Kevin is 3 years older than twice Jane's age. The sum of their ages is 39. How old is each person?

The probability of the message being "hi" given the ciphertext "st" is 0.

Consider a shift cipher with three possible messages, with a distribution of probabilities. The three possible messages are as follows:

Pr[M=‘hi’] = 0.3,

Pr[M=‘no’] = 0.2, and

Pr[M=’in’] = 0.5.

To solve this problem, we can use Bayes' theorem. We want to find the probability of the message being "hi" given the ciphertext "st".

Using Bayes' theorem, we have:

Pr[M=‘hi’ | C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] / Pr[C=‘st’]

We can break this down into three parts:

Pr[C=‘st’ | M=‘hi’]:

This is the probability that the ciphertext is "st" given that the message is "hi".

To find this probability, we need to encrypt the message "hi" using the shift cipher. If we shift each letter in "hi" by one (i.e., a becomes b, h becomes i, and i becomes j), we get the ciphertext "ij". Since "ij" does not contain the letter "s", we know that Pr[C=‘st’ | M=‘hi’] = 0.Pr[M=‘hi’]:

This is the probability of the message "hi", which is given as 0.3.Pr[C=‘st’]:

This is the probability of the ciphertext "st". We can find this probability by considering all the possible messages that could have been encrypted to produce "st".

There are three possible messages: "hi", "no", and "in". To encrypt "hi" to "st", we need to shift each letter in "hi" by two (i.e., a becomes c, h becomes j, and i becomes k). This gives us the ciphertext "jk".

To encrypt "no" to "st", we need to shift each letter in "no" by five (i.e., n becomes s and o becomes t). This gives us the ciphertext "st". To encrypt "in" to "st", we need to shift each letter in "in" by three (i.e., i becomes l and n becomes q). This does not give us the ciphertext "st", so we can ignore it.

Therefore, Pr[C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] + Pr[C=‘st’ | M=‘no’] * Pr[M=‘no’] = 0 + 0.2 * 1 = 0.2

Now we can plug in the values we have found:

Pr[M=‘hi’ | C=‘st’] = 0 * 0.3 / 0.2 = 0

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to get the equation of any straight line, we simply need two points off of it, let's use those points from the picture below.

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{4 +2}{3 -1} \implies \cfrac{ 6 }{ 2 }\implies 3\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \implies y +2= 3 (x -1) \\\\\\ y+2=3x-3\implies {\LARGE \begin{array}{llll} y=3x\underset{(0~~,~~-5)}{\stackrel{\stackrel{y-intercept}{\downarrow }}{-5}} \end{array}}\)

Answer:

A

Step-by-step explanation:

Answer:

3/5 of a foot

Step-by-step explanation:

1/5+2/5=3/5

Answer: The answer is where the n is the number of people in the club

Step-by-step explanation:

A)Write down an expression, in terms of n, for the number of people in the club.

B) Two of the people in the club are chosen at random. The probability that both these people are men is one tenth. Calculate the number of people in the club.

Answer:

b and d

Step-by-step explanation:

2(5x+2+x)=12x+4(b)

2(6x+2)=12x+4

First, solve the expression.

2(5x+2+x)

10x+4+2x

12x+4

So we know that one of the answers is B. and not A.

C. 2(5x+3)

10x+6

D. 2(6x+2)

12x+4

So the answers are B and D, or option B

---

hope it helps

Answer:

B=28

Step-by-step explanation:

The kind of sample that is described in the scenario is a lottery sample.

The lottery sample is the kind of sample that is described in the scenario in which 500 people attend a charity event, and each of them buys a raffle ticket.

The ticket stubs are placed in a drum and mixed thoroughly, and out of them, a few are drawn.

People whose tickets are drawn are declared winners of a prize. It is a type of probability sampling that depends on the element of chance.

In this type of sample, the probability of selecting an element is unknown and cannot be measured. I

t is a random process in which the probability of winning or being selected for the sample is entirely based on chance.

Hence, the lottery sampling technique is the appropriate one in the scenario.

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The estimation of cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2 is approximately 0.03490, rounded to five decimal places.

The 3rd degree "Taylor-polynomial" for the function cos(x) centered at a = π/2 is :

cos(x) = -(x - π/2) + (1/6)(x - π/2)³ + R₃(x),

We first convert the value of 88 degree to radians,

we get that 88° = (22/45)π,

So, we substitute this in the function above,

We get,

Cos(88°) = -((22/45)π - π/2) + (1/6)((22/45)π - π/2)³

Cos(88°) = 0.034899496

Cos(88°) ≈ 0.03490,

Therefore, the estimate of Cos(88°) is 0.03490.

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The given question is incomplete, the complete question is

The 3rd degree Taylor polynomial for cos(x) centered at a = π/2 is given by, cos(x) = -(x - π/2) + (1/6)(x - π/2)³ + R₃(x).

Using this, estimate cos(88°) correct to five decimal places

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

78

Step-by-step explanation:

add them all

Answer:16

Step-by-step explanation:

The statements "D1 = 5 is independent of D1 + Dz = 10" and "D1 = 6 is independent of Dz = 6" are true.

In the context of rolling two dice, independence refers to the outcome of one die not affecting the outcome of the other die. Let's analyze each statement to determine their truth.

"D1 = 5 is independent of D1 + Dz = 10"

Here, we are checking whether the event of the first die showing a 5 is independent of the event of the sum of the two dice being 10. These events are independent because the outcome of the first die does not impact the sum of the two dice. Regardless of whether the first die shows a 5 or any other number, the sum of the two dice could still be 10. Therefore, this statement is true.

"D1 = 6 is independent of Dz = 6"

This statement explores the independence between the first die showing a 6 and the second die also showing a 6. In this case, the events are independent since the outcome of the first die does not influence the outcome of the second die. The second die can show a 6 regardless of whether the first die shows a 6 or any other number. Hence, this statement is also true.

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The equation to determine the price of a pizza for a given number of toppings could be represented as follows: Price = Base Price + (Price per Topping x Number of Toppings)

Let's assume the base price of a medium pizza is $10, and the price per topping is $1. If you order your favorite medium pizza with, let's say, 3 toppings, we can calculate the expected price using the equation: Price = $10 + ($1 x 3) = $10 + $3 = $13. Therefore, you would expect to spend $13 for your favorite medium pizza with 3 toppings.

The equation allows for flexibility in pricing based on the number of toppings chosen. Each additional topping incurs an extra cost, which is added to the base price of the pizza. This pricing model enables customers to customize their pizza according to their preferences and budget, as they can choose the number of toppings they desire while knowing the corresponding price.

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The given surface is given by the relation,

xy²z=x²y−xz²+2yz

Let f(x,y,z) = xy²z - x²y + xz² - 2yz

                 = 0

The partial derivative of x with respect to y is given by;

∂x/∂y  = (- ∂f/∂y) / (∂f/∂x)

Let us first find the partial derivative of f with respect to x;

∂f/∂x = y²z - 2xy + z² ....(i)

Now, we will find the partial derivative of f with respect to y;

∂f/∂y = xz - 2x - 2z

        = z(x - 2) - 2x ....(ii)

∂x/∂y = (- ∂f/∂y) / (∂f/∂x)

         = [-{z(x-2) - 2x}] / {y²z - 2xy + z²}

After simplification, we get

∂x/∂y = [2x - z(x-2)] / {2xy - y²z - z²}

In Mathematics, partial differentiation is used to calculate the rate of change of a function concerning a particular variable, keeping all other independent variables constant. The partial derivative of x with respect to y is denoted as ∂x/∂y. It is essential to calculate partial derivatives to study the slope of a surface on a plane that is tangent to the surface at a given point.

The given surface is given by the relation, xy²z=x²y−xz²+2yz.

Let f(x,y,z) = xy²z - x²y + xz² - 2yz

                  = 0.

Now we have to find the partial derivative of x with respect to y.

We will first find the partial derivative of f with respect to x which is y²z - 2xy + z².

We can calculate the partial derivative of f with respect to y by differentiating the given function with respect to y and keeping the other variables constant.

We get ∂f/∂y = xz - 2x - 2z

                     = z(x - 2) - 2x.

The partial derivative of x with respect to y is given by ∂x/∂y = [-{z(x-2) - 2x}] / {y²z - 2xy + z²}.

After simplification, we get ∂x/∂y = [2x - z(x-2)] / {2xy - y²z - z²}.

The partial derivative of x with respect to y for the given surface is ∂x/∂y = [2x - z(x-2)] / {2xy - y²z - z²}.

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The matrix a is given such that a² - 3a - 2I = 0. It is shown that ai is invertible, and its inverse is  (1/2)(a_i - 3i).

Given: a² - 3a = 2i

Multiplying both sides by a⁻¹, we get

a - 3i = 2a⁻¹

Rearranging, we get

a⁻¹ = (1/2)(a - 3i)

Now, we need to show that a_i is invertible, i.e., we need to find (a_i)⁻¹.

We know that

(a_i)² - 3(a_i) = a

Multiplying both sides by a_i⁻¹, we get

a_i - 3i = a_i⁻¹ * a

Rearranging, we get

a_i⁻¹ = (1/2)(a_i - 3i)

Therefore, (a_i)⁻¹ exists and is given by (1/2)(a_i - 3i).

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Answer:

Correct answer is

\(165 {c}^{6} {b}^{6} \)

Answer:

{-1, 3, 7, 11, 15}

Step-by-step explanation:

we just substitute the set of even numbers in the function f(x) given to get our corresponding set of odds numbers

for 0

2(0)-1=0-1=-1

for 2

2(2)-1=4-1=3

for 4

2(4)-1=8-1=7

for 6

2(6)-1=12-1=11

for 8

2(8)-1=16-1=15

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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The quotient of 462 and 28 is 16.5 when written in decimal notation.

To calculate this, you divide 462 by 28:

462 ÷ 28 ≈ 16.5

The division process involves dividing the digits of the dividend (462) by the divisor (28) and obtaining the result. In this case, the result is approximately 16.5. The decimal point is placed after the digit 5, indicating the presence of a fractional part.

Please note that this is an approximation because the exact result would involve an infinite decimal expansion, which is typically rounded to a certain number of decimal places for practical purposes.

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Answer:

I love it when you think I will answer with 0oop

Answer:

32 is the final answer

Step-by-step explanation:

(-18 )+ 58 = 40

(-3 + 5) × -4

2 × -4 = -8

40 - (-8) = 32

Answer:

  $918.86

Step-by-step explanation:

You want the value of an account in which $800 is invested for 5 years earning interest of 2.78% compounded quarterly.

The account value is given by the formula ...

  A = P(1 +r/n)^(nt)

where P is the principal amount, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

  A = $800(1 +0.0278/4)^(4·5) ≈ $918.86

The value of the account after 5 years is $918.86.

Answer:

-5x+20

Step-by-step explanation:

Distribute the -5: -5(x) and -5(-4)

-5x+20

Since you cannot combine like terms, this is your final answer

Answer:

-5 × 4x = -20x

Step by Step Explanation:

Start with parenthesis

x - 4 = 4x

Multiply

-5 × 4x = -20x

Answer:

y' = (-3,6) z'= (1'-3)

Step-by-step explanation:

above

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

The probability is 0.5 tiles will be green

Step-by-step explanation:

Hope this helps