Express x^2 - 5x + 8 in the form of (x - a)^2 + b where a and b are too heavy fractions

Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

By applying the binomial distribution formula, it can be concluded that the probability of seeing at least one albino squirrel is 0.095.

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!)   where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

If n is the number of the squirrel, p is the probability of seeing albino squirrels and q is the probability of seeing non-albino squirrels, then:

n = 10000

p = 1/100000

q = 1 - 1/100000 = 99999/100000

The probability of seeing at least one albino squirrel:

= P (X ≥ 1)

= 1 - P(X< 1)

= 1 - P(X=0)

= 1 - C(10000,0) * (1/10000)⁰ * (99999/100000)¹⁰⁰⁰⁰⁻⁰

= 1 - (1 * 1 * (99999/100000)¹⁰⁰⁰⁰)

= 1 - 0.904836

= 0. 095164

≈ 0.095

Thus the probability of seeing at least one albino squirrel is 0.095.

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The probability that Tom is selected as President is 1 in 10, or 0.1.

The probability of Tom being selected as President is 1 in 10, or 0.1. This is because there are 10 members in the club, and each selection is equally likely. Therefore, the chance of Tom being chosen as President is the same as any other member of the club. This means that there is a 1 in 10 chance of Tom being selected as President, or a 0.1 probability. This probability can also be expressed as a fraction: 1/10, which is the same as 0.1. To calculate the probability of any other selection, such as the Vice-President or Treasurer, the same method can be applied. The probability of any one member of the club being selected for any position is 1 in 10, or 0.1.

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Answer:

$698

Step-by-step explanation:

Given that :

Principal = $5600

Rate = 4.75%

Time = 3 years

Simple interest = principal * rate * time

Simple interest = $5600 * 0.0475 * 3

simple interest = $798

Answer:

Discontinuity at (1, 7), zero at (-4/3 , 0)

Step-by-step explanation:

\(3x^{2} + x - 4\) = (3x + 4)(x - 1) = 0

                        x = -4/3   or 1

But x = 1 makes f(x) undefined, so there is discontinuity at x = 1

and there is a zero at x = -4/3.

3x + 4 = 3(1) + 4 = 3 + 4 = 7

If you were to graph this function, then you would get the line y = 3x + 4 with a hole at (1, 7).   The line would cross the x-axis at (-4/3, 0) with discontinuity at (1, 7)

4 feet.

The length of the rope from the ground to the top of the tent is 4 feet.

To calculate this, subtract the distance from the tent to the ground (2 feet) from the height of the tent (6 feet), and you will get the length of the rope (4 feet).

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Make sure to adjust the folder structure according to your needs when testing the code.

Here is the implementation of the `create_folders` function that takes a nested 2D list of strings representing folder structure and creates the corresponding folder structure:

```python

import os

def create_folders(structure):

   for item in structure:

       if isinstance(item, str):

           # Create the folder

           os.makedirs(item, exist_ok=True)

       elif isinstance(item, list):

           # Recursively create subfolders

           folder_name = item[0]

           subfolders = item[1:]

           os.makedirs(folder_name, exist_ok=True)

           os.chdir(folder_name)

           create_folders(subfolders)

           os.chdir('..')

```

You can test the function by creating your own folder structure and calling the `create_folders` function with it. For example:

```python

structure = ['f1', ['subf11', 'subf12'], 'f2', ['subf21', 'subf22', 'subf23'], 'f3']

create_folders(structure)

```

This will create the following folder structure:

```

- f1

   - subf11

   - subf12

- f2

   - subf21

   - subf22

   - subf23

- f3

```

Make sure to adjust the folder structure according to your needs when testing the code.

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Answer:

The standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

Step-by-step explanation:

To find the standard deviation for the number of people with the genetic mutation in groups of 900, we can use the properties of the binomial distribution. The binomial distribution describes the number of successes (in this case, people with the genetic mutation) in a fixed number of independent Bernoulli trials (in this case, selecting people), each with the same probability of success.

In our case, we have:

n = 900 (number of trials, i.e., the number of people in each group)

p = 0.05 (probability of success, i.e., the probability of having the genetic mutation)

The mean (μ) and variance (σ²) of a binomial distribution can be calculated using the formulas:

μ = n * p

σ² = n * p * (1 - p)

We are interested in finding the standard deviation (σ), which is the square root of the variance:

σ = sqrt(σ²)

So, in our case:

σ = sqrt(900 * 0.05 * (1 - 0.05))

σ = sqrt(900 * 0.05 * 0.95)

σ ≈ sqrt(42.75)

σ ≈ 6.54

Thus, the standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

To find the standard deviation for the number of people with the genetic mutation in groups of 900, you can use the formula for the standard deviation of a binomial distribution:

σ = √(n * p * (1-p))

Here, n = 900 (number of people randomly selected), p = 0.05 (5% of the population has the genetic mutation).

σ = √(900 * 0.05 * (1 - 0.05))
σ = √(45 * 0.95)
σ ≈ 6.48

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

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Answer:11/96

Step-by-step explanation:

1-(1/3)=2/3=14/24

(2/3)-(1/8)=(14/24)-(3/24)=11/24

11/24 divided into 4 again is 11/96

If the teen's ages that participated in a run are  {16, 18, 15, 14, 17, 16, 17, 15, 17} , then the Interquartile Range of the teen's ages is  2 .

The Interquartile range(IQR) is defined as the difference between third quartile (Q₃) and first quartile (Q₁) .

A running club's coach recorded ages of the teen's that participated in a 5k run ,

the teen's ages are ⇒ {16, 18, 15, 14, 17, 16, 17, 15, 17}

we first arrange the data of teen's ages in the increasing order .

we get ,  {14 , 15 , 15 , 16 , 16 , 17 , 17 , 17 , 18 } .

So , the lower half will be = {14 , 15 , 15 , 16}

the first quartile (Q₁) = (15+15)/2 = 30/2 = 15 ,

the upper half of the data is = {17 , 17 , 17 , 18}

the third quartile (Q₃) = (17 + 17)/2 = 34/2 = 17 .

So , the inter quartile range is = Q₃ - Q₁

= 17 - 15

= 2 .

Therefore , the Interquartile range is = 2 .

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Answer:

the increase is by 2

Step-by-step explanation:

You can add 17 plus 2 or subtract 17 from 19.

Answer:

2?

Step-by-step explanation:

Hey there!

72 * 1/8 = 9

= 72/1 * 1/8

= 72(1) / 1(8)

= 72 / 8

= 72 ÷ 8

= 9

Thus, the answer could either be:

• 72/1 * 1/8

• 72 / 8

OR

• 72(1) / 1(8) (hence how we possibly received answer number 2)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Answer:

Associates=7

Partners=10

Step-by-step explanation:

Let the number of associates be x while partners be y. Since they are a total of 17 then

x+y=17

Therefore, x=17-y

Also considering the charges then

800x+1800y=23600

Subsituting x with 17-y then

800(17-y)+1800y=23600

13600-800y+1800y=23600

1000y=10000

Y=10

X=17-y=17-10=7

Answer:

24

Step-by-step explanation:

The range is the biggest number subtracted by the smallest number.

45-21=24

I hope this helped <3

Answer:

150

Step-by-step explanation:

The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

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Answer:

971

Step-by-step explanation:

use the pemdas method

On solving the provided question, we can say that - Jasmine receives 2 shares, or $10 (2 x $5)and Holly receives 4 shares at $5 each, for a total of $20.

A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. For instance, the ratio might be represented as 1:3 if there were 1 boy and 3 girls (for every boy he has 3 girls) 3/4 are girls, while 1/4 are boys. A part is a quantity, ratio of amount or size between two or more items.

$30 is the entire sum.

Gertie distributes $30 in a 2:4 ratio.

2 plus 4 equals 6, the total number of shares.

$30 divided by six equals $5 for each share.

Jasmine receives 2 shares, or $10 (2 x $5).

Holly receives 4 shares at $5 each, for a total of $20.

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a) For a spinner with equally sized sectors, the probability distribution is uniform, meaning each outcome has an equal probability. This can be represented graphically with a flat line.

b) Given Simon's probability of hitting a home run is 0.34 and assuming each attempt is independent, Simon's expected number of home runs can be calculated using the binomial distribution.

a) For a spinner with equal sectors, the probability distribution is uniform. Since each sector has an equal chance of being landed upon, the probability of each outcome is the same.

Let's assume there are n sectors on the spinner. The probability of each outcome is 1/n. To graph the results on a Cartesian plane, we can plot the outcomes on the x-axis and their corresponding probabilities on the y-axis.

Each outcome will have a height of 1/n, resulting in a constant horizontal line at that height across all outcomes.

b) If the probability of Simon hitting a home run is 0.34, and he is expected to bat n times, we can use the binomial distribution to determine the probability of Simon hitting a certain number of home runs.

The probability mass function (PMF) of the binomial distribution can be used to calculate these probabilities. Each outcome represents the number of successful home runs (k) out of the total number of trials (n). We can calculate the probability of each outcome using the formula

P(k) = (n choose k) \(* p^k * (1-p)^{n-k},\)

where p is the probability of success (0.34) and (n choose k) is the binomial coefficient. We can plot the outcomes on the x-axis and their corresponding probabilities on the y-axis to graph the binomial distribution.

The resulting graph will show the probabilities of different numbers of home runs for Simon.

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The equation is V(t) = 10 - 5t, where V is the company's value in millions of dollars and t is the number of years since 2005. It represents a linear relationship where the company's value decreases by $5 million per year.

The equation that gives the company's value V in terms of t is V(t) = 10 - 5t, where V is the company's value in millions of dollars and t is the number of years since 2005.

In this equation, the initial value of the company in 2005 is $10 million, represented by the constant term 10. The value decreases by $5 million per year, which is represented by the term -5t, where t represents the number of years since 2005. As each year passes, the value decreases by $5 million, resulting in a linear relationship between the company's value and the number of years.

By substituting different values of t into the equation, we can determine the company's value at any given year. For example, if we substitute t = 2 into the equation, we get V(2) = 10 - 5(2) = $0 million, indicating that the company's value has reached zero after 2 years.

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70.65 cubic inches of the treasure chest is taken up by the coins. Option B is the correct option.

What is π in math?

The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.

Given that the radius of a coin is 1.2 inches and the height of the coin is  0.0625 inches.

The shape of the coin is a cylindrical in shape.

The volume of a cylinder is ∏r²h, where r is the radius of the coin and h is the height.

The volume of a coin is 3.14×1.2²×0.0625 = 0.2826  in³.

The number of coins is 250.

Multiply 250 by 0.2826 in³ to find the volume of 250 coins:

250×0.2826 in³ = 70.65 in³

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Answer:

Step-by-step explanation:

2, 2, 3, 3, 6, 8, 8, 8

Mean: ( 2 + 2 + 3 + 3 + 6 + 8 + 8 + 8 ) ÷ 8 = 5

Median: ( 3 + 6 ) ÷ 2 = 4.5

Mode: 8

Range: 8 - 2 = 6

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Step-by-step explanation:

1 rose is $1.50

and you have$15

15/1.5=10

the number of rose you can buy is 10

Answer:

12

Step-by-step explanation:

In this situation, interval measurement is being employed as the measurement level.

As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.

Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.

For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.

Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.

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Answer:

1. 5/12

2. 3/8

3. 1/4

Step-by-step explanation:

The initial population size of the fish species in the lake is 440. The exponential function represents growth.

In the given exponential function, P(t) = 440\((1.33)^t\), the initial population size is the value of P(t) when t is 0. Plugging in t = 0, we have P(0) = 440\((1.33)^0\) = 440(1) = 440. Therefore, the initial population size is 440.

To determine whether the function represents growth or decay, we can examine the base of the exponent. In this case, the base is 1.33. Since 1.33 is greater than 1, raising it to higher powers will result in increasing population size. Therefore, the function represents growth.

In summary, the initial population size of the fish species in the lake is 440, and the exponential function represents growth as the population increases over time.

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Answer:

44

Step-by-step explanation:

75-31=44

Answer:

44 books

Step-by-step explanation:

75-31=44

simple math