A sampling distribution of the sample means of many large samples of a probability distribution is normally distributed. Which statement is true according to the Central Limit Theorem?
A the original PD can have any shape
B the original PD must also be normal
C the original PD must be uniform
D the original PD must be symmetric
The statement that is true according to the Central Limit Theorem is B. the original PD must also be normal.
Which is the Central Limit Theorem?According to the central limit theorem, if you take sufficiently large samples from a population, the means of the samples will be normally distributed even if the population is not normally distributed. The central limit theorem (CLT) states that as sample size increases, the distribution of sample means approaches a normal distribution, regardless of the distribution of the population.
The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.
In conclusion, the correct option is B.
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The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5). The total length of the walking trail is
units. (Input whole numbers only.) (3 points)
Answer:
12
Step-by-step explanation:
a box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x1, x2, and x3 denote the amounts in the selected envelopes, the statistic of interest is m
The probability distribution for the statistic is ; for m = 0 , P(0) = 0.216 , for m = 5 ,P(5) = 0.296 and for m = 10 , P(10) = 0.488 .
In the question ,
it is given that ,
the box has 10 sealed envelopes , that contains number from 1,2,...,10 .
the first six envelopes has no money .
next two envelopes has $5
and the last two contains $10 bill .
if x₁, x₂, and x₃ denote the amounts in the selected envelopes,
the statistic of interest is m = maximum of X₁ , X₂ and X₃ .
we need to find probability distribution for the statistic m,
So , P(m = 0) = P( all three envelope contains no money) = (6/10)³ = 0.216
and P(m = 5) = P( all from 8 envelope which contains at most $5) - P(all three envelope with 0 money)
= (8/10)³ - 0.216
= 0.296
and P(m = 10) = 1 - (8/10)³ = 0.488
Therefore , the required probability is P(0) = 0.216 , P(5) = 0.296 and P(10) = 0.488 .
The given question is incomplete , the complete question is
A box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x₁, x₂, and x₃ denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X₁ ; X₂ , and X₃ . Obtain the probability distribution of this statistic ?
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In the Two Period Consumer model, the Net Effect from a decrease in the interest rate for a net borrower is:
Group of answer choices
C1↓; C2?; Savings ↑
C1↑; C2?; Savings ↓
C1↑; C2↓; Savings ↓
C1?; C2↓; Savings ?
C1?; C2↑; Savings ?
In the two period consumer model , the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.
What is two period consumer model?
The consumer lives for two cycles before passing away. Therefore, there is no use in saving during the second time period. Rearranging, our present disposable income minus our current consumption is what we call savings.By deciding not to spend their entire income during the present period, consumers conserve money. They borrow money from the credit market to cover the difference between their income and current expenditure, boosting their future period income by the amount they saved plus interest.A useful simplification, in fact. Maximum current expenditure exceeds maximum current income.Hence, the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.
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the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.
The domain of the function is: [0,∞), the range of the function is: [3500,∞)
What does domain and range mean?Domain and Range: The set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation. The set which contains all the second elements, on the other hand, is known as the range of the relation.
The potential input and output values of a function are its domain and range, respectively.
The formula for the function is C=130S+3500.
the region
This is a list of the function's potential S values.
Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)
The domain of the function is [0,∞)
Since S can have any value larger than 0.
The variety
This represents the function's potential C values.
The formula for the function is C=130S+3500.
Assuming S = 0, the following is true: C=130*0+3500=3500.
C must be more than 3500.
Any number higher than 3500 can be used as the value of C.
Consequently, the function's range is [3500,∞)
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test for an association between handeness and career for these 5 professions. state the null and alternative hypothesis
Null Hypothesis: There is no association between handedness and career for Accountants. And Alternative Hypothesis: There is an association between handedness and career for Accountants.
Profession 1: Lawyer
Null Hypothesis: There is no association between handedness and career for Lawyers.
Alternative Hypothesis: There is an association between handedness and career for Lawyers.
Profession 2: Pilot
Null Hypothesis: There is no association between handedness and career for Pilots.
Alternative Hypothesis: There is an association between handedness and career for Pilots.
Profession 3: Accountant
Null Hypothesis: There is no association between handedness and career for Accountants.
Alternative Hypothesis: There is an association between handedness and career for Accountants.
Profession 4: Nurse
Null Hypothesis: There is no association between handedness and career for Nurses.
Alternative Hypothesis: There is an association between handedness and career for Nurses.
Profession 5: Teacher
Null Hypothesis: There is no association between handedness and career for Teachers.
Alternative Hypothesis: There is an association between handedness and career for Teachers.
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Which is the equation of line b
The equation of line b that passes through the point (-3,2) is y=-1/4x+5/4
How do you find a line equation?to get the equation of a line given a point and its slope.
Recognize the slope.
Decide on the point.
In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .
Slope-intercept form should be used to write the equation.
What are the 3 different equations of lines?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
In the above question we see that,
The line b passes through the point (-3,2)
the equation of line should satisfy this point
In the given option the only line that satisfy the point is
option C
y=-1/4x+5/4
hence option C ,y=-1/4x+5/4 is the answer
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Graph the system of inequalities.
y>4 x-3
3 y-x≤9
Use the graphing tool on the right to graph the system of inequalities.
The graph of the inequality y > 4x - 3 , 3y - x ≤ 9 . is shown below.
In the question ,
the inequalities are given ,
we have to graph given inequalities ,
the inequalities are y > 4x - 3
3y - x ≤ 9 .
in the first inequality , y > 4x - 3
we put x = 0 , y is = -3 .
we put y = 0 , x is = 3/4 .
So ,the points for the line will be (0,-3) and (3/4,0) .
since the inequality does not have equal to sign , the line will be a dotted line .
in the second inequality ,3y - x ≤ 9 .
we put x = 0 , y is = 3 .
we put y = 0 , x is = -9 .
the points for the line will be (0,3) and (-9,0).
Since the inequality has equal to sign . Thus, line will be solid line .
Therefore , the for the given inequality is shown below.
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As part of her science project , Shay is making a model of a wind farm.She wants to put 24 turbines in her model.What arrays can Shay make using 24 turbines
Answer: In Shay's wind farm their can be 4 arrays
Search up the meaning of a Array if you are confused
Step-by-step explanation:
24 has 4 pairs of factors.
1,242,123,84,6Ben and Bob made a snowman been spent two hours more than double the time Bob spent
A piece of cardboard is 5 centimeters longer than it is tall. The area of the piece of cardboard is 66 square centimeters. How many centimeters long is the piece of cardboard?
Answer:
12.244 cm long
Step-by-step explanation:
The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:
height * (height + 5) = 66
To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:
height + 5 = 66 / height
We can then subtract 5 from both sides of the equation to get:
height = 66 / height - 5
We can then multiply both sides of the equation by the height to get:
height^2 = 66 - 5 * height
We can then use the quadratic formula to solve for the height of the piece of cardboard:
height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)
The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:
height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)
This simplifies to:
height = (5 + sqrt(61)) / 2
The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.
Therefore, the piece of cardboard is approximately 12.244 centimeters long.
Find the cosecant. Someone help me asap pls!
Answer:
sqrt2
Step-by-step explanation:
csc (x)= 1/sin(x)
sin(x)= (sqrt22)/(sqrt22*sqrt2)= 1/sqrt2
1/(1/sqrt2)=sqrt2/1=sqrt2
No matter what I've tried, nothing works. Hopefully you can help me
Answer:
see explanation
Step-by-step explanation:
given Δ ABD is isosceles with AB = AD then base angles are congruent, so
∠ ADB = ∠ ABD = 72°
then
∠ BAD = 180° - (72 + 72)° = 180° - 144° = 36° ( sum of angles in a triangle )
given Δ ABC is isosceles , then
∠ BCD = ∠ BAD = 36°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ ADB is an exterior angle of Δ BCD , then
∠ BCD + ∠ DBC = ∠ ADB
36° + ∠ DBC = 72° ( subtract 36° from both sides )
∠ DBC = 36°
So ∠ BCD = ∠ DBC = 36°
Thus the base angles of Δ BCD are congruent , then
Δ BCD is isosceles with BD = CD
Which of the following is true about the t-distribution? Assume a reference (random) sample of size 100 with sample mean 10 and sample standard deviation of 1 with unknown population mean and variance.
a. The t-distribution will look similar to the standard normal distribution as the sample size increases which results in the degrees of freedom increasing.
b. The t-distribution will look similar to the standard normal distribution as the sample size increases which results in the degrees of freedom decreasing.
c. The t-distribution will look similar to the normal distribution with mean 10 and standard deviation 1 as the sample size increases which results in the degrees of freedom decreasing.
d. The t-distribution will look similar to the normal distribution with mean 10 and standard deviation 1 as the sample size increases which results in the degrees of freedom increasing.
e. None of these
1000 times were added to the n=30 sample. Even with n=30, the sample variance distribution is still very biased.
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
The sample variance's variance (SD) is still very large. The range is from 20 to 30%.
Because we are utilizing estimated population variance rather than the genuine population variance, which has some degree of uncertainty, the e t distribution has a longer tail when degrees of freedom are limited. Given that the estimated population variance is nearer to the actual population variance when sample size = 30, the t distribution will be closer to the z distribution.
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Compute Shannon's %NMC. Round your answer to the nearest percent. For example, if your
computed answer is 99.4% your answer rounds down to 99%. If your computed answer is
99.5% you should round up to 100%.
The Shannon's %Net market contribution = 40%
What is NMC (Net market contribution)?
Net market contribution (NMC) is equal to total sales revenue less total costs (except market costs) minus market costs.
Cost overall (not including market expenses):
150000 packaged (in cans and bottles).
Kegs =80000
WIP Loss/Reduction = 42000
Labor Contracts = 9000
Total Direct Labor: 240000
18000 inbound pounds
180000 in compensation
Total= 719000
Consumer advertising costs 26850 on the market.
Marketing for trade = 31761
Promotional Sales = 18000
Total=76611 Net market contribution=1320271-719000-76611=$ 524660 %NMC=524660/1320271=0.3974=39.74%=40%
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Please answer the two following questions.
The transformed graph is attached
The domain is (-∝, ∝) and the range is (-3, ∝)
How to transform the graph?From the question, we have the following parameters that can be used in our computation:
y = eˣ
To transform the graph to y = e⁻ˣ - 3, we make use of the following rules:
Reflect across the y-axisShift down by 3 unitsSee attachment for the graph of y = e⁻ˣ - 3
The domain and the rangeFrom the attached graph, we have:
The graph extends across the x-axis i.e. domain = (-∝, ∝)
The graph opens upward from y > -3 i.e. range = (-3, ∝)
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A stage manager is trying to seat important guests in the front row of a theater. She would like to seat a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. If there are 3 diplomats, 2 singers, anf 2 directors attending the show, how many different front row plans are possible? (The workbook got the answer of 288) How?
Answer:
12 row plans
Step-by-step explanation:
the first seat has two possible options , the two directors. The second seat has another two options. With each director comes 2 options for the second seat so 2×2=4 possible options for the first and second seat . The 3rd seat has three options, that means for each combination of the 1st and 2nd seat three possible options 2×3=12 combinations
What is 1 1/2 + 5/7?
What properties of equality do you need to use to solve the equation 2.1x−1.6=6.8? Solve the equation. Question content area bottom Part 1 What properties of equality do you need to use to solve the equation? Select all that apply. A. The Division Property of Equality B. The Multiplication Property of Equality C. The Subtraction Property of Equality D. The Addition Property of Equality Part 2 The solution is enter your response here. (Type the value of x.)
it is 6.1
Step-by-step explanation:
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6
hours per week. The standard deviation of the sample was 2.3. Estimate the mean of the population with 99% confidence.
Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final
answers to one decimal place.
Answer:
With 99% confidence we can say that the mean of the population is between 43.1 and 46.1
Step-by-step explanation:
e. 2|x-4|-3y³ when x=3 and y=-2
Answer:
26
Step-by-step explanation:
To find the value of the expression 2|x-4|-3y³ when x=3 and y=-2, we need to substitute the values of x and y into the expression and then simplify. The absolute value part of the expression, |x-4|, is the distance between the number x and 4 on the number line. When x=3, this distance is |3-4|=1. So the expression becomes 2*1-3(-2)³ = 2-3(-8) = 2+24 = 26. Therefore, when x=3 and y=-2, the value of the expression 2|x-4|-3y³ is 26.
You can use induction. Here's a very very rusty sketch of the proof.
Given -
Union of two regular languages is regular.
Let f(n) be a function representing the union of n regular languages.
Question Is f(n) a regular language?
Lk+1 is the k+1th regular language, for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.
What is the purpose of the inductive hypothesis?The induction hypothesis's function The assumption made at the beginning of the induction phase is known as the induction hypothesis, and it is the situation where n = k for the proposition we are trying to prove ("P(k)"). If you don't bring this hypothesis into play at any point throughout the proof of the induction phase, something is amiss.
Given:
It is normal for two regular languages to be combined.
Give the function f(n) the name "union of n regular languages."
Question Is the language f(n) regular?
The union of a single regular language is regular
if n = 1. Base Case
The provided hypothesis tells us that f(2) is regular
if n = 2.
Assume that f(n) is regular for every n = k.
This is the inductive hypothesis.
Let n equal k+1 in the inductive step. The inductive premise tells us that f(k) is a regular language.
Consequently, f(n) = f(k+1) = Lk+1 U f(k) (k)
Lk+1 is the k+1th regular language,
for example. The presented hypothesis states that f(n) = f(k+1) is regular since f(k) and Lk+1 are both regular.
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can anyone please help me with this math question?
Answer:
a) (7-2x) +3 = 10 - 2X
b) x = y + 3 <=> y = x-3
c) (x-3).-2 +7 = -2x +6 +7 => -10 + 13 = 3
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2
The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5
Shell method:
The shell method is an integration for calculating the volume of a solid of revolution when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.
V=2π∫01(2-x). 27x³dx
= 2π.27([tex]x^{4}[/tex]/2 - [tex]x^{5}[/tex]/5)01
=54π(1/2-1/5)
= 81π/5
Therefore The volume V of the solid is obtained by rotating the region bounded by the given curves about the specified line. y = 27x^3, y = 0, x = 1; about x = 2 is 81π/5
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-1/2h(2h+3)=0 answer
Step-by-step explanation:
-1/2h(2h+3) = 0
Seperate the equation:
-1/2 = 0
h = 0
(2h+3) = 0
Subtract 3 from both sides:
2h+3 = 0
2h+3-3 = 0
Simply:
2h = -3
Final Answer:
h = 0
h = -3/2
Determine how many times the innermost loop will be iterated when the algorithm segment is implemented and run. (Assume that m and n are positive integers.)
for j := 1 to m
for k := 1 to n
[Statements in body of inner loop.
None contain branching statements that
lead outside the loop.]
next k
next j
Discrete mathematics
The inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.
Given program,
for j = 1 to m
k = 1 to n
statement in the body of innerloop. None contain branching statements that lead outside the loop.
next j
next k
Here, in the inner loop k iterates from 1 to n that is n times and j iterates from 1 to m that is m times.
Finally, the whole loop iterates m×n times because for every value of j from 1 to m, k value increases from 1 to n.
So, the inner loop iterates 'n' times, outer loop iterates 'm' times and total loop iterates (m×n) times.
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Escriba la ecuación en el formato y = mx + b, dada la siguiente información: Pasa por el punto A(7,2) es paralela a
3x-y=8
Answer:
El ecuación es y = 3x + 2
Step-by-step explanation:
Lo primero que tienes que hacer es poner 3x - y = 8 en la forma y = mx + b para para saber que 'm'. Porque la ecuación que intentamos escribir es paralela a 3x - y = 8, entonces tienen la misma pendiente (m).
3x - y = 8
-3x -3x
-y = -3x + 8
/-1 /-1 /-1 dividir todo por -1 para hacer 'y' positivo.
y = 3x - 8
Y como sabemos que la ecuación pasa por (7, 2), sabemos que pasa por 2 en el y-axis (vertical). Entonces 2 es el intercepto en y (b).
Solve for x.
3/7x +1/4x =38
Answer:
x = 56
Step-by-step explanation:
[tex]\frac{3}{7}[/tex] x + [tex]\frac{1}{4}[/tex] x = 38 The common denominator would be 28
[tex]\frac{12}{28}[/tex] x + [tex]\frac{7}{28}[/tex] x =38
[tex]\frac{19}{28}[/tex] x = 38 Multiply both sides by [tex]\frac{28}{19}[/tex]
[tex](\frac{28}{19})[/tex][tex]\frac{19}{28}[/tex] x = [tex](\frac{28}{19})[/tex][tex]\frac{38}{1}[/tex] Cross cancel the 19 and 38.
x = [tex](\frac{28}{1})[/tex][tex]\frac{2}{1}[/tex]
x = 56
Count the best-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. Preconditions: X = {x1, x2, x3, x4, x5} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1
For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.
Given that,
The following pseudocode snippet performs the maximum number of + operations. Assume that the probability of each potential piece of data is equal. Preconditions: X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1
We know that,
Here,
X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}
By doing the iteration method
Iteration process till 4th iteration we get 6
Therefore, For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.
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PLEASE HELP ME ASAP!!!
Consider the following quadratic function.
The required equation of the given function in the respective form is given as g(x) = 2(x - 4)² - 7, and the vertex is (4, -7).
What is the graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
g(x) = 2x² - 16x + 25
g(x) = 2[x² - 8x] + 25
g(x) = 2[x² - 8x + 16 -16] + 25
g(x) = 2(x - 4)² - 32 + 25
g(x) = 2(x - 4)² - 7
Now, the vertex is given as (h, k) = (4, -7).
And the graph of the given function is shown.
Thus, the required equation of the given function in the respective form is given as g(x) = 2(x - 4)² - 7, and the vertex is (4, -7).
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