Vanessa has 7 pieces of pizza and she wants to split them evenly between herself and 4 friends. How much will each person receive?​

Answer:

.04

Step-by-step explanation:

sin 5∅ - sin 7∅ - sin4∅ + sin8∅ divided by cos 4∅ - cos 5∅ - cos 8∅ + cos 7∅

= sin (5∅ - 7∅ - 4∅ + 8∅) / cos (4∅ - 5∅ - 8∅ + 7∅)

= sin 2∅ / cos -2∅

= .035 / .999 = .04

We have shown that every point in [a, b] is a limit point of B, and every limit point of B is in [a, b]. Therefore, B' = [a, b].

In mathematics, a limit point (also known as an accumulation point or cluster point) is a concept used in the study of topological spaces and sequences.

To prove that the set B' = [a, b] is equal to [a, b],

we need to show that every point in [a, b] is a limit point of B and every limit point of B is in [a, b].

1. Every point in [a, b] is a limit point of B:

Let x be an arbitrary point in [a, b]. We need to show that x is a limit point of B, which means that every open interval containing x contains a point of B other than x itself.

Since x is in [a, b], we know that a ≤ x ≤ b.

Consider an arbitrary open interval (x - ε, x + ε), where ε > 0.

We can choose ε small enough such that (x - ε, x + ε) is completely contained within [a, b].

Now, since (x - ε, x + ε) is an open interval containing x, we need to show that there exists a point y in B such that y ≠ x and y ∈ (x - ε, x + ε).

Since (x - ε, x + ε) is contained within [a, b],

we have a ≤ x - ε < x < x + ε ≤ b.

Therefore, there exists a point y in [a, b] such that y ≠ x and y ∈ (x - ε, x + ε). This implies that x is a limit point of B.

2. Every limit point of B is in [a, b]:

Let y be an arbitrary limit point of B. We need to show that y is in [a, b], which means that a ≤ y ≤ b.

Suppose, for the sake of contradiction, that y < a or y > b. Without loss of generality, assume y < a. Since y is a limit point of B, every open interval (y - ε, y + ε) contains a point of B other than y itself.

Consider the open interval (y - ε, a), where ε = (a - y)/2. This interval does not contain any point of B other than y itself, which contradicts the assumption that y is a limit point of B.

Therefore, it must be the case that y ≥ a. Similarly, we can show that y ≤ b. Hence, y is in [a, b].

Combining both parts, we have shown that every point in [a, b] is a limit point of B, and every limit point of B is in [a, b]. Therefore, B' = [a, b].

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Since a negative number's exponent is always positive, [(-4)⁴]⁵ will always be greater than -[(4¹²)³].

What is number system?

The Number System covers any of the several sets of symbols and usage guidelines for indicating numbers, which are used to indicate how many items are present in a particular group. Thus, the Roman numeral I, the Greek letter alpha, the first letter used as a numeral, the Hebrew letter aleph, or the modern number 1, which is nothing more than Hindu-Arabic in origin, can all be used to express the idea of "oneness."

A mathematical representation of the numbers in a given set is called a number system.

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Answer:

100%

1.00

Step-by-step explanation:

53/53 is one whole piece so it would be 100% because it's like saying a box is 100% full or 53/53 not 48/53 percent full.

when the denominator and numerator are the same that is 1 and then add decimal and zeros after it so 1.00

Hope this helps!

Answer:150, 4

Step-by-step explanation:

904/6=150 and 4/6.

There are 3 mangoes left behind after making 39 trays of 9 mangoes each

To find out how many trays can be made from 354 mangoes, we divide the total number of mangoes by the number of mangoes per tray.

Number of mangoes per tray = 9

Number of trays = 354 mangoes / 9 mangoes per tray

Number of trays = 39 trays

So, 39 trays can be made from 354 mangoes.

To determine how many mangoes are left behind, we subtract the number of mangoes used for the trays from the total number of mangoes.

Number of mangoes left behind = Total number of mangoes - Number of mangoes used for trays

Number of mangoes left behind = 354 mangoes - (39 trays * 9 mangoes per tray)

Number of mangoes left behind = 354 mangoes - 351 mangoes

Number of mangoes left behind = 3 mangoes

Therefore, there are 3 mangoes left behind after making 39 trays of 9 mangoes each

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Answer:

r = \(\frac{l}{pt}\)

Step-by-step explanation:

Given

l = prt ( isolate r by dividing both sides by pt )

\(\frac{l}{pt}\) = r

Answer:

\( ST = 5\sqrt{2} \)

Step-by-step explanation:

Given:

S(-3, 10)

T(-2, 3)

Required:

ST

SOLUTION:

Use the distance formula, \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \), to find ST.

Where,

\( S(-3, 10) = (x_1, y_1) \)

\( T(-2, 3) = (x_2, y_2) \)

\( ST = \sqrt{(-2 -(-3))^2 + (3 - 10)^2} \)

\( ST = \sqrt{(1)^2 + (-7)^2} \)

\( = \sqrt{1 + 49} \)

\( = \sqrt{50} = \sqrt{25*2} \)

\( ST = 5\sqrt{2} \)

Answer:

50

Step-by-step explanation:

the answer is 50 becuz it is

Answer:

8 and 2?

Step-by-step explanation:

I mean it days it right there

Answer:

B.) 5%

Step-by-step explanation:

You'll need to multiply 0.05 by 100. Since 100 = 1, we are only multiplying by 1 and not changing the value of our number.

0.05 × 100 = 5

5/100 is 5 over 100 and means 5 per 100. 5 "per 100" means 5 "percent" or 5%

Therefore, 0.05 = 5%

I hope this helps! ^-^

Step-by-step explanation:

square of 5 is 25 and it divided by the cube root of 27 means 3

Now ,

#25÷3

= 8 [1] (•°• 3×8 = 24)

Here,

we got 1 as a reminder .

Hope it is helpful to you

✌️✌️✌️✌️✌️✌️✌️

The remainder will be 1.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The square of 5 is divided by the cube root of 27.

Now,

Since, The square of 5 is divided by the cube root of 27.

Hence, We get;

⇒ 5² / ∛27

⇒ 25 / 3

After divide we get;

 3   )  25  ( 8

         24

       --------

          1

Thus, The value of remainder = 1

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=================================================

Work Shown:

P( (A u B u C)' ) = 0.33

P(A u B u C) = 1 - P( (A u B u C)' )

P(A u B u C) = 1 - 0.33

P(A u B u C) = 0.67

--------

P(AuBuC) = P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = P(C) + 0.37

P(C) = 0.67 - 0.37

P(C) = 0.30

For more information, search out "inclusion-exclusion principle". Also feel free to ask me if you have any questions.

The probability that the largest of n random samples is greater than the population median M is bounded above by\(1 - F(M)^(n-1) \times F(X(n))\).

Assumptions about the population and the sampling method.

Let's assume that the population has a continuous probability distribution with a well-defined median, and that we are taking independent random samples from this population.

Let \(X1, X2, ..., Xn\) be the random samples that we take from the population, where n is the sample size.

Let M be the population median.

The probability that the largest of these random samples, denoted by X(n), is greater than M.

Cumulative distribution function (CDF) of the population distribution to calculate this probability.

The CDF gives the probability that a random variable takes on a value less than or equal to a given number.

Let F(x) be the CDF of the population distribution.

Then, the probability that X(n) is greater than M is:

\(P(X(n) > M) = 1 - P(X(n) < = M)\)

Since we are assuming that the samples are independent, the joint probability of the samples is the product of their individual probabilities:

\(P(X1 < = x1, X2 < = x2, ..., Xn < = xn) = P(X1 < = x1) \times P(X2 < = x2) \times ... \times P(Xn < = xn)\)

For any x <= M, we have:

\(P(Xi < = x) < = P(Xi < = M) for i = 1, 2, ..., n\)

Therefore,

\(P(X1 < = x, X2 < = x, ..., Xn < = x) < = P(X1 < = M, X2 < = M, ..., Xn < = M) = F(M)^n\)

Using the complement rule and the fact that the samples are identically distributed, we get:

\(P(X(n) > M) = 1 - P(X(n) < = M)\)

= \(1 - P(X1 < = M, X2 < = M, ..., X(n) < = M)\)

=\(1 - [P(X1 < = M) \times P(X2 < = M) \times ... \times P(X(n-1) < = M) \times P(X(n) < = M)]\)

\(< = 1 - F(M)^(n-1) \times F(X(n))\)

Probability depends on the sample size n and the distribution of the population.

If the population is symmetric around its median, the probability is 0.5 for any sample size.

As the sample size increases, the probability generally increases, but the rate of increase depends on the population distribution.

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Answer:

(222 - 6) + 12

Step-by-step explanation:

You put B and C as the same thing but the correct option is this because first you take away 6 (subtract 6) from the 222 marbles then you replace them with 12 (add 12).

Answer: I hope it helps :)

Step-by-step explanation:

1.

\(Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}\)

2.

\(Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23\)

3.

\(Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6\)

4.

\(Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}\)

5.

\(Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y\)

Answer:

p = 10

Step-by-step explanation:

4 ^ 10 x 4 ^ 5 = 4 ^ 10+5 = 4 ^ 15

p = 10

Answer:

B

Step-by-step explanation:

PLS GIVE BRAINLIEST

Answer:

B

Step-by-step explanation:

The triangle reflects over the y-axis ,which is the vertical line, and then has a translation 2 units down

To obtain exactly one Democrat in a committee of six Congressmen from a group of four Democrats and nine Republicans, you can use the combination formula. In this case, you will choose one Democrat from four, and five Republicans from nine.

The combination formula is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items you want to choose.
For one Democrat: C(4, 1) = 4! / (1!(4-1)!) = 4
For five Republicans: C(9, 5) = 9! / (5!(9-5)!) = 126
Now, multiply the results to get the total number of ways to form a committee with exactly one Democrat:
4 (Democrats) * 126 (Republicans) = 504 ways.

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Answer:

Step-by-step explanation:

88 / 184 ≈ 0.48

96 / 184 ≈ 0.52

104 / 166 ≈ 0.63

62 / 166 ≈ 0.37

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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The required probability is 1.500.

f(x)=\begin{cases}\frac{10}{(x+5)}&\text{for }x<-1\\0&\text{for }-1\leq x\leq 1\\\end{cases}

a) We know that \int_{-\infty}^{\infty}f(x)dx=1

Therefore, the integral will be evaluated in two parts.

Integrating from -\infty to -1 and integrating from 1 to \infty.

For x<-1, \int_{-\infty}^{-1}\frac{10}{(x+5)}dx=10[\ln|x+5|]_{-\infty}^{-1}=10\ln6

For 1\leq x\leq \infty, \int_{1}^{\infty}0dx=0

Now, the integral of f(x) is equal to the sum of these two integrals. \int_{-\infty}^{\infty}f(x)dx=10\ln6+0=10\ln6

So, 10\ln6=1

Dividing by 10, we get \ln6=\frac{1}{10} 6=\text{e}^{1/10}

Now, \int_{-\infty}^{\infty}f(x)dx=\int_{-\infty}^{-1}\frac{10}{(x+5)}dx+\int_{1}^{\infty}0dx=1

Hence, the given function is a valid density function.

b) The probability P(0< X\leq 1) is the area under the curve from 0 to 1.

Therefore, P(0< X\leq 1)=\int_{0}^{1}f(x)dx

For -1\leq x\leq 0, the function is 0.

Therefore, P(0< X\leq 1)=\int_{0}^{1}\frac{10}{(x+5)}dx=10[\ln|x+5|]_{0}^{1}=10\ln6-10\ln5=10\ln\frac{6}{5}

Therefore, P(0< X\leq 1)=10\ln\frac{6}{5}\approx1.500

Hence, the required probability is 1.500.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

$36.35

Step-by-step explanation:

First, add -20.85 to 15.50:

20.85+15.50=36.35

Next, check to see if your answer is right:

36.35-20.85=15.50

or

36.35-15.50=20.85

Bam

Answer:

Step-by-step explanation:

1. 4x-4\(\leq\)x+6/2

2. 4x\(\leq\)x+6/2+4

3. 4x\(\leq\)x+7

4. 3x/3\(\leq\)7/3

5. x\(\leq\)2 1/3 or x\(\leq\) 2.33333333333

The correct answer is the Beta-binomial model. Bayesian analysis is a statistical approach that incorporates prior knowledge or beliefs about a parameter of interest and updates it based on observed data using Bayes' theorem.

In the case of a binary choice, where the outcome can be either yes or no, Bayesian analysis seeks to estimate the probability of success (yes) based on available information.

The Beta-binomial model is a commonly used model in Bayesian analysis for binary data. It combines the Beta distribution, which represents the prior beliefs about the probability of success, with the binomial distribution, which describes the likelihood of observing a specific number of successes in a fixed number of trials.

The Beta distribution is a flexible distribution that is often used as a prior for modeling probabilities because of its ability to capture a wide range of shapes. The Beta distribution is characterized by two parameters, typically denoted as alpha and beta, which can be interpreted as the number of successes and failures, respectively, in the prior data.

The binomial distribution, on the other hand, describes the probability of observing a specific number of successes in a fixed number of independent trials. In the context of Bayesian analysis, the binomial distribution is used to model the likelihood of observing the data given the parameter of interest (probability of success).

By combining the prior information represented by the Beta distribution and the likelihood information represented by the binomial distribution, the Beta-binomial model allows for inference about the probability of success in a binary choice.

The other options mentioned, such as the Normal-normal model and the Gaussian model, are not typically used for binary data analysis. The Normal-normal model is more suitable for continuous data, where both the prior and likelihood distributions are assumed to follow Normal distributions. The Gaussian model is also suitable for continuous data, as it assumes that the data are normally distributed.

In summary, the Beta-binomial model is the appropriate model for Bayesian analysis of a binary choice because it effectively combines the Beta distribution as a prior with the binomial distribution as the likelihood, allowing for inference about the probability of success in the binary outcome.

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