A scientist is measuring the temperature change in a decimal compound. The temperature dropped 11 f per hour from the original temperature. After four hours the temperature was 90 f find the compounds original temperature.

The domain of the given graph is (-4,4]

The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values.

"All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

Hence from the graph we get the domain as   (-4,4]

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Answer:

200

Step-by-step explanation:

20x for x=10

you are replacing the x for 10 which would be

20 x 10 = 200

x=1/2

Step-by-step explanation:

To find x, you divide both sides by the coefficient of x which is 20 so when you divide 10 by 20 it gives you 1/2

Answer:

the amount he gave his friend is a positive fraction, therefore to the right of 0 on the number line. the decimal is 3/8 which = 0.375

To solve the question:

9a x 3 + 8a + 4 -11a

First we will apply the rule of BODMAS

By applying the rules, we will first multiply before adding or subtracting

27a + 8a + 4 - 11a

Then we re-arrange after multiplying

27a + 8a -11a + 4

we will add all the numbers with "a" variable

24a + 4

Answer:

44

Step-by-step explanation:

33:11 = 132:44

Answer:

24 and 135

Step-by-step explanation:

let x and y represent the numbers

x=15+5y

x-y=111

making x the subject in equation 2

x=111+y put into eqn 1

111+y=15+5y

-4y=-96 y=24

x=15+5(24)

x=135

Numbers which represents the given condition are \(24\)and \(135\).

" Number is defined as the count of the given quantity as per the given condition."

According to the question,

\('x'\) represents the first number

As per the condition we have,

Second number \(= 5x + 15\)

Substitute the numbers in the given condition we get,

\(5x+15-x=111\)

Simplify it to get the value of \('x'\)

\(4x + 15 = 111\\\\\implies 4x = 96\\\\\implies x = 24\)

Substitute the value of \('x'\) to get second number,

\(5 (24) +15\\\\= 135\)

Hence , numbers which represents the given condition are \(24\)and \(135\).

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False. When multiple people access the same access point (AP), the communication to the wired world is not limited to approximately 1 Mbps per user.

The available bandwidth is shared among the users connected to the AP, but the exact speed each user experiences depends on various factors such as the total bandwidth provided by the AP, the number of users actively utilizing the network, and the nature of their online activities.

The speed experienced by each user can fluctuate depending on network congestion and the type of traffic being generated. For example, if all users are engaging in bandwidth-intensive activities like streaming high-definition videos or downloading large files simultaneously, it can impact the overall network performance, resulting in slower speeds for each individual user. However, if the network is underutilized or the users are engaged in less demanding tasks, each user may experience higher speeds closer to the maximum capacity provided by the AP.

Therefore, the statement that communication to the wired world is limited to approximately 1 Mbps per user when ten people access the same AP is false. The actual speed experienced by each user will depend on various factors and can vary significantly.

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Value of t0 for option a is ±1.895 and for option, b is 1.895 using symmetric and complement properties respectively.

Given  that t follows a t7 distribution let's understand what is t7 distribution

The t distribution (Student's t-distribution) is a "probability distribution used to estimate population parameters when the sample size is small (n<30) or the population variance is unknown".

The t-distribution describes a set of observations in which the majority of observations fall close to the mean and the remainder of the observations form the tails on either side. It is a type of normal distribution that is used for smaller sample sizes when the data variance is unknown.

The degrees of freedom of the t distribution determine its shape, and as the degrees of freedom increase, the t distribution approximates a normal distribution.

The degrees of freedom stand for "the number of distinct observations in a set of data. If we estimate a mean score from a single sample, for example, the number of independent observations is equal to the sample size minus one."

P(|t|<\(t_{0}\)) = 0.9

We can rewrite the expression using absolute value properties as follows:

P(-\(t_{0}\)<\(t_{7}\)<\(t_{0}\)) = 0.9

Using symmetric property we can write

1-2P(t7 < -t0) = 0.9

0.1 = 2P(t7 < -t0)

P(t7 < -t0) = 0.05

And we can find the value by typing "=T.INV(0.05,7)" into Excel.

So, in this case, the answer is t0 = ±1.895

for part B we have p(t>t0) = 0.05 for this we have to use complement rule

1- p(t7<t0) = 0.05

p(t7<t0) = 1 - 0.05  

p(t7<t0) = 0.95

And we can find the value by typing "=T.INV(0.95,7)" into Excel.

So, in this case, the answer is t0 = 1.895

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Answer:

El procedimiento para hallar el MCD de 12, 20, 36:Descomponer los números en su factores primos

12 2 6 2 3 3 1

   20 2 10 2 5 5 1

 36 2 18 2 9 3 3 31

Factores primos de 12 = 22 . 3

Factores primos de 20 = 22 . 5

Factores primos de 36 = 22.32

MCD = 21 = 2

Step-by-step explanation:

Neville's method is a mathematical technique used for polynomial interpolation and approximation. It was developed by Edward Neville in the early 20th century as an alternative to the Lagrange interpolation method.

Neville's method offers several advantages. Firstly, it provides a straightforward and efficient way to interpolate data points and approximate functions using a polynomial. It avoids the need to explicitly construct the Lagrange polynomial, which can be computationally expensive for large data sets. Additionally, Neville's method allows for the interpolation of data points at arbitrary locations within the given range, making it a flexible interpolation technique.

When comparing Neville's method with the Lagrange interpolation polynomial, both techniques aim to approximate a function using a polynomial. However, the main difference lies in the construction of the interpolating polynomial. While the Lagrange method constructs a single polynomial that passes through all the given data points, Neville's method constructs a table of polynomials. This table allows for the calculation of intermediate polynomial values at any desired point, providing a more efficient way to interpolate and approximate functions.

To approximate √3 using Neville's method with the given data points (Xo = -2, x₁ = -1, x₂ = 0, x₃ = 1, and x₄ = 2) and f(x) = 3, we can follow the steps of Neville's algorithm. By constructing the Neville's table and evaluating it at x = 3, we obtain the approximation for √3.

To determine the exact error of the approximation, we compare the obtained approximation to the actual value of √3. The difference between the two values provides an indication of the accuracy of Neville's method in this specific case.

References:

Neville's Algorithm for Polynomial Interpolation. Retrieved from [insert reference here].

Neville's Method: An Overview. Retrieved from [insert reference here].

Numerical Analysis - Mathematics of Scientific Computing (Chapter 3). Retrieved from [insert reference here].

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The probability of getting 15 or more heads is :

P (Z > -0.18) = 1 - 0.4289 =  0.5714

Now, According to the question:

Normal Approximation to Binomial:

The normal distribution is used to approximate for the binomial distribution. The condition when binomial distribution is approximated to normal is that n should be large and probability should be close to 0.5

"Information available from the question"

n = 30

Probability, p(heads) = 1/2

Since sample size is large, we check for normal approximation.

np = 30(1/2) = 15

and, n(1 - p) = 30(1 - (1/2)) = 15 both are greater than 5, we use normal approximation.

Mean, μ = np = 30(1/2) = 15

Standard deviation, σ = \(\sqrt{np(1-p)}\)

Standard deviation, σ = \(\sqrt{30(1/2)(1-1/2)}\)

Standard deviation, σ =2.739

We have to find P (X ≥ 15). Using continuity correction, we deduct 0.5

P(X ≥ 15) = P(X > 14.5)

The respective Z-score with X = 14.5 is

Z = (x - μ)/ σ

Z = (14.5 - 15)/2.739

Z = -0.18

Now, we use z-tables to find probability greater than -0.18

P (Z > -0.18) = 1 - 0.4289 =  0.5714

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The correct answer is (b) The probability is less than 0.5.

The odds of an event occurring are defined as the ratio of the probability of the event happening to the probability of the event not happening. If the odds of an event occurring are less than 1, it means that the probability of the event happening is less than the probability of the event not happening.

Since the probability of an event happening is always between 0 and 1, and the odds are less than 1, it implies that the probability is less than 0.5.

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Answer:

Variable: b

Equation: $12b + $16 = $112

Solution: 8 books

Step-by-step explanation:

$12b + $16 = $112

$12b + $16 - $16 = $112 - $16

$12b = $96

$12b ÷ $12 = $96 ÷ $12

b = 8

Hope that helps.

Answer:

9 and 5 I guess enjoy.

.

Step-by-step explanation:

and yeah no explanation

Step-by-step explanation:

Analytical Geometry if AB and CD are parallel they use the FUN method to calculate which means the angles are the same.

Answer:

$36.75

Step-by-step explanation:

The sales tax rate = 5 = 0.05  [Divide by 100 to convert in decimal]

The cost of a pair of shoes = $35.00

Tax amount to pay = Tax rate × Cost of a pair of shoes

5% of 35 = 1.75

35 + 5% = $36.75

The characters in the trailer would need to reach an initial velocity of at least 13.4 m/s in order to safely jump the crevice and escape the displacer beast.

In one of the trailers, the characters narrowly escape the displacer beast by jumping over a crevice. To calculate the minimum velocity required for the jump, we can use the equation for the distance of an object thrown vertically upwards:

v1 = √(2gh)

where v1 is the initial velocity, g is the acceleration due to gravity (9.81 m/s2), and h is the height of the crevice.

For example, if the crevice is 6 meters deep, the required initial velocity to safely jump over it would be:

v1 = √(2 * 9.81 * 6)

v1 = 13.4 m/s

Therefore, the characters in the trailer would need to reach an initial velocity of at least 13.4 m/s in order to safely jump the crevice and escape the displacer beast.

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Complete question:

How do you calculate the minimum velocity required to jump over a crevice to escape a displacer beast?

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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a.

= (5x)² - 3 = 25x² - 3

- 5f(x) = 5(x² - 3) = 5x² - 15

b.

- f(x - 2) = (x - 2)² - 3 = x² - 4x + 1

- f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

a. To calculate f(5x), we substitute 5x into the function f(x) and simplify the expression.

  f(5x) = (5x)² - 3 = 25x² - 3

  To calculate 5f(x), we multiply the function f(x) by 5.

  5f(x) = 5(x² - 3) = 5x² - 15

b. To calculate f(x - 2), we substitute (x - 2) into the function f(x) and simplify the expression.

  f(x - 2) = (x - 2)² - 3 = x² - 4x + 4 - 3 = x² - 4x + 1

  To calculate f(x) - f(2), we evaluate f(x) and f(2) separately and then find their difference.

  f(x) = x² - 3

  f(2) = 2² - 3 = 4 - 3 = 1

  f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

For the difference quotient of f(x) = -7x² - 5x + 9, we can calculate it as follows:

Difference quotient = [f(x + h) - f(x)] / h

Expanding the function and substituting into the difference quotient formula, we have:

[f(x + h) - f(x)] / h = [-7(x + h)² - 5(x + h) + 9 - (-7x² - 5x + 9)] / h

Simplifying and expanding further:

= [-7(x² + 2hx + h²) - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-7x² - 14hx - 7h² - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-14hx - 7h² - 5h] / h

= -14x - 7h - 5

The difference quotient of f(x) = -7x² - 5x + 9 is -14x - 7h - 5.

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Step-by-step explanation:

....................

Answer:

Follows are the solution to the given points:

Step-by-step explanation:\(a) \ \ (-5)^4 = -5 \times -5 \times -5 \times -5 =-625 \\\\ b) \ \ (+2)^6= 2 \times2 \times2 \times2 \times2 \times2 =64 \\\\ c)\ \ (+12)^2 = 12 \times 12 = 144 \\\\ d)\ \ (+15)^1= 15 \\\\ e)\ \ (-1)^{20} = -1 \times -1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1 \times-1\times-1= 1\)

\(\\\\ f) \ \ (-4)^5 =-4 \times -4 \times-4 \times-4 \times-4 =-1024\\\\ g)\ \ (-15)^0= 1 \\\\ h) \ \ (-2)^7= -2 \times-2 \times-2 \times-2 \times-2 \times-2 \times-2 =-128 \\\\ i) \ \ (+15)^{0}=1 \\\\ j)\ \ (+15)^1 =15\\\\ k)\ \ (+15)^2 = 15 \times 15=225\\\\ l)\ \ (-15)^2= -15 \times -15=225\)

The Volume percentage of the solution which is 1 cup of sugar to 2 quarts of water is 15.15%.

⇒The volume percentage of the solution,

               = Volume of solute / Volume of Solution × 100%       →  1

As per the question,

Substitute the values in 1,

Volume percentage of the solution   =   Volume of solute / Volume of

                                                                  Solution ×  100%

                                                             =   ( 50 / 330 ) × 100

                                                             =   0.1515 × 100

Volume percentage of the solution   =   15.15%

Therefore, 15.15% is the volume percentage of this solution.

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Answer:

\(19.79 - 2.8 = 16.99gallons\)

It will take Paris two hours to catch up with Helen.

Suppose Paris catches up with Helen after x hours, and in that time Paris travels d kilometers. Then, since Helen has a 4-km head start, Helen travels d + 4 kilometers in x hours. We can write a distance formula for each person as follows:

Distance covered by Helen = 6x + 4 (since Helen is traveling at 6 kph)

Distance covered by Paris = 8x (since Paris is traveling at 8 kph)

Since they will be at the same distance when Paris catches Helen, we can set both these equations equal. Solving for x, we get:

6x + 4 = 8x

2x = 4

x = 2

We can also verify our answer by finding the distance they each travel over the two hours. Since Paris is traveling at 8 kph for two hours, he will travel a distance of 16 km. Since Helen has a 4-km head start and is traveling at 6 kph for two hours, she will travel a distance of (6 x 2) + 4 = 16 km. This confirms that Paris has caught up with Helen after two hours.

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The tension in the string when the balloon is at equilibrium, we need to consider the forces acting on the balloon. The buoyant force, gravitational force, and tension in the string contribute to the equilibrium. By balancing these forces, we can find the tension in the string.

1. Start by calculating the volume of the balloon using the given radius. The volume of a sphere is given by V = (4/3)πr^3.

2. Substitute the radius value into the equation to find the volume of the balloon.

3. Calculate the weight of the displaced air. The weight of the displaced air is equal to the density of air times the volume of the balloon times the acceleration due to gravity.

4. Calculate the buoyant force. The buoyant force is equal to the weight of the displaced air.

5. Determine the net force acting on the balloon. The net force is the difference between the buoyant force and the weight of the balloon (mass of the skin times the acceleration due to gravity).

6. At equilibrium, the net force is zero. Therefore, the tension in the string must be equal to the net force.

7. Solve for the tension in the string by setting the net force equal to zero and rearranging the equation.

8. Substitute the given values for the density of air, density of helium, mass of the skin, and acceleration due to gravity into the equation to find the tension in the string.

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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