What is the probability that at least 2 students in a class of 36 have the same birthday?

Answers

Answer 1

Given a group of n students, and given the fact that there are 365 days in one year, the probability that there are no students with the same birthday is given by
[tex]p_{no} (n) = \frac{364}{365} \cdot \frac{363}{365} \cdot ... \cdot \frac{365-n+1}{365} = \frac{364!}{365^{n-1} (365-n)!} [/tex]
Therefore, the probabilty that there are at least 2 students with same birthday is the complementary of this value:
[tex]p_{yes} (n) = 1 -p_{no}(n) =1- \frac{364!}{365^{n-1} (365-n)!}[/tex]

And if we use n=36 (number of students), we find
[tex]p=1- \frac{364!}{365^{36-1} (365-36)!} \sim 0.83[/tex]
So, the probability that there are at least 2 students in a group of 36 with same birthday is approximately 83%.

Related Questions

A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

Answers

$400 have a nice one! :)

Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.

Let the number of cameras that can be sold be "x".

Total revenue = $ 14x

Total costs will be = $ 2100 + $9x

So, the equation that will be formed ⇒

14 x = 2100 + 9x

5x = 2100

x = 420

Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.

If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -

Total revenue = $ 14 × 470 cameras = $ 6,580

Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330

Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250

The height of a triangle is increasing at a rate of 2 2 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters per minute. at what rate is the base of the triangle changing when the height is 10 10 centimeters and the area is 80 80 square centimeters?

Answers

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 20 cm2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2. = 2, namely, the base of the triangle is increasing at a rate of 2 cm/min.

hey can you please help me posted picture of question

Answers

We have the following function:
C (t) = 6t - 180
Clearing t we have:
6t = c + 180
t = c / 6 + 180/6
Rewriting:
t (c) = (c + 180) / 6
Answer:
The inverse function for this case is given by:
t (c) = (c + 180) / 6
option A

At the sandwich shop, there are four different types of meat and three different types of cheese. If you select a sandwich without looking, what is the probability that it has your favorite type of meat on it?

give answer as a fraction

Answers

If you only have one favorite type of meat the probability 1/4
I don't know why you gave extra information about the cheese because the question didn't ask anything about the cheese

The solution is : 1/4 is the probability that it has your favorite type of meat on it.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, we have,

given that,

At the sandwich shop, there are four different types of meat and three different types of cheese.

If you select a sandwich without looking,

then we need to find the probability.

Solution

There are four different types of meat and three different types of cheese

Probability = number of required outcome / number of possible outcome

Total amount of meat = number of possible meat = 4

If you only have one favorite type of meat the probability 1/4

Hence, the correct answer is Option B.

The solution is : 1/4 is the probability that it has your favorite type of meat on it.

To learn more on probability click:

brainly.com/question/11234923

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Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased

Answers

50 is greater than or equal to 20 + 6x

50 is greater or equal to 20. How you do that is you write a greater than sighn and put a line under it.

hello can you please help me posted picture of question

Answers

The sample space will be: {1, 2, 3, 4, 5, 6}

Event A is: {Rolling 1,2 or 3}

Complement of event A will contain all those outcomes in the sample space which are not a part of event A.

So, complement of event A will be: {Rolling a 4,5 or 6}

Thus option A gives the correct answer

Q # 17 please solve the figures

Answers

Answer: First option:
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z

what kinds of symmetry does the capital letter E have

Answers

It has reflectional symmetry where the line of reflection (mirror line) is horizontal and it cuts through the middle of the letter

Answer[:]
The capital letter E has three kinds of symmetry(s):

1) Horizontal Line of Symmetry
2) One line of symmetry (NOT meaning they only have one type of symmetry, they have one LINE of symmetry)
3) Reflectional Symmetry (If you were to flip it on it's side, and cut it in half, then both sides would be the same)

[:] DustinBR [:]

Jim picked a card from a standard deck. What is the probability that Jim picked a heart or an ace?

Answers

Answer:

The answer is actually 16/52.

Step-by-step explanation:

There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.

13 hearts + 3 other aces = 16

There are 52 cards in a deck, so the probability would be 16/52.

a marble is selected at random from a jar containing 6 red marbles 3 yellow Marbles and 2 green marbles what are the odds in favor of selecting a red marble

Answers

Total Marbles = 6 + 3 + 2 = 11
Total Red marbles = 6

P(red) = 6/11

a customer buys three bottles of water at ninety nine cents each. there is seven percent tax on each bottle. what is the total bill?

Answers

If the tax was 7 cents then each bottle would cost 1.06 each, because tax doesn't mean it's three dollars plus tax which comes to 3.07, it's that if you have a water bottle coming out to 99 cents each and the tax was 7 cents, you add 7 to 99. Which in money, comes out to 1.06 each bottle. So the total bill is 3.18.
I hope this helped! I don't wanna get your answer wrong! >o<

The total bill of each bottle plus tax would be $5.04

please help!! I don't understand

Answers

Answer:

(4, 5)

Step-by-step explanation:

All the medians intersect at the same point. RU and PS are medians so they intersect at the same point that medians QT and PS intersect.

hey can you please help me posted picture of question

Answers

The correct answer is the las option (Option D), which is:

D. f(x)=(x+4)^4

The explanation is shown below:

1. The initial function was G(x)=x^4, whose graph shows that the shape has its vertex at 0,0.

2. If the it was shift 4 units to the left, you only has to add a 4 to the function.

3. Therefore, you obtain the the equation of the final shape is:

f(x)=(x+4)^4

As you can see, the answer is the option D.

What are the zeros of the polynomial function f(x)=x^2+5x+6

Answers

Find 2 numbers that multiply to 6 and add to 5.

3*2 = 6
3+2 = 5

x^2 + 5x+6 = (x+3)(x+2) = 0

Set each factor equal to zero.
x+3 = 0 ----> x = -3
x+2 = 0 -----> x = -2

Answer:
There are two zeros at -2 and -3.

Clabber company has bonds outstanding with a par value of $113,000 and a carrying value of $105,100. if the company calls these bonds at a price of $101,500, the gain or loss on retirement is:

Answers

Gain on retirement of bonds = book value of bonds - the amount paid to the bondholders = 105,100 - 101,500 = $3600

So, $3600 should be the gain or loss on the retirement.

which statement describes the ratio of weight to mass and the value of x in the table?

Answers

To find the ratio, pick any pair of corresponding table values.
weight/mass = (196 N)/(20 kg) = 98/10 N/kg

You can find x from ...
(98/10)x = 1078
x = 1078*10/98 = 110

The appropriate choice is ...
B The ratio is 98/10; x = 110

Solve for x
in the equation x^2-12x+36=90

Answers

This can be rewritten as
(x -6)² = 90 . . . . . the left side is already a perfect square
x -6 = ±√90 . . . . . take the square root
x = 6 ±3√10 . . . . add 6

Answer:

Using the identity rule:

[tex](a-b)^2 = a^2-2ab+b^2[/tex]

Given the equation:

[tex]x^2-12x+36 = 90[/tex]

Rewrite the above equation as:

[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]

Apply the identity rule:

[tex](x-6)^2 = 90[/tex]

Take square root to both sides we have;

[tex]x-6 = \pm \sqrt{90}[/tex]

Add 6 to both sides we have;

[tex]x = 6\pm \sqrt{90}[/tex]

[tex]x = 6 \pm 3\sqrt{10}[/tex]

Therefore, the value of x are:

[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]

Unit rate of 3 1/2 and 1/4

Answers

Hello.

3 1/2 ÷ 1 1/47/2 ÷ 5/47/2 · 4/528/102.8 2.8 is the unit rate

Have a nice day

what is the difference between the greatest amount and least amount of gasoline used to mow lawns?

1/8 2/8 3/8/4/8 5/8

Answers

Answer:
The difference is 4/8 which is equivalent to 1/2

Explanation:
The given values of gasoline amounts are as follows:
1/8 , 2/8 , 3/8 , 4/8 , 5/8

Since all the values have the same denominator, therefore, we can base our comparison on the numerator. The larger the numerator, the larger the value of the fraction.

Based on this, we can note that:
the least amount of gasoline is 1/8
the greatest amount of gasoline is 5/8

The difference between the two can be computed as follows:
difference = greatest amount - least amount
difference = 5/8 - 1/8
difference = 4/8 which can be simplified to give 1/2

Hope this helps :)

Solve for x. Use the completing the squares method. Round decimals to the nearest tenth. 2x2+16x=−18 (

Answers

To solve by completing square method we proceed as follows:
2x^2+16x=-18
dividing through by 2 we get:
x^2+8x=-9
but
c=(-b/2a)^2
c=(-8/2)=16
hence
x^2+8x+16=-9+16
x^2+8x+16=7
(x+4)(x+4)=7
(x+4)^2=7
thus getting the square root of both sides
x+4=+/-√7
x=-4+/-√7
x=

Answer:

[tex]x = -4 \frac{+}{-} 2\sqrt{5\\}[/tex]

Step-by-step explanation:

What is the volume of a right circular cylinder with a base diameter of 18yd. And a height of 3yd.

Answers

Answer:

[tex]Volume=254[/tex] to the nearest cubic yard.

Step-by-step explanation:

The volume of a right circular cylinder can be calculated using the formula;

[tex]Volume=\pi r^2h[/tex].

The diameter of the base is given to us. We divide it into two to obtain the radius.

[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].

We substitute these values into the formula to obtain;

[tex]Volume=9^2\times 3\pi yd^3[/tex]

[tex]Volume=243\pi yd^3[/tex]

[tex]Volume=763.4yd^3[/tex]

Answer:

answer= 254

Step-by-step explanation:

A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is

Answers

The net present value of the project can be calculated as follows:

NPV = - Cost + present value of all cash flows

Cost = $350,000
Present value of all cash flows = C*{[1-(1+r)^-n]/r}
Where C = Yearly cash flows = $140,000, r = discount rate = 9%, n = time of generating cash flows = 3 years.

Therefore,

NPV = -350,000 + 140,000*{[1-(1+0.09)^-3]/0.09} = $4,381.25

Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola

Answers

Think its hyperbola. Dont quote me.

Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola

Solution:

The general equation of circle is:-

(x-h)²+(y-k)=r²

The general equation of ellipse is:-

[tex] \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{{b^{2}}}=1 [/tex]

The general equation of parabola is:-

y = a(x-h)²+k

The general equation of hyperbola is:-

[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{{b^{2}}}=1[/tex]

The equation of conic section is: x^2/36-y^2=1

[tex]\frac{(x-0)^{2}}{36}-\frac{(y-0)^{2}}{1}}=1[/tex]

[tex]\frac{(x-0)^{2}}{6^{2}}-\frac{(y-0)^{2}}{{1^{2}}}=1[/tex]

Hence, this is hyperbola.

Answer: Hyperbola Option (D)

a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an intial speed of 130 feet per second. What is the maximum height, in feet, the ball will attain? round to the nearest hundredth

Answers

For this case, the first thing to do is write the equation of moving the ball.
We have then:
h (t) = - 16t ^ 2 + 130t + 2
Deriving we have:
h '(t) = - 32t + 130
We match zero:
-32t + 130 = 0
We cleared t:
t = 130/32
t = 4.0625 s
We evaluate the value of t = 4.0625 s in the equation of motion:
h (4.0625) = - 16 * (4.0625) ^ 2 + 130 * (4.0625) + 2
h (4.0625) = 266.0625 feet
Answer:
The maximum height, in feet, the ball will attain is:
h (4.0625) = 266.0625 feet

Final answer:

Using the kinematic equation for vertical motion, the maximum height a tennis ball will reach when fired at an initial speed of 130 ft/s from a height of 2 feet is approximately 264.91 feet.

Explanation:

Calculating the Maximum Height of a Tennis Ball

The maximum height that a tennis ball will attain when fired vertically can be calculated using the kinematic equations that describe projectile motion. Given that the initial speed of the ball is 130 feet per second and it is launched from a height of 2 feet, we can use the equation for vertical motion:

v^2 = u^2 + 2gh

where v is the final velocity (0 ft/s at the highest point), u is the initial velocity (130 ft/s), g is the acceleration due to gravity (-32.2 ft/s^2, negative because it is directed downwards), and h is the height gained. Rearranging the formula to solve for h we get:

h = (v^2 - u^2) / (2g) = (0 - 130^2) / (2 * -32.2)

After calculating h, we add the initial launch height of 2 feet to find the maximum height above ground:

Maximum Height = h + 2 feet

By plugging in the values, we can find the maximum height to be:

Maximum Height = (0 - 16900) / (-64.4) + 2 ≈ 264.91 feet (rounded to the nearest hundredth).

Therefore, the maximum height attained by the tennis ball is approximately 264.91 feet.

Simon has a scale model of the Concorde airplane. The actual length of the Concorde is approximately 200 feet. If the ratio of the actual length in feet to the length of the model in centimeters is 5 : 1, what is the approximate length of Simon's model?

Answers

The answer is: "40 cm " .
_________________________________________________________
Note:
_________________________________________________________

[tex] \frac{200 ft }{ (x) cm} = \frac{5}{1} [/tex] ;

Solve for "x" (in "cm" ) ;

→ 5x = 200 * 1 ;

→ 5x = 200 ;

Divide each side of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 5x / 5 = 200 / 5 ;

to get:

→ x = 40 .
___________________________________________________________
The answer is: " 40 cm " .
___________________________________________________________

Answer:

yur

Step-by-step explanation:

If we reject the null hypothesis, h0: ρ = 0 , what can we conclude about the population correlation coefficient?

Answers

If the null hypothesis, [tex]H_0:\:\rho =0[/tex] is rejected, then we can conclude that the correlation coefficient is significant. This means that there is enough evidence to conclude that a relationship exists between the two (or more) variables involved in the regression.

Volume and Surface Area

Math help 100 points

Answers

Part 1) we have that
volume smaller solid=512 cm³
volume larger solid=2197 cm³

we know that
volume larger solid=[scale factor]³*volume smaller solid
scale factor=∛[volume larger solid/volume smaller solid]
scale factor=∛[2197/512]-----> scale factor=1.625

Part 2)
the ratio of the surface areas is equal to [scale factor]²
1.625²-------> 2.64

Part 3)
surface area smaller solid=960 cm²
then
surface area larger solid=scale factor²*surface area smaller solid
surface area larger solid=[1.625]²*960-----> 2535 cm²
surface area larger solid is 2535 cm²

Answer:

1 - V = Smaller solid=512 cm³

V = Larger solid=2197 cm³

2- 1.625² = 2.64

3 - SA of big solid is found 2535 cm²

Juan is spinning a wheel with 4 unequal spaces marked with values of $200, $300, $400, and $600. The probability of landing on $200 is 2/9 . The probability of landing on $300 is 4/9 . The probability of landing on $400 is 2/9. The probability of landing on $600 is 1/9 . The expected value of spinning the wheel once is $, and the expected value of spinning the wheel three times is

Answers

a]
The expected value of spinning the wheel is given by:
E(x)=2/9(200)+4/9(300)+2/9(400)+1/9(600)
E(x)=44 4/9+133 1/3+88 8/9+66 2/3
E(x)=333 1/3

b] The expected value of spinning the wheel thrice will be:
(expected value of spinning once)*(number of spins)
=333 1/3*3
=1000/3*3
=1000

Answer:

333 and 1000

Step-by-step explanation:

The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?

Answers

It's the Geometric Sequence.

The n-th term of a geometric sequence with initial value a and common ratio r is given by:

[tex]a_n=a_1\cdot r^{n-1}\ for\ n\in\mathbb{N^+}[/tex]

We have:

[tex]a_1=-2;\ r=3;\ n=6[/tex]

Substitute:

[tex]a_6=-2\cdot3^{6-1}=-2\cdot3^5=-2\cdot243=-486[/tex]

Answer: The sixth term is equal -486.

Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a recurrence relation for the population of the world n years after 2010 (b) find an explicit formula for the population of the world n years after 2010. (c) what will the population of the world be in 2030

Answers

a1=6.9
a) an=(an-1)(1.1)
b) an=(6.9)(1.1^n-1)
c) 46.419 billion

Answer:

a 1=6.9

a an =

(an-1)(1.1)

b an=

(6.9)

(1.1^n-1)

46.419

billion

Step-by-step explanation:

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