The sample mean is 75.
Margin of error is 6.
Sample standard deviation is 17.53 .
What is the relationship between margin of error and confidence level?
Confidence level and marginal of error As the confidence level increases, the critical value increases and hence the margin of error increases. This is intuitive; the price paid for higher confidence level is that the margin of errors increases.
Part A:
The sample mean is at the midpoint of the lower and the upper values of the confidence interval.
Thus, the sample mean is given by:
=(69 + 81) / 2
= 150/2 = 75
Therefore, the sample mean is 75.
Part 2:
The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.
Thus, margin of error is given by 81 - 75 = 75 - 69 = 6 .
Therefore, margin of error is 6.
Part 3:
The margin of error is given by
ME = t₍ᵃ/₂₎ ([tex]\frac{s}{\sqrt{n} }[/tex] )
where t₍ᵃ/₂₎ is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.
Since the sample size is 25, the degree of freedom is 25 - 1 = 24.
[tex]\frac{a}{2}[/tex] = [tex]\frac{1-0.9}{2}[/tex] = [tex]\frac{0.1}{2}[/tex] = 0.05
From the t-distrbution table, we have:
t₍ᵃ/₂₎ = 1.710882
Thus, margin of error is given by:
6=1.710882 [tex](\frac{s}{\sqrt{25} })[/tex]
⇒[tex]\frac{s}{\sqrt{25} }[/tex] = [tex]\frac{6}{1.710882}[/tex]
⇒s= 17.53
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a committee of six people (four men and two women) need to select a chairman and secretary. they do so by drawing names from a hat. what are the probabilities that
The probability that they all are women is 0.0333 and that two of them are men is 0.50
There are 6 men and 4 women in your committee, that gives you a total of 10 people to choose from.
Without restrictions, there's a total of 10C3 ways to choose a subcommittee of 3 people.
a) A subcomitte of 3 people consisting of all women can be chosen in 6C0*4C3 ways.
So, the probability for the first problem is 6C0*4C3/10C3 = 0.0333
b) A subcommittee consisting of 2 men and 1 woman can be chosen in 6C2*4C1 ways.
So, the probability for this problem is 6C2*4C1/10C3 = 0.50.
Therefore, the probability that they all are women is 0.0333 and that two of them are men is 0.50.
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Disclaimer
the question given by you is incomplete, the answer is solved as per a similar question and the question is
A committee consist of six men and four women. A subcommittee is made by randomly choosing three of the committee members. What is the probability that: a. they are all women b. two of them are men?
How do you express .13 as a percentage?
.13 can be expressed in the form of percentage as 13%.
In order to convert numbers in decimal into percentage we only need to multiply the given number with 100 and after multiplying the number with hundred it can be written in percentage form. Like in the question given number is 0.13 and we need to express this in form of percentage. So in order to express this number in percentage we just multiply it with 100 which will be equal to 13% i.e
0.13 x 100 = 13%
By multiplying a decimal value by 100 and adding the percentage (%) sign, you can turn a decimal value into a percentage. A decimal multiplied moves the decimal point two places to the right.
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consider the curve defined by y2=x3−3x 3 for x>0. at what value of x does the curve have a horizontal tangent?
At x = 0 and x = 2, the curve defined by y² = x³ - 3x² has a horizontal tangent.
We have,
First, let's find the derivative of y with respect to x.
We can rewrite the equation as:
y² = x³ - 3x²
y = (x³ - 3x²)^(1/2)
Now, differentiating y with respect to x using the chain rule:
dy/dx = (1/2) * (x³ - 3x²)^(-1/2) * (3x² - 6x)
Next, we set the derivative equal to 0 to find the values of x where the curve has a horizontal tangent:
(1/2) * (x³ - 3x²)^(-1/2) * (3x² - 6x) = 0
We can disregard the constant factor of (1/2) since it doesn't affect the solution.
Thus, we have:
(x³ - 3x²)^(-1/2) * (3x² - 6x) = 0
To have a horizontal tangent, the slope of the curve should be 0, which means the derivative is equal to 0.
Now, we have two factors to consider:
(x³ - 3x²)^(-1/2) = 0, which means the expression inside the parentheses is equal to 0. However, this does not yield a real solution.
(3x² - 6x) = 0, which means the quadratic term equals 0.
Solving this quadratic equation:
3x² - 6x = 0
3x(x - 2) = 0
This equation has two solutions: x = 0 and x = 2.
Therefore,
At x = 0 and x = 2, the curve defined by y² = x³ - 3x² has a horizontal tangent.
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The graph shows the density of a substance. Find the density in grams per milliliter.
Answer:
2 grams per millimeter
Step-by-step explanation:
the point (2,1) shows us this.
How do you simplify (2−i) / (5+i) ?
To simplify [tex]\frac{2-i}{5+i} = \frac{9}{26} -\frac{7}{26} i[/tex] , multiply the numerator and denominator by the conjugate of the denominator.
A complex number's conjugate A+bi equals a-bi. A real number is the result of a complex number and its conjugate. That fact will be used here.
[tex]\frac{2-i}{5+i} =\frac{2-i}{5+i} . \frac{5-i}{5-i}[/tex]
[tex]= \frac{(2-i)(5-i)}{(5+i)(5-i)}[/tex]
[tex]=\frac{10-2i-5i-1}{25-5i+5i+1}[/tex]
[tex]=\frac{9-7i}{26}[/tex]
[tex]=\frac{9}{26}-\frac{7}{26}i[/tex]
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What is the length of AB
Answer: 11.5 maybe ? {sorry if its wrong]
Step-by-step explanation:
if my overall grade is 44 percent and a test is worth 60 percent of that grade and i get 50 percent on a test what would my overall grade be now?
What is the additive inverse of the polynomial -6x^3 +4x^2 -4
6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is -6x³ +4x² -4
Polynomial is minus six x cube plus four x square minus four.
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
6x³ -4x² +4 is the additive inverse of -6x³ +4x² -4
because -6x³ +4x² -4+6x³ -4x² +4=0
Hence, 6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4
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a certain acid has a ka equal to 5.57 x 10-5. determine the pkb of its conjugate base (give your answer to two decimal places)
The pk[tex]_b[/tex] of given acid conjugate base is 9.74 if k[tex]_a[/tex] of the same acid is equal to 5.57×10⁻⁵
The Bronsted-Lowry corrosive base hypothesis incorporates the ideas of form acids and form bases. At the point when a corrosive separates into its particles in water, it loses a hydrogen particle. The species that is shaped is the corrosive's form base.
A more broad definition is that a form base is the base part, X-, of a couple of mixtures that change into one another by acquiring or losing a proton. The form base can acquire or retain a proton in a synthetic response. The form corrosive gives the proton or hydrogen in the response.
In a corrosive base response, the substance response is:
Corrosive + Base ⇌ Form Base + Form Corrosive
We know very well that from equilibrium state theories that pk[tex]_b[/tex] +pk[tex]_a[/tex] =14
where pk[tex]_a[/tex] = - log( k[tex]_a[/tex] )
So, we have k[tex]_a[/tex] =5.57×10⁻⁵
Taking log of k[tex]_a[/tex] ,we get
=>pk[tex]_a[/tex]= -log(5.57×10⁻⁵)
Using properties of logarithm, log(a × b)=log(a)+log(b)
=>pk[tex]_a[/tex]= -log(5.57) -log(10⁻⁵)
=>pk[tex]_a[/tex]= -0.745 +5
=>pk[tex]_a[/tex]=4.25
Therefore, from above written formula, we get
=>4.25+pk[tex]_b[/tex]=14
=>pk[tex]_b[/tex]=14-4.25
=>pk[tex]_b[/tex]=9.74
Hence, pk[tex]_b[/tex] value is 9.74
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m×n , when m=13 and n=12
Answer:
156
Step-by-step explanation:
mxn
13x12= 156
......
1) Is the triangle right angled?
8cm
16cm
18cm
Answer:
for right angle triangle ...by Pythagoras theorem
18^2 = 8^2 + 16^2
324 = 64 + 256
324 = 320
which is not true ....
hence not a right angle triangle
I need help thanks for your help…
Answer: 2
Step-by-step explanation:
based on your site data sheet and your sample identification, do you feel that you determine an appropriate stream rating? (why or why not). do you feel using macroinvertebrates is a good method to evaluate stream conditions?
When collecting quantitative data you can use a statistical formula to give you a rough estimate of the sample size you will need. When collecting qualitative data, however, the rule of thumb is to have as representative of a sample as possible that will allow you to exhaust the knowledge you could learn from the population.
Macroinvertebrate sampling provides a relatively easy way to assess the water quality of a stream. The types and numbers of macroinvertebrates (mostly insect larvae/nymphs) that form the biological community at a particular stream location are shaped by both the nature of the stream and the quality of water that drains into the stream.
Work out the size of angle 0.
Give reasons for your answer.
Answer:
θ = 56°
Step-by-step explanation:
As OA and OB are both radii, triangle AOB is an isosceles triangle:
⇒ m∠ABO = m∠OAB = 48°
Interior angles of a triangle sum to 180°:
⇒ m∠ABO + m∠OAB + m∠AOB = 180°
⇒ 48° + 48° + m∠AOB = 180°
⇒ m∠AOB = 180° - 48° - 48°
⇒ m∠AOB = 84°
Angles on a straight line sum to 180°:
⇒ m∠AOB + m∠DOB = 180°
⇒ 84° + m∠DOB = 180°
⇒ m∠DOB = 180° - 84°
⇒ m∠DOB = 96°
The tangent of a circle is always perpendicular to the radius.
Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:
m∠OBC = 90°m∠ODE = 90°OBCD is a quadrilateral.
The interior angles of a quadrilateral sum to 360°:
⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°
⇒ 90° + θ + 28° + 90° + 96° = 360°
⇒ θ + 304° = 360°
⇒ θ = 360° - 304°
⇒ θ = 56°
A weather forecaster says that the temperature is changing at a rate of -8° per hour. At this rate, how long will it take for the temperature change to be -24°? It will take _____ hours for the change in temperature to be -24
The transition to -24 degrees will take three hours .The balance between energy coming into and going out of the planet's system determines its temperature.
What influences how the temperature fluctuates?The balance between energy coming into and going out of the planet's system determines its temperature. The Earth warms up when incoming solar energy is absorbed by the Earth system. Earth does not warm as a result of solar energy being reflected back into space. Earth cools as energy that has been absorbed is ejected back into space.Since 1880, the Earth's average temperature has increased by 0.14° F (0.08° C) every decade; however, since 1981, the pace of warming has increased by 0.32° F (0.18° C) per decade, or more than twice as fast. Using NOAA's temperature data, 2021 ranked as the sixth-warmest year ever.Explanation:
-8% / -24 = 3.
The transition to -24 degrees will take three hours.
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y varies directly with the square of x.
If x= 1/2 and y = 12, find x when y = 432.
Answer:
20.8
Step-by-step explanation:
y = x^2
Given the value of y = 432, the equation would be:
432 = x^2
x is found by finding the square root of 432
sqrt 432 = sqrt (x^2)
x = 20.8
Check:
20.8^2 = 432.64
Your final answer would be 20.8.
One basketball costs $2 more than another. The sum of their costs is $146. How much does each basketball cost?
Answer:
$72 and $74
Step-by-step explanation:
Let the cheaper ball cost x.
x + x + 2 = 146
2x = 144
x = 72
x + 2 = 74
Answer: $72 and $74
a study was conducted in which two types of engines, a and b, were compared. gas mileage, in miles per gallon, was measured. 50 experiments were conducted using engine type a and 75 experiments were done with engine type b. the gasoline used and other conditions were held constant. the average gas mileage was 36 miles per gallon for engine a and 42 miles per gallon for engine b. assume that the population standard deviations are 6 and 8 for engines a and b, respectively. we found a 95% confidence interval on the difference of population mean gas mileages for engines a and b is (-8.46,-3.54). how do you interpret this interval?
The Central Limit Theorem establishes that the sampling distribution of the sample means of size n can be approximated to a normal distribution with mean and standard deviation s = /n for a normally distributed random variable X, with mean and standard deviation.
The Central Limit Theorem can also be used with skewed variables if n is at least 30.
The sampling distribution of the sample percentage for a proportion p in a sample of size n will be about normal, with mean and standard deviation s = p(1-p)/n.
Between-normal-variables subtractionThe mean is the difference between the means when two normal variables are subtracted, and the standard deviation is the square root of the sum of the variances.
Calculation:Average gas mileage (A): Mean 36, SD 6, sample size 50:
So, μA = 36, sA = 6/√50 = 0.8485
Gas mileage B: Mean 42, SD 8, and sample size of 50:
So, μB = 42, sB = 8/√50 = 1.1314
Arrangement of the difference:
Mean: 36 - 42 = -6 where A - B
Standard deviation: 1.4142
Locate the point estimate.
This is the mean difference, which is -6 mpg.
B. Determine the error margin.To determine our level, we must deduct 1 from the confidence interval and divide the result by two. So: 1 - 0.95/2 = 0.025
Now that z has a pvalue of, we must locate it in the Ztable.
Z = 1.96 since it has a pvalue of.
Identify the margin of error M as follows.
M = zs = 1.96 * 1.4142 = 2.77
2.77 mpg is the error margin.
C. Create the 95% confidence interval for the variance in population mean fuel economy between engines A and B, then analyze the findings (5 pts)The sample mean plus M determines the interval's upper end. Therefore, it is -6 + 2.77 = -3.23 mpg.
The difference between the population mean gas mileage for engines A and B and how to interpret the data, in mpg, have a 95% confidence interval of (-8.77, -3.23) means, whereas the standard deviation is the sum of the variances' square roots.
Average gas mileage (A): Mean 36, SD 6, sample size 50:
So, μA = 36, sA = 6/√50 = 0.8485
Gas mileage B: Mean 42, SD 8, and sample size of 50:
So, μB = 42, sB = 8/√50 = 1.1314
Arrangement of the difference:
Mean: 36 - 42 = -6 where A - B
Standard deviation: 1.4142
Locate the point estimate.
This is the mean difference, which is -6 mpg.
B. Determine the error margin.
By subtracting 1 from the confidence interval and dividing the result by 2, we can determine our level. So: 1 - 0.95/2 = 0.025
We must now locate z in the Ztable because it has a pvalue of
Z = 1.96 since that has a p value of.
Find the margin of error now. such that M
M = zs = 1.96 * 1.4142 = 2.77
The error margin is 2.77 mpg.
C. Build the 95% confidence interval for the difference between the population-mean fuel economy for engines A and B, then analyze the findings (5 pts)
The sample mean multiplied by M determines the interval's upper end. Consequently, it is -6 + 2.77 = -3.23 mpg.
The 95% confidence interval for the difference between population mean gas mileage for engines A and B and how to interpret the data, in mpg, is (-8.77, -3.23).
When should you calculate the population standard deviation?You should calculate the population standard deviation when the dataset you’re working with represents an entire population, i.e. every value that you’re interested in. The formula to calculate a population standard deviation, denoted as σ.
What is the percent confidence interval for the population mean?A % confidence interval (CI) for the population mean is given by Example 6.2 A meat inspector has randomly measured 30 packs of acclaimed 95% lean beef. The sample resulted in the mean 96.2% with the sample standard deviation of 0.8%.
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SHOW WORK FOR BRAINLIST DUE TODAY
The graph of Stewart's assignment added as an attachment
How to draw the graph of the scenario?From the question, we have the following parameters that can be used in our computation:
Number of assignments = 36
Rate of assignment per day = 4
This means that the equation of the scenario is
Number of assignments remaining = Initial number of assignments - Rate of assignment per day * Number of days
Represent the number of assignments remaining with y and the number of days with x
So, we have the following representation
y = Initial number of assignments - Rate of assignment per day * x
Substitute the known values in the above equation, so, we have the following representation
y = 36 - 4 * x
Evaluate the products
y = 36 - 4x
So, the equation is y = 36 - 4x and the graph is added as an attachment
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Undergraduates
Graduates
Total
University Data
Receiving
Financial Aid
4222
1879
6101
Not Receiving
Financial Aid
3898
731
4629
Total
8120
2610
10730
If a student is selected at random, what is the
probability that the student receives aid
(rounded to the nearest percent)? [? ]%
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
in our case the desired cases are all students with financial aid : 6101
and the totally possible cases are 10730.
so, the probability to pick a student at random, who receives financial aid is
6101 / 10730 = 0.568592731... = 56.8592731...% ≈
≈ 57%
What is the solution to the following system of equations
7x+2y=24
8x+2y=30
queuing system a has a utilization of 80 percent, and queuing system b has a utilization of 90 percent. both have a single server. say the utilization of both systems increases by 5 percent; that is, a increases from 80 percent to 85 percent while b increases from 90 percent to 95 percent. which system is likely to experience the bigger change in the average time in queue?
For queuing system B, the average time in queue ids going to change significantly as a result of increased utilization.
This is because queuing system B is initially heavily loaded and has less capacity to handle more requests. As a result, an increase in utilization can cause a significant increase in average queue latency on system B compared to system A.
Average Queue Time is a measure of the time a customer or request spends being processed by a server. It is affected by several factors such as server load, customer or request arrival rate, and server service rate. As the load on the queuing system increases, it means that the server is being used more frequently and is no longer available to process incoming requests. This will increase the average time in the queue as more requests accumulate and have to wait to be processed. The greater the increase in occupancy, the greater the impact on average latency.
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What is the solution?
Answer:
336.
Step-by-step explanation:
8P3 = 8! / (8 - 3)!
= 8*7*6*5*4*3*2*1 / 5*4*3*2*1
= 8*7*6
= 336
1/8 of a number is 56. What is the number?
1/8 of a number is 56. The number is equal to 448.
let the number=x
1/8 of a number means we have to multiply 1/8 with x.
1/8 of a number =1/8x
now according to the condition, 1/8 of a number is 56 which means that we have 1/8x equal to 56.
1/8x=56
which gives us a simple algebraic equation in a single variable x. we can solve it accordingly .i,e multiplied 8 on both sides of the equation gives
x=56*8
x=448.
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Please answer all four questions (they are simple and go with the diagram)
(1) The measure of the angle CFD = 48°.
(2) The measure of the angle AFE = 48°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
What are the properties of angles?
The angle properties of lines are:
Vertically opposite angles are equal, for example, a = d, b = c.
Adjacent angles add to 180, for example, a + b = 180, a + c = 180. Corresponding angles are equal, for example, a = e, b = f, c = g, d= h.
(2) In the given figure, m∠BFC = 42°
By using the property of linear pair, we can write
∠BFC + ∠CFD = 180
42 + ∠CFD = 180
∠CFD = 58.
(2) Angle CFD and angle AFE are opposite angles and opposite angles are same in measurement so we can write
m∠AFE = 58°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
Hence,
(1) The measure of the angle CFD = 48°.
(2) The measure of the angle AFE = 48°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-3
Step-by-step explanation:
5 + ( -8 )
-8 - 5 = -3
so final answer: -3 because ( - 8 ) so the ( - ) would go on the answer
Answer: -3
Step-by-step explanation: It would be -3 because since we are adding a negative it would go toward the negative side. Also, it can be modeled as:
5 - 8
This would still = -3.
Please answer this question ty.
Answer:
u forgot the question...........
Is any additional information needed to show △≅△?
Answer:
No
Step-by-step explanation:
To prove 2 triangles an congruent we need three pieces of information
SSS or SAS or ASA or RHS
S - Side
A - Angle
R - Right angle
H - Hypotenuse
We have an angle side and another side
So these two triangles can be proved congruent by SAS
Hope this helped and have a good day
How do you find the nth term of the sequence 2,4,16,256,... ?
The [tex]n^{th[/tex] term of an exponentially increasing sequence can be found using the formula:
[tex]a_n = a_1[/tex] × [tex]r^(^n^-^1^)[/tex]
To find the [tex]n^{th[/tex] term of a sequence, you can use a formula that defines the relationship between the terms of the sequence. In this particular sequence, the terms seem to be increasing exponentially, with each term being the square of the previous term.
The [tex]n^{th[/tex] term of an exponentially increasing sequence can be found using the formula:
[tex]a_n = a_1[/tex] × [tex]r^(^n^-^1^)[/tex]
where [tex]a_n[/tex] is the nth term of the sequence, [tex]a_1[/tex] is the first term of the sequence, and r is the common ratio.
In this case, the first term is 2, and the common ratio is the previous term divided by the term before it. In this sequence, the common ratio is [tex]\frac{4}2=2[/tex]
Therefore, the [tex]n^{th}[/tex] term of the sequence can be found using the following formula:
[tex]a_n = 2[/tex] × [tex]2^{(n-1)[/tex]
So to find the [tex]n^{th[/tex] term, you would plug in the value of n into the formula. For example, to find the fifth term of the sequence, you would plug in 5 for n:
[tex]a_5 = 2[/tex] × [tex]2^{(5-1)[/tex]
= 2 × [tex]2^4[/tex]
= 2 × 16 = 32
So the fifth term of the sequence is 32
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A theater seats 500 people. Each adult ticket, a, sells for $7.50, and each student ticket, s, for $4.50. On a Friday evening, every seat was filled, and the theater made $3,150 in ticket sales. Which system of equations could be used to find the number of adult and student tickets sold on Friday evening?
a + s = 3,150
7.5a + 4.5s = 3,150
a + s = 500
7.5a + 4.5s = 3,150
a + s = 3,150
7.5s + 4.5a = 500
a + s = 500
7.5a + 4.5s = 500
Answer:
The two equations that can be used are 7.50a + 4.50s = 3150, and
a + s = 500.
----------------------
a + s = 3,150 NO
7.5a + 4.5s = 3,150 YES
a + s = 500 YES
7.5s + 4.5a = 500 NO
Step-by-step explanation:
We know that a + s = 500.
Total sales would be the product of the number of adult and student tickets times their repsective prices:
Total Sales ($) = $7.50a + $4.50s = $3150
Leaving off the units for the next steps, we have two equations and we can rearrange one of them to substitute into the other.
1) Rearrange the first equation to isolate a: a = 500-s
Now use this definition of a in the second equation:
7.50a + 4.50s = 3150
7.50(500-s) + 4.50s = 3150
3750 - 7.5s + 4.50s = 3150
-3s = -600
s = 200 student tickets were sold
Use a+s=500 to find a:
a+200 = 500
a=300 300 adult tickets were sold.
================
The two equations we used to find this answer were:
7.50a + 4.50s = 3150, and
a + s = 500
