1. Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years. (10 points)

Answers

Answer 1

at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.

To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.

Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.

1 - (1 - 1÷2922)^n >= 1

(1 - 1÷2922)^n <= 0

n >= log(0) ÷ log(1 - 1÷2922)

The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:

n >= log(10^-6) ÷ log(1 - 1/2922)

n >= log(10^-6) ÷ log(2921/2922)

n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)

n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)

n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)

n >= 23.

Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.

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Related Questions

what is (y-4)= -5/7 (x+28) in slope intercept form

Answers

Answer:

y = (-5/7)x - 16

Step-by-step explanation:

(y - 4)= -5/7(x + 28)

y - 4= -5/7x - 20

   +4             +4

------------------------

y = (-5/7)x - 16

I hope this helps!

Answer:  \(y =-\frac{5}{7}x -16\)

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope, and b is the y-intercept.

\((y-4)= -\frac{5}{7} (x+28)\)

\(y -4=(-\frac{5}{7})(x) + (-\frac{5}{7})(28)\)

\(y -4=-\frac{5}{7}x + (-20)\)

\(y -4=-\frac{5}{7}x -20\)      Add 4 on both sides.

\(y =-\frac{5}{7}x -16\)

An amount of Birr 500 is deposited in an account at the end of each six-month period with an interest computed at 6% compounded semi-annually. How many years does it take for the amount to reach Birr 56,398.43?​

Answers

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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The selling price of a refrigerator, is $775.00. If the markup is 25% of the dealer's cost, what is the dealer's cost of the refrigerator?

Answers

Answer:

$581.25

Step-by-step explanation:

A rectangular prism has a length of 6 cm, a width of 5 cm, and a depth of 4 cm. What is its volume? PL HURRY IT IS TIMED

Answers

Answer:

The answer should be 120

Step-by-step explanation: hope this helps

Let f(x) = x ^ 2 + 5 and g(x) = sqrt(x - 5) Find the rules for (fg)(x) (gf)(x)

Answers

Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

) In a geometric progression, the sum of the first two terms is equal to 16. The sum to infinity is equal to 25. Find the possible values of the first term. ​

Answers

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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Find an equation of the circle that satisfies the given conditions. Center (−1, 8); passes through (−3, −5)

Answers

Answer:

\((x + 1)^2 + (y-8)^2 = 173\)

Step-by-step explanation:

\(\textsf{The standard form of the equation of a circle is }\\\\ \sf (x -h)^2 + (y-k)^2 = r^2 \;where\; (h, k) \textsf{ are the coordinates of the center of the circle and \;r\; is the radius}\)

Here h = -1, k = 8

So we get
\((x - (-1)) ^2 + (y - 8)^2 = r^2\)

\((x + 1)^2 + (y - 8)^2= r^2\\\\\)

Since the circle passes through the point (-3, -5) we can plug in these values of x = -3 and y = -5 to get r squared

\((-3 + 1)^2 + (-5 -8)^2 = r^2\\\\(-2)^2 + (-13)^2 = r^2\\\\4 + 169 = r^2\\\\r^2 = 173\\\\\\\)

So the equation of the circle is
\((x + 1)^2 + (y-8)^2 = 173\)

If Janet rolls a fair 6-sided number cube 300 times, what is a reasonable prediction
on how many times she will roll a 5?

Answers

There are 50 predicted rolls for 5 in 300 times of rolls.

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Janet rolls a 6-sided number cube 300 times,

Probability = (Favourable Outcomes)/(Possible Outcomes)

Favourable Outcomes: 5 (1 total)

Possible Outcomes: 1,2,3,4,5,6 (6 total)

Probability of a 5 in any given roll of a die = 1/6

1/6x300 = 50 = 50 predicted roll with 5.

Hence, There are 50 predicted rolls for 5 in 300 times of rolls.

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What is the perimeter of a square with a side whose length is x +4?
4x² + 16
x² + 16
5x+4
4x + 16

Answers

Answer:

\(a. \: 4x ^{2} + 16\)

Step-by-step explanation:

\(1. \: gcf = 4 \\ 2. \: 4( \frac{4x^{2} }{4} + \frac{16}{4} ) \\ 3. \: 4(x^{2} + 4) \)

Use the associative property to simplify the expression 50 + 20 + 37​

Answers

Answer:

(50+20) +37=70+37=107

Archie bought 100 shares of stock in an ice cream company 2 years ago. He paid $60.65 per share. He just sold all of his shares for $67.68 per share. How much did he gain?

Answers

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.

Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11

Answers

Answer:do homework

Step-by-step explanation:

16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?

Answers

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

-6 - (-14) Please help And pleas show work or explane if you know the answer??

Answers

Answer:

8

Step-by-step explanation:

First, we have to simplify the equation. A negative term multiplied by a minus sign will ALWAYS be positive.

-(-14) = 14

Then, we will evaluate the expression.

-6+14 = 8

If it helps, you can rearrange the equation.

14-6 = 8.

Hope this helps!

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.

Assume that different groups of couples use a particular method of gender selection and each couple gives

Answers

a) The value of the mean is μ = 22.5

   The value of the standard deviation is σ = 3.5

b) The Value of 15 girls or fewer is significantly low.

   The value of 30 girls or more is significantly high.

c) The result 36 is significantly high because 36 is greater than 30 girls. A         result of 36 girls is not necessarily definitive proof of the method's effectiveness.

What is the standard deviation?

The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.

According to the given information

a) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.

Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.

The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:

μ = np = 45 x 0.5 = 22.5

Therefore, we expect to see around 22-23 girls in a group of 45 couples.

The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:

σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535

Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.

b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.

Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.

Significantly high:

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Significantly low:

Mean - 2σ = 22.5 - 2(3.535) = 15.43

c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.

This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.

It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.

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ABCD is a parallelogram.
E is the point where the diagonals AC and BD meet. Prove that triangle ABE is congruent to triangle CDE.
please write the justification for each value you find (e.g. Angle XYZ = 60° because.....)​

ABCD is a parallelogram.E is the point where the diagonals AC and BD meet. Prove that triangle ABE is

Answers

Answer:

the triangle (abe) is congruent to triangle (cde) becuase vertical angles are always congruent

√2x² + 7x + 5√2 = 0
find the roots of the following quadratic equation by factorization method



PLS HELP ME FAST

Answers

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

make e the subject
e-5=2f

Answers

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

which of the following is not the characteristics of numerical computing? a) aacuracy b) efficiency c) stability d)truncatating​

Answers

Based on the explanation below, the option which is not the characteristics of numerical computing d) truncatating​.

What is numerical computing?

Numerical computing is a technique for tackling difficult mathematical problems with only basic arithmetic operations.

The method entails the creation of mathematical models that can be solved using arithmetic procedures.

The three characteristics of numerical computing are accuracy, efficiency, and stability.

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NO LINKS NO FILES. Write the next two integers: -48, -24, -12, _, _

Answers

Answer:

-6,-3

hope this helps

have a good day :)

Step-by-step explanation:

-(x+2)+3(5+x)=41. please help me solve this equation

Answers

Answer:

Step-by-step explanation:

-x - 2 + 15 + 3x = 41

2x + 13 = 41

2x = 28

x = 14

Complete the long division problem on your own sheet of paper. Be sure to show all steps to show your teacher. Then enter the answer in the essay box. 16)13

Answers

0.8

------------------

16 | 130

128

Milani's teacher draws students names at random, calls on the student, and replaces the name so that students know they should always be prepared to respond. There are 20 students in Milani's class. Let X be the number of names it takes for the teacher to draw Milani's name. Find the probability that the teacher first draws Milani's name as the 7th name. You may round your answer to the nearest hundredth.​

Answers

Answer: 0.04

Step-by-step explanation:

Khan

Answer: 0.04

Step-by-step explanation:

In ΔWXY, w = 170 inches, x = 590 inches and y=630 inches. Find the measure of ∠Y to the nearest 10th of a degree.

Answers

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

To find the measure of angle ∠Y, we need to use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of its angles.

The formula for the law of cosines is:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to side c.

In our case, we know the lengths of the sides w, x, and y, and we want to find the angle ∠Y, which is opposite to side y. So, we can use the formula as follows:

\(y^2 = w^2 + x^2 - 2wx cos(Y)\)

Substituting the values, we have:

\(630^2 = 170^2 + 590^2 - 2(170)(590) cos(Y)\)

Simplifying and solving for cos(Y):

\(cos(Y) = (170^2 + 590^2 - 630^2) / (2170590)\)

cos(Y) ≈ -0.236

Note that the cosine of an angle is negative if the angle is between 90 and 180 degrees, which is the case for angle ∠Y in this triangle. Therefore, we need to use the inverse cosine function to find the measure of angle ∠Y:

Y ≈ 103.2 degrees

Rounding to the nearest tenth of a degree, we get:

Y ≈ 103.2°

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

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You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0 . You calculate a p-value of 0.0667. What is the highest possible significance level you can have?

Answers

Answer:

95%

Step-by-step explanation:

We have the following information:

n = 25, p-value = 0.0667

Besides that H0 is not rejected.

With this information we can affirm that the highest possible significance level you can have is 95%

Because alpha = 0.05

We reached this conclusion thanks to the fact that:

p-value> 0.05 hence we do reject the null hypothesis

There are 400 boxes arranged in 3 groups. The second group has twice as many boxes as the
first group. The third group has 4 more boxes than the first group. How many boxes are in the first group? Solve this problem in two ways: with the aid of a strip diagram and with algebraic equations. Explain your reasoning.

Answers

The number of boxes in the first group is 99

What is word problem?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem is solved into mathematical equation or expression.

Represent the first group by a, second group by b and third group by c

therefore;

b = 2a

c = 4+a

a+b+c = 400

therefore

a+2a+4+a= 400

4a + 4 = 400

4a = 400-4

4a = 396

a = 396/4

a = 99

therefore there are 99 boxes in the first group

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I think that 1 cannot be an even or an odd number because it cannot be divided by 2. am I correct?​

Answers

It’s a odd number , a even number is multiples of two

I will mark brainliest for best answer!

I will mark brainliest for best answer!

Answers

Answer:

a) 8 b)9 c)1 d) 3

Step-by-step explanation:

Raymond has a credit card with a 21.99% Apr. His balance this month is 3,000. Calculate how much interest he will pay this month. Round to the nearest cent.

Answers

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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The amount of tax on a chair was $3.60. The tax rate was 5%. Find the original price of the chair.

Bianca solved the problem below. Find Bianca’s error.

0.05(3.60) = Original price

The original price is $0.18.

Answers

9514 1404 393

Answer:

  $72.00

Step-by-step explanation:

The relationship between price and tax is ...

  tax amount = (tax rate) × (price)

Then the price can be found by dividing by the tax rate:

  price = (tax amount)/(tax rate)

  price = $3.60 / 0.05 = $72.00

The original price of the chair was $72.00.

__

Bianca apparently did not pay any attention to the way tax is computed. Nor did she check her work. The original price is not a small fraction of the tax. It is the other way around. Bianca used a wrong relationship between tax and price.

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