Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer:

15 percent

Step-by-step explanation: You will substract the new value from the old value.

23-20

Now you will get the difference between them and divide that by the original amount.

3/20

This will equal 0.15 in which you now multiply by 100

15 percent

\((\stackrel{x_1}{5}~,~\stackrel{y_1}{9})~\hfill \stackrel{slope}{m}\implies 2 ~\hfill \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{2}(x-\stackrel{x_1}{5})\)

Answer:

\( \boxed{\sf Length \ of \ the \ rectangle = 16 \ in} \)

Given:

Perimeter of rectangle = 48 in

Length = Twice the width

To Find:

Length of the rectangle

Step-by-step explanation:

Let width of the rectangle be 'w'.

So,

Length of the rectangle = 2w

\(\sf \implies Perimeter \ of \ rectangle = 2(Length + Width \\ \\ \sf \implies 48 = 2(2w + w) \\ \\ \sf \implies 48 = 2(3w) \\ \\ \sf \implies 48 = 6w \\ \\ \sf \implies 6w = 48 \\ \\ \sf \implies \frac{ \cancel{6}w}{ \cancel{6}} = \frac{48}{6} \\ \\ \sf \implies w = \frac{48}{6} \\ \\ \sf \implies w = \frac{8 \times \cancel{6}}{ \cancel{6}} \\ \\ \sf \implies w = 8 \: in\)

Width of the rectangle (w) = 8 in

Length of the rectangle = 2w

= 2 × 8

= 16 in

The code opens the file "paragraph.txt" in read mode, reads its contents using the `read()` method, and assigns the result to the `paragraph` variable. ```python

paragraph = open("paragraph.txt", "r").read()

```

Problem 1: To solve the problem,  use a dictionary data structure to store the frequencies of each letter or special character. Here's an example implementation in Python:

```python

def build_frequency_table(frequency_data):

   frequency_table = {}

   for line in frequency_data:

       letter, frequency = line.split()

       frequency_table[letter] = int(frequency)

   return frequency_table

# Example usage:

frequency_data = [

   "a 10",

   "b 5",

   "c 3",

   "-" 15,

   "." 8,

   "!" 4,

   "+" 1

]

frequency_table = build_frequency_table(frequency_data)

print(frequency_table)

```

In this example, the `build_frequency_table` function takes the `frequency_data` as input, which is a list of strings representing the frequency information for each character. It splits each line by the space character, extracts the letter and frequency, and adds them to the `frequency_table` dictionary. The function returns the resulting frequency table.

Problem 2: To read all the lines of a paragraph from a text file, you can use the `readlines()` method of a file object. Here's an example:

```python

filename = "paragraph.txt"  # Replace with the actual filename

with open(filename, "r") as file:

   paragraph_lines = file.readlines()

for line in paragraph_lines:

   print(line)

```

In this example, the `paragraph.txt` file is opened in read mode using the `open()` function. The `readlines()` method is then used to read all the lines from the file and store them in the `paragraph_lines` list. Finally, you can iterate over the `paragraph_lines` list to process each line individually.

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After 20 years, the wetland will have decreased in area by 20/5 = 4 times.

If the area has decreased by a sixth every 5 years, it will decrease by 4/6 = 2/3 after 20 years.

Therefore, the percent of the total area that disappears after 20 years is 2/3 = 66.67%.

Rounding to two decimal places, the answer is 66.67%.

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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Answer:

  14 square units

Step-by-step explanation:

You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.

The diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:

  b = -4 -(-11) = 7

The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...

  h = 8 -4 = 4

We now have the information we need to use the area formula:

  A = 1/2(7)(4) = 14 . . . . square units

The area of ∆ABC is 14 square units.

__

Additional comment

You can use the diagram and count grid squares to find the dimensions of the triangle.

Answer:

Step-by-step explanation:

Domain of a function is given by the set of x-values (Input values) on the graph.

Range of a function is given by the set of y-values (output values) on the graph.

From the graph attached,

Set of time will represent the "domain" and set of snowfall will represent the "range" of the function graphed.

a). Domain of the function: 0 ≤ x ≤ 5

b). Range of the function: 0 ≤ y ≤ 10

Answer:

The first one!

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Geometric sequences have a common ratio while arithmetic sequences have a common difference.

On the left table, we can see that it's an arithmetic sequence because 3+2=5, 5+2=7, and so on.

On the right table, we can see that it's a geometric sequence because 3*2=6, 6*2=12, and so on.

Basically, if you see a multiplication pattern for the output, it's a geometric sequence. If you see an addition (or subtraction) pattern for the output, it's an arithmetic sequence

For this study, what is the response variable is b. Whether or not a student graduates from college.

The outcome of an experiment in which the explanatory variable is altered is the response variable. It is a variable whose variation can be accounted for by other variables. It is also known as the outcome variable or the dependent variable. As an illustration, the students wish to utilise height to predict age; hence, height is the explanatory variable and age is the response variable.

Whether a student in the example graduates from college. The university official is interested in examining this variable to see whether it has any associations with the predictor variable, which is whether students declare their majors before their junior year. A is the predictor variable. if a student chooses a major prior to entering their junior year.

Complete Question:

A university official wants to determine if a relationship exists between whether students choose their majors before their junior year and whether they graduate from college. For this study, what is the response variable?

a. Whether a student decides on his/her major before their junior year

b. Whether or not a student graduates from college.

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Answer:

Slope=4

x−intercept=−  

4

16

​  

=−4

b−intercept=  

1

16

​  

=16.0000

Step-by-step explanation:

Answer:

720cm³

Step-by-step explanation:

Volume of a cylinder is given by Base Area (A) x Height (h)

or V = Ah

Volume of cylinder A = 18 x 5 = 90 cm³

Base Area A = πr² where r is the radius of the base

For cylinder A, if radius = rₐ

Area = π x (rₐ)² = 18

We can see that cylinder B has twice the height of cylinder A. That means cylinder B radius is twice the radius of cylinder A

So radius of cylinder B = 2 x rₐ = 2rₐ

Base Area of Cylinder B = π x (2rₐ)² = 4π(rₐ)² = 4 x Base Area of cylinder A = 4 x 18 = 72

So while the heights are in the ration 1:2, the base areas are in the ratio 1:4 because the areas are directly proportional to the square of the radius

Hence Volume of Cylinder B = 72 x 10 = 720 cm³

Another way to look at this is that the volume of cylinder B = 8 (2 x 2 x2) times the volume of cylinder A = 8 x 90 = 720cm³

The partial fraction decomposition of the function f(x) = x^4 - x^5 + 5x^3 can be written in the form:
f(x) = A/(x-a) + B/(x-b) + C/(x-c) + D/(x-d) + E/(x-e),
where A, B, C, D, and E are coefficients to be determined, and a, b, c, d, and e are the roots of the polynomial.

To find the partial fraction decomposition, we need to factorize the denominator of the function into linear factors. In this case, the denominator is x^4 - x^5 + 5x^3.

Step 1: Factorize the denominator
x^4 - x^5 + 5x^3 can be factored as x^3(x-1)(x^2 + 5).

Step 2: Set up the decomposition
Now that we have the factors of the denominator, we can set up the partial fraction decomposition:
f(x) = A/(x-a) + B/(x-b) + C/(x-c) + D/(x-d) + E/(x-e).

Step 3: Determine the coefficients
To determine the coefficients A, B, C, D, and E, we need to find the values of a, b, c, d, and e. These values are the roots of the polynomial x^4 - x^5 + 5x^3.
The roots can be found by setting each factor equal to zero and solving for x:
x^3 = 0 → x = 0 (a root of multiplicity 3)
x - 1 = 0 → x = 1 (a root of multiplicity 1)
x^2 + 5 = 0 → x = ±√(-5) (complex roots)

Step 4: Substitute the roots into the decomposition

Substituting the roots into the partial fraction decomposition, we get:

f(x) = A/x + A/x^2 + A/x^3 + B/(x-1) + C/(x+√(-5)) + D/(x-√(-5)) + E.

Note: The coefficients A, B, C, D, and E are determined by solving a system of linear equations formed by equating the original function f(x) with the decomposition and evaluating at the different roots.

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The factors of of the quadratic equations are (4c+5) and (c + 1) .

Given,

Quadratic equation :  4c²+9c+5

Now,

Factorize the quadratic equation,

4c² + 4c + 5c + 5 = 0

4c(c + 1) + 5(c+1) = 0

(4c+5)(c + 1) = 0

So,

4c + 5 = 0

c = -5/4

c + 1 = 0

c = -1

Thus the values of c are -5/4 and -1 and the quadratic equation is factorable .

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The estimated number of bacteria present in the culture after 5 hours as per exponential growth is equal to 5,240.

Initial population size (N₀) = 500 bacteria

Population size after 1 hour (N) = 800 bacteria

let us consider,

N₀ is the initial population size,

N is the population size at a given time,

k is the growth rate constant,

t is the time in hours,

e is the base of the natural logarithm (approximately 2.71828).

To determine the number of bacteria present in the culture after 5 hours,

Use the exponential growth formula for uninhibited growth,

N = N₀ × \(e^{(kt)\)

To find the growth rate constant (k), rearrange the formula as follows,

⇒k = ln(N / N₀) / t

⇒k = ln(800 / 500) / 1

⇒k = ln(1.6)

Using a calculator, we find that k ≈ 0.470

Now, use the growth formula to calculate the population size after 5 hours,

N = N₀ × \(e^{(kt)\)

N = 500 ×\(e^{(0.470 \times 5)\)

N = 500 × \(e^{2.35\)

Using a calculator, we find that \(e^{2.35\) ≈ 10.48

⇒N ≈ 500 × 10.48

⇒N ≈ 5240

Therefore, it is estimated that there will be approximately 5,240 bacteria present in the culture after 5 hours using exponential growth .

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Answer:

32 degrees

Step-by-step explanation:

If AB and BC are perpendicular, that means the angle is 90 degrees. They already give you 24 and 24 which add up to 48 and then you subtract 90 by 48 to find the missing value

The given differential equation is not exact. To determine if a differential equation is exact, we need to check if its partial derivatives satisfy a specific condition.

In this case, the given equation is dy/dx = 9xe^x – y + 6x^2. Let's find the partial derivatives of the expression on the right-hand side with respect to y and x.∂/∂y (9xe^x – y + 6x^2) = -1∂/∂x (9xe^x – y + 6x^2) = 9e^x + 12x

The condition for exactness is that these partial derivatives are equal: ∂/∂y (∂/∂x) = ∂/∂x (∂/∂y). However, in this case, we have -1 ≠ 9e^x + 12x, which means the equation is not exact.As the equation is not exact, we cannot directly solve it by finding a potential function. Other methods, such as using integrating factors or applying specific techniques for solving non-exact equations, may be required.

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Answer:

The third answer is correct

Step-by-step explanation:

Given:

A net of a rectangular prism

l (length) = 11,75 cm

w (width) = 5,75 cm

h (height) = 4 cm

Find: A (surface area) - ?

The surface area is equal to the sum of the areas of all the sides

There are:

2 sides with dimensions of 11,75 cm and 4 cm

2 sides with dimensions of 5,75 cm and 11,75 cm

2 sides with dimensions of 4 cm and 5,75 cm

\(a(surface) = 4 \times 11.75 \times 2 + 5.75 \times 11.75 \times 2 + 4 \times 5.75 \times 2 = 275.125 = 275 \frac{1}{8} \: {cm}^{2} \)

Answer:

50%

Step-by-step explanation:

it's just half 80 so it's 50%

The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.

To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.

To explain this mathematically, we can use the formula:

where Inches/Foot = 12 and Feet/Yard = 3.

Plugging in the appropriate variables, we can calculate the number of inches in a football field as:

Inches = 120 x 3 x 12 = 4320 inches.

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Answer:

16

Step-by-step explanation:

Multiply it by 1/3 and it equals 16

Answer:

16

Step-by-step explanation:

48/3=16

Answer:

29

Step-by-step explanation:

The value of b by assuming that the two lines are parallel will be equal to 29°.

When two lines converge at a point, they produce an angle. The word "angle" refers to the length of the "gap" between these two rays. The symbol is used to denote it.

Radians, a unit of roundness or rotation, and degrees are the 2 most common units used to measure angles. In daily life, angles are present.

As per the given information provided by the given figure,

The angle is corresponding in nature,

So, the equation will be,

3b + 5 = 92

3b = 92 - 5

3b = 87

b = 87/3

b = 29°.

Therefore, the angle b is 29°.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

The variable of summation is represented by an index which is placed beneath the summation sign. The index is often represented by i. (Other common possibilities for representation of the index are j and t.) The index appears as the expression i = 1.

Step-by-step explanation:

~Feitan Portor~

Answer:

2πrh+2πr2

Step-by-step explanation:

I'm a genius...

Answer:

Closed= 2πrh+2πr²

Open= 2πrh+πr²

Answer:

-2+5x+2x-4

Step-by-step explanation:

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

The rank that should be assigned to a score of x=6 is 4.

The given scores are already sorted from smallest to largest. The scores before x=6 are 1, 1, and 3, which are ranked 1, 2, and 3, respectively. The next score after x=6 is also 6, and since we are asked to rank x=6, we need to skip the next two 6s and assign it the rank 4.

Arrange the given scores in ascending order, which has already been done: 1, 1, 3, 6, 6, 6, 9 Identify the position of the first occurrence of the score x = 6. In this case, the first 6 appears in the 4th position.

The rank assigned to a score of x = 6 is 4, based on the order of the given scores.

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Answer:

(4x - 3)(3x² - 1)

Step-by-step explanation:

12x³ - 9x² - 4x + 3 ( factor the first/second and third/fourth terms )

= 3x²(4x - 3) - 1 (4x - 3) ← factor out (4x - 3) from each term

= (4x - 3)(3x² - 1)