The probability of getting a specific number on the first roll of the die is 1/6. The probability of getting that same number on five successive rolls is (1/6)^5 = 1/7776. Because there are six different ways to get the same number on five rolls, multiply by 6 to get the probability of the same number on five successive rolls to be 6/7776 =1/1296.
Determining the probability that all five rolls will be different starts with asking how many ways can you choose 5 numbers from six with replacement and without repetition where order does not matter, then dividing that number by the total number of outcomes in five rolls of the die.
The total number of possible rolls is easy. There are six possible outcomes for each of the five rolls, so the total number of possible combinations after 5 rolls is 6^5 = 7776.
Now if each roll has to be a different number, consider that there are six acceptable outcomes on the first roll of the die. There are only five acceptable outcomes on the second roll, four on the third, three on the fourth, and two on the fifth. Multiplying all these together gives 6x5x4x3x2 = 6! = 720 ways to get a different number on five successive rolls of the die. This probability is 720/7776 ( 0.0926 or 9.26% or 120 times greater than getting the same number on each of five rolls.
Consider a game in which six true dice are rolled. What is the probability of obtaining exactly one ace, at least one ace and exactly two aces?
Exactly 1 ace(one) =6C1 * 5^5 = 18750 / 6^6 = 0.401877572
At Least 1 ace(one) =6C1 *5^5 +6C2 * 5^4 + 6C3 * 5^3......6C6 * 5^0= 31031/6^6 = 0.6651020233
Exactly 2 aces(ones) =6C2 * 5^4 = 9375 / 6^6 = 0.200938786
If you require two specific times(e.g. first time and second time) to be 5(probability 1/6), others to be non-5(probability 1−1/6=5/6). The probabiliy is (1/6)2(5/6)3, you have C52=10 different ways to roll two 5. Therefore the answer is 10(1/6)2(5/6)3, which is approximately 0.1608.
To learn more about five standard (six-sided) dice visit:
https://brainly.com/question/27994198?
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(10x – 2) - (2x - 7)
O 8x + 5
O 12.2 + 5
o 12c - 9
O 83 -9
Answer:
the first one
8x+5
Step-by-step explanation:
10x-2-2x+7= 8x+5
3) Consider the function f defined by
f(x) = (3 - x)(4 + 3x). At what point does
the curve y=f(x) intersect the y-axis?
Answer:
(0,12)
Step-by-step explanation:
Let x = 0, solve the equation.
Find the 13th term of the arithmetic sequence 4x – 9, x – 16, -23 – 23,...
Answer: thumbs up
Step-by-step explanation:
The teachers at Eastside High School were asked the number of years they have been teaching. The results are as follows.
3, 4, 9, 12, 7, 5, 4, 12, 3, 9, 11, 4, 14, 9, 2, 10, 3, 10, 9, 7
Use the data to fill in the box-and-whisker plot below.
Answer:
I'm not your Slave
Step-by-step explanation:
do it yourself
PLEASE HELP
3/4x - 7 = 3 (1/6x +1)
Solve the linear equation and determine whether it’s one solution or infinite solution or no solution
Answer:
One SolutionStep-by-step explanation:
[tex] \frac{3}{4} x - 7 = 3( \frac{1}{6} x + 1)[/tex]
[tex] = > \frac{3}{4} x - 7 = \frac{1}{2} x + 3[/tex]
[tex] = > \frac{3}{4} x - \frac{1}{2} x = 3 + 7[/tex]
[tex] = > \frac{3 - 2}{4} x = 10[/tex]
[tex] = > \frac{1}{4} x = 10[/tex]
=> x = 10 × 4
=> x = 40
Here,
The variable x whose only one value 40 will solve the equation.
Hence,
It has only one solution. (Ans)
Find the value of x.
Answer:
13.8
Step-by-step explanation:
https://www.calculator.net/triangle-calculator.html
It gives you everything you need to know about the triangle
Determine whether the equation represents direct, joint, or inverse variation. Then identify the constant.
t = 100/s
y/5 = x
p/qr = 4
C = 2πr
V = 1/3πr^2h
xy = 2/5
Urn 1 contains 3 blue tokens and 2 red tokens; urn 2 contains 2 blue tokens and 4 red tokens. All tokens are indistinguishable. You roll a die to determine which urn to choose: if you roll a 1 or 2 you choose urn 1; if you roll a 3, 4, 5, or 6 you choose urn 2. Once the urn is chosen, you draw out two tokens at random from that urn (no replacement). How many possible outcomes are possible
Answer:
RR = 0.4
RB = 0.3
BB = 0.22
BR = 0.30
Step-by-step explanation:
P( Urn 1 ) = 2/6 = 1/3
P( Urn 2 ) = 1 - 1/3 = 2/3
Urn 1 contains : 3 blue and 2 red
P( blue | urn 1 ) = 3/5 ( with replacement ) , P( blue | urn 1 ) = 3/4 ( without replacement )
P( red | urn 1 ) = 2 / 5 ( with replacement ) , P(red | urn 1 ) = 1/2 ( without replacement )
Urn 2 contains : 2 blue and 4 red
P ( blue | urn 2 ) = 1/3 ( with replacement ) , P( blue | urn 2 ) = 2/5 ( without replacement )
P ( red | urn 2 ) = 2/3 ( with replacement) , P( red | urn 2 ) = 4/5 ( without replacement )
Determine
i) Possible outcomes when two tokens are drawn from either Urn without replacement
RR = [[ ( 2/5 * 1/3 ) + ( 2/3 * 2/3 ) ] * [( 1/2 * 1/3 ) + ( 4/5 * 2/3 ) ]] = 0.4
RB = [[ (2/5 * 1/3 ) + ( 2/3 * 2/3 ) ] * [ ( 3/4 *1/3 ) + ( 2/5 * 2/3 ) ]] ≈ 0.3
BB = [[ ( 3/5 * 1/3 ) + ( 1/3 * 2/3 ) ] * [ ( 3/4 *1/3 ) + ( 2/5 * 2/3 ) ]] ≈ 0.22
BR = [[ ( 3/5 * 1/3 ) + ( 1/3 * 2/3 ) ] * [ ( 1/2 * 1/3 ) + ( 4/5 * 2/3 ) ]] ≈ 0.30
260 students were surveyed on whether they prefer apple juice or orange juice. A table of relative frequencies is shown. How many more girls prefer apple juice than boys
Answer:
We need a picture of the screen plz
Step-by-step explanation:
The perimeter of any polygon is the?
Choose a right answer :
a) Product of all the sides.
b) sum of the all sides.
c) sum of any two sides.
d) sum of the diagonals.
Answer:
B
Step-by-step explanation:
perimeter is the sum of all sides. it's the distance around the figure.
solve the following equation for x: y = 2 x-5 , x + y = 4
Answer:
(3,1)
Step-by-step explanation:
Y=2x-5
x+y=4
substitute the answer for y in the first equation (2x-5) with the y in the second equation
x+(2x-5)=4
x+2x-5=4
3x-5=4
add 5 to both sides to isolate 3x
3x=9
x=3
To find y, replace x in either of the original equations and solve for y.
x+y=4
3+y=4
y=1
so, x=3, y=1
chech answer by subbing x and y values into either original equation.
y=2x-5
1=2(3)-5
1=6-5
1=1
or
x+y =4
3+1=4
4=4
PLEASE HELP !!!!!!!!!!!!
9514 1404 393
Explanation:
The figure will be a rectangle only if the angles between adjacent congruent sides are 90°.
__
Attached is an example of a quadrilateral with 3 congruent sides. It is not a rectangle, but could be an isosceles trapezoid if the top and bottom sides were parallel. It would be a parallelogram (rhombus) if opposite congruent sides were parallel.
1 pts
So
Sales
SE
According to
the data given, sza
what is the
sales amount
when the
temperature is
18 degrees C?
Temperature
A certain test preparation course is designed to help students improve their scores on the USMLE exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 3 students' scores on the exam after completing the course:
15,20,18
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Answer:
The 90% confidence interval for the average net change in a student's score after completing the course is (13.42, 21.92).
Step-by-step explanation:
Average change in the sample:
[tex]M_{s} = \frac{15+20+18}{3} = 17.67[/tex]
Standard deviation of the sample:
[tex]s = \sqrt{\frac{(15-17.67)^2+(20-17.67)^2+(18-17.67)^2}{2}} = 2.52[/tex]
We have the standard deviation for the sample, so the t distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 3 - 1 = 2
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 2 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.92
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.92\frac{2.52}{\sqrt{3}} = 4.25[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 17.67 - 4.25 = 13.42
The upper end of the interval is the sample mean added to M. So it is 17.67 + 4.25 = 21.92
The 90% confidence interval for the average net change in a student's score after completing the course is (13.42, 21.92).
According to the Central Limit Theorem, which statements(s) are TRUE. There may be more than 1 correct answer. A. An increase in sample size from n = 16 to n = 25 will produce a sampling distribution for the sample means that has a smaller standard deviation. B. The larger the sample size, the more the sampling distribution of sample means will resemble a normal distribution C. The mean of the sampling distribution of sample means for samples of size n = 15 will be the same as the mean of the sampling distribution for samples of size n = 100. D. The mean of a sampling distribution of sample means is equal to the population mean divided by the square root of the sample size. E. The larger the sample size, the more the sampling distribution of sample means resembles the shape of the population.
Answer:
Options A, B and C are correct.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
From the Central Limit Theorem, we have that:
The larger the sample size, the closer to the normal distribution the distribution of sample means is.
No matter the sample size, the mean is the same.
The larger the sample size, the smaller the standard deviation.
The smaller the sample size, the larger the standard deviation.
So the correct options are:
A, B, C
Divide 10 by t. Then, add 2.
Which of the following expressions matches the statement above?
A.
t + 10 + 2
B.
10 + (t + 2)
C.
10 + + 2
D.
10 + 2 +
85% of x is 51. Write an equation that represents the situation
Answer:
85%*x =51
Step-by-step explanation:
of means multiply
Hence,
85% times x =51
Stefan has a bag that contains 3 blue marbles and 5 red marbles only.What fraction of the marbles in the bag are blue?
Answer:
3/8
Step-by-step explanation:
vecause there are 8 in total and 3 of them are blue.
hope this helps
What is the value of the following
expression when d=2?
3d + (2.d)-4
Answer:
6
Step-by-step explanation:
I used a calculator and the answer is 6
The graph below shows how the monthly rent for an apartment changed over time
Answer:
Its C. If you look at the graph and match it with the years it increases by 50
Step-by-step explanation:
Which of the following is the additive inverse of
1/2
Answer:
2
Step-by-step explanation:
1/2 x 2 = 1
Answer:
2
Step-by-step explanation:
beacuse 2/1 is actually 2
math question helppppppppp
Answer:
it would be 17 m second one is 20inch third one is 6 meters
Step-by-step explanation:
np give it a heart
Answer:
1st) area = 12 x 3.7 = 44.4 m²
2nd) area = 24 x 18 = 432 in²
3rd) area = 7.3 x 5 =36.5 m²
Step-by-step explanation:
if a city with a population of 500,000 doubles in size every 64 years, what will the population be 256 years from now?
Answer:
8,000,000
Step-by-step explanation:
This is because 256 divided by 64 is 4, meaning 64 goes into 256 4 times. If 500,000 is being doubled every 64, it means that in 256 years, the population will have been doubled 4 times.
Meaning? Well...
500,000 x 2 = 1,000,000 = 64yrs
1,000,000 x 2 = 2,000,000 = 128yrs
2,000,000 x 2 = 4,000,000 = 192yrs
4,000,000 x 2 = 8,000,000 = 256yrs
This is 4 times.
so every time it's doubled, it means the sum of that number times 2.
MUST HELP!!!! (+10 POINTS +BRANILEST +5 STARS +THANKS ON PROFILE)
any absurd answers will result in a ban.
Answer:
Imagery
Imagery includes language that appeals to all of the human senses, including sight, hearing, taste, touch, and smell.
I think its imagery because the narrator describes that the character stood firmly, was held, rootless in mid air, etc..
Step-by-step explanation:
:))
I will give brainleist pls
Answer:
C
Step-by-step explanation:
We can immediatly rule out A and B because the Quotient is bigger than the Divisor.
We can then rule out D because 2,016 does not round to 2,200.
The answer is C. 2,184 can round to 2200 and the Divisor is bigger than the quotient.
Answer:
C
Step-by-step explanation:
This is quite simple as we can find the answer out on the first hint itself. The first hint says the divisor, 2 number in the equation or number you are dividing by, can be rounded to 50, which means it is in the range of 45-54. We can see the only divisor in that range is C. To go with the other hints, though, the dividend, first number, can be rounded to 2,200 which means it is in the range of 2,151-2,250. All of them pass that, so on to the next hint. It says the quotient, number you get as answer, is smaller than the divisor, which we found is in the range of 45-54. Answer choices A and B do not follow this as the divisors of their equation are obviously smaller than the quotient, so we can conclude C to be our answer
Problem 1.(32 points) A random sample of 100 Uber rides in Chicago has on average 5.4miles per ride. Assume the distribution of the distance of Uber rides to be approximatelynormal with a standard deviation of 1.3 miles.(a) (5 points) Construct a 99% confidence interval for the average distance (in miles) ofan Uber ride. (round to one decimal place)(b) (4 points) What can we assert with 99% confidence about the possible size of our errorif we estimate the average distance of an Uber ride to be 5.4 miles
Answer:
a) CI = ( 5,1 ; 5,7 )
b) SE = 0,1
Step-by-step explanation:
a) Sample random n = 100
Mean = μ = 5,4
Standard deviation s = 1,3
CI = 99 % α = 1 % α = 0,01 α/2 = 0,005
z(c) for 0,005 is from z-table z(c) = 2,575
z(c) = ( X - μ ) /s/√n CI = μ ± z(c) * s/√n
CI = 5,4 ± 2,575* 1,3/10
CI = 5,4 ± 0,334
CI = ( 5,1 ; 5,7 )
b) SE = Standard deviation / √n
SE = 1,3 /10 SE = 0,1
We can support that with 99 % of probability our random variable will be in the CI.
I need help pleaseee
Answer:
H
Step-by-step explanation:
There are 6 flavors of candy in a bag. The probability of randomly selecting strawberry is 1/4, lime is 3/16, lemon is 4/32, cherry is 1/8, and grape is 14/64. What is the probability of randomly selecting a piece of the 6th flavor?
Easy question look at photo
Answer:
I would go with yes, since we know BC=UV
Step-by-step explanation:
Each interior angle of a regular nonagon has a measure 13x+10°. What is x?
Answer:
Step-by-step explanation:
A nonagon has nine sides.
The sum of exterior angles = 360°, so each exterior angle is 360°/9 = 40°.
Each interior angle = 180°-exterior angle = 140°.
13x + 10° = 140°
x = 10°