Final answer:
Madison can choose from 4368 different combinations of 9 movies, including all 4 dramas and 5 out of the 16 non-drama movies.
Explanation:
Madison is picking out movies to rent and wants all 4 dramas out of her 9 selections. With 7 foreign films, 3 horror films, 6 action movies, and 4 dramas, the total number of non-drama movies is 16 (7+3+6). Since she must select all 4 dramas, she needs to choose the remaining 5 movies from the 16 non-drama movies available.
To find how many different combinations of 9 movies she can rent, we use the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items to choose from, r is the number of items to choose, and ! denotes factorial, representing the product of all positive integers up to that number.
The question asks us to calculate C(16, 5) because Madison is choosing 5 movies out of the 16 non-drama movies. This calculation yields:
C(16, 5) = 16! / [5!(16-5)!] = 4368
Therefore, there are 4368 different combinations of 9 movies Madison can rent if she wants all 4 dramas.
If the area under the standard normal curve to the left of zequalsminus1.72 is 0.0427, then what is the area under the standard normal curve to the right of zequals1.72?
Answer: 0.0427
Step-by-step explanation:
Given : The area under the standard normal curve to the left of z = -1.72 is 0.0427
We know that the normal curve is a bell shaped curve that is symmetric such that half of the data falls to the left of the mean (Mean lies at the middle of the curve) and half of data falls to the right.
Now, z=-1.72 lies on the left side and z=1.72 lies right side.
Since, normal curve is symmetric and the magnitude of the values if same , then the area under the standard normal curve to the left of z = -1.72 is equals to the area to the right of z = 1.72 is 0.0427
Therefore, the area under the standard normal curve to the right of z = 1.72 is 0.0427
The area under the standard normal curve to the right of z=1.72 is 0.9573 or 95.73%, which can be calculated by subtracting the area to the left of z from 1 (1 - 0.0427 = 0.9573).
Explanation:The area under the standard normal curve to the left of z=-1.72 is 0.0427. This essentially means that 4.27% of all observations fall under this score. Conversely, the area to the right of the z-score represents the proportion of observations that are greater than z. In a normal distribution, the sum of the areas to the left and to the right of a z-score must always equal to 1 (0.0427 + x = 1), because all possible outcomes are accounted for by a normal distribution. Hence, we can find out the area to the right by simply subtracting the area to the left from 1. So, the area under the standard normal curve to the right of z=1.72 is 1 - 0.0427 = 0.9573 or 95.73%.
Learn more about Standard Normal Curve here:https://brainly.com/question/36467349
#SPJ3
Question 11 (2.5 points)
The perimeter of a rectangular poster is 108 in. The length is 12 in, greater than the
width. Find the length,
a) 21
b) 42
c) 33
d) 48
Answer:
42 in
Step-by-step explanation:
108 in = 2l + 2w
l = 12 in
108 = 24 + 2w
84 = 2w
w = 42
The width is 21 inches, leading to a length of 33 inches, which corresponds to option c.
To find the length of the rectangular poster, we will use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width. According to the question, we have a perimeter P of 108 inches and the length is 12 inches greater than the width. If we let w represent the width, then the length can be represented as w + 12. Plugging into the perimeter formula we get: 108 = 2(w + 12) + 2w.
Now, let's solve for w:
108 = 2w + 24 + 2w
108 = 4w + 24
108 - 24 = 4w
84 = 4w
w = 84 / 4
w = 21 inches
Now that we have the width, we can find the length by adding 12 inches:
Length = w + 12
Length = 21 + 12
Length = 33 inches
Therefore, the length of the poster is 33 inches, which corresponds to option c.
In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r2 is reported as .40. Which of the following would be a correct interpretation? Mobility explains 40% of the variation in number of friends There is a strong positive relationship between number of friends and mobility As mobility increases, number of friends decreases Mobility explains 16% of the variation in number of friends
Answer:
Option A
Step-by-step explanation:
Given that in a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r^2 is reported as .40.
r square, being the coefficient of determination explains the variablity of one variable due to the variability of the other. Here Mobility explains 40% variation in the number of friends is right answer.
Option B is wrong because r = ±6324, so cannot say positive or negative.
Similarly option c is wrong because we are unsure whether negative correlation. Option d is wrong since 16% is not right .
In a certain study comma the chance of encountering a car crash on the roadstudy, the chance of encountering a car crash on the road is stated as 66%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
The probability is 0.66.
Step-by-step explanation:
Given,
The chance of encountering a car crash on the road is stated as 66%,
That is, out of 100% cases the percentage of the number of car crash cases is 66%,
⇒ Total outcomes = 100%, favourable outcome = 66 %
So, the probability of occurrence a car crash = [tex]\frac{66\%}{100\%}[/tex]
[tex]=\frac{66/100}{100/100}[/tex]
[tex]=\frac{66}{100}[/tex]
[tex]=0.66[/tex]
Where, 0 < 0.66 < 1.
Hence, the indicated degree of likelihood as a probability value between 0 and 1 inclusive is 0.66.
Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach? 1.3 ft 2.6 ft 26.0 ft 27.6 ft
Answer:
Option D.
Step-by-step explanation:
Arianna kicks a soccer ball into the air with an initial velocity = 42 feet per second
If the starting height of the ball is 0 feet then we have to find the approximate maximum height the soccer ball attached.
Since we know vertical motion is represented by
v² = u² - 2gh
Where v = final velocity of the object
u = initial velocity of the object
g = gravitational force
h = h = maximum height achieved by the object
Here v = 0, u = 42 feet per second and g = 32 feet per second²
Now we plug in these values in the formula
0 = (42)² - 2(32)(h)
1764 = 64h
[tex]h=\frac{1764}{64}[/tex]
h = 27.56 feet
≈ 27.60 feet
Therefore, maximum height achieved by the soccer ball is 27.6 feet.
Option D is the answer.
Answer:
Option D is 2.76 ft
Step-by-step explanation:
Its correct
hi, I would greatly appreciate if someone left the work step by step to solve one of these questions so I can understand it? if it's possible
Answer:
see below
Step-by-step explanation:
a
y = 2x -3
Standard form is Ax + By =C where A is a positive integer and B and C are integers
Subtract 2x from each side
y-2x = 2x-2x -3
-2x+y = -3
We want A to be positive
Multiply each side by -1
2x -y = 3
This is in standard form
b
y = 2/3 x -7
Subtract 2/3x from each side
y-2/3x = 2/3x-2/3x -7
-2/3x+y = -7
We want A to be positive integer
Multiply each side by -3
-3*(-2/3x+y) = -7*-3
2x -3y = 21
c
y = -3x +1/2
Add 3x to each side
3x +y = -3x+3x +1/2
3x+y = 1/2
Multiply each side by 2
2(3x+y) = 1/2*2
6x+2y = 1
Calculate the amount of money you'll have at the end of the indicated time period You invest $2000 in an account that pays simple interest of 4 % for 20 years. The amount of money you'll have at the end of 20 years is S
Answer:
The amount would be $ 3600.
Step-by-step explanation:
Given,
The invested amount, P = $ 2000,
Annual rate of interest, r = 4 %,
Time, t = 20 years,
So, the simple interest would be,
[tex]I=\frac{P\times r\times t}{100}[/tex]
[tex]=\frac{2000\times 4\times 20}{100}[/tex]
[tex]=\frac{160000}{100}[/tex]
[tex]=\$1600[/tex]
Hence, the amount of money after 20 years,
[tex]A=P+I[/tex]
[tex]=2000+1600[/tex]
[tex]=\$ 3600[/tex]
if abc=1 prove that 1/(1+a+b^-1) + 1/(1+b+c^-1) +1/(1+c+a^-1) =1
Answer with explanation:
It is given that, abc=1
[tex]\rightarrow \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}\\\\\rightarrow \frac{b}{b+ab+1}+\frac{c}{c+bc+1}+\frac{a}{a+ac+1}\\\\abc=1\\\\\rightarrow \frac{b}{b+ab+abc}+\frac{c}{c+bc+abc}+\frac{a}{a+ac+abc}\\\\\rightarrow \frac{1}{1+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1}{abc+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1+a}{a(bc+1+c)}+\frac{c}{c+bc+1}\\\\\rightarrow\frac{1+a+ac}{a(bc+1+c)}\\\\\rightarrow\frac{1+a+ac}{abc+a+ac)}\\\\\rightarrow\frac{1+a+ac}{1+a+ac)}\\\\=1[/tex]
Hence proved.
Answer:
ABC=1
Step-by-step explanation:
20. Use Barrow's a, e method to determine the slope of the tangent line to the curve x^3 + y^3=C^3
Answer: Slope would be,
[tex]-\frac{x^2}{y^2}[/tex]
Step-by-step explanation:
Here, the given curve,
[tex]x^3 + y^3=C^3[/tex]
[tex]\implies x^3 + y^3 - C^3=0[/tex]
In Barrow's method,
Steps are as follows,
Step 1 : put, x = x - e, y = y - a
[tex](x-e)^3 + (y-a)^3 - C^3=0[/tex]
[tex]x^3-3x^2e+3xe^2-e^3+y^3-3y^2a+3ya^2-a^3+C^3=0[/tex]
Step 2 : Reject terms which do not contain a or e,
[tex]-3x^2e+3xe^2-e^3-3y^2a+3ya^2-a^3=0[/tex]
Step 3 : Reject all terms in which a or e have exponent greater than 1,
[tex]-3x^2e-3y^2a=0[/tex]
Step 4 : Find the ratio of a : e,
[tex]-3y^2a=3x^2e[/tex]
[tex]\implies \frac{a}{e}=-\frac{x^2}{y^2}[/tex]
Hence, the slope of the given curve is [tex]-\frac{x^2}{y^2}[/tex]
consider the function represented by the table
the ordered pair given in the bottom row can be written using function notation as,
a) f(9)=5
b) f(5)=9
c) f(5,9)=14
d) f(9,5)=14
Answer:
f(9) =5
Step-by-step explanation:
We have an input x and an output f(x)
The input in the last row is 9 and the output is 5
The input x=9 and the output f(9) =5
f(9) =5
The correct option is (a) because [tex]f(9)=5[/tex].
Important information:
The given table represents the ordered pairs.Function notation:The function notation of a point [tex](x,f(x))[/tex] or [tex](x,y)[/tex] is [tex]f(x)=y[/tex].
Using the definition of function notation. The function notation of given ordered pairs [tex](2,6),(7,3)[/tex] and [tex](9,5)[/tex] are:
[tex]f(2)=6[/tex]
[tex]f(7)=3[/tex]
[tex]f(9)=5[/tex]
Thus, option (a) is correct and the other options are incorrect.
Find out more about 'Function notation' here:
https://brainly.com/question/26253633
2. According to a well-known legend, the game of chess was invented many centuries ago in northwestern India by a certain sage. When he took his invention to his king, the king liked the game so much that he offered the inventor any reward he wanted. The inventor asked for some grain to be obtained as follows: just a single grain of wheat was to be placed on the first square of the chessboard, two on the second, four on the third, eight on the fourth, and so on, until all 64 squares had been filled. If it took just 1 second to count each grain, how long would it take to count all the grain due to him?
Answer:
2^64. I know 2^20 is 1048576. Cube that and multiply by 16 or grab a calculator. I'm too lazy to solve this.
The time taken to count all the grain due to him is [tex]2^{64}-1[/tex] or 18,446,744,073,709,551,615 sec .
What is Geometric Progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
What is sum of Geometric Progression?. The sum of infinite, i.e. the sum of a GP with infinite terms is [tex]S_{∞} = \frac{a}{(1 - r) }[/tex]such that 0 < r < 1.
The formula used for calculating the sum of a geometric series with n terms is Sn = [tex]\frac{a( r^{n} -1 )}{(r - 1)} ,[/tex] where r ≠ 1.
According to the question
A chess board has 64 squares and all had been filled with grain
1st squares of chess board has grain = 1 = [tex]2^{0}[/tex]
2nd squares of chess board has grain = 2 = [tex]2^{1}[/tex]
3nd squares of chess board has grain = 4 = [tex]2^{2}[/tex]
4nd squares of chess board has grain = 8 = [tex]2^{3}[/tex]
so on ..
As this is an Geometric Progression
Where
First term (a) = 1
common ratio (r) = 2
Number of terms = n = 64
Now,
it took just 1 second to count each grain ,
Time taken to count all the grains
By using formula of sum of Geometric Progression
Sn = [tex]\frac{a( r^{n} -1 )}{(r - 1)} ,[/tex] where r ≠ 1.
substituting the values in formula
S₆₄ = [tex]\frac{1( 2^{64}-1 )}{(2-1)} ,[/tex]
S₆₄ = [tex]2^{64}-1[/tex]
S₆₄ = 18,446,744,073,709,551,615
Hence, The time taken to count all the grain due to him is [tex]2^{64}-1[/tex] or 18,446,744,073,709,551,615 sec .
To know more about Geometric Progression and sum of Geometric Progression here:
https://brainly.com/question/14256037
#SPJ2
I need the answer to these math questions.
1) Multiply 8 minutes 31 seconds by 17.
Answer:
2 h 16 min 23 sec
Step-by-step explanation:
Hello
the time is expressed in the sexadecimal system, which uses the number 60 as an arithmetic base,hence
1 min=60 sec
1 hora =60 min
Now, we have
[tex](8 min + 31 sec)*17=136 min +527 sec\\\\\\we\ need\ to\ convert\ this\ in\ our\ base\ 60\, using\ a\ rule\ o\ three\\\\ 60 min=1\ hour\\136 min=x ?\\\\x=\frac{ 136 h}{60}\\ x=2.26 hours\\\\[/tex]
we take the whole part as an hour, and the decimal part is multiplied by 60 to get minutes
Step 1
[tex]8min*17=136 min =2.26 h\\\\2.26h = 2\ h + 0.26h(\frac{60 min}{1 h}) \\2.26h =2h+15.6 min\\\\[/tex]
we repeat the procedure to leave the minutes as a whole part
[tex]2.26\ h =2\ h+15\ min + 0.6\ min*(\frac{60 \sec}{1 m} )\\2.26\ h =2\ h\ 15\ min\ 36\ sec[/tex]
Step 2
[tex]\\527\s*(\frac{1 min}{ 60\ sec})=8.78\ min\\ \\8.78\ min= 8\min\0.78\ min\\8.78\ min=8\ min\ 0.78\min(\frac{60\ seg}{min})\\8.78\min=8\ min \ 47\ sec\\\\now, add\\\\8 min *17 =2\ h\ 15\ min\ 36\ sec\\31 sec *17 =8\ min \ 47\ sec\\(8\ min\ 31\ sec)*17=2\ h\ 15\ min\ 83\ sec\\83 s(\frac{1 min}{60 sec})=1.38 min\\1.38\ min\ =1\ min\ 0.38\ min*(\frac{60 sec}{1\ min})\\1.38\ min=1\min\ 23 s.\\( 8min 31 sec)*17=2 h 16 min 23 sec[/tex]
Have a great day
Two marbles are drawn without replacement from a box with 3 White, 2 green, 2 red, and 1 Blue Marble.
Find the probability. Both marbles are white
Answer:
[tex]\frac{3}{28}[/tex]
Step-by-step explanation:
Te meaning of without replacement is once the ball is picked from the stock it cannot be put back
Hre there are total 8 balls and 3 white balls
probability of picking 1st white is [tex]\frac{3}{8}[/tex]
now only 2 white and total is 7( one ball has already been picked)
therefore probability of picking 2nd white ball is [tex]\frac{2}{7}[/tex]
both the action are independent events
therefore, probability of picking 2 white balls is [tex]\frac{3}{8}[/tex] × [tex]\frac{2}{7}[/tex]
= [tex]\frac{3}{28}[/tex]
Answer:[tex]\frac{3}{28}[/tex]
Step-by-step explanation:
Given a box contains 3 White ,2 green,2 red & 1 Blue marble
We have to draw two marbles without replacement
therefore for first draw we have 3 white marble to choose among 8 marbles
i.e.
[tex]_{1}^{3}\textrm{C}[/tex] choices among the total of [tex]_{1}^{8}\textrm{C}[/tex] options
For second draw we 2 white marbles left therefore no of ways in which a white marble can be choosen is
[tex]_{1}^{2}\textrm{C}[/tex]
Therefore required probability is =[tex]\frac{favourable\ outcome}{Total\ outcome}[/tex]
P[tex]\left ( required\right )[/tex]=[tex]\frac{3\times2}{8\times7}[/tex]
P[tex]\left ( required\right )[/tex]=[tex]\frac{3}{28}[/tex]
1. Assume that R and S are symmetric relations on a set A. Prove that Rns is symmetric.
Answer with explanation:
Suppose, A={(a,b),(b,a), (c,d),(d,c),(p,q),(q,p),(a,a),(b,b)}
A Relation M is Symmetric , if (p,q)∈M , then (q,p)∈M.
⇒It is given that, R and S are symmetric Relation on a Set A.
⇒If R is symmetric, then if (a,b)∈R, means,(b,a)∈R.So, R={(a,b),(b,a)}.
⇒If S is Symmetric, then if (c,d)∈S, means,(d,c)∈S.So, S={(c,d),(d,c)}.
⇒R ∩ S ={(a,b),(b,a),(c,d),(d,a)}
⇒If you will look at the elements of Set , R∩S, there is (a,b)∈ R∩S,so as (b,a)∈ R∩S.Also, (c,d)∈ R∩S,so as (d,a)∈ R∩S.
Which shows Relation in the set , R∩S is symmetric.
On their first date, Kelly asks Mike to guess the date of her birth, not including the year. Complete parts a through c below. a. What is the probability that Mike will guess correctly? (Ignore leap years.)
Answer:
The probability that mike will guess correctly is 0.0027397 or [tex]\frac{1}{365}[/tex].
Step-by-step explanation:
Consider the provided information.
The number of days in a year is 365 (Ignore leap years).
[tex]Probability = \frac{favorable\ outcomes}{possible\ outcomes}[/tex]
Here, favorable outcomes is 1 and total number of outcomes are 365.
Substitute these value in above formula.
[tex]Probability = \frac{1}{365}[/tex]
[tex]Probability = 0.0027397[/tex]
Thus, the probability that mike will guess correctly is 0.0027397 or [tex]\frac{1}{365}[/tex].
Probability of an event represents the chances of occurrence of that event.
The probability that Mike will guess Kelly's birth date correctly (ignoring leap years) is [tex]\dfrac{1}{365} \approx 0.00027[/tex]
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]
Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Since we know that in a year (non leap year), there are 365 days, and Kelly's birthday can be on any one of those date, so the total number of days to chose from is 365 and since birthday of Kelly is going to be on single day of whole year, so favorable case is only single.
Thus,
if E = Selecting Kelly's birth date correctly,
Then
[tex]P(E) = \dfrac{1}{365} \approx 0.00027[/tex]
Thus,
The probability that Mike will guess Kelly's birth date correctly (ignoring leap years) is [tex]\dfrac{1}{365} \approx 0.00027[/tex]
Learn more about probability here:
brainly.com/question/1210781
A cell of some bacteria divides into two cells every 10 minutes.The initial population is 3 bacteria. (a) Find the size of the population after t hours (function of t) (b) Find the size of the population after 7 hours. # Preview | Preview (c) When will the population reach 21? t42 Preview
Answer:
(a) [tex]P_{t}=3(2)^{6t}[/tex]
(b) [tex]3(2)^{42}[/tex]
(c) 28.07 minutes
Step-by-step explanation:
A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.
That means sequence formed will be 3, 6, 12, 24............
We can easily say that this sequence is a geometric sequence having common ratio (r) = [tex]\frac{T_{2}}{T_{1}}=\frac{6}{3}[/tex]
r = 2
Now we know the explicit formula of a geometric sequence is given by
[tex]P_{t}=P_{0}(r)^{\frac{60t}{10}}=P_{0}(r)^{6t}[/tex]
Where a = Initial population = 3 bacteria
r = common ratio = 2
and t = time in hours
So explicit formula will be [tex]P_{t}=3(2)^{6t}[/tex]
(a) Now we have to calculate the size of population after t hours
[tex]P_{t}=3(2)^{6t}[/tex]
(b) We have to find the size of population after 7 hours or 420 minutes
[tex]P_{t}=3(2)^{6\times7}[/tex]
= [tex]3(2)^{42}[/tex]
After 7 hours bacteria population will be [tex]3(2)^{42}[/tex]
(c) Time to reach population as 21
By the explicit formula
[tex]21=3(2)^{6t}[/tex]
[tex]2^{6t}=\frac{21}{3}=7[/tex]
Now we take log on both the sides of the equation
[tex]log(2^{6t})=log(7)[/tex]
6t log2 = log 7
6t(0.301) = 0.845
t(1.806) = 0.845
t = [tex]\frac{0.845}{1.806}=0.468[/tex] hours
Or t = 0.468×60 = 28.07 minutes
Therefore, after 28.07 minutes bacterial population will be 21
The bacteria population grows following an exponential pattern, therefore the population after t hours can be calculated using the exponential growth formula with the initial population as 3 and each cell dividing every 10 minutes. To calculate the time when the population reaches a certain size, solve the exponential growth equation for t.
Explanation:The growth of bacteria population can be described as exponential growth, with each cell dividing into two every 10 minutes. Given the initial population as 3 bacteria, we would need to calculate the number of divisions that occur within the specified time frame to calculate the population after t hours.
(a) To find the population after t hours, we convert the hours to minutes (since each division occurs every 10 minutes) and then calculate the number of divisions. Each bacterial division results in a doubling of the population, so we use the formula for exponential growth: N = N0 * 2^n, where N0 is the initial population (3), and n is the number of divisions (6t, because t hours is 60t minutes and each division occurs every 10 minutes, making a total of 6t divisions per hour). So the population after t hours is N = 3 * 2^(6t).
(b) To find the size of the population after 7 hours, we substitute t = 7 into the formula, to get N = 3 * 2^(6*7) = 3 * 2^42.
(c) To find out when the population reaches 21, we equate N to 21 in the formula and solve for t. So, 21 = 3 * 2^(6t). Solving this equation gives the time t in hours when the population will reach 21.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
#SPJ11
PLEASE HELP THIS SHOULD BE MY LAST ONE
Answer:
g(-4) = -4
g(-2) = 1
g(1) = -4
Step-by-step explanation:
The value of the given function is -4 for all values of x other than -2 and 1 if x=-2
So,
For x=-4 the value of function will be -4.
g(-4) = -4
For x=-2
The value of function is -2.
g(-2) = 1
And for x=1, the value will be -4.
g(1) = -4 ..
A given binomial experiment has n=100 trials and p=1/3. Is it more likely to get x=20 successes or x=45 successes. Why?
Answer:
The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.
Step-by-step explanation:
Given information: n=100 and p=1/3.
According to the binomial distribution, the probability of getting r success in n trials is
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
where, n is total trials, p is probability of success and q is probability of failure.
Total trials, n = 100
Probability of success, p = [tex]\frac{1}{3}[/tex]
Probability of failure, q = [tex]1-\frac{1}{3}=\frac{2}{3}[/tex]
The probability of 20 successes is
[tex]P(x=20)=^{100}C_{20}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{100-20}[/tex]
[tex]P(x=20)=\frac{100!}{20!(100-20)!}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{80}\approx 0.001257[/tex]
The probability of 45 successes is
[tex]P(x=45)=^{100}C_{45}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{100-45}[/tex]
[tex]P(x=45)=\frac{100!}{45!(100-45)!}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{55}\approx 0.004296[/tex]
The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.
Suppose that a movie theater snack bar turns over its inventory of candy 3.3 times per month. (Round your answer to 2 decimal places.) If the snack bar has an average of 340 boxes of candy in inventory, what is its average daily sales rate for candy
Answer:
The average daily sales rate for candy is 37.4.
Step-by-step explanation:
We know that,
[tex]\text{Inventory turnover }= \frac{\text{Total sale}}{\text{Average inventories}}[/tex]
[tex]\implies \text{Total sale}=\text{Inventory turnover }\times \text{Average inventories}[/tex]
Given,
Inventory turnover of candies = 3.3,
Average inventories = 340
So, sale of candies = 3.3 × 340 = 1122
Now,
[tex]\text{Average daily sales rate}=\frac{\text{total sale}}{\text{Number of days}}[/tex]
Since, 1 month = 30 days ( approx ),
Hence, the average daily sales rate for candy = [tex]\frac{1122}{30}[/tex]=37.4
If a ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that a. the ball is not even numbered? b. the ball red and even numbered? c. the ball red or even numbered? d. the ball is neither red or even numbered?
Answer:
a. 50%
b. 33%
c. 17% (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)
d. 67%
Step-by-step explanation:
a. We have a total of 18 balls, 13 are red and 5 are white. They are numbered from 1 to 18. In this case, we don't care about the color of the ball, we just need it to be not even. We have to count how many not even numbers are between 1 and 18, that is 9. So, the chances of getting a ball not even numbered are 9 in 18, that's
[tex]\frac{9}{18}*100=50\%[/tex]
b. Now we do care about the color of the ball. The red balls are numbered from 1 to 13, so we have 6 balls even numbered. That makes the chances 6 in 18 (we still have 18 in total), that's
[tex]\frac{6}{18}*100=33\%[/tex]
c. (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)
The white balls are numbered from 14 to 18, so we have 3 balls even numbered. That makes the chances 3 in 18,
[tex]\frac{3}{18}*100=17\%[/tex]
d. Let's notice that "the ball is neither red or even numbered" is the complement (exactly the opposite) of "the ball is red and even numbered", that means
100% = Probability (ball red and even numbered) + Probability (ball neither red or even numbered)
So, Probability (ball neither red or even numbered) = 100% - Probability (ball red and even numbered) = 100% - 33% = 67%
The probability that a randomly selected teenager watched a rented video at least once during a week was 0.75. What is the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week? (Round your answer to four decimal places.)
Answer:
0.7564
Step-by-step explanation:
Let X be the event of watching a rented video at least once during a week,
Given,
The probability of watching a rented video at least once during a week was, p = 0.75,
So, the probability of not watching a rented video at least once during a week was, q = 1 - p = 0.25,
Binomial distributive formula,
[tex]P(x)=^nC_x p^x q^{n-x}[/tex]
Where,
[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]
Hence, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week,
P(X ≥ 5) = P(X=5) + P(X=6 )+ P(X=7)
[tex]=^7C_5 0.75^5 0.25^{7-5}+^7C_6 0.75^6 0.25^{7-6}+^7C_7 0.75^7 0.25^{7-7}[/tex]
[tex]=21 (0.75)^5 (0.25)^2 + 7 (0.75)^6 0.25 + 0.75^7[/tex]
[tex]=0.756408691406[/tex]
[tex]\approx 0.7564[/tex]
The probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week is 0.3015.
Explanation:The probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week can be calculated using the binomial probability distribution formula:
P(X ≥ k) = 1 - P(X < k)
where X is the number of teenagers who watched a rented movie at least once, k is the minimum number of teenagers (5 in this case), and P(X < k) is the probability that less than k teenagers watched a rented movie at least once.
In this case, the probability that a randomly selected teenager watched a rented video at least once during a week is 0.75. Therefore, the probability that a randomly selected teenager did not watch a rented video at least once is 1 - 0.75 = 0.25.
Using the binomial probability distribution formula, we can calculate the probability that less than 5 teenagers watched a rented movie at least once:
P(X < 5) = C(7, 0) * (0.25)^0 * (0.75)^7 + C(7, 1) * (0.25)^1 * (0.75)^6 + C(7, 2) * (0.25)^2 * (0.75)^5 + C(7, 3) * (0.25)^3 * (0.75)^4 + C(7, 4) * (0.25)^4 * (0.75)^3
where C(n, r) is the number of combinations of n items taken r at a time:
C(n, r) = n! / (r! * (n-r)!)
Substituting the values and evaluating the expression, we get:
P(X < 5) = 0.698486328125
Therefore, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week is:
P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.698486328125 = 0.301513671875
Learn more about probability here:https://brainly.com/question/32117953
#SPJ3
If a 42-piece set of stainless steel flatware costs $113.40 at a certain store, what is the cost (in dollars) per piece?
Answer:$2.7 dollars per piece
Step-by-step explanation: Divide 113.40 by 42
$2.7 per piece is the answer.
$113.40 / 42 piece set of stainless steel = $2.7
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
What are problem-solving and examples?Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about Problem-solving here: brainly.com/question/13818690
#SPJ2
discrete math:
find the rule for determining when a number is divisible by 11.
Answer:
Step-by-step explanation:
Divisibility rule when a number is divisible by 11:
Take the alternating sum of digits in a number read from left to right .If that is divisible by 11 then the the given number is divisible by 11.
It is a divisibility rule of 11.
Let 1342 is a number .The number is divisible by 11 or not
Alternating sum of digits =1-3+4-2=0
The alternating sum of digits is divisible by 11 .
Therefore, the number 1342 is divisible by 11.
Let a number 2728
Alternating sum of digits = 2-7+2-8=-11.
The alternating sum of digits is divisible by 11 .
Therefore, the number 2728 is divisible by 11.
The rule for determining divisibility by 11 involves alternately adding and subtracting a number's digits; if the result is 0 or divisible by 11, the original number is too. Examples illustrate the application of the divisibility test.
Rule for Divisibility by 11
The rule for determining when a number is divisible by 11 is quite straightforward. To apply the rule, you alternate between adding and subtracting the digits of the number in question from left to right. If the resulting sum (which may be negative) is 0 or divisible by 11 itself, then the original number is divisible by 11. For example, consider the number 2728. Apply the rule like this: 2 - 7 + 2 - 8 = -11. Since -11 is divisible by 11, 2728 is also divisible by 11.
Examples
Another example: Take the number 5831. Using the rule: 5 - 8 + 3 - 1 = -1, which is not divisible by 11, hence 5831 is not divisible by 11.
This divisibility test is a fantastic example of how certain mathematical rules are used to quickly determine properties of numbers without needing to perform long divisions.
Solve the inequality and graph the solution on a number line.
–3(5y – 4) ≥ 17
please show work!
Answer:
Step-by-step explanation:
In order to solve the inequality, follow the simple steps:
–3(5y – 4) ≥ 17 .
Dividing both sides with -3:
5y - 4 ≤ -17/3 (the sign of the inequality becomes opposite whenever a negative number is either multiplied or divided on both the sides of the inequality).
Adding 4 on both sides:
5y ≤ -5/3
Dividing 5 on both sides:
y ≤ -1/3.
This shows that all the values of y less than and equal to -1/3 satisfy the inequality.
The number line has been attached. Since it involves ≤ sign, therefore, a filled circle will be used to plot the inequality. Less than means that all the values on the left hand side of the number line will be included. This is denoted with an arrow (see the diagram)!!!
Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired, whereas the other 40% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty?
The probability that exactly two telephones will end up being replaced under warranty is found to be 0.147.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Suppose the total number of telephones be x.
Then, the telephones submitted under warranty is 20% × x = 0.2x.
The number of telephones to be repaired is 60% × 0.2x = 0.12x
And, those to be replaced are given as 40% × 0.2x = 0.08x.
Now, the probability of exactly two units being replaced out of 10 is given by binomial distribution as,
P(Exactly two units being replaced) = ¹⁰C₂(0.08)²(0.92)⁸
⇒ P(Exactly two units being replaced) = 0.147
Hence, the probability for the given case is obtained as 0.147.
To know more about binomial distribution click on,
https://brainly.com/question/14565246
#SPJ5
To solve this problem, we can use the concept of conditional probability. Given that 20% of telephones are submitted for service while under warranty and of these, 60% can be repaired and 40% must be replaced with new units, we can calculate the probability that exactly two telephones will be replaced under warranty.
Explanation:To solve this problem, we can use the concept of conditional probability. Let's break down the information given:
20% of all telephones are submitted for service while under warranty.Of these, 60% can be repaired.40% must be replaced with new units.Now, let's calculate the probability that exactly two telephones will be replaced:
First, calculate the probability of a telephone being replaced: 20% (probability of being submitted) * 40% (probability of needing replacement) = 8%.Now, calculate the probability of a telephone being repaired: 20% (probability of being submitted) * 60% (probability of being repaired) = 12%.Since we need exactly two telephones to be replaced, we need two telephones to be replaced and eight telephones to be repaired. The probability of two telephones being replaced and eight telephones being repaired can be calculated as 10C2 (number of ways to choose 2 out of 10) * (8%)^2 * (12%)^8 = 45 * 0.08^2 * 0.12^8 ≈ 0.0572 (rounding to four decimal places).Therefore, the probability that exactly two telephones will end up being replaced under warranty is approximately 0.0572, or 5.72%.
A grocery bag can be classified as either paper or plastic. Suppose that 97% of grocery bags are classified as plastic. (a) Two grocery bags are chosen at random. What is the probability that both grocery bags are plastic? (b) Five grocery bags are chosen at random. What is the probability that all five grocery bags are plastic? (c) What is the probability that at least one of five randomly selected grocery bags is paper? Would it be unusual that at least one of five randomly selected grocery bags is paper?
Answer with explanation:
Given : The probability of grocery bags are classified as plastic = 0.97
(a) f two bags are chosen at random.
Then , the probability that both grocery bags are plastic is given by :-
[tex]^2C_2(0.97)^2(1-0.97)^0=0.9409[/tex]
(b) If five grocery bags are chosen at random.
Then , the probability that all five grocery bags are plastic is given by :-
[tex]^5C_5(0.97)^5(1-0.97)^0\approx0.8587[/tex]
(c) The probability of getting paper = 1-0.97=0.03
The probability that at least one of five randomly selected grocery bags is paper :-
[tex]P(x\geq1)=1-P(0)\\\\1-^5C_0(0.03)^0(0.97)^5\\\\=1-(0.03)^0(0.97)^5=0.1412659\approx0.14>0.05[/tex]
Thus , it would not be unusual that at least one of five randomly selected grocery bags is paper.
Probability is used to determine the chances of an event
The probability that both grocery bags are plastic is 0.9409The probability that all five grocery bags are plastic is 0.8587The probability that at least one grocery bags is paper is 0.1413It would not be unusual that at least one of five randomly selected grocery bags is paper.[tex]p = 97\%[/tex] -- chances that a bag is plastic
(a) Both plastics selected are plastic
This is calculated as:
[tex]P(2) = p^2[/tex]
So, we have:
[tex]P(2) = (97\%)^2[/tex]
[tex]P(2) = 0.9409[/tex]
Hence, the probability that both grocery bags are plastic is 0.9409
(b) All five are plastic
This is calculated as:
[tex]P(5) = p^5[/tex]
So, we have:
[tex]P(5) = (97\%)^5[/tex]
[tex]P(5) = 0.8587[/tex]
Hence, the probability that all five grocery bags are plastic is 0.8587
(c) At least one of the five is paper
The probability that none of the five is paper is the same as the probability that all five is plastic.
So:
[tex]P(None) = 0.8587[/tex]
Using complement rule,
[tex]P(At\ least\ 1) = 1 - P(None)[/tex]
So, we have
[tex]P(At\ least\ 1) = 1 - 0.8587[/tex]
[tex]P(At\ least\ 1) = 0.1413[/tex]
Hence, the probability that at least one grocery bags is paper is 0.1413
The above probability is greater than 0.05
Hence, it would not be unusual that at least one of five randomly selected grocery bags is paper.
Read more about probabilities at:
https://brainly.com/question/11234923
Which of the following is equivalent to the formula =C2+C3+C4+C7?
=SUM(C2:C7)
=SUM(C2,C4:C7)
=SUM(C2, C3, C4:C7)
=SUM(C2:C4, C7)
Answer:
=SUM(C2:C4, C7)
Step-by-step explanation:
In excel 'C' represent the cell ( intersection of row and column ),
Also, '=sum( )' represents the function of addition in the excel,
Also, when we operate all consecutive cells from [tex]Cn[/tex] to [tex]Cm[/tex]
Then under the function formula we write [tex]Cn:Cm[/tex]
And, when we operate a cell [tex]Cn[/tex] with non consecutive cell [tex]Cl[/tex]
Then under the function formula we write [tex]Cn, Cl[/tex]
Hence, C2+C3+C4+C7 can be written as,
=SUM(C2:C4, C7)
Graduation is 3 years away and you want to have $850 available for a trip. If your bank is offering a 3-year CD (certificate of deposit) paying 2% simple interest, how much do you need to put in this CD to have the money for your trip?
Answer:
We need to put $801.88 amount in the bank.
Step-by-step explanation:
given that
t=3 yr
Need amount $850 after 3 yr so P= $850
Interest rate=2%
We know that for simple interest
[tex]P=A\left(1+\dfrac{rt}{100}\right)[/tex]
Where r is the Interest rate,t is the time,A is the present amount and P is principle amount after t time.
Here given that P= $850
So now putting the values
[tex]850=A\left(1+\dfrac{2\times 3}{100}\right)[/tex]
So A=$801.88
We need to put $801.88 amount in the bank.
Find the general solution to 2y ′′ − y ′ − y = 0.
Answer: y(x) = [tex]C_{1} e^{x} + C_{2} e^{\frac{-x}{2} }[/tex]
Step-by-step explanation:
2y ′′ − y ′ − y = 0
The characteristic equation is:
[tex]2r^{2} - r - 1 = 0[/tex]
[tex]2r^{2} - 2r + r - 1 = 0[/tex]
2r(r-1) + 1(r-1) = 0
(r-1)(2r+1) = 0
[tex]r_{1} = 1 , r_{2} = \frac{-1}{2}[/tex]
∴ there are two distinct roots
so the general equation is as follows:
y(x) = [tex]C_{1} e^{r_{1}x } + C_{2} e^{r_{2}x }[/tex]
y(x) = [tex]C_{1} e^{x} + C_{2} e^{\frac{-x}{2} }[/tex]
Imagine the average time to complete a “4-year” bachelors degree is actually 4.3 years based on national data. You collect data on the 20 psychology students who started school during the same semester as you, finding an average time to complete at 4.5 years, with a sample standard deviation of 0.5 years. What is your 95% confidence interval? (for your FINAL answers, round to the nearest TWO decimal places)
Answer:
To answer you question, we need the confidence internals formula, μ±Zc*(σ/[tex]\sqrt{N}[/tex]); N is the 20 psychology students, 0.5 the desviation standar and 4.3 is the medium based on national data, every fact in years.
Step-by-step explanation:
You need to consult the Zc value, you can find this table attached in this question; for 95%, we have a Zc value of 1.96.
Next step replace values: 4.3±1.96*(0.5/[tex]\sqrt{20}[/tex]) = 4.3±0.22 (rounding the result)
So, the confidence interval are:
4.08cm≤X≤4.52cm