Express 48 1/4 in simplest radical form.

In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).

The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.

Section formula is given as follows:

\((\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})\)

It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and   AP/PB = 3/2

Let the coordinates of the point P be (a, b).

By using section formula,

(a, b) = \((\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})\)

(a, b) =  \((\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )\)

(a, b) = \((\frac{18 - 4}{5} , \frac{3-8}{5})\)

(a, b) = \((14/5, -5/5)\)

(a, b) = \((14/5, -1)\)

Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).

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Answer: Domain is \([0,\infty)\) and range is [0,4000].

Step-by-step explanation:

It is given that, the set of ordered pairs (t,d), where

t = the time in seconds after  someone jumps out of a plane at  4000 meters to go skydiving

d = is the displacement above the  ground.

It means t is independent variable and it is represented on the x-axis.

d is dependent variable and it is represented on the y-axis.

We need to find the domain and Range.

Domain is the set of input values.

Here, input is time and time can not be negative.

Domain \(=0\leq t=[0,\infty)\)

Range is the set of output values.

Here, output is displacement above the  ground which can not be negative or more than 4000 meters.

Range \(=0\leq d\leq 4000=[0,4000]\)

Therefore, domain is \([0,\infty)\) and range is [0,4000].

Answer:

Step-by-step explanation:

Given:

N₀ = 298 pages

N = 20 pages

You can apply the formula:

Number of days

D = [N₀ / N] + 1 = [298 / 20 ] + 1 =

= [14.9] + 1 = 14 + 1 = 15 day,

where the square brackets are the integer part of the number

If a book has 298 pages, and I read 20 pages a day, then it will take 15 days to read the entire book.

Total pages in the book= 298

Total pages that I daily read= 20

Then it will take 15 days to read the entire book.

The formula for this problem:

The solution to this type of problem can be figured out with the help of unitary method.

20 pages of a book can be read in = 1 day

1 page of a book can be read in = 1/20 days

298 pages of a book can be read in = 1/20×298 days = 14.9 days

But days cannot be 14.9, so it will be 15 days which is the nearest value of 14.9.

15 days it will take to read the entire book.

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The number of days would be 10 and the maximum percent of the population infected would be 25.752%.

What are exponential functions?

The exponential function, denoted by \(e^x\), is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

\(p(t) = 7te^{-\frac{t}{10}}\)

percentage of infected people a maximum when p '(t) = 0

                    \(p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10\)

Hence percentage of infected people reaches a maximum after 10 days

maximum percent of the population infected = p(10)

    \(p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%\)

Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.

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Answer:

$4.53

Divide 18.12 by 4

Using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

Recall:

Given the trigonometry ratio of sin A = 3/5

Recall that, sin ∅ = opp/hyp (SOH)

Thus, this means that, in sin A = 3/5,

Thus, find the value of b by applying the Pythagorean theorem.

\(b = \sqrt{c^2 - a^2}\) (Pythagorean Theorem)

\(b = \sqrt{5^2 - 3^2}\\\\\mathbf{b = 4}\)

Therefore, using the trigonometry ratio and Pythagorean Theorem, the value of b in the triangle is: 4.

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The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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Answer:

ion kno

Step-by-step explanation:

Using the probability distribution The variance, σ² is 400.

Variance is the anticipated squared deviation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a set of numbers are from one another.

Descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling are just a few of the concepts that make use of variance. In the sciences, where statistical data analysis is common, variance is a crucial tool.

The variance, which is frequently represented by σ², is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself.

E(X) = ∑X P(X)

       = 2.52

E(X²)  = ∑X² P(X)    

         = 406.4

Variance, σ² = E(X²) - [E(X)]²

                     = 406.4 - 2.52²

                     = 400.496

                     ≈ 400

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To perform saturating arithmetic on unsigned 8-bit integers, we need to ensure that the result remains within the valid range of 0 to 255.

To calculate the sum of 151 and 214 using saturating arithmetic, follow these steps:

Add the two numbers:

151 + 214 = 365

Check if the result exceeds the maximum value of an 8-bit unsigned integer (255).

Since 365 is greater than 255, we need to saturate the result.

Set the result to the maximum value (255) to ensure it remains within the valid range.

Therefore, the result of 151 + 214 using saturating arithmetic is 255.

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Answer: angle x= 20 degrees

Step-by-step explanation: sum of angles in triangle is 180 degrees.

You count 2x + 3x +(x+60) = 180

6x=120

The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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Answer:

#1- definition #2

#2- definition #1

#3- definition #3

Step-by-step explanation:

Answer:

(x-2) (x+1) (x+4)

Step-by-step explanation:

x^3+3x^2-6x-8

Rearranging the terms,

(x^3 - 8) + (3x^2 - 6x)

a^3 - b^3 = (a-b) (a^2 + ab + b^2)

(x^3 - 8) = (x^3 - 2^3) = (x-2) (x^2 + 2x + 4)

(3x^2 - 6x) = 3x(x-2)

So, x^3 + 3x^2 -6x -8

= (x-2) (x^2 + 2x +4) + 3x(x-2)

(x-2) is the common factor,

= (x-2) ( x^2 +2x+4 + 3x)

= (x-2) (x^2 + 5x + 4)

= (x-2) (x^2 + 4x + x + 4)

= (x-2) (x(x+4) +1(x+4))

= (x-2) (x+1) (x+4)

Answer:

-4

Step-by-step explanation:

4+3+5/ 3-6

12/-3

-4

hope this helps

Approximately 1.023 x 10^12 ounces of soda were consumed in the US in 2010 altogether.

To answer this question, we need to multiply the number of people in the United States by the average amount of soda each person drank.

So, using scientific notation to simplify the calculation, we can write:
3.1 x 10^8 people x 3.3 x 10^3 ounces of soda =
(3.1 x 3.3) x (10^8 x 10^3) ounces of soda =
10.23 x 10^11 ounces of soda.
To convert this back to standard notation, we can write:
1.023 x 10^12 ounces of soda.

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The complete response x(t), with initial conditions and input, can derived using Laplace transform and inverse Laplace transform techniques.

To derive the complete response x(t), we first take the Laplace transform of the given differential equation, applying the initial conditions to obtain the transformed equation in the Laplace domain.

Next, we solve the transformed equation for the Laplace transform X(s) of x(t) using algebraic manipulations and inverse Laplace transforms

We consider the input u(t) = 5t, and take its Laplace transform U(s) to express it in the Laplace domain.

By substituting X(s) and U(s) into the transformed equation, we solve for X(s) to obtain the Laplace transform of the complete response.

Finally, we use inverse Laplace transform techniques to find the time-domain expression for x(t), the complete response of the system.

Sketching the response x(t) involves plotting the function x(t) with respect to time, considering the given initial conditions and input.

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The equation Ant can use to determine the total cost (y) for any large pizza, regardless of the number of toppings ordered (x), is y = 12 + 0.50x.

The equation is formed by considering the base cost of a large cheese pizza, which is $12. Each additional topping adds $0.50 to the total cost.

The variable x represents the number of toppings ordered, and y represents the total cost of the pizza. Multiplying the number of toppings (x) by the cost per topping ($0.50) gives the additional cost of the toppings.

By adding the base cost of the large cheese pizza ($12) to the additional cost of the toppings (0.50x), we obtain the equation y = 12 + 0.50x. This equation allows Ant to calculate the total cost for any large pizza based on the number of toppings chosen.

For example, if a customer orders 3 toppings, substituting x = 3 into the equation gives y = 12 + 0.50 * 3 = 12 + 1.50 = $13.50. Hence, the total cost for a large pizza with 3 toppings would be $13.50.

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The expression that gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours is option d: 20 - 20e^-0.5.

The rate of snowfall is given by the function r(t) = 2e^-0.1t inches per hour. To find the amount of snow that falls from time t = 0 to time t = 5 hours, we need to integrate the rate function with respect to time over this interval.

Integrating the function r(t) from 0 to 5 gives us ∫(0 to 5) 2e^-0.1t dt. This integration evaluates to 20 - 20e^-0.5.

Option d: 20 - 20e^-0.5 is the correct expression because it represents the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours. The constant term 20 represents the initial amount of snowfall at t = 0, and the exponential term accounts for the decrease in the rate of snowfall over time.

Therefore, the correct expression to calculate the amount of snowfall in this time interval is 20 - 20e^-0.5.

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A conclusion about the value of a population parameter based on information from the corresponding sample statistics and the associated the associated probability distributions.

Statistical inference is the process of making conclusions or inferences about the characteristics of a population based on information obtained from a sample.

It involves using statistical techniques to draw generalizations or estimates about population parameters using sample data.

A conclusion about the value of a population parameter based on information from the corresponding sample statistics and the associated the associated probability distributions.

Statistical inference involves two main components:

1. Estimation: Estimation involves using sample data to estimate or approximate the value of a population parameter.

2. Hypothesis Testing: Hypothesis testing is used to make decisions or draw conclusions about the population based on sample data.

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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Answer:

Step-by-step explanation:

recall that rate of change is the slope of a line,   this also  is called a derivative ,  for later in calculus.  :P

given

Point 1  =  p1= (0 , -4)

Point 2 = p2 = (2 , 2 )

slope = m

m = (2-(-4)) / (2-0)

note that this question is aimed at messing you up by putting in the extra negative.  so it's always important to use the brackets, like i've done, to keep that correct

m = (2+4) / 2

m = 6/2

m = 3

slope is 3

Answer:

B

Step-by-step explanation:

Because if you multiply the fractions by 6, the denominator would be a multiple.

For example, 2/3y x6/1= 12/3y= 4y

The two negatives cancel out when we divide or multiply. Think of negative as opposite. Having two opposites cancel.

The slash means fraction and it also means division

6/7 = 6 divided by 7

6/7 = six sevenths

So that allows us to go from fraction to decimal form 6/7 = 0.857 approximately after using your calculator or long division.

Answer:

$125.00

Step-by-step explanation:

4 walls (2 at 18 foot and 2 at 15 foot). height of each wall = 10 foot.

total area of 2 wide walls = 2 (10 X 15) = 300 square foot.

total area of 2 long walls = 2 (10 X 18) = 360 square foot.

area of ceiling = 18 X 15 = 270 square foot.

total area = 930 square foot.

200 square foot for one gallon of paint.

she will need 930/200 = 4.65 tins of paint = 5 tins.

one tin costs $25.

she will have to budget 5 X 25 = $125.00  

The statement is generally true.

In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.

In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.

This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.

In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.

However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.

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Answer:

If you have a calculator with a "Y^X" function, you can raise 27 to the (1/3) power to get the cube root. Or, take the logarithm of 27, divide it by 3, and then find the anti log. That is, find the base 10 log of 27, divide it by three, and then compute 10 ^ that number. (Or of course you can use the base e log and raise e to the number.)

If you are willing to get into complex numbers, you can find that there are actually three cube roots of 27. One of them is 3. To find the other two, use de Moivre's formula (from Wikipedia):

If z is a complex number, written in polar form as

then the n nth roots of z are given by

where k varies over the integer values from 0 to n − 1.

This formula is also sometimes known as de Moivre's formula.

This leads to the two complex roots,

3 x ( (cos 120 degrees) + i x sin(120 degrees) ) and

3 x ( (cos 240 degrees) + i x sin(240 degrees) ).

These work out to be approximately:

3 x (-0.5 + i x 0.866) and

3 x (-0.5 - i x 0.866).

Step-by-step explanation:

The number of bricks needed to cover the patio is approximately 1811 bricks.

To find the number of bricks needed for the patio in the English system, we follow these steps:

Step 1: Find the total width and length of the patio in inches.

Convert the width and length in meters to inches:

Width: 5 m = 5 x 39.37 = 196.85 in.

Length: 6 m = 6 x 39.37 = 236.22 in.

Add these values to the portion of the width and length of the patio expressed in inches to find totals:

Total width: 196.85 in. + 16 in. = 212.85 in.

Total length: 236.22 in. + 19 in. = 255.22 in.

Step 2: Find the area of each brick in square inches.

Multiply its width by its length:

Brick area: 3.75 in. x 8 in. = 30 in².

Step 3: Find the number of bricks needed by dividing the patio area by the brick area (round up to the nearest whole brick):

Patio area: 212.85 in. x 255.22 in. = 54,318.837 in².

Number of bricks needed: 54,318.837 in² / 30 in² ≈ 1810.63 bricks.

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Answer:

B

Step-by-step explanation:

using the rule of radicals

\(\sqrt{\frac{a}{b} }\) × \(\sqrt{\frac{c}{d} }\) = \(\sqrt{\frac{ab}{cd} }\) , then

\(\sqrt{\frac{3x}{2} }\) × \(\sqrt{\frac{x}{6} }\)

= \(\sqrt{\frac{3x^2}{12} }\)

= \(\sqrt{\frac{3x^2}{3(4)} }\)

= \(\sqrt{\frac{x^2}{4} }\)

= \(\frac{\sqrt{x^2} }{\sqrt{4} }\)

= \(\frac{x}{2}\)