E(z),the expected value of z in which at least one member has a birthday in 12 months is (11/12)^10
Define the random variable Zi’s as
[tex]Z_{i}[/tex]= 1 : if no member of the club has a birthday in the month
= 0: otherwise for, i =1,2, ......,12 .
Now, we have,
= P ([tex]Z_{i}[/tex] =1) .
=p( no member of the club has a birthday in month i).
= p, say.
Now, there are a total of 10 members in the club and their birthdays are assumed to be independently and uniformly distributed over the 12 months of the year. So, there are 12 possible choices of months for each of the 10 members for their birthday. Thus, the total no. of exhaustive mutually exclusive and equally likely no. of ways of birthdays 12^10.
Again, if no member of the club has a birthday in month 'i'; then, all of their birthdays should be on the remaining (12 - 1) = 11 months of the year. So, there are possible choices of birthday months for each of the 10 members of the club. So, the no. of cases for the event (Zi=1) is 11^10.
So, p([tex]Z_{i}[/tex]=1) = Favorable no. of cases for Zi=1) / Total no. of all possible cases
= 11^10 / 12^10
By the classical definition of probability.
= (11/12)^10
p([tex]Z_{i}[/tex] = 1) = (11/12)^10
E(Zi).= (11/12)^10
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What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
A. 660 cm2
B. 652 cm2
C. 326 cm2
D. 432 cm2
Answer:
The answer is b I searched it on goggle and did the math.
Step-by-step explanation:
Somebody please help me plsssss
Given:
The radius of the cylinder = 2 cm
Height of the cylinder = 5 cm
To find:
The volume of the cylinder.
Solution:
We know that, the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
Where, r is the radius and h is the height of the cylinder.
Putting [tex]r=2,h=5[/tex] in the above formula, we get
[tex]V=\pi (2)^2(5)[/tex]
[tex]V=\pi (4)(5)[/tex]
[tex]V=20\pi [/tex]
Therefore, the volume of the cylinder is [tex]20\pi [/tex] cubic cm and its approximate value is 62.832 cubic cm.
Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.15%. They
have 500 grams of substance B which decays at a rate of 0.37%. They are trying to determine how many years it will be before the substances
have an equal mass.
If Mrepresents the mass of the substance and trepresents the elapsed time in years, then which of the following systems of equations can be
used to determine how long it will be before the substances have an equal mass?
Answer:
231.59 years
Step-by-step explanation:
To model this situation we are going to use the exponential decay function:
f(t)= a (1-b)^t
where f(t) is the final amount remaining after t years of decay
a is the final amount
b is the decay rate in decimal form
t is the time in years
For Substance A:
Since we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:
r = 0.15/100 = 0.0015. Replacing the values in our function:
f(t) = a (1-b)^t
f(t) = 300 (1-0.0015)^t
f(t) = 300 (0.9985)^t equation (1)
For Substance B:
Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:
r=0.37/100= 0.0037. Replacing the values in our function:
f(t) = a (1-b)^t
f(t)= 500 (1-0.0037)^t
f(t)=500(0.9963)^t equation (2)
Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:
M=300(0.9985)^t equation (1)
M=500(0.9963)^t equation (2)
We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :
{M=300(0.9985)^t
{M=500(0.9963)^t
Without doing any calculations, compare Expression A to Expression B.
A (34 + 25) ÷ 14
B 34 + 25
Answer:
A < B
Step-by-step explanation:
well lets see, they are both adding 34 and 25
But in a, they are dividing, and because dividing usually makes the number smaller, B is larger
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Expression A is less than expression B
Step-by-step explanation: Connexus
(Write the equation) Thank you if you answer it <3
Answer:
10 - 2 = (x + 6)Explanation:
The Sum Of x And 6 Is Two Less Than Ten.The Sum Of x And 6: x + 6
Two Less Than Ten: 10 - 2
Put The Two Terms Together10 - 2 = (x + 6)I need help FAST pleaseeeee
Answer:
20 i think
Step-by-step explanation:
HELP!! 4 questions !!! easy points!! 25 points!! please answer quick!
Step-by-step explanation:
(i) From the graph value of x varies -3 to 3 i.e.
[tex]-3\leq x\leq 3[/tex]
and domain in the input values which function can take
So, option (d) is correct.
(ii) option (d) is correct as it represent the function [tex]y=x[/tex]. While all the other function does not satisfy the given conditions.
(iii) [tex](-14,-15), (-9,-10)[/tex] are the parts of solution pair.
(iv) Option (c) and (d) represents the function as each element of the first set has a unique image in the second set.
A population of 120 beetles increases at an annual rate of 30%. How many beetles will there be in 16 years? Write an expression to represent the equivalent monthly population increase rate.
Answer:
Expression: [tex]120(1.3)^{16}[/tex]
Beetles after 16 years: 7984 beetles
Step-by-step explanation:
Since the population increases 30% annually every year on the population size of that year, then we need to use a compound interest formula which would be the following
A = P (1 + r/n) (nt)
A = the future amount
P = the initial amount
r = the annual increase rate (decimal)
n = the number of times that interest/increase is compounded per unit t
t = the number of years
Using the values in the question the expression for this scenario would be the following
120(1 + (0.30 / 1))^(1*16)
[tex]120(1.3)^{16}[/tex]
7984.99
What is 1/3÷9? hurry!
Exact Form:
1/27
Decimal Form:
0.037 (with a line over 037)
I will mark brainliest
Answer:
I think that it is positive 650.
Answer:
you got it
Step-by-step explanation:
that is itdescribe your answer to gt i wrie u are doing a test
A computer randomly selects a number from the given set. {1.2 5 10 25 30 36} What is the probability that an even number is selected? Enter your answer as a fraction, in simplest form, in the box. Pleven) =
Answer:
4/7 (I may be wrong)
Step-by-step explanation:
There are 7 numbers, of which 4 are even. This could be %100 wrong/right.
Challenge How many flowers, spaced every 6 in., are needed to surround a circular garden with a
200-ft radius? Use 3.14 for it.
Williams, Aaily
flowers are needed to surround the circular garden.
Answer:
1,256 flower
Step-by-step explanation:
First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:
C
=
2
π
r
If we substitute
100
ft
for
r
and use
3.14
to approximate
π
we get a circumference of:
C
=
2
⋅
3.14
⋅
100
ft
C
=
6.28
⋅
100
ft
C
=
628
ft
We can now convert the circumference in feet to inches;
628
ft
×
12
in
1
ft
⇒
628
ft
×
12
in
1
ft
⇒
628
×
12
in
⇒
7536
in
To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:
7536
in
×
1
flower
6
in
⇒
7536
in
×
1
flower
6
in
⇒
7536
×
1
flower
6
⇒
7536
flower
6
⇒
1256
flower
You would require 1,256 flowers
i need help btw i am in middle school
Answer: J
Step-by-step explanation: It is very cool you are in middle schopol
A person paid by the hour works 22 hours a week and makes $459. How much would they make if they work 39 hours?
Answer:
813.681818182
(That's the exact number, but you can circle it to 813.7 )
Step-by-step explanation:
459%22=20.8636363636
20.8636363636 x 39= 813.681818182
[tex]\sqrt[3]{11}[/tex]
Answer:
2.22
Step-by-step explanation:
[tex]\sqrt[3]{11} =2.223980091[/tex]
Rounded to hundredths: 2.22
15 is 9 than j what is j in this question
Answer:
6
Step-by-step explanation:
15 is 9 more hence you subtract 9 from15
Hope this helps
A house that costs $125,400 appreciates at a rate of 3% each year. What is the value of the
home after 3 years.
a.$137027.97
b.$275503.80
c.$114449.19
d.$3385800
Answer:
The value after three years is $137,027.97
Step-by-step explanation:
Here, we want to get the value of the home after 3 years
Generally, we have the exponential formula as follows;
y = P(1 + r)^t
where P is the original cost which is $124,400
r is the rate of increase which is 3% = 3/100 = 0.03
t is the time which is 3 years
Substituting these values;
y = 125400(1 + 0.03)^3 = $137,027.97
Is u = 105 a solution to this equation
Answer:
im sorry what?
Step-by-step explanation:
What best describes how many real number solutions the equation has?
Answer:
zero, because the discriminant is negative
Step-by-step explanation:
By writing the quadratic formula, we have the discriminant written in the root as;
b^2-4ac
Now, given the expression, we can see that the discriminant here is -19
What this mean is that we have a negative discriminant
Hence, we can conclude that the roots are complex and as such, none of the roots are real
Simplify the following equation
Answer:
3x - 2
Step-by-step explanation:
Answer:
3x−2
Heart if this helped!
The ratio of cyclists to pedestrians on a certain trail was 2 to 7. If there were 27 people on the trail, how many more pedestrians were there than cyclists?
Answer:
15 more pedestrians than cyclists
Step-by-step explanation:
2:7 ratio tells us two cyclists for every seven pedestrians so out of every 9 people 2 are cyclists and 7 are pedestrians.
27/9=3
So we have 3 groups of 9...
3×2=6
&
3×7=21
so
6 cyclists and 21 pedestrians
subtract cyclists from pedestrians to find difference...
21-6=15
0.25% of 42 is what number
Answer:
0.105
Step-by-step explanation:
0.25/100 x 42 = 0.105
Answer: The answer is 0.105
Kelly has $100 she received for her birthday She saves $10 each week from doing chores Which function can be used to find t the amount of money Kelly will have saved
Answer:
$620 every year
Step-by-step explanation:
Since the question didn't specify how long she would have to save for, let's just assume that it's one year. There are 52 weeks in a year which is $520, and on her birthday she would have an extra $100, so every year she saves $620 in total.
Can someone help me with this. Will Mark brainliest. Need answer and explaination/work. Thank you.
Answer:
Yes, quadrilateral MATH is a rectangle.
Step-by-step explanation:
If you plot the coordinates onto a graph, you will get a rectangle. You can determine it is a rectangle because there are four right angles, and two adjacent sides that are equal in length.
M (-4,-1)
A (-3,2)
T (3,0)
H (2,-3)
Josea went out to dinner at an Indian restaurant. The
total bill was $38. She wanted to leave a 15% tip.
If you use the idea of scaling to find the tip amount,
what would she need to multiply by?
Please help me with this question!!
Answer:
Step-by-step explanation:
Mabye 7?
The senior classes at Portland High School and Biddeford High School planned separate
trips to New York City. The senior class at Portland High School rented and filled 1 van
and 6 buses with 372 students. Biddeford High School rented and filled 4 vans and 12
buses with 780 students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry?
Write the linear equation given slope and point.
(-4,-7); slope = 3
Answer:
Step-by-step explanation:
Use the "point-slope" formula for the equation of a straight line,
y - k = m(x - h)
Here the slope, m, is 3 and the line passes through (h, k): (-4, -7), so the proper equation in this case is
y - (-7) = 3(x + 4), or:
y + 7 = 3(x + 4).
If you wish you may rewrite this equation in slope-intercept form, as follows:
y = 3x - 7 + 12, or y = 3x + 5
Giving brainlist to whoever answers
Answer:
10 I believe I really hope it helped!
Step-by-step explanation:
Answer:
That's easy! 10 times
Step-by-step explanation:
60 divided by 6 is 10
Danielle has to walk 2 miles to reach a hidden temple. She has walked 1 1/4 miles, how many more miles does Danielle need to walk to reach the hidden temple.
Answer:
[tex]\dfrac{3}{4}\ miles[/tex]
Step-by-step explanation:
Total distance to a temple = 2 miles
She has walked 1 1/4 miles or 5/4 miles
More miles to reach the hidden temple = total distance - walked distance
[tex]=2-\dfrac{5}{4}\\\\=\dfrac{8-5}{4}\\\\=\dfrac{3}{4}[/tex]
So, she has to travel [tex]\dfrac{3}{4}[/tex] miles to reach the hidden temple.