Suppose that we ask n randomly selected people whether they share your birthday. (a) Give an expression in terms of n for the probability that no one shares your birthday (ignore leap years). $$ Correct: Your answer is correct. (b) What is the least number of people we need to select so that the probability is at least 0.8 that at least one person shares your birthday
Using the binomial distribution, it is found that:
a) The expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
b) You need to select at least 587 people.
For each person, there are only two possible outcomes, either they share your birthday, or they do not. The probability of a person sharing your birthday is independent of any other person, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[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.There are 365 days in a non-leap year, hence, the probability of each person sharing your birthday is [tex]p = \frac{1}{365}[/tex]
Item a:
This probability is P(X = 0), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{n,0}.\left(\frac{1}{365}\right)^{0}.\left(\frac{364}{365}\right)^{n} = \left(\frac{364}{365}\right)^{n}[/tex]
Hence, the expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
Item b:
The probability that at least one person shares your birthday is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We want that:
[tex]P(X \geq 1) \geq 0.8[/tex]
Hence:
[tex]1 - P(X = 0) \geq 0.8[/tex]
[tex]P(X = 0) \leq 0.2[/tex]
Hence:
[tex]\left(\frac{364}{365}\right)^{n} \leq 0.2[/tex]
[tex]n\log{\left(\frac{364}{365}\right)} \leq \log{0.2}[/tex]
[tex]n \geq \frac{\log{0.2}}{\log{\left(\frac{364}{365}\right)}}[/tex]
[tex]n \geq 586.6[/tex]
Rounding up: You need to select at least 587 people.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
please help me with geometry
Answer:
x = 5Step-by-step explanation:
triangol BCD = triangle BDA
so
3x - 1 = 34 - 2x
5x = 35
x = 35 : 5
x = 5Answer:
x = 7
Step-by-step explanation:
BD is an angle bisector , so
∠ ABD = ∠ DBC , that is
3x - 1 = 34 - 2x ( add 2x to both sides )
5x - 1 = 34 ( add 1 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
Kofi is 3 years older than Ama.If Ama is now x years old, what is kofi age
Answer:
x+3
Step-by-step explanation:
Kofi is 3 years older than Ama, so the answer is "x+3".
Jim, Katrina, Larry, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim last?
c. Find the probability that Jim will arrive first and Kim last.
a.___ (Type an integer)
b.___ (Type an integer.)
c.___ (Type a fraction. Simplify your answer)
Answer:
24
6
1/12
Step-by-step explanation:
a) This is a counting problem 4*3*2*1 = 24 different ways.
b) 1 * 2 * 1 * 1 = 2 ways
This is one you should try.
Jim Kat Larry Kim
Jim Larry Kat Kim
You can't get another way.
c)
There are 2 ways that Jim can arrive first and Kim Last shown in b
2/24 = 1/12
Suppose you are starting your own company selling chocolate covered strawberries. You decide to sell the milk chocolate covered strawberries for a profit of $2.25/box and the white chocolate covered strawberries at $2.50/box. Market tests and available resources, however, have given you the following constraints. The combined production level should not exceed 800 boxes per month. The demand for the white chocolate is no more than half the demand for milk chocolate strawberries. The production level for white chocolate should be less than or equal to 200 boxes.
Using the information in the problem, write the constraints. Let x represent number of milk chocolate boxes produced, and y represent number of white chocolate boxes produced.
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
Answer
200
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
Answer
Minimum amount of white chocolate production: y Answer
Answer
Vertices of the feasible region: (0,0)(400, Answer
)( Answer
, Answer
)( Answer
,0)
Optimization equation: Profit = Answer
x+ Answer
y
Your maximum profit is $ Answer
. You should produce Answer
boxes of milk chocolate and Answer
boxes of white chocolate.
Answer:
Step-by-step explanation:
I answered this question in question #24285520
Answer:
Step-by-step explanation:
Total number of chocolate boxes that can be produced: x+y Answer
≤
Answer
800
Restrictions based on demand of each: y Answer
≤
Answer
1/2
x
Maximum amount of white chocolate production: y Answer
≤
Answer
200
Minimum amount of milk chocolate production: x Answer
≥
Answer
0
Minimum amount of white chocolate production: y Answer
≥
Answer
0
Vertices of the feasible region: (0,0)(400, Answer
200
)( Answer
600
, Answer
200
)( Answer
800
,0)
Optimization equation: Profit = Answer
2.25
x+ Answer
2.5
y
Your maximum profit is $ Answer
1850
. You should produce Answer
600
boxes of milk chocolate and Answer
200
boxes of white chocolate.
4 pounds of oranges costs $ 12 . What is the unit price per pound?
Answer:
3 dollars per pound
Step-by-step explanation:
Unit Price = Cost / Pounds of oranges
Unit Price = 12 / 4
Unit Price = 3
The unit price per pound is $3
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances? A. The populations are independent. B. One of the populations is normally distributed. C. The two samples are simple random samples. D. This test requires that both populations have normal distributions.
Answer:
B. One of the populations is normally distributed.
Step-by-step explanation:
To test a claim about two population standard deviation or variance, it is imperative that the data meets certain requirements which include :
Randomness : Data must not be biased as such it must be drawn as a random sample from a larger group.
The data must be independent. That is not related to one another, the outcome of one should not rely on the outcome or value of another.
Both groups must be drawn From a population which is normally distributed.
One group being normally distributed by stribuyed while the other isn't a requirement for hypothesis testing in this scenario.
Question 1 (Fill-In-The-Blank Worth 4 points)
(05.02)The area of the parallelogram below is
square meters
6 m
7 m
2 m
Numerical Answers Expected!
Answer for Blank 1
Step-by-step explanation:
we don't see the parallelogram nor any description of it.
so, it is impossible to tell you the right answer.
as I only answer questions by don't ask any, I don't know how you can add a picture.
Which number shows four hundredths
.004 .04 .400 4.00
Answer:
hello the answer is .04/0.04
Answer:
.04 is four hundredths
Step-by-step explanation:
I hope this helps
Factorise 2x3+9x2+10x+3
Answer:
Hello,
Answer is (x+1)(x+3)(2x+1)
Step-by-step explanation:
[tex]p(x)=2x^3+9x^2+10x+3\\p(-1)=2*(-1)^3+9*(-1)^2+10*(-1)+3=-2+9-10+3=0\\p(x)\ is\ divisible\ by\ (x+1)We\ arrange\ to\ put\ a\ factor\ of\ x+1\\\\2x^3+9x^2+10x+3\\\\=2x^3+2x^2+7x^2+7x+3x+3\\\\=2x^2(x+1)+7x(x+1)+3(x+1)\\\\=(x+1)(2x^2+7x+3)\\\\=(x+1)(2x^2+6x+x+3)\\\\=(x+1)(2x(x+3)+1(x+3))\\\\=(x+1)(x+3)(2x+1)\\[/tex]
PLEASE ANSWER
The distance from the vertex of the curve to the focus is equal to _____.
Here’s the options
the distance from the vertex to the directrix
the distance from the vertex to the y-axis
the distance from the vertex to the origin
a constant
Answer:
The distance from the vertex to the directrix.
Step-by-step explanation:
According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.
Hence, the right answer is: The distance from the vertex to the directrix.
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 50 m. (Round your answer to two decimal places.)
Answer:
2.75 m²
Step-by-step explanation:
From the information given:
the thickness of the paint = 0.07 cm = (0.07/100) m
= 0.0007 m thick
the diameter hemispherical dome = 50 m
∴
radius of the dome = 50m /2 = 25 m
The volume of a hemispherical dome is expressed as:
[tex]V = \dfrac{2}{3}\pi r^3[/tex]
Thus, the change in the volume now is:
[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]
[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]
[tex]{dV} = 2 \pi r^2 (dr)[/tex]
∴
dV = 2π × (25)² (0.0007)
where;
dr = 0.0007
dV = 2π × (25)² (0.0007)
dV = 2.75 m²
Write the equation of a line in slope intercept form that passes through the two points. 4,-1 and 6,-7
A line has an equation of,
[tex]y=mx+n[/tex].
m is called a slope
n is called y-intercept
We are also given two points [tex](x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7)[/tex].
We begin with computing the slope,
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}[/tex]
We have computed the slope m and our equation is almost done,
[tex]y=-3x+n[/tex]
Next step is to find out what y-intercept n is. I will use point [tex](4,-1)[/tex] and insert x and y it into already known equation, then solve for n,
[tex]-1=-3(4)+n[/tex]
[tex]-1=-12+n\implies n=\boxed{11}[/tex]
The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,
[tex]\boxed{y=-3x+11}[/tex]
Hope this helps. :)
Write a linear equation representing the information shown in the table.
A) y = 2x + 10
B) y = –2x + 10
C) y = 10x – 2
D) y = 10x + 2
Answer:
b
Step-by-step explanation:
y=-2x+10
y=-2×0+10 y=10
y=-2×1+10 y=8
y=-2×2+10 y=6
y=-2×3+10 y=4
Answer: B. y = –2x + 10
Step-by-step explanation:
A company wants to decrease their energy use by 17%. If their electric bill is currently $2500 a month, what will their bill be if they are successful
Please help with this while part!!!!
Step-by-step explanation:
1. The given expression is, [tex]A=lw[/tex]
We need to solve it for w.
[tex]w=\dfrac{A}{l}[/tex]
2. The given expression is, [tex]C=\pi D[/tex]
We need to solve it for D.
[tex]D=\dfrac{C}{\pi}[/tex]
3. The given expression is, [tex]v=s+gt[/tex]
We need to solve it for s.
[tex]s=v-gt[/tex]
4. The given expression is, [tex]5x-2y=11[/tex]
We need to solve it for y.
[tex]D=\dfrac{5x-11}{2}[/tex]
5. The given expression is, [tex]P_1V_1=P_2V_2[/tex]
We need to solve it for P₂. So,
[tex]P_2=\dfrac{P_1V1}{V_2}[/tex]
For each kilogram of a persons weight 2.5 milligrams of a drug is to be given. what dosage should be given to a child who weighs 84 pounds? Use the fact that 1 lb = 0.45 kg
Answer:
A child who weighs 84 pounds should be given 94.5 milligrams of the drug.
Step-by-step explanation:
Givens:
1kg=2.5 milligrams of dosage
Weight of child = 84 pounds
1 pound = 0.45 kg
Solution:
Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg
Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.
Find how much money needs to be deposited now into an account to obtain $7,300 (Future Value) in 6
years if the interest rate is 2.5% per year compounded monthly (12 times per year).
The final amount is $
Round your answer to 2 decimal places
Answer:
x= $6,284.15
Step-by-step explanation:
7300 = x(1 + .025/12)^72
x = [tex]\frac{7300}{(1 + \frac{.025}{12} )^{72} }[/tex]
x= $6,284.15
helpppp asap pleaseee
Answer:
29/3 is your answer
Step-by-step explanation:
pls mark as brainliest
Find the missing length
Answer:
x=5.9
i think this the answer
There are 1000 students in a college.Out of 20000 in the whole university in a study of 200 were found to be smokers in the college and 1000 in whole university. Is there any significant difference between the proportion of smokers in college and university
Answer:
1000 students in college
2000 students in University
200 out of 2000 are smokers
200 out 1000 are smokers
200 : 2000
1 :10
200 : 1000
1 : 5
Ed decides to include more fruit in his diet. He goes to the grocery store over the weekend and buys 6 apples, 6 oranges, and 6 avocados. The total cost is $19.50.
Ed finishes the apples very quickly, and has some leftover avocado. The following weekend he buys 12 apples, 2 oranges, and 1 avocado. This time he pays just $9.50.
The following week, Ed reads an article on the benefits of avocado, so over the weekend he buys 5 avocados along with 2 apples and 4 oranges. His total this time is $14.
Assume that Ed pays a unit price rather than a price per pound for the apples, oranges, and avocados.
9514 1404 393
Answer:
apples: $0.50 eaoranges: $0.75 eaavocados: $2.00 eaStep-by-step explanation:
Let a, o, v represent the prices of one each of apples, oranges, and avocados, respectively. Then the equations describing the purchases can be written ...
6a +6o +6v = 19.50
12a +2o +1v = 9.50
2a +4o +5v = 14.00
__
Dividing the first equation by 6 makes it ...
a +o +v = 3.25
Subtracting this from the second equation gives ...
(12a +2o +v) -(a +o +v) = (9.50) -(3.25)
11a +o = 6.25
Subtracting the third equation from 5 times the reduced first equation gives ...
5(a +o +v) -(2a +4o +5v) = 5(3.25) -(14.00)
3a +o = 2.25
The difference of these last two equations is ...
(11a +o) -(3a +o) = (6.25) -(2.25)
8a = 4.00
a = 0.50
Then the other values are ...
o = 2.25 -3(a) = 0.75
v = 3.25 -a -o = 2.00
The unit prices are:
apples -- $0.50
oranges -- $0.75
avocados -- $2.00
_____
Additional comment
Most graphing or scientific calculators will solve systems of equations like these. Using an appropriate tool, it takes less time to find the solution than to read this one.
Note that the last purchase description in the problem statement has the items in a different order than in the first two descriptions. Care must be taken to make sure the correct equations are written.
Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.
16. Find the equation of the line that has slope m = 1/2 and passes through (4, 10).
Give your answer in slope-intercept form
Answer:
Step-by-step explanation:
Recall that the equation of a line is y = mx + b.
Excellent. Let's plug in the values we are given into the general equation for a line. We get 10 = 1/2 * 4 + b.
Simplify to 10 = 2 + b, and we get b = 8.
Our final equation, then, is y = 1/2 x + 8.
Hope this helps!
(b) If 124n= 232 five, find n.
Answer:[tex]n=\frac{58}{31}[/tex]
Step-by-step explanation:
[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]
The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five
Let's first convert "232 five" into a numerical value:
"232 five" means 2325 (since five is in the units place).
Now, the equation becomes:
124n = 2325
To solve for n, divide both sides of the equation by 124:
n = 2325 / 124
Now, perform the division:
n = 18.75
So, the value of n is 18.75.
To know more about equation:
https://brainly.com/question/10724260
#SPJ2
find the missing segment below brainly
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]
[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]
[tex]\\ \sf\longmapsto 120-6x=4x[/tex]
[tex]\\ \sf\longmapsto 120=6x+4x[/tex]
[tex]\\ \sf\longmapsto 120=10x[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
where are parabolas on your hand?
parabolas are there on my hand palms and it must be there on your hands too but why are you asking this question?
Use the discriminant to determine all values of k which would result in the graph of the equation
y
=
3
x
2
+
k
x
+
75
y=3x
2
+kx+75 being tangent to the x-axis.
Answer:
sauce is 177013
Step-by-step explanation:
integrate with respect to x 2tanx secant^2x/(1+ tan²x)
[tex] \displaystyle \int \bf \: \frac{2 \: tan \: x. {sec}^{2} \: x }{1 + {tan}^{2} \: x } \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{tan \: x \: . \: \cancel{ {sec}^{2} \: x}}{ \cancel{ {sec}^{2} \: x}} \: \: dx \: \: \: \: \pink{ \{ \because \: {sec}^{2} \: x - {tan}^{2} \: x = 1 \}} \\ \\ = 2 \displaystyle \int \bf \: tan \: x \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{sin \: x}{cos \: x} \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = - 2 \displaystyle \int \bf \: \frac{ - \: sin \: x}{ \: cos \: x} \: \: dx\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \bf \: - 2 \ln \: |cos \: x| + c\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{ \{ \because \: \displaystyle \int \bf \: \frac{ {f}^{′} (x)}{f(x)} \: dx = \ln \: |f(x)| + c \}}[/tex]
