b. Total Sample = 300 college students
The question is asking how many people were in the sample of 300 college students that were asked if they were interested in playing video games. The answer is option B: 300.
To answer this question, we must first understand the context of the question. It is asking about the number of English-speaking people on the planet who want to play a new kind of online video game. To answer this, 300 college students were asked if they were interested in playing video games. Of those 300 students, 100 said yes, and 20 of those students preferred this new game to an existing game that is widely used. Therefore, the sample size was 300.
The sample size is 300 college students. From the 300 college students, 100 said yes to playing video games. Of these 100, 20 preferred the new game to an existing game. Therefore, the sample size is 300 college students.
Total Sample = 300
No. of Yes = 100
No. of Prefers new game = 20
So, Total Sample = 300 college students
Learn more about total sample here:
https://brainly.com/question/1477952
#SPJ4
at memorial hospital, jamie operates a new state-of-the-art mri scanner that serves approximately 10 patients during an 8-hour shift. patients are scheduled for various lengths of time, depending on the complexity of their scan. the image quality is significantly superior to what it was on previous scanners, but the number of patients served per day remains the same. this situation attests to the fact that
The image quality is significantly superior to what it was on previous scanners, but the number of patients served per day remains the same. this situation attests to the fact that the service sector has seen improvement in quality of service, but productivity remains about the same.
Improvement in quality of service:
Putting the customer first, balancing efficiency and customer satisfaction (experience), and focusing on employee engagement are three key strategies for improving contact center service quality.
Productivity:
Productivity is the efficiency with which goods and services are produced and is represented by a scale. A measure of productivity is often expressed as a ratio of total output to a single input or total input in a production process. Typically the output per unit of input over a period of time. The most common example is a measure of (aggregate) labor productivity, an example of which is GDP per worker. There are various definitions of productivity (including those not defined by the ratio of outputs to inputs), and the choice depends on the purpose of measuring productivity and the availability of data gain. The main reason for differences in different measures of productivity usually has to do with how outputs and inputs are aggregated (directly or indirectly) to obtain such relative measures of productivity doing conduct.
Importance of Productivity:
Productivity gains are defined as the process of getting more out of every hour of work. Improving productivity can take many forms, including: Capital, Investments in equipment, software, infrastructure, machinery, etc. equate to labor. Productivity is important for individuals (workers and consumers), business leaders, and analysts(such as policy makers and government statisticians).
Learn more about Number:
https://brainly.com/question/3589540
#SPJ4
Bora paid $10.00 for 45 tokens to play arcade games. Use a ratio table to find how many tokens he would receive for $16.00.
Answer: 72
Step-by-step explanation: (Look at the attachment for the best experience)
First, we need to know how to set up our table. So, sometimes we need to divide and then multiply to find the equivalent ratio. So now we can piece information together to find the missing numbers. So, the far left is the information we are given. So, both of them can be divided by 5 (as the highest) and then we get 2 and 9. Then, since we know that we can multiply 2 by 8 to get 16, we do the same for 9. So, 9 x 8 = 72, making that how many tokens Bora can pay with only 16 dollars. I hope this helped!
c) calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%
The tolerance interval that included 99% of the cadence values with a 95% confidence is equal to (0.634,1.218).
A tolerance interval is constructed using the following formula:
TI= overline x plus/minus t * o l k,n (s)
Let, k = 0.99 and n = 20
to l 0.99,20 =3.615
The following calculations are done to compute the tolerance interval:
TI= overline x plus/minus t * o l k,n (s)
= 0.9255 plus/minus 3.615 * (0.0809)
approx (0.634, 1.218)
In summary, with a 95% level of confidence, 99% of the cadence values fall within the tolerance interval of (0.634, 1.218).
Learn more about Tolerance interval here: brainly.com/question/14985398
#SPJ4
College freshmen were asked if they were currently enrolled in Composition I. The results are shown in the table.
Enrolled in Composition I Not enrolled in Composition I Row Totals
Males 87 122
Females 46
Column Totals 81 251
How many females are currently not enrolled in Composition 1?
46
83
129
170
Answer:
Step-by-step explanation:
83
To find the number of females who are not enrolled in Composition I, we can look at the table and find the total number of females and subtract the number of females who are enrolled in Composition I.
The total number of females is found in the "Column Totals" row, in the second column, and is 251.
The number of females enrolled in Composition I is found in the "Males" row, in the second column, and is 46.
So the number of females who are not enrolled in Composition I is:
251 (total number of females) - 46 (females enrolled in Composition I) = 205
Therefore, the answer is 83.
8/5 times what equals 2?
Answer:
5/4 should be the answer.
Step-by-step explanation:
2 divided by 8/5 = 5/4
Answer:
Step-by-step explanation:
x is 5/4
8x/5=2
8x=10
x=5/4
if theta is an angle in q2, will sec (theta) be positive or negative
The reading of the angle sec θ in the second quadrant of the given problem is; Negative
How to interpret trigonometric ratios?There are 6 main trigonometric ratios and if we can use which are;
sin θ
cos θ
tan θ
secθ
cotan θ = sin θ/cosθ
cosec θ = 1/sin θ
sec θ = 1/cos θ
Now, we are told that sec θ is in the second quadrant and we know that in the second quadrant only sin θ and cosecθ are positive and as such sec θ will be negative.
Read more about trigonometric ratios at; https://brainly.com/question/13276558
#SPJ1
Cameron and his children went into a movie theater where they sell drinks for $6 each and candies for $5 each. Cameron has $100 to spend and must buy at least 18 drinks and candies altogether. If xx represents the number of drinks purchased and yy represents the number of candies purchased, write and solve a system of inequalities graphically and determine one possible solution.
One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
We can write a system of inequalities to represent the situation as follows:
6x + 5y ≥ 90 (because Cameron must spend at least $90 on drinks and candies)
x + y ≥ 18 (because Cameron must buy at least 18 drinks and candies altogether)
x ≥ 0, y ≥ 0 (because Cameron can't buy negative number of drinks or candies)
To graphically represent the solution set of this system, we can plot the inequalities on a coordinate plane. We can start by drawing the line representing the first inequality: 6x + 5y = 90. To find the slope-intercept form of this equation we can subtract 90 from both sides, 6x + 5y - 90 = 0, and we get: 6x + 5y = 90.
The second inequality is x + y ≥ 18 which is a boundary line.
The third inequality is x ≥ 0 and y ≥ 0 which means that both x and y should be non-negative.
The solution set of this system of inequalities is the intersection of the half-planes defined by the inequalities. This is the set of all points that lie in all three half-planes. One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
Therefore, One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
To learn more about inequalities,
Visit; brainly.com/question/30231190
#SPJ4
In the grating equation nλ=d sin θ, the quantity θ will be determined in the labusing the angular scale on the experimental apparatus.using meter sticks and geometry/trigonometry.using a protractor.
In the grating equation nλ=d sin θ, the quantity θ will be determined in the lab by using meter sticks and geometry/trigonometry
The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign
Here we have given that the grating equation nλ=d sin θ, the quantity θ will be determined in the lab.
The term grating equation in math states that d = 1/N where N is the grating constant, and it is the number of lines per unit length and n is the order of grating, which is a positive integer, representing the repetition of the spectrum.
And the term trigonometry is defined as a branch of mathematics concerned with relationships between angles and ratios of lengths.
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
A store owner bought a batch of teddy bears for $120. She sells the teddy bears at a markup of 20% and made a profit of $24. How many teddy bears did she buy in the batch?
EA and ED are perpendicular. EB intersects AEC. Given that measure angle AEB equals 4x+1 and measure angle CED equals 3x, determine the missing measures.
Answer:
x= 12.714°
Step-by-step explanation:
<AEB + <CED = 90°
4x+1+3x = 90°
7x+1= 90°
7x=89
x= 12.714°
The data pairs (x,y) represent the average annual tuition y (in dollars) for public colleges in the United States x years after 2005. Use the linear regression feature on a graphing calculator to find an equation of the line of best fit. Round the value of the slope and the value of the y-intercept to the nearest hundredth. Then estimate the average annual tuition in 2020 to the nearest hundred dollars. (0, 11,386), (1, 11,731), (2, 11,848), (3, 12,375), (4, 12,804), (5, 13,297)
Average annual tuition in 2020 is 14,286.70.
What is value?Value is the worth of something in terms of its usefulness, quality, or importance. It is the importance that an individual, group or organization places on something and is an important concept in economics, business and politics. Value can be seen as a measure of how much someone or something is worth, both in terms of money and in terms of intangible qualities, such as respect or admiration. Value is subjective, meaning that it is based on personal opinion and perspective.
Using a graphing calculator, the equation of the line of best fit is y = 96.98x + 11145.46. The slope of the line is 96.98 and the y-intercept is 11145.46.
By substituting x = 15 into the equation, the estimated average annual tuition in 2020 is 14,286.70. This can be rounded to the nearest hundred dollars, giving an estimate of 14,300 dollars.
To know more about value click-
https://brainly.com/question/24281057
#SPJ4
Solve the absolute value equation.
|x−2| – 7 = –3
Answer: x =6 or x =-2
Step-by-step explanation:
|x−2|−7=−3
Step 1: Add 7 to both sides.|x−2|−7+7=−3+7|x−2|=4
Step 2: Solve Absolute Value.|x−2|=4 We know either x−2=4orx−2=−4x−2=4(Possibility 1)x−2+2=4+2(Add 2 to both sides)
x=6
and for other
x−2=−4(Possibility 2)x−2+2=−4+2(Add 2 to both sides)x = -2
Sandy Schabel owns 400 shares of Exxon
Mobil (XOM) stock. After the quarterly dividends are reinvested
under a dividend reinvestment program (DRIP), she owns
401. 6 shares. XOM is selling at $86. 40 a share. Find the annual
dividend per share and the annual yield for XOM
The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%. Multiply the result by 100 to get the annual yield in percentage: 0.0415 x 100 = 4.15%
Annual dividend per share: $3.60
Annual yield: 4.15%
1. To find the annual dividend per share, divide the increase in shares (1.6) by the number of shares owned before the reinvestment (400).
1.6/400 = 0.004
2. Multiply the result by the current share price of XOM ($86.40):
0.004 x 86.40 = $3.60
3. To find the annual yield, divide the annual dividend per share by the current share price of XOM ($86.40):
3.60/86.40 = 0.0415
4. Multiply the result by 100 to get the annual yield in percentage:
0.0415 x 100 = 4.15%
The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%.
Learn more about percentage here
https://brainly.com/question/16797504
#SPJ4
A locat sollege hosts a science competition for 1,014 elementary and middle school students. Three awards are given at each grade level. An equal number of students enters the competition from each grade. 3 through 8, How many students from each grade level enter the science competition?
When there are 1,014 elementary and middle school pupils, X2 = 175 students from each grade level participate in the science competition.
What is standard deviation ?When the standard deviation is low and high, it is argued that data are more evenly distributed and more densely clustered around the mean, respectively. The standard deviation is a measurement of how widely the data are scattered from the mean value. Comparing data sets that may have the same mean but a distinct range may be aided by it. For example, the means of the two integers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are identical. The second, though, is obviously wider.
given
X1
u1 = 400 u2 = 100
20 25
X2
Z1 score = Z2 score
X1 - u1 / 20 = X2 - u2 / 25
460 - 400 / 20 = X2 -100 / 25
3 = X2 - 100 /25
X2 = 175 score on exam b
When there are 1,014 elementary and middle school pupils, X2 = 175 students from each grade level participate in the science competition.
To know more about standard deviation visit :-
brainly.com/question/23907081
#SPJ1
Could any of you guys help me answer this question pls the homework is due today!
Step-by-step explanation:
y = 37 + x
the 4th angle (bottom right) is
360 - 90 - 90 - 125 = 55°
because the sum of all angles in any quadrilateral is 360°.
now we can assume a right-angled triangle on the right side of the trapezium.
one leg is 15 cm (like the left side), the other leg is x cm. and the right side of the trapezium is the Hypotenuse.
the bottom right angle is 55°.
the upper angle is 125 - 90 = 35°.
we can use the law of sine to get x.
the law of sine is
a/sin(A) = b/(sin(B) = c/sin(C)
with a, b, c being the sides of the triangle opposite of the corresponding angles A, B, C.
so,
15/sin(55) = x/sin(35)
x = 15×sin(35)/sin(55) = 10.50311307... cm
y = 37 + 10.50311307... = 47.50311307... ≈
≈ 47.5 cm
How can you check to see if the ratio 1/2 is equivalent to another ratio?
To check if two ratios are equivalent, you can divide both ratios by the same number until you reach the same result. For example, if you divide both 1/2 and 3/6 by 2, you will get the same result of 1/3.
To check if two ratios are equivalent, you can divide both ratios by the same number until you reach the same result. For example, if you divide both 1/2 and 3/6 by 2, you will get the same result of 1/3.
1. Take both ratios, 1/2 and 3/6
2. Divide both ratios by the same number, in this case 2.
3. This will give you the equivalent results of 1/3.
4. Therefore, 1/2 is equivalent to 3/6.
To check if two ratios are equivalent, divide both ratios by the same number until you reach . In this case, 1/2 is equivalent to 3/6.
Learn more about ratio here
https://brainly.com/question/13419413
#SPJ4
A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. after one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. the fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. have the conditions for inference been met?
Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.
Describe statistics.It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.
The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.
To know more about statistics visit:
brainly.com/question/29342780
#SPJ4
find the general solution of the given differential equation. x dy/ dx − y = x^2 sin x
To find the general solution of the given differential equation x dy/ dx − y = x^2 sin x, we must use a series of calculations.
First, we need to separate the variables, so y can be expressed as a function of x. To do this, we divide both sides of the equation by x, giving us the equation dy/dx = x sin x + y/x.
Next, we will need to use integration to find the general solution. To integrate, we need to find an antiderivative of the equation dy/dx = x sin x + y/x. To do this, we can use the formula ∫xdx = 1/2 x^2 + c. Using this formula, we can integrate both sides of the equation to get 1/2 x^2 + c = x sin x + ∫ y/x dx.
We can then solve for the antiderivative of y/x, which is ln|y| + c. Therefore, the general solution of the equation is 1/2 x^2 + ln|y| + c = x sin x + c.
Finally, we can solve for y in terms of x to get y = x^2 sin x + c'e^(1/2 x^2), where c' is the integration constant. This is the general solution of the given differential equation.
To learn more about equation, click here:
https://brainly.com/question/29657988
#SPJ4
i am stuck with this question please help with this!!
-thank you!
Answer: 60in²
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
So to solve this, you need to know how to find the area of a trapezoid.
In case you don't know this equation, I'll explain it briefly.
The area of a trapezoid = (a+b)*h/2, where a and b are the base lengths and h is the height of the trapezoid.
We can solve this problem using this equation, which would look like:
Area = (9+11)*6/2
= 20*6/2
= 60
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 25.0
Step-by-step explanation:
[tex]\frac{x}{\sin 65^{\circ}}=\frac{22}{\sin 53^{\circ}}\\\\x=\frac{22 \sin 65^{\circ}}{\sin 53^{\circ}}\\\\x \approx 25.0[/tex]
assume your professor has given you 60 minutes to complete a specific assignment. you have worked on the assignment for 45 minutes but have not yet completed the assignment. a friend stops by and asks you to go out for a couple of hours. what should you do?
The best course of action would be to politely decline the offer and explain to your friend that you still have to finish the assignment.
What is minutes?Minutes is a record of the proceedings of a meeting or other event. It is typically written by the secretary of the meeting and contains a summary of the main points discussed, decisions taken, and any action points arising from the meeting. Minutes are an important part of any organization as they provide a record of the decisions taken and an opportunity for review. Minutes can also help to keep everyone on track and ensure that everyone is aware of their responsibilities.
Even though your friend may be disappointed, they will understand. It is important to prioritize your school work and stay on top of assignments, so you should continue to work on the task at hand.
If you find yourself struggling to stay focused, it can help to break down the assignment into manageable chunks and set a timer for each chunk. This can also help you stay on track with the time limit that your professor gave you. Additionally, taking a few minutes to get up and stretch or grab a snack can help you stay energized and productive.
If you need additional help, reach out to your professor or a tutor. You can also ask a classmate for help or advice. Your professor likely will not mind if you ask for an extension on the assignment, as long as it is reasonable and you provide a valid reason.
Remember, it is important to prioritize your school work and stay on top of assignments. It is ok to take breaks and accept help, but be sure to stay focused on the task at hand.
To know more about minutes click-
https://brainly.com/question/2078551
#SPJ4
Use the distributive property to remove the parentheses
(-4+v+4x)(-6)
Answer:
24-6v-24x
Step-by-step explanation:
(-4 +v + 4x) × (-6)
Apply the Distributive Property:
- (-6) × 4+ (-6) × v + (-6) × 4x
Determine the sign:
6 × 4 - 6v - 6 × 4x
Calculate the product or quotient:
24 - 6v -6 × 4x
Multiply the monomials:
24 - 6v - 24x
Hope this helps you :)
Answer:
24-6v-24
Step-by-step explanation:
first distribute -6 to all other numbers as shown below.
(-4 . -6)+(v . -6)+(4x . -6)
then we will get 24-6v-24x
A cylinder and the Sphere below have the same radius and the same volume. What is the height of the cylinder
Answer:
8 m
Step-by-step explanation:
Volume of a sphere is V = 4/3 π r³.
Volume of a cylinder is V = π r² h.
The two volumes are equal, so:
4/3 π r³ = π r² h
4/3 r = h
The radius is 6 m, so the height of the cylinder is:
h = 4/3 (6 m)
h = 8 m
Answer:
The height of the cylinder is 8m.
Step-by-step explanation:
Given, the Radius and Volume of the cylinder and sphere are equal.
Radius, r = 6m
Formula,
Volume of the sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
⇒ Volume of the cyliner = Volume of Sphere
⇒ [tex]\frac{4}{3}\pi r^{3}[/tex] = [tex]\pi r^{2}h[/tex]
⇒ [tex]h = \frac{4\pi r^{3} }{3\pi r^{2} }[/tex]
⇒ [tex]h = \frac{4r}{3}[/tex]
⇒ [tex]h = \frac{4 * 6}{3}[/tex]
⇒ h = 8m
Sorry for the fact that this is in French but i have exams coming up and i don’t understand this concept. You can translate and explain in English, idc. It’s Annuities
Annuité : Une série d'un nombre donné de versements ou de retraits périodiques.
Annuité de fin de période : Une annuité dont les versements sont effectués à la fin de
chaque période.
M = (R[(1 + i)^n −1])/i
M représente le montant total au moment du dernier versement
R représente la somme versée périodiquement, en dollars
i représente le taux d'intérêt par période de capitalisation, sous forme décimale
n représente le nombre de périodes de capitalisation.
Ex1. À la fin de chaque mois, pendant 3 ans, Patrick dépose 100 $ dans un compte qui
rapporte 6% d'intérêt par année, composé mensuellement.
a) Détermine le solde du compte au bout de 3 ans
b) Quel est le total de l'intérêt accumulé ?
a) Pour déterminer le solde du compte au bout de 3 ans, nous devons utiliser la formule de l'annuité de fin de période. Il y a un total de 3 ans x 12 mois/an = 36 mois de capitalisation. Le taux d'intérêt par mois est de 6%/12 = 0.005. La somme déposée chaque mois est de 100 $. En utilisant la formule, nous pouvons calculer le solde final:
M = (R[(1 + i)^n −1])/i
M = (100 [(1 + 0.005)^36 −1])/0.005 = $51,664.23
b) Pour calculer le total de l'intérêt accumulé, nous pouvons soustraire le montant total des dépôts (100 $ x 36 mois = $3,600) au solde final du compte.
Intérêt accumulé = Solde final du compte - Montant total des dépôts
Intérêt accumulé = $51,664.23 - $3,600 = $48,064.23
En résumé, le solde final du compte après 3 ans est de 51,664.23 $ et l'intérêt accumulé est de 48,064.23 $.
J'espère que cela aide et a été correctement traduit haha
henry find he can type 70 words in 5 minutes and that in 8 minutes he can type 112 words
If henry can 70 words in 5 minutes and that in 8 minutes he can type 112 words the rate of change is 14.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Henry can type 70 words in 5 minutes and that in 8 minutes he can type 112 words.
m=112-70/8-5
=42/3
=14
Hence, the rate of change is 14.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ1
the sum of the first 5 terms of an arithmetic series is $70$. the sum of the first 10 terms of this arithmetic series is $210$. what is the first term of the series?
Therefore ,as a result, 42/5 is the value of the first term in the equation for the arithmetic mean.
What does arithmetic mean?The arithmetic average or means of the group is calculated as the sum of each value in a list divided by the total number of things in that list. The progression in mathematics is the same as this. The average of the integers 5, 7, and 9 is 4, as shown by the equation 5 + 7 + 9 being equal to 21, and 21 divided by 3 (there are actually three numbers) being equal to 7.
Here,
Given :
5 a + 10 d = 70 in the first five terms (1)
The first ten terms add up to 10 a + 45 d = 210. (2)
This means that in order to solve the system for a, multiply equation (1) by 2, then subtract it from equation (2):
=> 10a - 10a + 45d - 20d = 210-140
=> 25d = 70
=> d = 70/25
=> d = 14/5
A value then becomes:
5a + 10*14/5 = 70;
5a = 70-140/5;
5a = 350-140/5;
a = 42/5.
42/5 is the response.
As a result, 42/5 is the value of the first term in the equation for the arithmetic mean.
To know more about arithmetic mean , visit
brainly.com/question/13000783
#SPJ4
Triangle ABC is congruent to Triangle PDF. Side AC corresponds to what side in Triangle PDF?
Answer:
the angle that corresponds to AC IS PF
Find the exact value of the area
of the shaded region. The length
of the side of the grid squares
is I unit.
Answer:
91.1cm²
Step-by-step explanation:
since all of them are quarters of circles
area of figure 1 = (π(r.1)²)÷4 = (64π)÷4= 16π cm²
area of figure 2 = (π(r.2)²)÷4 = (25π)÷4= 6.25π cm²
area of figure 3 = (π(r.3)²)÷4 = (9π)÷4= 2.25π cm²
area of figure 4 = (π(r.4)²)÷4 = (4π)÷4= 4π cm²
area of figure 5 = (π(r.5)²)÷4 = (π)÷4 cm²
area of figure 6 = (π(r.6)²)÷4 = (π)÷4 cm²
the total area = 16π+6.25π+2.25π+4π+2(π÷4)=
28.5π+0.5π = 29π = 91.1cm²
a fair die is rolled four times. what is the proba bility that each of the final three rolls is at least as large as the roll preceding it?
The probability is 7/72 that each of the final three rolls is at least as large as the roll preceding it.
Let [tex]N_{i}[/tex] represent the number appearing on die when die is rolled ith time,
i=1,2,3,4
Given that [tex]N_{1}[/tex]≤[tex]N_{2}[/tex]≤[tex]N_{3}[/tex]≤[tex]N_{4}[/tex]
Each time when a die is rolled, six options are there.
Let we have four equal sets
{1,2,3,4,5,6}, now we have to select four numbers such that, exactly one number is selected from each set
Case 1: All four are same
Number of ways:⁶C₁ =6
Case 2: Three are same but one is different
Number of ways: ⁶C₁ ⁵C₁ =30
Case 3: Two are same of one kind and two are same of second kind
Number of ways: [tex]\frac{1}{2}[/tex] ⁶C₁ ⁵C₁=15
Case 4: Two are same and two are different
Number of ways: ⁶C₁ ⁵C₂=60
Case 5: All four are different
Number of ways: ⁶C₄=15
Required probability:
=[tex]\frac{6+30+5+60+15}{6*6*6*6}[/tex]
=[tex]\frac{126}{36*36}[/tex]
=[tex]\frac{72}{7}[/tex]
For further information regarding die probability, click the link below:
brainly.com/question/4407739
#SPJ4
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5. 4 years and a standard deviation of 2. 1 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined
Using the central limit theorem to find the mean is 5.4 and the standard error of the mean of the indicated sampling distribution is 0.6.
We must utilize the central limit theorem to determine the mean and standard error of the mean of the sample distribution in the given query.
Considering the posed query,
The company has a mean age of 5.4 years and is normally distributed.
2.1 years of standard deviation.
The population is sampled at random with an n = 12 size, and the mean of each sample is calculated.
The mean is determined using the central limit theorem.
μ(x) = μ = 5.4
The standard error of the mean of the indicated sampling distribution is:
σ(x) = σ/√n
σ(x) = 2.1/√12
σ(x) = 2.1/3.5
σ(x) = 0.6
To learn more about the central limit theorem
brainly.com/question/18403552
#SPJ4