How many people have to be in a room to have a 50% probability of at least two people having the same birthday?

Order of fractions from smallest to largest:

If sorted we first equate the denominator to 60.

18/60, 16/60, 54/60, 44/60, 51/60

So if sorted from smallest to largest, the order becomes:

4/15, 3/10, 11/15, 17/20, 9/10

If sorted we first equate the denominator to 60. it becomes:

15/60, 20/60, 40/60, 45/60, 24/60

So if sorted from smallest to largest, the order becomes:

1/4, 1/3, 2/5, 2/3, 3/4

If sorted we first equate the denominator to 60. it becomes:

135/60, 80/60, 100/60, 105/60, 84/60

So if sorted from smallest to largest, the order becomes:

4/3, 7/5, 5/3, 7/4, 9/4

If sorted we first equate the denominator to 30. it becomes:

126/30, 65/30, 125/30, 66/30, 39/30

So if sorted from smallest to largest, the order becomes:

13/10, 13/6, 11/5, 25/6, 21/5

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Answer: i don't know I just did this so i can get points to ask a question super sorry.

Step-by-step explanation:

The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.

The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.

In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.

The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.

Mathematically, we can write this sum as:

S = (6xi-3)/n for i = 1, 2, ..., n

And the limit of S as n approaches infinity can be written as:

lim n -> infinity S = lim n -> infinity (6xi-3)/n

Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.

In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].

Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:

∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3

And this value is 9, so the limit of S as n approaches infinity is 9.

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The ordered pair that is in the solution set of the given inequality is (-1, -9). The correct answer would be an option (C).

An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.

We can substitute each of the ordered pairs into the inequality to see if it satisfies the inequality:

A: (2, -1)

5x - 2y > 12

5 × 2 - 2 × -1 > 12

10 - 2 > 12

8 > 12 (False)

B: (1, 5)

5x - 2y > 12

5 × 1 - 2 × 5 > 12

5 - 10 > 12 (False)

C: (-1, -9)

5x - 2y > 12

5 × -1 - 2 × -9 > 12

-5 + 18 > 12 (True)

D: (0.2, 0.5)

5x - 2y > 12

5 × 0.2 - 2 × 0.5 > 12

1 - 1 > 12 (False)

So, the only ordered pair that is in the solution set of the inequality is C: (-1, -9).

Hence, the correct answer would be option (C).

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The number of ways that baking club form an executive committee with 2 people will be 6.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

A baking club wants to form an executive committee. There are 4 people in the baking club, including Mark.

The number of ways that baking club form an executive committee with 2 people will be given as,

⁴C₂ = 4! / [(4 - 2)! x 2!]

⁴C₂ = 4 x 3 x 2! / (2! x 2 x 1)

⁴C₂ = 2 x 3

⁴C₂ = 6

The number of ways that baking club form an executive committee with 2 people will be 6.

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The number corresponds to the given string  is 237880

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

The shortlex ordering places the shortest sequences at the front of the list of sequences by cardinality (length), while sequences of the same length are arranged lexicographically.

Given:  cbbca cba cbc

  length =11

We need to find the number of strings that precede the given string over {a,b,c}

Number of strings of length 0 = 1

Number of strings of length 1 = 3

Number of strings of length 2 = 3²

'

'

'

'

'

Number of strings of length 10 = 3¹⁰

In general, number of strings formed withy length n = 3ⁿ

Add all the strings of length 0 to 10

1+3+3²+......................+3⁻¹⁰

By simple geometric sum formula ,

we have

= (3¹¹⁻¹)/(3-1) =  88573

Number of strings of length 11 starting with either 'a' or 'b' = 2*3¹⁰

Number of strings of length 11 starting with 'ca' = 3⁹

Number of strings of length 11 starting with 'cba' = 3⁸

Number of strings of length 11 starting with 'cbba' or 'cbbb' = 2*3⁷

Number of strings of length 11 starting with 'cbbcaa' or 'cbbcab' = 2*3⁵

Number of strings of length 11 starting with  'cbbcaca' = 3⁴

Number of strings of length 11 starting with 'cbbcacbab' or 'cbbcacbaa' = 2*3²

Number of strings of length 11 starting with 'cbbcacbaca' = 3

Number of strings of length 11 starting with 'cbbcacbacba'  or 'cbbcacbacbb'  = 2

Total number of strings of length 11 preceding the given string is :

  2+3+2*3² +3⁴+ 2*3⁵+ 2*3⁷+3⁸+3⁹ + 2*3¹⁰

= 149306

The number corresponds to the given string

=  88573 + 149306 +1

= 237880

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Step-by-step explanation:

Outliers: In this data set, the value of 501 is an outlier as it is significantly higher than the other values.

Median: To find the median, we arrange the data in order and find the middle value. In this case, since there are an odd number of values, the median is the middle value: 290.

Mean: To find the mean, we add up all the values and divide by the number of values:

(248 + 260 + 267 + ... + 311 + 501) / 21 = 293.67

10% Trimmed Mean: To find the 10% trimmed mean, we delete the bottom 10% of the values (2 values) and the top 10% of the values (2 values) and then find the mean of the remaining values:

(278 + 282 + 284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 15 = 286.87

20% Trimmed Mean: To find the 20% trimmed mean, we delete the bottom 20% of the values (4 values) and the top 20% of the values (4 values) and then find the mean of the remaining values:

(284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 12 = 288.92

The median, mean, 10% trimmed mean, and 20% trimmed mean can be compared to see how resistant each measure is to outliers. The median is the most resistant measure as it only considers the middle value, whereas the mean is the least resistant measure as it considers all values in the data set. The trimmed means are intermediate measures that are more resistant to outliers than the mean but less resistant than the median. In this case, we can see that the 10% trimmed mean is more resistant to outliers than the mean but less resistant than the 20% trimmed mean.

Answer:

Step-by-step explanation:

A) The equation for the perimeter of a rectangle is given by 2 * (length + width), so we can write the equation for this rectangle as:

2 * (30 + w) = 108

B) To find the width of the rectangle, we can solve for w:

60 + 2w = 108

2w = 48

w = 24

So, the width of the rectangle is 24 cm.

(a) If 10 < 7, then 3 = 4.

This statement is true. Because  False ------> False has the truth value T

(b) If 7 < 10, then 3 = 4

This statement is False. Because  True ------> False has the truth value F

(c) If 10 < 7, then 3 + 5 = 8.

This statement is true. Because  False ------> True  has the truth value T

(d) If 7 < 10, then 3 + 5 = 8

This statement is true. Because  True ------> True  has the truth value T

What is a conditional statement?

A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.

(a) If 10 < 7, then 3 = 4.

This statement is true. Because  False ------> False has the truth value T

( 10 is not less than 7 and 3 is not equal to 4)

(b) If 7 < 10, then 3 = 4

This statement is False. Because  True ------> False has the truth value F

( 7 < 10 and 3 is not equal to 4 )

(c) If 10 < 7, then 3 + 5 = 8.

This statement is true. Because  False ------> True  has the truth value T

(  10 is not less than 7 , but  3 + 5 = 8 )

(d) If 7 < 10, then 3 + 5 = 8

This statement is true. Because  True ------> True  has the truth value T

( 7 < 10 and 3 + 5 = 8, both are true )

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(a) If 10 < 7, then 3 = 4.

This statement is true. Because  False ------> False has the truth value T

(b) If 7 < 10, then 3 = 4

This statement is False. Because  True ------> False has the truth value F

(c) If 10 < 7, then 3 + 5 = 8.

This statement is true. Because  False ------> True  has the truth value T

(d) If 7 < 10, then 3 + 5 = 8

This statement is true. Because  True ------> True  has the truth value T

What is a conditional statement?

A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.

(a) If 10 < 7, then 3 = 4.

This statement is true. Because  False ------> False has the truth value T

( 10 is not less than 7 and 3 is not equal to 4)

(b) If 7 < 10, then 3 = 4

This statement is False. Because  True ------> False has the truth value F

( 7 < 10 and 3 is not equal to 4 )

(c) If 10 < 7, then 3 + 5 = 8.

This statement is true. Because  False ------> True  has the truth value T

(  10 is not less than 7 , but  3 + 5 = 8 )

(d) If 7 < 10, then 3 + 5 = 8

This statement is true. Because  True ------> True  has the truth value T

( 7 < 10 and 3 + 5 = 8, both are true )

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The required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5

The expression model is defined as the model of the given situation in the form of an expression using variables and constants.

Here,
From the figure,
It can be concluded that it is 2/5 times the sum of 8 and 4,
Also
= 2/5[8 + 4]

Simplify
= 2/5[12]
= 24/5
= 4 4/5

Thus, the required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5

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Answer:

28 cm^2

Step-by-step explanation:

The area will be the height (4)   times the average of the bases (8 and 6 , average = 7 )

4 x 7 = 28 cm^2

12n+250

because you don't know the amount of tickets

Answer:

p = (39x +30 -5q)/13x

Step-by-step explanation:

16px + 10q + 10px = 78x + 60

Solve for p.

Subtract 10 q from  each side.

16px + 10q-10q + 10px = 78x + 60 -10q

16px + 10px = 78x + 60-10q

Combine like terms.

26px = 78x + 60-10q

Factor out p.

p(26x) =  78x + 60-10q

Divide each side by 26x.

p =  (78x + 60-10q)/(26x)

Simplify.

p = (39x +30 -5q)/13x

There are 31 19/24 miles Trish drive in all.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Trish drive 18 1/8 miles yesterday she drove 13 2/3 miles today.

Hence, Total miles Trish drive in all is,

⇒ 18 1/8 + 13 2/3

⇒ 145/8 + 41/3

⇒ (145 × 3 + 41 × 8 ) /24

⇒ (435 + 328) / 24

⇒ 763/24

⇒ 31 19/24 miles

Thus, Total miles Trish drive in all is, 31 19/24 miles.

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The amount of grape in bin using probability distribution =253 gm

Probability is simply the chance that something will happen.

Whenever the outcome of an event is uncertain, we can talk about the likelihood or likelihood of a particular outcome. Analyzing events according to their probabilities is called statistics.

The best example of understanding probability is coin tossing.

Heads or tails, he has two possible outcomes. Crisps

The probability of an event is between 0 and 1 and can also be expressed as a percentage. event probability

P(A)>P(B)P, left parenthesis, A, right parenthesis, greater than, P, left parenthesis, B, right parenthesis, then event

P(A)=P(B)P, left parenthesis, A, right parenthesis, equal, P, left parenthesis, B, right parenthesis, event AA and BB occurs with equal probability. 

Now for the given Question:

You need to find the z-score which is closest to .2000 (20%)

 Look at your negative z-score table

  Look at  z= -.84

So -.84 standard deviations below the mean represents 20%                          

 261  - .84 X (9.4) = 253.1 gm

Hence the amount of grapefruit in bin= 253 gm

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The perfect square polynomial is x² - 32x + 256 and the factored form is (x - 16)(x - 16)

A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.

A perfect square polynomial can be represented as follows;

ax² + bx - c = 0

Hence, the perfect square trinomial is x² - 32x + 256.

Now, let's factorise it.

x² - 32x + 256.

x² - 16x - 16x + 256

x(x - 16) -16(x - 16)

Therefore,

(x - 16)(x - 16)

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Answer:    x²-32x+16²

Step-by-step explanation:

   (x-a)²=x²-32x+a²   where .2ax=-32x so, 2a=32  then a=16

   then  (x-16)²=x²-32x+16²

The following results are:

a. Average height: 58.84

b. Median height: 58

c. Mode height: 55

d. Range of data: 73 - 44 = 29

e. Standard deviation: 8.23

f. Z-score for 65 inches: (65 - 58.84) / 8.23 = 0.83

Statistics is a process in which we collect, interpret, study and understand the data. We took a small sample from the large quantity and then we did study of the sample then according to results, we did our predictions for events which can happen in future.

Given that,

The height of 25 trees,

following results (recorded in inches).

60 57 62 69 46 54 64 60 59 58 75 51 49

67 65 44 58 55 48 62 63 73 52 55 50

a.   Average = Sum of  height of all the trees/Total number of trees

                     = 58.84

b.  Median =  (N + 1)/2th term after arranging into ascending order

                  = 58

c.  Mode = Highest frequency

               = 55

d. range = Highest value - Lowest value

              = 73 -44

              = 29

e. the standard deviation of the given data, you would need to perform the following steps:

Calculate the mean of the data:

(60 + 57 + 62 + 69 + 46 + 54 + 64 + 60 + 59 + 58 + 75 + 51 + 49 + 67 + 65 + 44 + 58 + 55 + 48 + 62 + 63 + 73 + 52 + 55 + 50) / 25 = 58.84

Find the deviation of each data point from the mean:

60 - 58.84 = 1.16, 57 - 58.84 = -1.84, 62 - 58.84 = 3.16, and so on...

Square each deviation:

1.16^2 = 1.3536, (-1.84)² = 3.3876, 3.16^2 = 9.9876, and so on...

Sum all the squared deviations:

1.3536 + 3.3876 + 9.9876 + ... = 519.24

Divide the sum by the number of data points minus 1 (for a sample) or by the number of data points (for a population):

519.24 / 24 = 21.63

Take the square root of the result:

√21.63 = 4.65

The standard deviation of the given data is 4.65.

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y = 0.3x + 1.8 matches f(x) = 0.1x³ + 2

y = 1.2x + 7.4 matches f(x) = 0.1x³ + 2

y = 2.7x + 3.6 matches f(x) = 0.1x³ + 2

y = 4.8x + 1.8 does not match f(x) = 0.1x³ + 2

y = 4.8x - 10.8 does not match f(x) = 0.1x³ + 2

y = 0.3x - 10.8 does not match f(x) = 0.1x³ + 2

A tangent line is a straight line that touches a given curve at a single point and has the same slope as the curve at that point. In other words, it is a line that locally approximates the curve at that point. The tangent line is often used to study the behavior of a function near a particular point and can provide valuable information about the properties of the curve

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Answer:

1, 2, 3, 6, 9, 18, 27 and 54

Step-by-step explanation:

A factor is a number that divides another number without leaving a remainder

Factors of 54:

1 × 54 = 54

2 × 27 = 54

3 × 18 = 54

6 × 9 = 54

9 × 6 = 54

18 × 3 = 54

27 × 2 = 54

54 × 1 = 54

The factors are: 1, 2, 3, 6, 9, 18, 27 and 54

The double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.

Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration.  The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

To evaluate the double integral  [tex]\int\limits^a_b {} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3), we first need to find the limits of integration for x and y.

The x-coordinates of the vertices of the rectangle range from 0 to 4, so the limits of integration for x are 0 to 4. The y-coordinates of the vertices of the rectangle range from 1 to 4, so the limits of integration for y are 1 to 4.

So, the double integral becomes:

[tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] =  (2 × 4² + 8 × 4) - (2 × 1² + 8 × 1) = 32 - 10 = 22.

Therefore, the double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.

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A'(15) = 2 * 15 = 30.The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm^2 when the side length is 15 mm.

The area A(x) of a square wafer is given by A(x) = x², where x is the side length of the wafer. The derivative of A(x) with respect to x, denoted A'(x), represents the rate of change of the area with respect to the side length. To find A'(15), we need to find the derivative of A(x) at x = 15.

A'(x) = 2x

Therefore, A'(15) = 2 * 15 = 30.

The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm² when the side length is 15 mm. This means that for every 1 mm increase in the side length, the area of the wafer will increase by 30 mm², and for every 1 mm decrease in the side length, the area of the wafer will decrease by 30 mm².

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Answer:

no

Step-by-step explanation:

5.9 is close to 5.10

5.99 is close to 6

5.9 + 0.1 = 5.10

5.99+0.1 = 6

Answer:

Hi there! 5.9 is NOT bigger than 5.99

Step-by-step explanation:

5.9 is 0.09 less than 5.99.

Hope this helps!

Brainiest? Can you click on the crown on this answer? Thanks!

-4-1/3m+8n is the simplified form of the expression -2/5(10+5/6m-20n)

An expression is combination of variables, numbers and operators.

The given expression is -2/5(10+5/6m-20n)

Minus two by five times of ten plus five by six m minus twenty n.

In the expression m and n are the variables and minus and plus are the operators.

Apply distributive property to solve the expression.

-2/5(10)-2/5(5/6)m+2/5(20n)

-4-1/3m+8n

Hence, -4-1/3m+8n is the simplified form of the expression -2/5(10+5/6m-20n)

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The electric field at points A and C is the same, since they are both the same distance away from the center of the charge. Therefore, the electric field at A and C is the largest, while the electric field at B and D is the smallest. Thus, the correct answer is A. A, C, B, D.

The electric field is determined by the magnitude of the charge, the distance between the charge and the point where the electric field is measured, and the direction of the electric field. In this case, point A and C are the same distance away from the center of the charge, while points B and D are further away. Therefore, the electric field at points A and C is the strongest.

the complete question is :

which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?

Options :

A. a, b, c, d

B. b, c, d, a

C. b, d, c, a

D. d, c, b, a

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The earning of the store is $62.55.

What is an equation?

An equation is expression with one or more variables. It can also have more than 1 degree. it is a linear combination of constants and variables.

We are given that a box contains 74.25 ounces of pecans

These pecans are divided in 8.125 ounces of containers

First let us see how many such containers can be made

To find that we divided the two we get

74.25/ 8.125 = 9 such containers can be made

Now Each container is being sold for $6.95

Hence the total earnings are

9 * 6.95 = $62.55

The earning of the store is $62.55

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Based on the volume of the solid, the value of K is 8960.

The volume of the solid = volume of the cone + volume of the hemisphere

The volume of the cone = ¹/₃hπr²

The volume of the hemisphere = ²/₃πr³

where;

r is radius = 20 cm

h is the height of the cone = ?

The curved surface area of the cone = πrl

The curved surface area of the cone = 580π cm²

πrl =  580π

l = 580/20

l = 29 cm

h = √(29² - 10²)

h = 27.2 cm

The volume of cone = ¹/₃ * 27.2 * 20² * π

The volume of the cone = 3626.7π cm³

The volume of the hemisphere = ²/₃ * π * 20³

The volume of the hemisphere = 5333.3 cm³

The volume of the solid = 5333.3π cm³ + 3626.7π cm³

The volume of the solid = 8960π cm³

The volume of the solid is kπcm³ = 8960π cm³

K =  8960

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The function f(x) is linear and equation is y = 4x + 6 where x=0,1,2,3,4

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a co-domain, as well as a range. In general, a function is denoted as f(x), where x represents the input. A function's generic representation is y = f(x).

In mathematics, there are several types of functions. Some examples include:

When there is a mapping for a range for each domain between two sets, this is referred to be an injective function or a one to one function.

Surjective functions, also known as Onto functions, are used when more than one element is transferred from domain to range.

Polynomial function: A function made up of polynomials.

Inverse Functions: A function that may be used to inverse another function.

Now,

For function f(x)=6,10,14,18,22, g(x)=8,10,12,16,22 for x=0,1,2,3,4

f is a function because y increases 4 for each increase of 1 in x

slope = 4

intercept = f(0) =6

Hence Equation is y = 4x + 6 where x=0,1,2,3,4

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Answer:

Step-by-step explanation:

ss