Consider rolling a fair die until the total of the outcomes
surpasses 6. Let X represent the number of throws necessary to
complete this task. Find P(X ≤ 7), P(X ≤ 2), and P(X ≤ 1).
Answers
The probability of getting 6 or greater than 6 is 7/18.
The total number of outcomes surpasses 6 when the sequence is (2,2,2,2,2), and (1,1,1,1,1,2) in 6 and 7 rolls respectively. Let X be the number of times the die is rolled until the total outcome surpasses 6.P(X ≤ 7) can be calculated as follows: Since the probability of getting 2 for each roll is 1/6 and we need at least 6 to end the sequence, it means that we need to roll a dice at least five times before getting 6 or higher.
Now, we need to calculate the probability of having an outcome equal to 6 or greater than 6 in 6 rolls, which means we need to sum the probability of each sequence of outcomes that gives 6 or greater than 6. 6 = 2 + 2 + 2, and there are five ways of getting this outcome, as each roll can give two or more.
Each outcome has a probability of (1/6) x (1/6) x (1/6) = (1/216). 7 = 2 + 2 + 2 + 2 + 2 + 1, and there are 6 ways of getting this outcome as each of the five rolls can give two or more, and the sixth roll gives one.
Each outcome has a probability of (1/6) x (1/6) x (1/6) x (1/6) x (1/6) x (5/6) = (5/7776). Therefore, P(X ≤ 7) = 5/216 + 6 x 5/7776 = 35/1296P(X ≤ 2) can be calculated as follows: If the first roll gives a 5 or a 6, we stop, and it means we need only one roll. The probability of getting 5 or 6 in one roll is 2/6 = 1/3.
If the first roll gives 1, 2, 3, or 4, we need to roll a second time. In the second roll, we can get any value from 1 to 6. Therefore, the probability of getting 6 or greater than 6 is 4/6 = 2/3.
The probability of getting less than 6 is 1/3. Therefore, the probability of getting 6 or greater than 6 in two rolls is (1/3) + (2/3 x 1/3) = 5/9.
Therefore, P(X ≤ 2) = 1/3 + (2/3 x 5/9) = 11/18P(X ≤ 1) can be calculated as follows: If the first roll gives 6, we stop, and it means we need only one roll. The probability of getting 6 in one roll is 1/6.
If the first roll gives 5, 4, 3, 2, or 1, we need to roll a second time. In the second roll, we can get any value from 1 to 6. Therefore, the probability of getting 6 or greater than 6 is 4/6 = 2/3.
The probability of getting less than 6 is 1/3. Therefore, the probability of getting 6 or greater than 6 in two rolls is (1/3) + (2/3 x 1/3) = 5/9. Therefore, P(X ≤ 1) = 1/6 + (5/9 x 1/6) = 7/18.
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Related Questions
Once again i need help its worth 90 points so id say its worth it
Answers
Answer:
EXPLANATION BELOW
Step-by-step explanation:
7 | 0, 4, 8
8 | 0, 8, 9
9 | 5
10 | 1, 9
11 | 6, 7
hope this helps!! you basically just divide the number into two-
True or False?
When rainfall increases, the water level in the lake goes up. Rainfall is the independent variable in this situation. (4 points)
True
False
2.
(07.07)
Alexander can earn money for the cans he recycles. Which of the following statements describes the variables in this situation correctly? (4 points)
The number of cans recycled is the independent variable because it affects the amount of money earned.
The number of cans recycled is the dependent variable because it affects the amount of money earned.
The amount of money earned is the independent variable because it affects the number of cans recycled.
The amount of money earned is the dependent variable because it affects the number of cans recycled.
3.
(07.07)
Calvin's plane is flying at a speed of 600 miles per hour. If y represents the distance the plane has traveled and z represents the time it has spent traveling, which of the following equations shows the relationship between y and z? (4 points)
y = 600 + z
z = 600 + y
z = 600y
y = 600z
4.
(07.07)
It costs $1.58 to buy a bag of popcorn. Which of the following equations shows the amount of money needed, z, to buy n bags of popcorn? (4 points)
z = 1.58 + n
n = 1.58 + z
z = 1.58n
n = 1.58z
5.
(07.07)
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f).
Elapsed Time
(seconds) Distance Traveled
(feet)
1 6.2
2 12.4
3 18.6
4 24.8
Which of the following equations represents the relationship between the distance traveled and the elapsed time? (4 points)
f = 6.2 + n
n = 6.2 + f
f = 6.2n
n = 6.2f
Answers
It is a true statement that when rainfall increases, the water level in the lake goes up. The rainfall is the independent variable in the situation.
Is rainfall the independent variable?The answer is yes because independent variable is the one that is manipulated or changed in an experiment. The dependent variable is the one that is observed or measured.
In this situation, rainfall is independent variable because it is what is being manipulated or changed. The water level in the lake is the dependent variable because it is what is being observed or measured.
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V has coordinates (11,-14), and W has coordinates (x,10)
what is the value of X if VW =25?
Answers
Answer:
Step-by-step explanation:
The value of X would be 18
x=18
Kin made a Picture frame for a square picture with sides that are 5f-4 inches long. Framing the picture adds 2 inches to the length of each side. Use the distributive property to write two expressions for the perimeter of the frame picture.
SHOW YOUR WORK
Pls help Tysm!
Answers
The perimeter of a shape is the sum of its side lengths
The expressions for the perimeter of the frame are 4(l + 2) and 4l + 8
How to determine the perimeter of the shapeThe side length of the frame is given as l
So, the perimeter of the frame is
:\(P = 4l\)
When 2 inches are added to each length, the perimeter of the frame becomes
\(P =4(l + 2)\)
Expand
\(P =4l + 8\)
Hence, the expressions for the perimeter of the frame are 4(l + 2) and 4l + 8
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The table shows the number of points scored by a basketball team in their first seven games.
Answers
Answer:
15
Step-by-step explanation:
the range is the largest number take away the smallest number
56-41=15
is this a function if not what is it?
Answers
Answer:
Not a function but a relation
Step-by-step explanation:
It is not a function because 10 is matched with both 4 and 20.
a tank contains 1000 l of brine with 15 kg of dissolved salt. pure water enters the tank at a rate of 10 lymin. the solution is kept thoroughly mixed and drains from the tank at the same rate. how much salt is in the tank (a) after t minutes and (b) after 20 minutes?
Answers
The salt is in the tank (a) after t minutes is 20 minutes and (b) after 20 minutes there are 150 kg of salt.
Salt in Brine Tank CalculationLet's call the amount of salt in the tank after t minutes "S(t)".Since pure water is entering the tank and brine is leaving at the same rate, the volume of the solution in the tank remains constant at 1000 liters.However, the concentration of salt in the solution is changing over time. At any given time, the amount of salt in the tank can be found by multiplying the volume of the solution by its concentration, which we can call "C(t)".So, we have:S(t) = C(t) * 1000
The rate of change of salt in the tank is equal to the rate at which salt is entering the tank (from the dissolved salt in the brine that is leaving the tank) minus the rate at which salt is leaving the tank (from the brine that is leaving).dS(t)/dt = (C(0) - C(t)) * 10
where C(0) is the initial concentration of salt in the
brine (15 kg / 1000 liters = 0.015 kg/liter).
We can solve this differential equation to find the concentration of salt in the tank as a function of time. However, this can be a bit complicated, so let's just consider the answer for the specific times asked:(a) After 20 minutes, we have:C(20) = C(0) - (S(20) / 1000 - S(0)) / 10
= 0.015 - (S(20) / 1000) / 10
And (b) the amount of salt in the tank after 20 minutes is:S(20) = C(20) * 1000
Plugging in the value of C(20) from part (a), we get:S(20) = (0.015 - S(20) / 1000 / 10) * 1000
S(20) = 15 - S(20) / 10
S(20) = 150
So, after 20 minutes, there are 150 kg of salt in the tank.Learn more about Salt in Brine Tank Calculation here:
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the cost for a bakery to make a dozen muffins is 2.52. the sale price of an individual muffin is 2.99. for one day, the bakery will donate 1/2 of the profits from muffin sales to charity. what is the bakeries donation, in dollars, if 88 muffins are sold that day
Answers
Answer:
I'm pretty sure it would be $131.56
Step-by-step explanation:
I think it will be $131.56 because if you take an multiply the 2.99 times 88 the number of muffins that were sold that day, then you would get $263.12. If you donated 1/2 of the profits made, then you would take 263.12 and divide it by 2 because half of it would be divided by 2. So therefore you would get $131.56! Hope this helps!
Correct me if I'm wrong!
The goal of this project is to apply combinations and permutations to determine the number of possibilities of various scenarios.
1. (10 pts) Define combination and permutation, and provide the formulas for both.
2. Here is a real-life example of a combination and a permutation. I love ice cream and one of my favorite shops has 31 flavors. I can either get a 3-scoop bowl or a 3-scoop cone.
Answers
Combination refers to a way of grouping the elements of a set into a subset in an undered form whereas Permutation is a way of grouping the elements of a set into a subset in an ordered form.
The formula for combination is: C(n,q) = n!/[q !(n-q)!]
The formula for permutation is: P(n,q) = n!/(n-q)!
Real life and specific examplesA real life example of permutation involves selecting 10 people to join a group where they are assigned different duties and a real life example of permutation is selecting 10 people to join a group where they are assigned duties on a first come first served basis.
A specific example of combination is this: In a collection of 17 individuals, 7 $2 cards will be given. In how many ways can the cards be shared? This is combination because there is no set order.
A specific example of permutation is this: In a competition, three individuals contest. In how many ways can they have the 1st, 2nd, and 3rd positions?
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What is the perimeter?
Answers
Answer:
41.13m
Step-by-step explanation:
the circumference of the circle is 25.13 and the 8 on both sides equals to 16
12
Mackenzie wants to buy a backpack that cost $60. If the tax rate is 7.5%, how much tax will she
pay?
Answers
Answer:
$4.5
Step-by-step explanation:
I'm gonna do my work on paper.
If AB=BC=15 feet and AC=24 feet, what is, BD, the height of the camp tent entrance?
Answers
The solution is, the value of BD is 9, the height of the camp tent entrance.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².
here, we have,
If AB=BC=15 feet and AC=24 feet,
now, we have to find BD, the height of the camp tent entrance.
we get,
BD is a perpendicular bisector of AC.
now, we have,
AD = DC = 24/2 = 12
by using Pythagorean theorem, we get,
BD² = AB² - AD²
solving we get,
BD = 9
Hence, The solution is, the value of BD is 9, the height of the camp tent entrance.
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15
The fraction 15 is the same as 15 divided by ___
Answers
Answer:
If its just 15 then its 1
Step-by-step explanation:
Because 15 divided by 1 is 15 which is the fraction.
Answer:
Below,...!
Step-by-step explanation:
15 is not a fraction as is you can put any number over a one and that whole number immediately becomes a fraction:
\(\frac{7}{1} or \frac{43}{1} or \frac{987}{1} or \frac{1}{1} or \frac{15}{1}\)
15/1 is your fraction so 15/1 divided into 15 equals 1
\(\frac{15}{1} / 15 = 1/1 = 1\)
Answer: 1
Chow,...!
It takes Carrie 585858 minutes to get home. If Carrie leaves for home at 1{:}321:321, colon, 32, what time will she arrive?
Answers
Carrie will arrive at home at 4:02 PM on the same day she leaves.
To determine the time Carrie will arrive, we need to add the number of minutes it takes her to get home to her departure time.
Carrie leaves for home at 1:32 PM. To convert this time to minutes, we multiply the hours (1) by 60 and add the minutes (32). This gives us a total of 92 minutes.
Next, we add the 58,858 minutes it takes Carrie to get home to the departure time of 92 minutes:
92 minutes + 58,858 minutes = 58,950 minutes.
Now, we need to convert the total minutes back to hours and minutes. Since there are 60 minutes in an hour, we divide 58,950 by 60:
58,950 minutes ÷ 60 = 982.5 hours.
The decimal part represents the remaining minutes. To convert this decimal to minutes, we multiply it by 60:
0.5 (decimal part) × 60 = 30 minutes.
Therefore, Carrie will arrive at 982 hours and 30 minutes after her departure time.
To convert this back to a 12-hour clock format, we divide 982 by 12, which gives us a quotient of 81 with a remainder of 2. This means Carrie will arrive 81 days after her departure time, with an additional 2 hours and 30 minutes.
As for the exact time she will arrive on the day she leaves, we need to add the 2 hours and 30 minutes to her departure time:
1:32 PM + 2 hours and 30 minutes = 3:62 PM.
However, since we are using a 12-hour clock format, we need to adjust the time to the correct format:
3:62 PM can be rewritten as 4:02 PM.
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Find the number of units x that produces a maximum revenue R.R = 171x2 − 0.06x3x = units
Answers
The number of units x that produces a maximum revenue with the expression given is x = 0.
To find the value of x that maximizes the revenue function R, we can take the derivative of R with respect to x and set it equal to 0. This will give us the critical point of the function.
The derivative of the function R with respect to x is:
R'(x) = 342x - 0.18x²
Setting this equal to 0, we get:
342x - 0.18x² = 0
Solving for x, we find that x = 0 or x = 1900.
However, we need to consider the constraints of the problem to determine which value of x is the optimal solution. If x is a number of units, then x cannot be negative. Therefore, the only valid solution is x = 0.
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A teacher put out 6 pegs to mark a 450m running race the pegs are in a straight line and are spaced evenly there is a peg at the start and a peg at the end of the race. Later the teacher removes the two end pegs to make a shorter race
Answers
The teacher removes the two end pegs to make a shorter race of 270 metres long.
The distance between each peg in a 450-meter running competition marked by 6 pegs is:
Overall distance / Each peg's separation (Number of pegs - 1)
450 metres divided by (6 - 1) equals 90 metres between each pin.
If the teacher removes the two end pegs, then there are only 4 pegs remaining, and the distance between each peg is still the same:
90 metres separate each pin.
Consequently, the shortened race's length is:
Distance of lesser race is equal to the sum of the distances between the two end pegs.
Shorter race's distance is equal to 450m – 2(90m) = 270m.
The shortened race therefore measures 270 metres.
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at a dinner party, guests were served dishes of soup, rice, and tofu. every dish of soup was shared by two guests, every dish of rice was shared by three guests, and every dish of tofu was shared by four guests. every guest ate from exactly one dish of soup, one dish of rice, and one dish of tofu. if the total number of dishes was 65, then how many guests were there?
Answers
In Korea, tofu is typically offered during breakfast.
Describe breakfast.
The first meal of the day, known as breakfast, is often had in the morning. After an overnight fast, it is a crucial meal that gives the body and brain fuel. Protein and carbs are generally found in breakfast foods such eggs, bacon, oatmeal, toast, pancakes, yoghurt, cereal, and fruits. A nutritious breakfast may boost energy levels, jump-start the metabolism, and enhance focus and memory. A nutritious breakfast can also aid in lowering mid-day snacking and preventing overeating in the evening. Make sure to incorporate breakfast in your daily schedule since eating breakfast is crucial to living a healthy lifestyle.
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The ratio of cattle to horses on the ranch was 12 to 3. The combined number of cattle and horses was 960. How many horses are on the ranch?
Answers
Answer: There are 192 horses in the ranch
Step-by-step explanation:
The combined number of cattle and horses = 960.
Ratio of cattle to horses =12 :3
Total ratio =12+3=15
Number of horses on the ranch = ratio of horse / Total ratio x total number of horses and cattle
3/15 x 960 = 192
Therefore there are 192 horses in the ranch
What's the circumference of a
circle with a radius of 6 inches?
Use 3.14
C = [?] inches
Answers
Answer:
37.7
Step-by-step explanation:
Answer:
C=2πr=2·π·6≈37.69911in
Bank ABC offers a 10 -year CD that pays a 5.0% interest compounded annually.
Bank XYZ also offers a 10 -year CD that pays 4.95% interest compounded daily.
How much would a $1,000 initial investment in each bank's CD be worth at maturity?
Bank ABC: ______
Bank XYZ: ______
(Enter answer in the form: $x,x×x.xx )
Answers
A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity. A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.
The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:
A = P(1 + r/n)^(nt)
where P is the principal,
r is the annual interest rate,
n is the number of times compounded per year,
t is the number of years, and
A is the value of the CD at maturity.
Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.
Let's calculate the value of a $1,000 investment in Bank ABC's CD.
P = $1,000
r = 5.0% compounded annually
t = 10 years
n = 1
We have all the values; let's put them in the formula and solve:
A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89
Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.
Let's calculate the value of a $1,000 investment in Bank XYZ's CD.
P = $1,000
r = 4.95% compounded daily
t = 10 years
n = 365
We have all the values; let's put them in the formula and solve:
A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82
Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.
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Diane works at a hair salon and earn $150 after working 6 hours write an equation that describe her rate of pay then graph
Answers
Answer:
150 dived by 6=$25/hr
Step-by-step explanation:
i cant graph on here so srry
arithmetic operations are performed on selected records in a database using statistical functions
T/F
Answers
The answer is false as arithmetic operations are performed using arithmetic functions, not statistical functions. Arithmetic operations are performed on selected records in a database using arithmetic functions, not statistical functions.
Arithmetic operations in a database involve basic mathematical calculations such as addition, subtraction, multiplication, and division. These operations are used to manipulate numerical data in a database and perform calculations on selected records. Statistical functions in a database are used to analyze and summarize data. These functions include measures such as mean, median, mode, standard deviation, and variance. Statistical functions are used to provide insights into the data, identify trends and patterns, and make predictions. However, they are not used for arithmetic operations on selected records.
Finally, it is important to note that both arithmetic and statistical functions are essential tools for working with data in a database. Depending on the nature of the data and the analysis required, either type of function may be used. However, it is crucial to understand the differences between the two and use them appropriately to ensure accurate and meaningful results.
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Carroll bikes 111 kilometer east, 444 kilometers north, and then 555 kilometers east again. How far is Carroll from her starting position
Answers
Answer:
the Carroll is 1110 kilometer far
The sum of three numbers is 41.
The second number is 5 times the first.
The third number is 14 less than the second.
What is the third number?
Answers
Answer:
look below
Step-by-step explanation:
a = the 1 st# b = 2nd # c= 3rd #
a+b+c=41
b=5a
c=14-b
plug in one of those values
a+b+14-b=41
a+14=41
-14
a=27
plug in the "a" value
-7(x + 6) = 14
PLEASE HELPPPP
Answers
Answer:
x = -8
Step-by-step explanation:
-7(x + 6) = 14
-7x + -42 = 14
-7x = -56
x = 8
3. XY has an equation of x = 8. What is the equation, in point-slope form, of a line that is
perpendicular to XY and passes through (6, 9)?
(i'm looking for an explanation)
Answers
Answer: y=9
Step-by-step explanation:
Plug in (6,9) into the slope intercept form equation:
9=0(6) +b
Then get
9=b
When you make the equation you would end up with:
y=0x+9
which simplifies to y=9
ALGEBRA 1:
FIND THE PRODUCT OF THE FOLLOWING:
(2x+1)^2
please somebody help me, if you’re correct i’ll give you an extra 50 points for helping. please do not use my question for points as i am failing and truly need help i’m so stressed lol.
Answers
=(2x+1)(2x+1)
=4x^2+2x+2x+1
=4x^2+4x+1
Answer:
Step-by-step explanation:
(2x-1)(2x-1) Work outside then inside
4x^2 and +1 are the outside terms
-2x and -2x are the inside terms
so the answer will be
4x^2 - 4x +1
2.
Identify the axis of symmetry of the parabola.
A. x= 3
B. x= 6
C. x= 5
D. x= 4
Answers
Answer:
x=4
Step-by-step explanation:
The imaginary line that divides it goes through 4 on the x axis
Answer:
A. x= 3
Step-by-step explanation:
Round 4.872 to the nearest tenths
Answers
Your answer is below.
4.9
are 4(-2b+5) and 2(-4b+10) are equivalent expressions
Answers
Answer:
Yes
Step-by-step explanation:
they are both −8b+20
4(-2b+5)
4 x -2b is -8b
4 x 5 is 20 which gives you
-8b+20
2(-4b+10)
2 x -4b is -8b
2 x10 is 20
Which also gives you -8b+20