No matter what the shape of the parent population is, as long as our sample size is 10 or greater, we can conclude that the sampling distribution of the sample mean is approximately normally distributed. This statement is False.
We know that,
the Central limit theorem says that no matter what the distribution of the population is, as long as the sample is "large", meaning of size 30 or more, the sample mean is approximately normally distributed. If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size.
So therefore we need sample size greater than 30 and we have given 10 or greater.
Hence the given statement is false.
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a spiral staircase in a building is in the shape of a helix of radius 5 meters. between two floors of the building, the stairs make one full revolution and climb by 4 meters. a person carries a bag of groceries up two floors. the combined mass of the person and the groceries is m
Using formula Work done against gravity,
The work done by person against the gravity is 5880 J .
Work done against gravity:
The work done in lifting an object against gravity becomes the potential energy of the object-earth system. The change in gravitational potential energy Δ P.Eg is Δ P.Eg = mgh, where h is the increase in altitude and g is the acceleration due to gravity.
Mathematically, work done against gravity is given by,
W = Fg×d×cosθ
where, Fg --->force of gravity = weight = m×g
m --> mass
g --> gravity
d---> displacement
θ--> angle between force and displacement
we have given that
g = 9.8 m/s²
d = displacement = height = 2×4 = 8m
θ =angle between force and displacement = 180°
Combined mass = 75 kg
So, W = 75×9.8×8×cos 180°
W = -5880 J
Hence, the required work done is -5880J.
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Complete question:
A spiral staircase in a building is in the shape of a helix of radius 5 meters Between two floors of the building; the stairs make one full revolution and climb by 4 meters A person carries a bag " of groceries up two floors The combined mass of the person and the groceries is 75 kg and the gravitational force is 75g downward, where g 9.8 m/sec? is the acceleration due to gravity: Calculate the work done by the person against gravity in joules. Enter an exact answer.
Jaspir invested £2400 for years in a savings account. He was paid 7.5% per annum compound interest. At the end of the years he had £3445.51 in the savings account. Work out the value of .
Answer:
5
Step-by-step explanation:
FV =PV(1+r)^n
3445.51= 2400(1+0.075)^n
n=4.836
n is about 5
solve the system by the method of elimination. (if there is no solution, enter no solution. if the system is dependent, enter a for x and enter y in terms of a.) 2x-4y=6
-4x+8y=-12
There is no solution for the given system of equations, 2x-4y = 6 and -4x+8y = -12, by the elimination method.
According to the question,
We have the following system of equations:
2x-4y = 6 ...(1)
-4x+8y = -12 ...(2)
Now, we will multiply equation 1 by 2 and add the obtained result to equation 2:
2(2x-4y) = 2*6
4x-8y = 12
Now, adding this equation to second one (note that the left hand side will be added to only left hand side):
-4x+8y+4x-8y = -12+12
Now, there is no variable left on the left hand side.
Hence, there is no solution for the given system of equations.
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he actual voltages of power packs labeled as 12 volts for a sample are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, 11.77. true or false: it is possible that the 99% confidence interval calculated from these data will not contain the mean voltage for the entire population.
The statement is false, the true statement is "the mean voltage will be contained in the 99% confidence interval calculated from these data."
Given,
sample=11.77, 11.90, 11.64, 11.84, 12.13, 11.99, 11.77
A 99% confidence interval gives you more assurance that the interval represents the true value in the population. It does, however, provide a wider interval than a 95% confidence interval. For most analyses, a 95% confidence interval is sufficient to extend your results to the general population.
These intervals are simply a way of providing a range of values that we are reasonably confident (either 95% or 99%) includes the true population mean. A 99% confidence interval gives you more assurance that the interval represents the true value in the population.
As a result, the 99% confidence interval calculated from these data will include the mean voltage for the entire set of data.
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Data was recorded for the temperature, in degrees celsius, of a cup of coffee over a 30-minute period. given the regression equation, , what is the predicted temperature after 3 minutes? 33.45 oc 62.24 oc 65.17 oc 66.69 oc
The regression equation between temperature of a cup of coffee and time period is In(Temp) = 4.20 - 0.023(Time). The predicted temperature after 3 minutes is 33.45⁰C.
Least-square regression is a representation of data in a linear equation:
y = ax + b
where x, y are data variables.
The regression equation is obtained by minimizing the distance from regression line to each data points.
In the given problem, the equation of the least-squares regression line is:
In(Temp) = 4.20 - 0.023(Time),
In this case,
y = In(Temp)
x = Time
Where ln is the natural logarithmic operator.
When Time = 30 minutes, then,
In(Temp) = 4.20 - 0.023 x 30
In(Temp) = 4.20 - 0.023 x 30
In(Temp) = 3.51
Temp = e^(3.51) = 33.45
Hence, the predicted temperature after 3 minutes is 33.45⁰C
Your question is incomplete, but most probably your question was:
Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation,
In(Temp) = 4.20 - 0.023(Time), what is the predicted temperature after 3 minutes? 33.45 °C 62.24 °C 65.17 °C 66.69 °C
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A machine can make 56 parts in 4 hours. It can also make in . Which rates could you use to write an equation of the form ykx that represents the number of parts y the machine can make in ? What is that equation? Question content area bottom Part 1 Which of these rates could you use to write an equation of the form ykx that represents the number of parts y the machine can make in ? Select all that apply.
choose all the statements which are correct: group of answer choices using the ratio test: if , then the series is absolutely convergent according to the alternating series test, the series is convergent if the terms are decreasing with limit a series is called conditionally convergent if it is convergent but not absolutely convergent every absolutely convergent series is also convergent the series is called absolutely convergent if the series is convergent
The Ratio Test says that the series converges absolutely it is convergent but not absolutely convergent every absolutely convergent series is also convergent the series is called absolutely convergent
What is the ratio test used for?
Ratio test is one of the tests used to determine the convergence or divergence of infinite series. You can even use the ratio test to find the radius and interval of convergence of power series! Many students have problems of which test to use when trying to find whether the series converges or diverges.
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What does having the sprinter gene mean?.
The sprinter gene means having Alpha-actinin-3(ACTN3) gene.
In the given question we have to find what does having the sprinter gene mean.
The ACTN3 gene is the recently identified "sprinters gene."
A gene, as we already stated, codes for a protein. Alpha-actinin-3 is designated by ACTN3. This protein, which can only be found in fast twitch muscle fibres, gives muscles their explosive ability.
The fast twitch muscle fibres of sprinters like Usain Bolt and other Olympic athletes would create a lot of alpha-actinin-3.
In order to summarise the genetic component, an individual has the ACTN3 gene if alpha-actinin-3 is present in muscle cells. They are therefore better suited for quick movements.
However, if a person lacks alpha-actinin-3, they have a variant copy of the ACTN3 gene. In other words, they are appropriate for long-distance activities.
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On july 15, piper company sold $10,000 of merchandise (costing $5,000) for cash. The sales tax rate is 4%. On august 1, piper sent the sales tax collected from the sale to the government. On november 3, the milwaukee bucks sold a six-game pack of advance tickets for $300 cash. On november 20, the bucks played the first game of the six-game pack (this represented one-sixth of the advance ticket sales).
The entries for July 15 and August 1 transaction and entries for November 3 and November 20 transaction are given below.
What is sales tax?
A tax that is paid to a governing body for the sale of particular goods and services is known as a sales tax. Typically, laws let the merchant to collect money from the customer at the time of purchase to cover the tax. It is typically referred to as a usage tax when a tax on goods or services is paid directly to a governing body by a customer.
The entries for July 15 and August 1 transaction and entries for November 3 and November 20 transaction are as below.
1) Journal entry
Date account and explanation debit credit
July 15 Cash 10400
Sales revenue 1000
Sales tax payable 400
(To record sales)
Cost of goods sold 5000
Inventory 5000
(To record cost of goods sold)
Aug 1 Sales tax payable 400
Cash 400
2) Journal entry
Date account and explanation debit credit
Nov 3 Cash 300
Unearned ticket revenue 300
(To record revenue)
Nov 20 Unearned ticket revenue 50
Ticket revenue 50
(To record adjusting entry)
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To estimate the mean lifetime of a certain type of truck tire, a mechanic put of the tires on an -wheeler. The mean lifetime of the tires is miles, with a standard deviation of miles. The sample had no outliers and no strong skewness. Is it appropriate to use the methods of this section to construct a confidence interval for the mean lifetime of this type of tire?
No, because the sample size is insufficient and the sample does not represent a distribution that is roughly normal.
What do the numbers mean?
Statistics is the study and manipulation of data, including methods for data collection, evaluation, analysis, and interpretation. Descriptive statistics and inferential statistics are the two main subfields of statistics.
What three sorts of statistics are there?
They are (i) the mean, (ii) the median, and (iii) the mode. The study of statistics involves gathering, analyzing, interpreting, presenting, and organizing data in a particular way.
The population must have a normal distribution, or the sample size must be sufficient to use the central limit theorem, in order to generate a confidence interval. It is not appropriate to create the confidence interval for mean because neither of the two conditions were met in this instance.
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lucy scored a 85, 64 and 76 on her math exams. what score must lucy obtain on the next math test to have an average of exactly 80?
Answer:
95
Step-by-step explanation:
To find the average you take the sum of the scores and then divide it by the number of exams. Let x equal the score Lucy must obtain on the next math test.
[tex]\frac{85+64+76+x}{4} =80[/tex]
Add the scores and multiply both sides by 4
225 + x = 320
Subtract 225 from both sides
x = 95
The proportional relationship between the total number of minutes, m, that mariam practices the piano after some number of days, d, can be represented by the equation m = 34dm=34d. At what rate did she practice, in minutes per day?.
The Rate at which she practices piano per day will be 34 minutes.
We know that Proportional relationships are relationships between two variables like x and y when their ratios got equivalent.
For example, [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex]. This is the proportional relationship between the variables, a, b, c, and d. In this a is equal to c (a = c) and b is equal to d(b = d).
In our question, the proportional relationship between total minutes (m) and the number of days (d) is given by:
m = 34d.
We need to find the rate, which can be defined as the total minutes spent on practice piano per day.
Minutes spent = m
Days = d
Rate = [tex]\frac{m}{d}[/tex]
So, we know, m = 34d
[tex]\frac{m}{d}[/tex] = [tex]\frac{34}{1}[/tex] = 34
Hence, The rate is 34 minutes per day.
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multiply by 12.50 x 52.75
Answer:
659.375
Step-by-step explanation:
big brain
use a calculator
a rectangle is sometimes similar to another rectangle, because we can sometimes map one onto the other using only dilations and rigid transformations.
A rectangle and another rectangle can occasionally be mapped onto one another using solely stiff transformations and dilations.
By altering the initial shape, shapes can be mapped to other comparable shapes.
The following needs to be accurate for a shape to change.
The forms must be comparable.The shapes have to be of the same kind.The shapes need to have equivalent side lengths.The respective side lengths of the rectangles must have an equivalent ratio in order for one rectangle to be transferred to another.
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8. a) The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year. Again, it was increased by 20% this year. (i) How much was his salary last year? (ii) How much is he drawing this year? 2010
The last year's salary was Rs 8250 and he is drawing this year Rs 9075.
What is the percentage of a number?
The percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%' known as percentage symbol.
The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year.
So, The last year's Salary was 7500 +750 = 8250
Again, it increased by 20% this year.
Then, Drawings of current year = 7500 + 20% of 7500
7500 + 1500 = 9000
8250 + 10% of 8250 = 9075
Drawings of current year = 9075.
Hence, the last year's salary was Rs 8250 and he is drawing this year Rs 9075.
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What does it mean to pilot program?.
Pilot program means is a small scale, short term experiment that helps an organization or company to learn how a large scale project might work in practice.
Pilot program:
The best pilot program provides a platform for the organization to test logistics, prove value before spending a significant amount of time, energy or money on a large scale project.
The pilot program is also called as feasibility study or experimental trial.
Steps for pilot program:
1.
set clear goals
2.
Decide on a length of time
3.
Choose your testing group
4.
Develop a plan for on-boarding
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What is the volume, in cubic inches, of a packing box if its dimensions are 40 inches long, 30 inches wide, and 20 inches high?.
The volume, in cubic inches, of a packing box is 24000 cubic inches
What is a cuboid?
A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
The box is a cuboid.
Volume = length*width*height
= 40*30*20
= 24000 cubic inches
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In the united tate, the birth rate B of unmarried women (birth per 1000 unmarried women) for women whoe age i a i modeled by the function B(a)=-0. 355a^219. 17a-213. 37. A) what i the age of unmarried women with the highet birth rate?
b)what i the highet birth rate of unmarried women?
Using the Quadratic function,
a) The age of unmarried women with the highet birth rate is 27.1
b) The highet birth rate of unmarried women is 61.42..
Quadratic Function:
A quadratic function is a polynomial function of degree 2 which can be written in the general form, f(x) = ax²+ bx + c
here a, b , c are real numbers and a not equal to zero.
The quadratic function f(x) will have only the maximum value when the the leading coefficient or the sign of 'a' is negative.
when "a" is negative then maximum value of f(x) is -b/2a .
We have given that,
United State ,the birth rate B of unmarried women (birth per 1000 unmarried women) for women whoe age say a modeled function is
B(a) = −0.30a² + 16.26a −158.90 ---(*)
which is a quadratic function .
comparing (*) with ax²+bx +c = 0
we get, a = - 0.30 , b = 16.26, c = - 158.90
we have to find out the age of unmarried women with highest birth rate .
Highest birth rate means B(a) is maximum.
and using above facts , B(a) is Maximum at -b/2a
a) so, the age of unmarried women with highest birth rate = - b/2a = - 16.26/2×(-0.30) = 27.1
b) birth rate will be highest or max. when a = 27.1
the highet birth rate of unmarried women = B(27.1)
= −0.30(27.1)²+ 16.26(27.1) −158.90
= 61.42
Hence, the age of unmarried women with the highet birth rate is 27.1 and the highet birth rate of unmarried women is 61.42..
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Which description of the graph of the linear inequality y ≥ 7x 4 is correct?.
The graph of the linear equality will be a solid line with a y-intercept of negative four and a slope of seven. Description of the graph is The graph will be shaded above the line.
The inequality is expressed as y ≥ 7x - 4
Now, just focusing on the equality sign
y = 7x - 4
y = 7x + (-4) --- (1)
Any linear equation in slope-intercept form has the following generic form:
y = mx + c --- (2)
so by equation 1 and 2
mx = 7x
m = 7
the equation y ≥ 7x - 4,
Put x = 0
y = 7(0) - 4
y = -4
As a result, the graph will look like a solid line with such a negative y-intercept of 4 and a seven slope. It will be shaded above the line on the graph.
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This graph represents the first hypothetical described in the video. Imagine someone invests $10,000 with 7% returns compounding each year for 30 years.
Using the formula of compound interest, the amount compounded annually for 30 years at a rate of 7% is $76,122.55
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeSubstituting the values into the equation above;
A = 10000(1 + 0.07/1)^1 * 30
A = $76,122.55
The amount at the end of 30 years is equal to $76,122.55
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let a be a finite non-empty set. does there exist a relation r on a that is both an equivalence relation and an order relation?
The required relation on R on A is explain below
What is finite non-empty set?It is a set where either the quantity of components is large or just beginning or finishing is given. In this way, we mean it with the quantity of components, n(A), and on the off chance that n(A) is a characteristic number, it's a limited set.
According to question:Let A be finite non-empty set.
Then the exist relation R on A which is both equivalence and order relation.
Suppose A = {a₁, a₂, a₃........an}
And, R = {(a₁, a₁)(a₂, a₂).......}
R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.
Then R is equivalence relation and an order relation.
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YALL SOLVE this with solutions thank uu.
Answer:
[tex] - 12.6x - 4.9x = - 154 \\ \\ - 17.5x = - 154 \\ \\ x = \frac{ - 154}{ - 17.5} \\ \\ x = 8.8[/tex]Answer:
x= 8.8
Step-by-step explanation:
-12.6x-4.9x=-154
-17.5x=-154
-17.5x/-17.5 = -154/-17.5
x = 8.8
n a certain game, the integer variable bonus is assigned a value based on the value of the integer variable score. if score is greater than 100, bonus is assigned a value that is 10 times score. if score is between 50 and 100 inclusive, bonus is assigned the value of score. if score is less than 50, bonus is assigned a value of 0.
The integer variable bonus is assigned a value based on the value of the integer variable score
score > 100 implies bonus = 10 * score
score between 50 and 100 implies bonus = score
score < 50 implies bonus = 0
First, we need to analyze the conditions:
score > 100 implies bonus = 10 * score
score between 50 and 100 implies bonus = score
score < 50 implies bonus = 0
Writing the above as programming instructions, we have:
if(score > 100){//This represents the first condition
bonus = 2 * score;
}
else if(score >=50 && score<=100){//This represents the second
bonus = score;
}
else{//This represents the last condition
bonus = 0;
}
Hence, if score > 100 implies bonus = 10 * score
score between 50 and 100 implies bonus = score
score < 50 implies bonus = 0
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What does it mean when the graph touches the x-axis?.
When the graph touches the x-axis then, it makes contact with the x - axis and not passes through the x - axis,
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph touches the x-axis.
Now,
Let the function of graph is circle.
Then, If it is touches the x-axis then, the y-co-ordinate of the center will be equal to the radius of the circle.
Thus, When the graph touches the x-axis then, it makes contact with the x - axis and not passes through the x - axis.
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Ged: in a certain high school, the probability that a student drops out is , and the probability that a dropout gets a high-school equivalency diploma (ged) is. What is the probability that a randomly selected student gets a ged? round your answer to four decimal places, if necessary.
Using the concept of probability and the information given, it is determined that the probability of a randomly selected student receiving a GED is 0.0175 = 1.75%.
The specified percentages are:
7% of students drop out and 25% of them get GED.
So 100 - 7 = 93% of students will not drop out. So 0% have a diploma so they doesn't need a GED.
as a result:
p = 0.07 (0.25) + 0.93 (0) =0.0175
A randomly selected student has a 0.0175 = 1.75% chance of receiving her GED.
your question is incomplete but most probably your full question was
In a certain high school, the probability that a student drops out is 0.07 , and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25 . What is the probability that a randomly selected student gets a GED?
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In exercie 9-12, write a plan to prove that angle 1 i congruent or equal to angle 2
The angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.
Given, two triangles ABC and XYZ,
we have to prove that the angle A is congruent to the angle X.
Now, as AB = XY (Given)
BC = YZ (Given)
AC = XZ (Given)
By using the Side-Side-Side congruence rule, we get
Δ ABC ≅ ΔXYZ
Now, ∠A = ∠X (By CPCT)
So, the angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.
Hence, the angle 1 is proved congruent to the angle 2 in the triangle ABC and XYZ respectively.
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A baker would like to tore 12 3\4 pound of flour in container that each hold 3 1\2 pound of flour. How many container will the baker need
The answer to the given word problem is:
4 containers will be required by the baker.
What is a word problem?
A word problem is a mathematical exercise used in the science classroom where key background information is presented in everyday language rather than mathematical notation.
Word puzzles give you a chance to work on your close reading, visualizing, interpreting, and analyzing skills. In a word problem, a story is presented to the students. They must carefully read to comprehend what information is crucial and visualize it to fully comprehend the objective.
Solution Explained:
Given in question,
Total amount of flour = [tex]12\frac{3}{4}[/tex] pounds = 51/4
Each container has a capacity of = [tex]3\frac{1}{2}[/tex] pounds = 7/2
Therefore, Total number of containers required = 51 X 2/ 4 X 7 = 51/14 = 3.6
So if we round it off to a whole number we get, total number ≈ 4
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design a function that accepts an integer argument and returns the sum of all the integers from 1 up to the number passed as an argument. for example, if 50 is passed as an argument, the function will return the sum of 1, 2, 3, 4, . . . 50. use recursion to calculate the sum.
The function will be designed in the python computing language
Python is an interpreted, object-oriented, high-level, dynamically semantic programming language. Its straightforward syntax prioritizes readability and makes it simple to understand, which lowers the cost of program sustenance.
The code will be -
def main():
number = int(input('Enter a positive integer: '))
finalSum = addition(number)
print("The integral of this number is ", finalSum, ".")
def addition(num):
if num == 1:
return 1
else:
return num + addition(num-1)
main()
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Subtract -5x^2-9x-5 from 4x^2-5x+3
Answer:
9x² + 4x + 8
Step-by-step explanation:
(4x² - 5x + 3) - (-5x² - 9x - 5)
4x² - 5x + 3 + 5x² + 9x + 5
9x² + 4x + 8
I hope this helps!
a set of students take a multiple choice exam, all guessing randomly on each question. what distribution would the student grades follow?
Binomial distribution will be followed for grade of student.
Binomial Distribution:
When an experiment or survey is repeated numerous times, the likelihood that the results will be SUCCESS or FAILURE is known as the binomial distribution. The prefix "bi" implies "two" or "twice," therefore the term "binomial" refers to a distribution type with two probable outcomes. A coin flip, for instance, can only result in one of two outcomes: heads or tails, and completing a test can result in either passing or failing.
What do we need for a Binomial Distribution?
1. one base experiment which will be repeated many times (n times).
2. only two outcomes in the base experiment: success or no success; property fulfilled or not fulfilled.
3. a success probability p that does not change from one experiment to the next (this means the experiments are independent).
So,
Binomial distribution will be followed for grade of student.
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