Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then
The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..
Indicator method :
This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.
let X₁ be the outcome of a 10 sided die
X₂ be the outcome of 13 sided die
X₃ be the outcome of 5 sided die
let l₁ ,I₂ ,I₃ be three indicator functions such that
I₁ =1 if X₁ = 1
=0 otherwise
I₂ = 1 if X₂ = 1
=0 otherwise
I₃ = 1 if X₃ = 1
=0 otherwise
so Z denotes the number of ones showing when the three dice are rolled once.
so Z=I₁ +I₂ +I₃
so E[Z]=E[I₁]+E[I₂]+E[I₃]
so E[I₁]=1×P[X₁=1] = 1/10
E[I₂]=1×P[X₂=1] = 1/13
E[I₃]=1×P[X₃=1] = 1/5
so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769
the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.
V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09
V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071
V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16
so V[Z]= 0.09 + 0.071 + 0.16 = 0.321
Hence, the expectation value i.e, E(Z) is 0.3769..
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suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000 with a standard deviation of $2,500. use the 68-95-99.7 rule to find the percentage of buyers who paid.b) more than $155,000
Percentage of buyers who paid more than $155,000 is equal to 2.78%.
What is standard deviation?The standard deviation is a metric that reveals the degree of variation (such as spread, dispersion, and spread) from the mean. The standard deviation represents a "average" departure from the mean. Because it uses the original units of measurement from the data set, it is a well-liked measure of variability. Similar to variance, there is little variation when data points are close to the mean, but there is much variation when data points are widely scattered from the mean. The amount of departure from the average is determined by standard deviation. The most common measurement of dispersion, the standard deviation, is based on all values. Therefore, a change in even one value has an impact on the standard deviation's value. It is
Given:
Mean is $150,000, and
Standard deviation is $2500.
We need to determined the percentage of buyers who paid more than $1,55,000 as per given mean and standard deviation.
By using z score formula can be use to calculate the percentage of the buyer who paid,
z= [tex]\frac{x-μ}{σ}[/tex]
As given in question sample mean i.e. X= 150,000
= [tex]\frac{1,55,000- 1,50,000}{2500}[/tex]
=2
By using standard normal distribution table,
P(X > 155000) = P( z > 2 )
= 1 - 0.9772
=0.0278
Hence, it is equal to 2.78%.
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I need help thank you. (pls give a proper explanation) here is the question I need this asap pls answer quick
...............................
To keep track of each student's preferred hue, Mr. Roberson constructed a frequency table. According to the frequency chart, the following statements are accurate:
Twice as many students prefer green than purple.Two more students prefer blue than purple.Hence, Options B and D are correct.
What is the meaning of the term “frequency table”?The number of times a specific value appears in the data is the value's frequency. Frequency tables or charts are used to represent frequency distributions.
A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.
Therefore, Options B and D are correct.
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mary has 16 forks and 12 knives to place in silverware holders at the fast food restaurant where she works. she wants to distribute them equally, with no forks or knives left over. what is the greatest number of silverware holders mary can stock?
The greatest number of silverware holders Mary can stock is 4, each containing 4 forks and 3 knives so that no fork or knife is left over and are distributed equally.
What is distribution?
When a quantity is to be distributed equally into a certain number of groups, we divide the quantity by the number of groups.
Equating number of silverware stocks :Given: 16 Forks and 12 knives
To find: number of silverware stocks = ?
As we know that the knives and forks should be distributed equally in each silverware holder, 4 forks and 3 knives will go into each of the silverware holder.
Now, we need number of silverware holders each having same number of forks and knives.
4 forks×4 = 16
3 knives× 4 = 12
∴ Number of silverware holders Mary requires to distribute knives and forks equally with no left over is 4.
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Jenna received some gift cards for music and movie downloads for her birthday. Using one of
them, she downloaded 16 songs and 2 movies, which cost a total of $46. Using another, she
purchased 1 movie, which cost a total of $15. How much does each download cost?
Answer:
Step-by-step explanation: 500
4. Find the value of x and the length of the three sides.
Answer:
I think the values are :
Step-by-step explanation:
AC= -5
CB= -2
AB= -3
help please got the answer -.75 but don't think it's the right answer, please help or
Verify. The first to answer correctly will be rewarded the brainleyest
Answer:
f = 8
Step-by-step explanation:
First, let's multiply this equation out
10 = 3f - 15 + 1
Simplify:
10 = 3f - 14
Add 14 to both sides:
24 = 3f
Divide both sides by 3:
f = 8
Let's plug this in to make sure:
10 = 3(8 - 5) + 1
10 = 24 - 15 + 1
10 = 24 - 14
10 = 10
Thus, the answer is not -75, but I applaud you for trying before coming here!
I hope this helped!
an executive hires 3 office workers from 8 applicants. (a) in how many ways can the selection be made?
The number of ways can the selection be made is 84.
Given:
an executive hires 3 office workers from 8 applicants.
a ) .
Number of ways = C ( 8 , 3 )
C ( n , r ) = n! / ( n - r ) ! r!
C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!
= 8! / 5! * 3 !
= 8 * 7 * 6 * 5! / 5! * 3!
= 56 * 6 / 3!
= 56 * 6 / 3 * 2 * 1
= 56 * 3 / 2 * 1
= 28 * 3 / 1
= 28 * 3
= 84 ways
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The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each
year from 2010 through 2016 can be approximated by the models = 254 − 9 + 1. 12 and = 341 +
3. 2 where t is the year.
Write a function P that represents the annual profit of the company.
(Profit = Revenue − Cost)
A function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
Describe the term Function?Function: A relationship between two variables, one of which is dependent on the other and the other of which is independent, is represented by an expression.The overall cost incurred by a business (or organization) for one employee over the course of a year is known as the annual cost.We provided Cost C. ( in thousand of dollar)
And a company's revenue R (in thousands of dollars).
C is the cost function.
C = 254 - 9t + (1.1)t²Revenue function R = 341 - 3.2t where t time in year .The value t = 9 is 9 years.
If P is the Annual profit. Then,
Profit = Revenue − Cost
P = R - C
P = 341 - (3.2)t - 254 - 9t + (1.1)t²
= (1.1)t² - (12.2)t + 87
Thus, a function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
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Complete Question:
The annual cost C in thousands of dollars and revenue R in thousands of dollars for a company each year from 2010 through 2016 can be approximated by the models C = 254 − 9t + 1.1t2 and R = 341 + 3.2t where t is the year, with t = 10 corresponding to 2010.
(a) Write a function P that represents the annual profit of the company.
Help fast due soon
Given: AC = CB
CD Bisects AB
Prove: AADC= ABDC
What are the statements and reasons
Answer:
Step-by-step explanation:
Given: AC = CB
CD Bisects AB
Prove: ΔADC= ΔBDC
AC≅CB Given
AD ≅ DB are congruent because of the segment bisector theorem.
DC≅DC reflexive property
ΔADC≅ ΔBDC SSS theorem
five hamburgers cost 5.25 at this rate what is the cost of 8 hamburgers
Answer: 8.4
Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4
Find the absolute extrema for the given function on the interval [15.6, 19.2). Write your answer in the form (x.f(x)). Round your answers to two decimal places. f(x) = In (12x^2 - 11x + 2)
Absolute Minimum: Absolute Maximum
we use is the derivative of top times bottom times top over bottom squared. At the critical point, we want eight X ln x minus four X to equal zero.
Only one answer—two x minus one and one x minus half—will satisfy the condition. The largest and smallest endpoints on the left and right must be determined. On each of these items, there is an E square root. A maximum for the minimums occurs at critical point or endpoints. We can see that these will be absolute according to the extreme value theorem, and here is our maximum.
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Select the correct answer. How many solutions does this system of equations have? y = x^2 + x + 3, y = -2 - 5
A. No solution
B. 1 solution
C. 2 solutions
D. 3 solutions
The system of equations has no solutions, the correct option is A.
How many solutions does the system of equations has?
The system of equations is:
y = x^2 + x + 3
y = -2x -5
The system can be solved if we solve the equation:
-2x - 5 = x^2 + x + 3
So we need to solve that quadratic equation, we can rewrite it as:
x^2 + x + 3 + 2x + 5 = 0
x^2 + 3x + 8 = 0
Let's check the discriminant to see how many solutions we have:
D = (3)^2 - 4*1*8
D = 9 - 32 = -23
We have a negative discriminant, so we only have complex solutions, thus, the system of equations has no solutions.
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Madelyn launches a toy rocket from a platform. The height of the rocket in
feet is given by h(t) = -16t² + 16t+ 96 where t represents the time in
seconds after launch. What is the appropriate domain for this situation?
Answer:
The domain of the function (t) in h(t) = -16t² + 16t+ 96 should be greater than or equal to 3 seconds.
What are inequalities?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The symbol a < b indicates that a is smaller than b. When a > b is used, it indicates that a is bigger than b.
Given that height of the rocket in feet is given by h(t) = -16t² + 16t+ 96 where t represents the time in seconds after launch
We know that height can not be negative.
∴ h ≥ 0.
So, - 16t² + 16t+ 96 ≥ 0.
- t² + t+ 6 ≥ 0.
t ≥ 3 seconds.
Therefore the domain of the function (t) in h(t) = -16t² + 16t+ 96 should be greater than or equal to 3 seconds.
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At Master Street Elementary School
there are 22 classrooms. If there are
30 students in each classroom, how
many students are there in the entire
school?
660 or it may not be that because only said that theres 22 classrooms. So yeah ;)
30 x 22 = 660 its just multiplication
length
Quantity
amount of substance
luminous intensity
US Customary Units
inch (in), foot (ft), yard (yd), mile (mi)
ounce (oz), pound (lb), ton (tn)
fluid ounce (fl oz), pint (pt), quart (qt),
gallon (gal)
second (sec), minute (min), hour (hr)
degrees Fahrenheit ("F)
SI Units
kilometer (km), meter (m), centimeter
(cm), millimeter (mm)
second (s)
Kelvin (K)
kilogram (kg), gram (g), milligram (mg)
ampere (A). milliampere (mA)
mole (mol)
candela (cd)
Answer:
Step-by-step explanation:
All units of a physical measure are linked via a conversion factor. On this web page for every unit you can find the conversion factor compared to the base unit (SI unit).
To do a conversion (or equivalent) you must multiply the value to be converted by the conversion factor of the start unit and then divide the result by the conversion factor of the destination unit.
For example, we want to know how many centimeters equals 12 yards?
# convert the units in meters (which is the SI base unit for the lengths)
# 1 yard = 0.9144 meters
# 1 centimeters = 0.01 meters
# derive the conversion factor between the yard and centimeters by dividing the factors found
# 0.9144/0.01 = 91.44
# 1 yd = 91.44 cm
# now we multiply the amount to be converted by the conversion factor found
# 12 * 91.44 = 1097.28
# result: 12 yd equals 1097.28 cm
Unit conversion tool implements this simple algorithm.
1. Claude can do 120 jumping jacks in 2 minutes.
Write an equation to represent how many jumping
jacks Claude can complete in 5 minutes.
the number of golf balls in tigers golf bag (y) after x rounds of golf is represented by the equation y=-3x+28 what is the meaning of the value of "-3" in the context of this situation? question 8 options: tiger loses 3 balls each round. tiger begins with 3 balls in his golf bag. tiger finishes with 3 balls in his bag. tiger adds 3 balls to his bag each round.
Question 8 options:
Tiger begins with 3 balls in his golf bag.
Tiger finishes with 3 balls in his bag.
Tiger adds 3 balls to his bag each round.
The value of "-3" in the context of this situation is "tiger loses 3 balls each round".
The correct answer option is option A
How to determine the parameters in an equation?y = -3x + 28
Where,
The number of golf balls in tigers golf bag = yRounds of golf = xNumber of balls lost each round = -3For instance, if the tigers played 8 rounds of golf,
The number of golf lost = - 3x
= -3(8)
= -24
Then,
The number of golf balls in tigers golf bag,
y = -3x + 28
= -3(8) + 28
= -24 + 28
= 4 golf balls.
Therefore, the situation can be solved using equation and determining the parameters of the equation.
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Answer:
Tiger begins with 3 balls in his golf bag.
Step-by-step explanation:
:)
Find an equation that is perpendicular to 4x+3y=12
Answer:
Step-by-step explanation
x=2
The of the degrees of each factor is the degree of the product.
Answer:The degree of the product is equal to the sum of the degrees of the factors.
Step-by-step explanation:
there are 38 different time periods during which classes at a university can be scheduled. if there are 677 different classes, what is the minimum number of different rooms that will be needed?
The minimum number of different rooms that will be needed = 18
We know that the Pigeonhole Principle states that if N objects are placed into k boxes, then at least one box contains at least N/k objects.
In this question, we have been given there are 38 different time periods during which classes at a university can be scheduled.
if there are 677 different classes, we need to find the minimum number of different rooms that will be needed.
There exists a time period will have at least 677/38 = 18 classes during
it.
Therefore, 18 different rooms will be needed.
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Which criteria for triangle congruence allows you to immediately conclude that the triangles.
We may determine that the triangles are congruent based on the (B) HL criterion right away.
What are HL criteria?According to the HL Postulate, a right triangle's hypotenuse and leg are congruent if they are also congruent with the hypotenuse and leg of another right triangle.
So, we can see from the accompanying figure that these two triangles share a center line that is parallel to the base.
The two triangles are therefore right-angled triangles.
The hypotenuse of two triangles being congruent is then mentioned as a further argument.
Triangle congruence according to the HL criterion allows for a quick determination of congruence.
Therefore, we may determine that the triangles are congruent based on the (B) HL criterion right away.
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Complete question:
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?
A) SAS
B) HL
C) AAS
D) none
I need help what is Three times a number is less than twice the number added to 8 ?
Answer:
Step-by-step explanation:
The answer is 3.
X=2X-3
X+3=2X
3=2X-X
3=X
Answer:
3x < 2x + 8
Step-by-step explanation:
Use the unit fraction 1/5 to represent the space between the tick marks on the number line. Write an expression involving subtraction that is being modeled. Then find the difference.
In triangle XYZ, m2Y = 63.25° and mzZ= 28.8°. Determine the measure of the exterior angle to X.
O92.05°
87.95°
061.20⁰
26.75°
ASAP!!
The value of the exterior angle of the measure of the angle X is found as 120.85°.
Explain the term linear pair?When two lines cross at one point, a linear pair with angles is created. If the angles follow the intersections of the two lines in a straight line, they are referred to as linear. A linear pair's total angles are always proportional to 180°.For the stated question-
Three angles of the triangle XYZ are-
∠Y = 63.25°
∠Z = 28.8°.
then, by angle sum property of triangle.
∠X + ∠Y + ∠Z = 180
∠X = 180 - 63.25° - 28.8°.
∠X = 87.95
Thus, exterior angle to X.
Exterior angle = 180 - ∠X (linear pair)
Exterior angle = 180 - 87.95
Exterior angle = 120.85°
Thus, the value of the exterior angle of the measure of the angle X is found as 120.85°.
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Answer:
the answer is 87.95
Step-by-step explanation:
explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
Nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
What is birth weight?
The body weight of a newborn is referred to as birth weight. Infants of European descent typically weigh between 2.5 and 4.5 kilogrammes at birth, with an average of 3.5 kilograms. South Asian and Chinese babies weigh about 3.26 kilogrammes on average.
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grammes. Babies born to smokers often ranged in weight from 500 to 4500 grammes.
However, we also notice some significant variations between the two groups' normal ranges of birth weights. With fewer infants in the lower weight ranges, nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
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what is the recursive formula
Answer: The recursive formula generate term at a time by relating the term to one or more previous terms
Step-by-step explanation: The formula for recursive is
f(1)=6,f(n)=f(1)+f(n-1),n>1
Please help me solve
Answer:2sin(x)
Step-by-step explanation:.
Answer: D.
Step-by-step explanation:
suppose that the mean weight of king penguins found in an anarctic colony last year was 15.4 kilograms and the standard deviation was 2.5 kilograms. you want to test the null hypothesis that the mean penguin weight this year does not differ from last year. assume that the standard deviation has not changed. you are planning to measure a random sample of 100 penguins. at 10% significance level, find the critical values for the test.
we are 90% confident that the mean penguin height lies in the range:
14.99 and 15.81
A popular deviation (or σ) is a degree of the way dispersed the facts is on the subject of the imply. Low popular deviation way facts are clustered across the imply, and excessive popular deviation shows facts are greater unfold out. What is the usual deviation example? Consider the facts set: 2, 1, 3, 2, four.
The imply and the sum of squares of deviations of the observations from the imply could be 2.four and 5.2, respectively. Thus, the usual deviation could be √(5.2/5) = 1.01. Standard deviation tells you ways unfold out the facts is. It is a degree of the way some distance every determined fee is from the imply. In any distribution, approximately 95% of values could be inside 2 popular deviations of the imply.
Given sample mean=x=15.4 kg
sample standard deviation=s=2.5 kg
sample size=n=100 penguins
z multiplier for 90 CI is 1.645
90% CI for population mean is given by:
[tex]X+Z_{\frac{\alpha }{2} } * \frac{Z}{\sqrt[]{N} }[/tex]
15.4 (±)1.645(2.5)/sqrt(100)
15.4(±)1.645(2.5)/10
15.4 (±) 0.41125
15.4-.41125<μ<15.4+.41125
14.98875<μ<15.81125
we are 90% confident that the mean penguin height lies in the range
14.99 and 15.81
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The formula A=6V^2/3 related the surface Area ‘A’, in square units, of a cube to the volume ‘V’, in cubic units. What is the volume, in cubic inches, of a cube with surface area of 396.
536.2 cubic inches is the volume of a cube with surface area of 396.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
[tex]A=6V^{\frac{2}{3}}[/tex]
A is surface Area ‘A’, in square units, of a cube
V is volume of cube in cubic units.
We need to find the volume, in cubic inches, of a cube with surface area of 396.
A=396
We need to find V
[tex]V^{\frac{2}{3} } =A/6[/tex]
=396/6
=66
[tex]V=66^{\frac{3}{2} }[/tex]
V=536.2 cubic inches
Hence, 536.2 cubic inches is the volume of a cube with surface area of 396.
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PLS HELP!!! I really need help!
Use substitution to solve the system.
5x + 4y = 9
-2x + y = -14
Answer:
x = 9/5 − 4y/5
x = 7 + y/2
Step-by-step explanation:
Move all terms that dont contain x to the right side and solve.