If there are 30 people in a classroom, what is the probability that at least two have the same birthday

Answer:

The Domain of the relationship is the set: {-5, -4, -2, -1, 0, 1, 3, 4} (Answer D)

Step-by-step explanation:

Let's recall that the Domain of a relationship is the set of values in the starting set for which there is a correspondent value in the final set.

In this case, we have a set of numbers on the x axis, which are connected with values in the y axis as indicated by the plotting of the points on the (x,y) plane.

The Domain will consist of all those x-values for which we see in the given plot connected to a corresponding y-value.

So, we see that:

the x-value -5 is connected to the y-value -4

the x-value -2 is connected to the y-value -1

the x-value -1 is connected to the y-value 0

the x-value 0 is connected to the y-value 1

the x-value 3 is connected to the y-value 4

and the x-value 2 is connected to two y-values:  3 and 4

Therefore all those x-values are part of the Domain of this relationship. That is, the set: {-5, -4, -2, -1, 0, 1, 3, 4}

The GED of 2076 and 1076 is 4 and it can be expressed as a linear combination of the two integers that was used to obtain it as follows:

4 = -8 × 248 + 21 × 1076.

Given the numbers 2076 and 1076, we are required to find the GED of the integers using the Euclidean algorithm and then express the GED of the pair as a linear combination of the given numbers.

The Euclidean Algorithm states that,

If a and b are two non-negative integers and a > b, then

gcd(a, b) = gcd(b, a mod b).

Euclidean Algorithm: To find the gcd of the given pair of integers, we can apply the Euclidean algorithm.

Division Algorithm

2076 / 1076 = 1 with a remainder of 1000

Since the remainder is not equal to zero, we will divide the divisor with the remainder of the first division.

1076 / 1000 = 1 with a remainder of 76

Again, divide the divisor with the remainder of the previous division.

1000 / 76 = 13 with a remainder of 28

Once again, divide the divisor with the remainder of the previous division.

76 / 28 = 2 with a remainder of 20

Similarly, divide the divisor with the remainder of the previous division.

28 / 20 = 1 with a remainder of 8

Again, divide the divisor with the remainder of the previous division.

20 / 8 = 2 with a remainder of 4

Divide the divisor with the remainder of the previous division.

8 / 4 = 2 with a remainder of 0

As we have obtained the remainder of the division as 0, we stop the process of division.

Hence, the GED of 2076 and 1076 is 4.

GED as a linear combination to find the GED as a linear combination of the given numbers, we will express each remainder as a linear combination of the two integers that was used to obtain it.

The process is given as follows:

1000 = 2076 - 1 × 107676

         = 1076 - 1 × 100076

         = 2076 - 2 × 107620

         = 1076 - 2 × 528

         = 2076 - 3 × 760

         = 528 - 1 × 248

         = 2076 - 4 × 5288

         = 528 - 2 × 248

         = 1076 - 4 × 5284

         = 248 - 1 × 208

         = 528 - 2 × 248

         = 1076 - 4 × 528

         = 2076 - 8 × 248

Hence, the GED of 2076 and 1076 is 4 and it can be expressed as a linear combination of the two integers that was used to obtain it as follows:

4 = -8 × 248 + 21 × 1076.

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Answer:

The answer is 2163.57142857 rounded equals 2164 is the answer

Step-by-step explanation:

all you have to do is 15145 divided by 7 and you get your answer then round

Answer:

To do this, just do 12 divided by 4.80 = 2.5 dollars per can at Corner Grocery, and at Max's Market 15 divided by 5.25 = 2.85 per can. So the Corner Grocery has a better unit price by 35 cents.

Thanks for your question.

Answer:

i dont know

Step-by-step explanation:

i dont know

Answer:

8/3 < 8/2

D

Step-by-step explanation:

8/3 = 2.67

8/2 = 4

So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.

There is more left if 8 is divided by 2 than when it is divided by 3

[Answer]8/3 < 8/2

[Answer] D

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

8/3 < 8/2

Step-by-step explanation:

D. When fractions have equivalent numerators, the one with the lesser denominator is the greater fraction.

8/2 = 4

8/3 = 2.667

Answer:   2.4 calories

Step-by-step explanation: all you would need to do is divide 144 calories by 60 goldfish.

Answer:

22 mm

Step-by-step explanation:

Answer:

https://socratic.org/questions/a-card-is-drawn-from-a-standard-deck-a-second-card-is-drawn-without-replacing-th-1#131182

Step-by-step explanation:

:)

The answers are:

(a) The jet turns upwards out of the dive at approximately 8.50 seconds.

(b) The altitude of the jet when it begins its turn upwards is approximately 4987 meters.

a) To find the time at which the jet turns upwards, we need to find the value of t when the altitude function, h(t), changes from decreasing to increasing.

This occurs when the velocity of the jet changes from negative (indicating descent) to positive (indicating ascent).

The velocity function, v(t), is the derivative of the altitude function.

Let's find the velocity function first by taking the derivative of the altitude function:

h(t) = 16t³ - 204t² + 9900

v(t) = d/dt [h(t)] = d/dt [16t³ - 204t² + 9900]

v(t) = 48t² - 408t

Now we can solve for the time when the velocity changes sign (i.e., when v(t) = 0) to find the time at which the jet turns upwards:

48t² - 408t = 0

48t(t - 17/2) = 0

We have two solutions: t = 0 and t = 17/2.

(a) At t = 0, the jet starts its diving motion, so we disregard this solution.

(b) At t = 17/2, the jet turns upwards out of the dive.

b) Let's calculate the altitude of the jet at t = 17/2:

h(17/2) = 16(17/2)³ - 204(17/2)² + 9900

h(17/2) = 4987 meters

Therefore, the answers are:

(a) The jet turns upwards out of the dive at approximately 8.50 seconds.

(b) The altitude of the jet when it begins its turn upwards is approximately 4987 meters.

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A statistically significant negative correlation coefficient of r = -0.91 was obtained from a sample of n = 30. This indicates a strong and significant negative relationship between the variables.

The researcher conducted a correlation analysis and found a correlation coefficient (r) of -0.91, which indicates a strong negative relationship between the variables under investigation. The negative sign indicates that as one variable increases, the other variable tends to decrease, and vice versa.

The statistical significance of the correlation coefficient is crucial in determining whether the observed relationship is likely to be due to chance or if it truly exists in the population. In this case, the report should highlight that the obtained correlation coefficient is statistically significant.

To establish statistical significance, the researcher likely conducted a hypothesis test, such as a t-test or a permutation test, to determine the probability of obtaining a correlation coefficient as extreme as -0.91 under the null hypothesis of no correlation. Since the obtained correlation coefficient is statistically significant, it suggests that the observed negative relationship is unlikely to be a result of chance and provides evidence for a genuine association between the variables in the population from which the sample was drawn.

Reporting this finding is important for conveying the strength and significance of the negative relationship to the readers, providing valuable insights for further analysis and interpretation of the variables under investigation.

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Answer:

x < 0

Step-by-step explanation:

Since the arrow is going to the left, we know it is less than.

Since the dot is open, we know that it cannot be equal to 0.

Hence, the answer is x < 0.

Answer:

2030.4

Step-by-step explanation:

divided 85 and 7.0

It provides character details that indicate Mrs. This function Faxon's interaction with this character serve in the given excerpt. Therefore, the correct option is option A.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt. It provides character details that indicate Mrs. This function Faxon's interaction with this character serve.

Therefore, the correct option is option A.

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Answer:

x=4, y=-11. (4, -11).

Step-by-step explanation:

3x+2y=-10

5x+y=9

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

3x+2y=-10

-2(5x+y)=-2(9)

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

3x+2y=-10

-10x-2y=-18

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

-7x=-28

7x=28

x=28/7=4

5(4)+y=9

20+y=9

y=9-20=-11

the area of a circle with a rectangle will be [π w²2]/4.

What is the area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

area of the circle will be πr².

The area of a circle inscribed in a rectangle if the length of the rectangle is l and the width is w

= [π w²2]/4.

Hence the area of a circle with a rectangle will be [π w²2]/4.

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The most appropriate choice for Probability will be given by-

Probability of rolling a sum of 10 on a standard pair of six sided dice = \(\frac{1}{12}\)

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here,

Total number of outcomes = 36

Favourable outcomes = {(4,6), (5,5), (6,4)}

Number of favourable outcomes = 3

Probability of rolling a sum of 10 on a standard pair of six sided dice = \(\frac{3}{36}\)

                                                                                                                  = \(\frac{1}{12}\)

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The calculated value of the total population of the country is 8530000

From the question, we have the following parameters that can be used in our computation:

3582600 is 42%. of the total population of the country

This means that

42%. of the total population of the country = 3582600

Express as product

So, we have

42% * the total population of the country = 3582600

Divide both sides by 42%

the total population of the country = 3582600 /42%

Evaluate

the total population of the country = 8530000

Hence, the total population of the country is 8530000

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The transformation is explained below.

The transformation is merely a translation of points vertically and horizontally.

The original triangle must have its original coordinates. All you have to do is subtract 1 from their x-coordinate and add 5 units to their y-coordinates.

For example, if the original coordinate is (1,2), then the translated point would now be (0,7). Once you get all the translated points, you can plot them as the new translated triangle.

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Without the original triangle, we cannot graph the image. However, I will provide the steps to apply the given transformation to any triangle:

1. Plot the vertices of the original triangle.

2. For each vertex, shift the x-coordinate left by 1 unit and shift the y-coordinate up by 5 units.

3. Connect the corresponding vertices to form the image of the triangle.

For example, let's say the original triangle has vertices A(2,3), B(5,6), and C(7,2). Applying the given transformation:

- Vertex A becomes A'(1,8) [x - 1 shifts left by 1, y + 5 shifts up by 5]

- Vertex B becomes B'(4,11)

- Vertex C becomes C'(6,7)

Connecting the corresponding vertices, we form the image of the triangle with vertices A'(1,8), B'(4,11), and C'(6,7).

Hope this helps you

Answer:

75.36 is the answer.

Step-by-step explanation:

trust me bro.

Answer:

75.39822

Step-by-step explanation:

2πrh+2πr2=2·π·2·4+2·π·22≈75.39822

It said don't round your answer...

By adapting Euclid's proof for prime integers, we can show that there are infinitely many monic irreducible polynomials in the polynomial ring K[x], where K is a field.

Let's consider the polynomial ring K[x], where K is a field. To show that there are infinitely many monic irreducible polynomials in K[x], we can adapt Euclid's proof for prime integers.

Assume we have a finite list of monic irreducible polynomials in K[x], denoted as P1(x), P2(x), ..., Pn(x). We want to find a monic irreducible polynomial that is not divisible by any of these polynomials.Consider the polynomial Q(x) = P1(x)P2(x)...Pn(x) + 1. This polynomial is monic and has a degree greater than any of the polynomials in our list.

Now, let's assume that Q(x) is reducible. This would mean that Q(x) can be factored as Q(x) = R(x)S(x), where R(x) and S(x) are non-constant polynomials in K[x].Since Q(x) is monic and has a degree greater than any polynomial in our list, both R(x) and S(x) must have a degree less than Q(x).

However, this implies that R(x) and S(x) are not divisible by any of the polynomials in our list, contradicting the assumption that we had a finite list of monic irreducible polynomials.

Therefore, Q(x) must be irreducible, and we have found a monic irreducible polynomial that is not in our initial list.Since this argument can be repeated infinitely, we conclude that there are infinitely many monic irreducible polynomials in K[x], where K is a field.

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The domain of f(x) is all real numbers.

Option D is the correct answer.

We have,

The given function is f(x) = 36 - x².

This function represents a parabola with its vertex at (0, 36) and opening downwards.

The domain of a function is the set of all possible values of x for which the function is defined.

For the given function f(x) = 36 - x²,

The function is defined for all real numbers of x since we can plug in any real number for x and get a real number output.

Therefore,

The domain of f(x) is all real numbers.

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Answer:

535 students passed and 107 students failed

Step-by-step explanation:

Create a system of equations where p is the number of students who passed and f is the number of students who failed:

p + f = 642

p = 5f

Solve by substitution by plugging in 5f as p into the first equation, then solving for f:

p + f = 642

5f + f = 642

6f = 642

f = 107

So, 107 students failed.

Find how many students passed by multiplying this by 5:

107(5)

= 535

535 students passed and 107 students failed.

(a) Let's substitute u(x, t) = F(x)G(t) into the wave equation ∂t^2u = c^2∂x^2u. We have:

∂t^2u = c^2∂x^2u

∂t^2(F(x)G(t)) = c^2∂x^2(F(x)G(t))

F(x)∂t^2G(t) = c^2G(t)∂x^2F(x)

Dividing both sides by c^2F(x)G(t), we obtain:

1/G(t)∂t^2G(t) = 1/F(x)∂x^2F(x)

Since the left side depends only on t and the right side depends only on x, both sides must be constant. Let's denote this constant by -λ^2. We then have two separate ordinary differential equations:

1/G(t)∂t^2G(t) = -λ^2

1/F(x)∂x^2F(x) = -λ^2

(b) Using the given initial conditions, we can derive the expressions of the Fourier coefficients of the solution u(x, t). By substituting u(x, 0) = f(x) into the expression for u(x, t), we obtain:

u(x, 0) = ∑[n=1 to ∞] (a_n cos(cnπt) + b_n sin(cnπt)) sin(nπx)

Since u(x, 0) = f(x), we can equate the corresponding coefficients:

f(x) = ∑[n=1 to ∞] a_n sin(nπx)

By comparing the coefficients, we can determine the values of a_n. Similarly, we can derive the expressions for b_n by considering the boundary condition u(0, t) = u(L, t) = 0.

Note: The above derivation assumes that the Fourier series expansion is appropriate for the given function f(x) and the boundary conditions. It is important to ensure that the function f(x) satisfies the necessary conditions for Fourier series representation, such as periodicity and integrability, and that the boundary conditions are consistent with the chosen form of the solution u(x, t).

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Answer: ITS B (-5,3,-4 + i, -4 - i)

The correct answer is B, or –5, 3, –4 + i, –4 – i

Just got it right on edge 2020, hope this helps!! :)

Answer:

m = y2 - y1 / x2 - x1

Step-by-step explanation:

It takes the balloon to descend to an altitude of 20 feet after 5 seconds

From the question, we have the following parameters that can be used in our computation:

y = -20x + 80

When the height is 20, we have

-20x + 80 = 20

So, we have

-20x = -100

Divide

x = 5

Here, y - 0

So, we have

-20x + 80 = 0

This gives

-20x = -80

Evaluate

x = 4

Hence, the time is 4 seconds

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A house that has 2,100 sq ft of living area is more unusual than a house that sells for ​$125,000. This is because the probability of finding a house with 2,100 sq ft of living area is only 38.21% which is less than 5.86% which is the probability of finding a house that sells for ​$125,000.

A real estate agent has surveyed houses in twenty nearby zip codes in an attempt to put together a comparison for a new property that she would like to put on the market. The 1057 houses she surveyed have a mean price of ​$172,000, with a standard deviation of $30,000. The mean living area is 1567 sq​ ft, with a standard deviation of 210 sq ft. We are to find out which is more unusual, a house in that market that sells for ​$125,000 or a house that has 2,100 sq ft of living​ area? Let's answer this question step by step. We have,Mean of Price

= $172,000

Standard Deviation of Price

= $30,000

Mean of Living area

= 1567 sq ft

Standard Deviation of Living area

= 210 sq ft

The price of the house that is being sold is $125,000.The calculation to find the Z-score for the house that is selling at $125,000 is given by:

Z = (X- μ)/ σ

Where, X = Price of the house

= $125,000μ

= Mean Price

= $172,000σ

= Standard Deviation

= $30,000

Substitute the values and find the Z-score,

Z = (125,000-172,000) / 30,000 = -1.5667

We then look at the Z-table to find the probability of getting the Z-score value -1.5667. From the Z-table, we get the value of 0.0586 or 5.86%. The probability of finding a house that sells at $125,000 is 5.86% in that area.Now let's calculate the Z-score for a house that has 2,100 sq ft of living area using the formula,

Z = (X- μ)/ σ

Where, X = Living area

= 2100 sq ftμ

= Mean Living Area

= 1567 sq ftσ

= Standard Deviation

= 210 sq ft

Substitute the values and find the Z-score,

Z = (2100-1567) / 210

= 0.3

We then look at the Z-table to find the probability of getting the Z-score value 0.3. From the Z-table, we get the value of 0.3821 or 38.21%. The probability of finding a house with 2,100 sq ft of living area is 38.21% in that area.Therefore, a house that has 2,100 sq ft of living area is more unusual than a house that sells for ​$125,000. This is because the probability of finding a house with 2,100 sq ft of living area is only 38.21% which is less than 5.86% which is the probability of finding a house that sells for ​$125,000. Hence, a house with 2,100 sq ft of living area is more unusual in that area.

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Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.

Answer:

option 1

as the sides were already given, A and D are the only way that the triangle can have SAS.

The option 1 . ∠A ≅ ∠D is correct and needed to apply SAS similarity theorem in this given condition.

The  SAS theorem states that if two triangles have a congruent angles and the sides that define the angle  are proportional, the two triangles are similar.

Given are two triangles ΔABC and ΔDEF and their sides AB =7 , AC = 12, DE =14, DF = 24

Then AB/ DE = 7/14 = 1/2

 and AC / DF = 12/24 = 1/2

∴ AB / DE = AC/ DF

Therefore the sides AB and AC are proportional to DE and DF

And for the application of SAS the angle defined by these pairs must be congruent.

AB and AC defines ∠A and DE and DF defines ∠D

Thus, ∠A must  be congruent to  ∠D so that SAS can be to applied to make the given triangles similar.

Therefore, option 1. ∠A ≅ ∠D  is correct option

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