Since there is a fixed number of trials and the trials are independent, it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The game is played n times.In each game, each of the 8 participants is equally as likely to win the game, hence p = 1/8.Thus, the binomial distribution is appropriate.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)
Answer:
Step-by-step explanation:
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook coats $3. Which of the following graph represents the possible combinations of pens and notebooks that she may purchase?
Answer:
3p + 8n, 12p + 2n, 9p+4n, 6p+6n
8 columns bar graph.
Step-by-step explanation:
$2 = pen
$3 = notebook
This could be written as a bar graph in multiples of $6.00 along y axes.
3 pens + 8 notebooks. Then 12 pens + 2 notebooks.
Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks
3p + 8n, 12p + 2n, 9p+4n, 6p + 6n
3p = $6
8n = $24
12p = $24
2n = $6
9p = $18
4n = $12
6p = $12
6n = $18
and so on...
Find the midpoint of the line segment.
Answer:
-2,-3
Step-by-step explanation:
How many numbers lie between the squares of 39 and 40
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
Given the system of equations, what is the solution? 2x+y = -1 х- у = -5
Answer:
x=-2, y=3
Step-by-step explanation:
make it easy first, solve for x in the second equation: x= -5+y.
then sub that in for the other x: 2(-5+y)+y= -1
now combine like terms: -10+3y= -1
solve for y: 3y=9, y= 3
then replace y for your second equation: x-3= -5
solve for x= -5+3.... so then its -2
check by replacing all variables with your new solutions:
2(-2), which is -4+3 does equal -1
(-2) -3 does equal -5.
your answers are x=-2, y=3
Suppose we are sending a digital signal which is a string of 0s and 1s of length five. (Example stringsare 00101, 11000, 10101 are all 5 bit strings.) When we send the message, each bit (0 or 1) is sentindependently and there is some chance that the bit is corrupted. Namely, each time we send a 0 thereis a 5% chance that a 1 is received and each time we send a 1 there is a 5% chance a 0 is received.Suppose we send a message of length 5, what is the probability that an incorrect message is received
Answer:
0.7738 = 77.38% probability that an incorrect message is received.
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is corrupted, or it is not. The probability of a bit being corrupted is independent of any other bit. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
5% probability a bit is sent incorrectly:
This means that [tex]p = 0.05[/tex]
Message of length 5
This means that [tex]n = 5[/tex]
What is the probability that an incorrect message is received?
This is the probability of at least one incorrect bit, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.05)^{0}.(0.95)^{5} = 0.7738[/tex]
0.7738 = 77.38% probability that an incorrect message is received.
Help pls ASAP this need to be done
D
Because slope of section D is greater than the others and hence speed is highest.
1. The curved surface area of a cylinder of height 21cm is
660cm", find its radius. please help me .....
I will give brainliest.
Answer:
21 times 660 and then you will get the answer
Can someone please help me?
characteristics of the median
Answer:
Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.
How do I solve this and do the explanation of it
Answer:
180-66
114
hope it helps mark as brainlist
Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.
Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).
TV(X,X+a) = ?
Answer:
1
Step-by-step explanation:
Computing Tv(X, X + a ) for any a∈(0,1)
Given that : X∼Ber(0.5)
∴ The probability mass function
P(X = 1 ) = 0.5
P(X = 0) = ( 1 - 0.5 )
and expectation E[X] = 0.5
hence ; TV ( X, X + a ) = 1
Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them.
Answer:
Step-by-step explanation:
1 . Sphere :
[tex]Surface \ Area = 4\pi r^2\\\\ Volume = \frac{4}{3} \pi r^3[/tex]
Variable is ' r '
Others Constants.
2. Cone :
[tex]Surface \ Area = \p r^2 + \pi rs[/tex] [tex][ \ s = \sqrt { r^2 + h^2 } \ , r = base \ radius, h = height \ ][/tex]
[tex]Volume = \frac{1}{3} \pi r^2 h[/tex]
Variables are ' r ' and ' h '
Others constants.
3. Cuboid ( Rectangular Prism )
[tex]Surface \ Area = 2 ((l\times b) + ( b \times h) + ( l \times h)) \\\\Volume = l \times \ b \times \ h[/tex]
Variables : l , b , h
Constant is 2
4. Cylinder
[tex]Surface \ Area = 2 \pi r h + 2 \pi r^2 \\\\Volume = \pi r^2 h[/tex]
Variables : ' r ' and ' h '
Others constants..
Answer:
shapes. cuboid. cube. cylinder. prism. sphere. pyramid. rightcircularcone. volumeformula. l×w×h. v=a . 3. v=πr . 2. h. v=b×h. v=( 3. 4)πr . 3. v=( 3. 1)×h×b. v=( 3. 1)πr . 2. h. variables. l=length,w=width,h=height. a=side. r=radius,h=height. b=base,h=height. r=radiusofthesphere. b=areaofthebase,h=heightofthepyramid. r=radiusofthecircularbase,h=height
Step-by-step explanation:
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.
Clothes Food Toys
43 30 52
24 38 58
42 46 43
35 54 49
28 47 63
31 42 53
17 34 48
31 43 58
Required:
a. Find the values of mean and standard deviation.
b. Is there a difference in the mean attention span Of the children for the various commercials?
Answer:
(a)
Mean
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
Standard deviation
[tex]\sigma_1 = 8.73[/tex]
[tex]\sigma_2 = 7.65[/tex]
[tex]\sigma_3 = 6.04[/tex]
(b) Yes, there is a difference in the mean
Step-by-step explanation:
Solving (a): The mean and standard deviation of each commercial
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
For clothes:
[tex]\bar x_1 = \frac{43+24+42+35+28+31+17+31}{8}[/tex]
[tex]\bar x_1 = \frac{251}{8}[/tex]
[tex]\bar x_1 = 31.375[/tex]
For food:
[tex]\bar x_2 = \frac{30+38+46+54+47+42+34+43}{8}[/tex]
[tex]\bar x_2 = \frac{334}{8}[/tex]
[tex]\bar x_2 = 41.75[/tex]
For toys:
[tex]\bar x_3 = \frac{52+58+43+49+63+53+48+58}{8}[/tex]
[tex]\bar x_3 = \frac{424}{8}[/tex]
[tex]\bar x_3 = 53.00[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For clothes:
[tex]\sigma_1 = \sqrt{\frac{(43 - 31.375)^2 +.............+(31 - 31.375)^2}{8-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{533.875}{7}[/tex]
[tex]\sigma_1 = \sqrt{76.2678571429}[/tex]
[tex]\sigma_1 = 8.73[/tex]
For food:
[tex]\sigma_2 = \sqrt{\frac{(30 - 41.75)^2 +............+(43 - 41.75)^2}{8-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{409.5}{7}}[/tex]
[tex]\sigma_2 = \sqrt{58.5}[/tex]
[tex]\sigma_2 = 7.65[/tex]
For toys:
[tex]\sigma_3 = \sqrt{\frac{(52-53.00)^2+...................+(58-53.00)^2}{8}}[/tex]
[tex]\sigma_3 = \sqrt{\frac{292}{8}}[/tex]
[tex]\sigma_3 = \sqrt{36.5}[/tex]
[tex]\sigma_3 = 6.04[/tex]
Solving (b): Difference in mean in the commercials;
In (a), we have:
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
[tex]\bar x_1 \ne \bar x_2 \ne \bar x_3[/tex]
Hence, there is a difference in their means
Please help me understand
Answer:
A is is correct since the interquatile or a is 15 since 15 plus 15 equals 30 and 20 plus 20 equals 40
B is incorrect since the interquare are not both 30
C is incorrect since both interquatiles are wrong
D is incorrect since the standrard devations are off
If f(x)=x^2−8x and g(x)=−12x^2 what is g(f(−4))?
Answer:
-27648
Step-by-step explanation:
In this problem, we are looking for the function of g in terms of the function f. Simply put, we just replace the variable x in the function g with f(-4).
Step 1, writing g(f(-4)):
[tex]g(f(-4))=-12(f(x))^2[/tex]
Great! Let us substitute f(x) with the given expression.
Step 2, substituting and simplifying:
[tex]\\g(f(-4))=-12(x^2-8x)^2\\g(f(-4))=-12((-4)^2-8*(-4))^2\\g(f(-4))=-12(16+32)^2\\g(f(-4))=-12*2304\\g(f(-4))=-27648[/tex]
g(f(-4) is [tex]\fbox{-27648}[/tex].
I hope this helps! Let me know if you have any questions :)
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2
Answer:
C. 90√3
Step-by-step explanation:
5√2 . 9√6 = 45√12 = 45×2√3
= 90√3
The simplified form is 90√3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given expression is, 5√2×9√6
=5×9×√(2×6)
=45×√12
=45×2√3
=90√3
Hence, the simplified form is 90√3 .
To learn more on multiplication click:
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Which of the following is not an example of a parent function?
y=x
y=2x^3
y=1/2
y=2^x
9514 1404 393
Answer:
(b) y=2x^3
Step-by-step explanation:
The function y=2x^3 is an example of the parent function y=x^3 being vertically scaled by a factor of 2. As such, it is not the parent function.
_____
Additional comment
A parent function is one that has not been translated or scaled in any way. One could argue that the parent function of the form y=constant is y=1, so that the function y=1/2 has been scaled by a factor of 1/2. In this problem, we recognize the parent function y=x^3 has clearly been scaled to get y=2x^3, so the latter is not an example of a parent function.
If this is a "check all that apply" question, then y=1/2 is another reasonable answer.
Answer:(b) y=2x^3
Step-by-step explanation:
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE CYLINDER
Answer:
Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7
Hope this helps :)
Answer:
If we want to find volume of cone we must use this formule: πr²*high/3.
Step-by-step explanation:
let's solve step by step
firstly you know the radius is 3 and high is 4
if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³
Can someone help me with this question please.
Answer:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Step-by-step explanation:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
4 minutes is what fraction in a day
Answer:
4/1440 or 1/360
Step-by-step explanation:
A day has 24 hours and 60 minutes in each hour.
24 × 60 = 1440
I hope this helps.
Answer:
4/1440 or 1/360
Step-by-step explanation:
one day have 24hr .when we convert it to minutes,it becomes 1440minutes. so fraction of 4 min in a day us 4/1440 or in equavalent fraction 1/360.
The weight, in pounds , of Mike's five pet dogs are listed below.What is the mean absolute deviation (MAD) of the weights?
16 , 23 , 27 , 41 , 53
Type the answer in the box.
______ pounds
Answer:
it would be 32
Step-by-step explanation:
you would add them all up then divide it by five
Answer: The answer is 32
Someone please help with the questions on this picture!! URGENT!!!
Answer:
A) Independent
B) Dependent
Step-by-step explanation:
A) If we take a marble out and put the marble back, it means we have restored the sample to what it was initially and thus it doesn't affect probability of making another selection.
Thus, this is an independent event.
B) A card is taken from a deck of cards without replacement and set aside. Then after that another card is taken from the first sample, this means that the first sample size has now reduced and thus the first card taken affects the probability of the second card to be picked. Thus, this is a dependent event.
Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
Answer:
if I am understood your question correctly, X would be 84/29
Step-by-step explanation:
What is 34% plus 29% times 60
Answer:
34%+29%=63% 63%x60=37.8
Step-by-step explanation:
because math
Answer:
[tex] { \tt({34\% + 29\%) \times 60}} \\ = 63\% \times 60 \\ = \frac{63}{100} \times 60 \\ = 37.8[/tex]
How many exterior walls does the building have?
Answer:
18
Step-by-step explanation:
360÷20=18
twentycharactersignorethis
the building has 16 exterior walls
A system of equations is shown below:
y = 3x − 7
y = 2x + 1
What is the solution to the system of equations?
(8, 17)
(−8, 17)
(−8, −17)
(8, −17)
Answer:
(8, 17)
Step-by-step explanation:
y= 3x -7 -----(1)
y= 2x +1 -----(2)
Substitute (1) into (2):
3x -7= 2x +1
Being x terms to one side, constant to the other:
3x -2x= 7 +1
x= 8
Substitute x= 8 into (2):
y= 2(8) +1
y= 16 +1
y= 17
∴ The solution is (8, 17).
you can never divide any one angle into smaller angle. true or false
Answer:
true.
hope it helps..
Consider functions f, g, and h.
F(x) = 3x^3 + 9x^2 al- 12x g(x) = x - 1 h(x) = 3x2 + 12x
Which expression defines function h?
The relation between the functions f(x), g(x), and h(x) will be f(x)/g(x) is equal to h(x). Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The functions are given below.
f(x) = 3x³ + 9x² - 12x
g(x) = x - 1
h(x) = 3x² + 12x
The function f(x) can be written as
f(x) = 3x(x² + 3x - 4)
f(x) = 3x(x² + 4x - x - 4)
f(x) = 3x(x + 4)(x - 1)
f(x) = (x - 1)(3x² + 12)
Then divide the function f(x) by the function g(x), then we have
f(x) / g(x) = (x - 1)(3x² + 12) / (x - 1)
f(x) / g(x) = (3x² + 12)
f(x) / g(x) = h(x)
More about the function link is given below.
https://brainly.com/question/5245372
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Answer:
B
Step-by-step explanation:
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