more terms that are not similar terms. That is, they do not have the same variable or exponentiation. The order of the variables does not matter unless there are exponentiations.
To simplify and combine the like terms of the given question
7) -4x^2 - y^2 - 6x^2 + 2xy - 4x^2 + 7xy - xy +4y^2-9xy - 4x^2 + xy
Now, arranging them with the like terms
= -4x^2- 4x^2- 4x^2- 6x^2- y^2 +4y^2+ 2xy- xy-9xy + xy
= -10x^2 + 3y^2 - 7xy
8) n+n^2-5n+40n-10+3n^2+1-5n+n^2+18n-2
Now, arranging them with the like terms
= n^2+n^2+3n^2+n-5n+40n-5n+18n-10+1-2
= 5n^2 + 49n - 11
9) 14y - y^2 + 9y^2 + 12 - 5y^2 + 25y - y +8y^2 - 9y +25y + y
Now, arranging them with the like terms
= 9y^2- y^2- 5y^2+8y^2+ 25y- y - 9y + y +25y + 14y +12
= 11y^2 + 45y + 12
10) 12b + 2b^2 + 6a^2 + a - 5b + 2a - ab + 4a^2 - b - ab + 10b
Now, arranging them with the like terms
= 2b^2+ 6a^2+ 4a^2 + a+ 2a + 12b - 5b - b+ 10b - ab- ab
= 10a^2 + 2b^2 + 3a + 16b - 2ab
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Help please!!!!!!!!!!!!
An estimate of the quotient is in improper fraction [tex]\frac{133}{60}[/tex]. An estimate of the quotient is in mixed fraction [tex]2 \frac{13}{60}$$[/tex]
[tex]6 \frac{1}{3} \div 2 \frac{6}{7}$$[/tex]
Convert mixed numbers to improper fractions: [tex]$\quad 6 \frac{1}{3}=\frac{19}{3}$[/tex]
[tex]=\frac{19}{3} \div 2 \frac{6}{7}$$[/tex]
Convert mixed numbers to improper fractions: [tex]$2 \frac{6}{7}=\frac{20}{7}[/tex]
[tex]$=\frac{19}{3} \div \frac{20}{7}$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b} \times \frac{d}{c}$[/tex]
[tex]=\frac{19}{3} \times \frac{7}{20}$$[/tex]
Multiply fractions: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{19 \times 7}{3 \times 20}$$[/tex]
Multiply fractions:[tex]\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{19 \times 7}{3 \times 20}$$[/tex]
Multiply the numbers: [tex]$19 \times 7=133$[/tex]
[tex]=\frac{133}{3 \times 20}$$[/tex]
Multiply the numbers: [tex]$3 \times 20=60$[/tex]
[tex]=\frac{133}{60}$$[/tex]
Convert improper fractions to mixed numbers: [tex]$\frac{133}{60}=2 \frac{13}{60}$[/tex]
[tex]=2 \frac{13}{60}$$[/tex]
When it comes to adding Mixed or Improper fractions, we can have either the same denominators for both the fractions to be added or the denominators can differ too.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
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What is 7.68 rounded to the nearest half's
The nearest half of 7.68 is 7.5
Given,
A number is given by:
7.68
and, to find the rounded to the nearest half
Now, The number 7.68 is between 7.5 and 8.
Let's find which of these two numbers 7.68 is closer too.
We can do this by subtracting 7.68 from each of those numbers:
8 - 7.68 = 0.32
7.5 - 7.68 = -0.18
So, 7.68 is 0.32 away from 8, but it's only 0.18 away from 7.5
Hence, The nearest half of 7.68 is 7.5
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write a two-step equatipn that involves division and addition and has a solution of x=-25
The equation that involves division and addition and has a solution of x=-25 will be 3x - 40 = x + 90
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables that are given.
The equation that involves division and addition and has a solution of x = -25 will be:
3x - 40 = x - 90
Collect like terms
3x - x = -90 + 40
2x = -50
Divide
x = -50 / 2
x = -25
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5. If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be either:
The population proportion when the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200 must be D. 0.35 or 0.65.
How to illustrate the information?Based on the information, it should be noted that the formula for the standard error for the population will be:
✓p(1 - p)/n
where
p = population proportion
n = sample size
Therefore, this will be illustrated as:
✓p(1 - p)/n = 0.0337
Remove the square root
p( 1 - p)/200 = 0.00113569
Cross multiply
p(1 - p) = 0.227138
p - p² = 0.227138
Equate to 0
p² - p + 0.227138 = 0
Using almighty formula, P1 = 0.6512 and P2 = 0.3488
Therefore, the correct option is D.
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If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be:
A) 0.25
B) 0.75
C) 0.20 or 0.80
D) 0.35 or 0.65