Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm. Use function notation to respond to each item below. To answer these questions, you do not need to know the area of a circle in terms of its radius r . All answers must include f. A circle has a radius of 26 cm. A second circle has an area that is 52 square cm more than the first circle. Represent the area of the second circle.

Step-by-step explanation:

the answer is 2(l+b) and it is verified

Thus, the value of x in the figure is 9.

Collinear refers to a term used in figure to describe a set of three or further points that lie on the same straight line. In other words, if you can draw a straight line that passes through two or further points, those points are said to be collinear.

We can use the member addition hypothetical to break for x. According to the member addition hypothetical, if three points A, B, and C are collinear, also AB BC = AC.

In this case, points D, E, and F are collinear, so we can write

DE EF = DF

Substituting the given values, we get

x- 1 4x 5 = 6x- 5

Simplifying the equation, we get

x 4 = 6x- 5

Abating 5x from both sides, we get

= x- 5

Adding 5 to both sides, we get

x = 9

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Answer:

              Hello there! If the circular device has a diameter of 4.5 inches, the radius of the device would be 2.25 inches.

Step-by-step explanation:

              The diameter of the circle is a line segment that not only passes through the center of the circle, but also has endpoints that are on the circle and opposite sides to each other. The radius, on the other hand, is half the distance of the diameter, or the distance from any point on the circle to the center of the circle. I've attached a picture below to show you what that would look like, if you're a visual learner.

             Since we know the diameter of the circular device is 4.5 inches, and we know that the radius of a circle is half the length of the diameter of that same circle, that means the radius of the circular device would be [tex]\frac{4.5}{2}[/tex] or 2.25 inches long.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

0

Step-by-step explanation:

Probability (also known as chance) is the number that indicates how likely an event is to occur. If something has a low probability, it is unlikely to happen. If something has a high probability, it is likely to happen.

If we look at a phone keypad, you will see the numbers 0-9, but you will never see a number greater than 9.

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the numbers, but none are greater than 9.

We are aware that ([tex]1^2[/tex] + a1 + b) = 15 represents the sequence's initial term. The second term is determined by the formula ([tex]2^2[/tex] + a2 + b) = 22. These equations can be expressed as a set of linear equations:

a + b = 14 ...(1)

a + b = 14 ...(1)

The results of the simultaneous solving of these equations are a = -3 b = 17.

Thus, [tex](n-3)^2 + 17[/tex] is the nth term in the series in the form of (n+a)2 + b.

An Arithmetic Progression (AP) is a sequence of numbers in which each term is obtained by adding a fixed value to the previous term. This fixed value is called the common difference of progression.

For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic progression with a common difference of 3. To find the next term, we add 3 to the previous term:

2 + 3 = 5

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14

And so on.

In general, the nth term of an arithmetic progression can be calculated using the formula:

an = a1 + (n - 1)d

where:

an is the nth term of the sequence

a1 is the first term of the sequence

the common difference between terms

n is the number of the term you want to find

So, if we wanted to find the 10th term of the sequence 2, 5, 8, 11, 14, ..., we would use the formula:

a10 = 2 + (10 - 1)3

a10 = 2 + 27

a10 = 29

Therefore, the 10th term of the sequence is 29.

To find the nth term of the sequence in the form of (n+a)² + b, we need to first find the values of a and b.

Let's begin by finding the difference between consecutive terms in the sequence:

The difference between the first and second terms is 22 - 15 = 7.

The difference between the second and third terms is 31 - 22 = 9.

We can observe that the difference between consecutive terms is not constant, which means that the sequence is not arithmetic. However, we can check if the second differences are constant:

The second difference is 2.

Since the second differences are constant, we can conclude that the sequence can be represented by a quadratic equation of the form (n² + an + b). Now, we need to solve for the values of a and b.

We know that the first term of the sequence is given by (1² + a1 + b) = 15. Similarly, the second term is given by (2² + a2 + b) = 22. We can write these equations as a system of linear equations:

a + b = 14 ...(1)

4a + b = 11 ...(2)

Solving these equations simultaneously, we get:

a = -3

b = 17

Therefore, the nth term of the sequence in the form of (n+a)² + b is:

(n-3)² + 17

So, for example:

The 1st term is (1-3)² + 17 = 9 + 17 = 26

The 2nd term is (2-3)² + 17 = 1 + 17 = 18

The 3rd term is (3-3)² + 17 = 0 + 17 = 17

The 4th term is (4-3)² + 17 = 1 + 17 = 18

The 5th term is (5-3)² + 17 = 4 + 17 = 21

and so on.

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Substitute the value of y in the first equation with the second equation.

6x + 3(1-x) = 15

Simplify and solve for x:

6x + 3 - 3x = 15

3x + 3 = 15

3x = 12

x = 4

Now, substitute the value of x in the second equation to solve for y:

y = 1 - x

y = 1 - 4

y = -3

Therefore, the solution to the system of equations is (4, -3).

The following Python function, star string(), receives the integer n as an input and outputs a string of stars (asterisks) that is 2n characters long:

What is a Recursive Python Function?

A recursive function is one that uses self-referential language to define itself. This indicates that the function will continue to call itself and perform its activity until a condition is met and a result is returned.

Here's a possible implementation of the recursive function "star_string" in Python:

   def star_string(n):

   if n == 0:

       return "*"   # base case

   else:

       return star_string(n-1) + star_string(n-1)

The function takes an integer parameter "n", which represents the exponent of 2 in the length of the resulting string (i.e., 2 to the nth power). The base case occurs when n equals 0, in which case the function returns a single asterisk ("*"). Otherwise, the function recursively calls itself with n-1 as the argument, and concatenates the results of those two calls to produce a string that is twice as long.

Here's an example of how to call the function and print the result:

n = 3  # for example

result = star_string(n)

print(result)   # prints "********"

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The possible measure of the side AB is 9.09 cm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The sum of all the interior angles in a triangle is 180°.

So, The measure of angle 'f' = 180° - (72 + 59)°.

f = 49°.

We also know the cosine rule for a triangle ABC is, cosA = (b² + c² - a²)/2bc.

cos49° = (49 + 144 - m²)/168.

110.22 = 193 - m².

m² = 82.78.

m = 9.09.

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Answer:

x = 10182634

y = - 462847/46

Step-by-step explanation:

Divide both sides of the equation by the coefficient of variable

x =   -1012y

y = - 10182634/ 1012

x =   -1012y(  - 10182634/ 1012)

The student's grade point average is 2.32.

The student will not be admitted to the business college.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

(a)

Total grade points earned

= (6 x 4) + (15 x 3) + (31 x 2) + (8 x 1)

= 24 + 45 + 62 + 8

= 139

Total credit hours.

= 6 + 15 + 31 + 8

= 60

Now,

The student's grade point average:

= Total grade points earned / Total credit hours taken

= 139 / 60

= 2.32

(b)

2.32 < 2.5

This means,

The student's grade point average is lower than the required 2.5 GPA for admission to the business college.

Thus,

The student's grade point average is 2.32.

The student will not be admitted to the business college.

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The meaning or impact of the regression data residual not being normally distributed is that the assumptions of the regression model are not met. This can result in biased or misleading estimates of the regression coefficients and the overall fit of the model.

When the residuals are not normally distributed, it can indicate that there are other factors influencing the relationship between the independent and dependent variables that are not accounted for in the model. This can lead to incorrect predictions and unreliable conclusions about the relationship between the variables.

To address this issue, it may be necessary to transform the data or use a different type of regression model that does not assume normality of the residuals. It is also important to check for outliers and influential points, as these can also affect the distribution of the residuals.

In conclusion, the normality of the residuals is an important assumption of the regression model, and if it is not met, it can have a significant impact on the reliability and validity of the results.

The true statement on the height of the ball when thrown from a building, given the equation, can be found to be A. The ball reaches the ground in 3 seconds.

The equation given of the ball being thrown from a building, gives us the height when solved.

The height of the ball when it reaches the ground is 0 feet so we can insert this in the formula to find the time:
0 = - 5 ( t - 3 ) ( t + 5 )

We can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, we can set each factor equal to zero and solve for t:

t - 3 = 0 or t + 5 = 0

Solving for t in the first equation, we get:

t - 3 = 0

t = 3

Seeing as t is 3 seconds the first option is correct.

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The range of heights for lots in New York City is:

1776 feet - 0 feet = 1776 feet.

Height is a mathematical term that refers to the vertical distance between an object's top and base. On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

The range of heights for lots in New York City is the difference between the tallest and shortest lots.

The tallest lot is 1 World Trade Center, which is 1776 feet tall.

The shortest lot is empty and 0 feet tall.

Therefore, the range of heights for lots in New York City is:

1776 feet - 0 feet = 1776 feet

So, the answer is A. 1776 feet.

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The kind of evidence geologists use to make geological timelines of events in Earth's history is the fossil remains.

A geological timeline shows a calendar of events in Earth's history.

To develop geological timelines, scientists understudy physical objects or structures on the Earth.  These objects or structures enable them to prove a phenomenon of interest.

Generally, the best form of evidence for the study of the history of life on earth is fossils, as they give clues about geological events and past climates, including the ages of rocks.

Other kinds of evidence for developing geological timelines include the following:

Thus, fossils provide the best kind of evidence for geological timelines.

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Answer:

The trigonometric function that models the ocean tide for a period of 12 hours is f(x) = 6 sin (2πx/12).

the sale price of a fishing rod is $28.16.

How to do?

The markup of 220% means the store sells the rods for 100% + 220% = 320% of the cost price.

So, the selling price of one fishing rod before the discount is:

320% of $11 = (320/100) x $11 = $35.20

Now, the rods are marked down by 20%, which means the selling price is reduced by 20% of $35.20:

20% of $35.20 = (20/100) x $35.20 = $7.04

Therefore, the sale price of one fishing rod after the 20% discount is:

$35.20 - $7.04 = $28.16

So, the sale price of a fishing rod is $28.16.

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A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.

Step-by-step explanation:

f(x)= x¹ - x² +9

g(x) = x³ + 3x² + 12

To find (f-g)(x):

The operations on functions are as easy as the operations on numbers or polynomials.

We have to subtract the functions to find the above mentioned operation.

(f-g) (x)= f(x)-g(x)

         = (x¹ - x² +9)-(x³ + 3x² + 12)

The minus will change the signs of function g.

The probability that a randomly selected teacher earns more than $525 a week is 0.1820. Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

This is calculated by using the standard normal distribution formula:

P(x > 525) = 1 - P(x ≤ 525) = 1 - 0.8413 = 0.1820

The probability that a randomly selected teacher earns more than $525 a week can be found by calculating the z-score for $525 and then using the standard normal table to find the probability.

The z-score is calculated as follows:

z = (x - μ)/σ

Where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values from the question, we get:

z = (525 - 490)/45 = 0.78

Now, we can use the standard normal table to find the probability that a randomly selected teacher earns more than $525 a week. The table gives us the probability that a value is less than a given z-score, so we need to subtract the probability from 1 to find the probability that a value is greater than the z-score.

The probability that a value is less than 0.78 is 0.7823. So, the probability that a value is greater than 0.78 is 1 - 0.7823 = 0.2177.

Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

Answer: 0.2177

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Answer: The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

Step-by-step explanation: We know,

Area of the square = p^2 where p is the side of the square.

The perimeter of the square = 4p cm where p is the side of the square.

thus, The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

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Answer:

400m³

Step-by-step explanation:

Multiply each section individually. First, multiply 8 x 5 x 4.  This gives you 160.  Now you multiply 5 x 12 x 4, which equals 240.

Now you add them together to get 400.

Answer:

x=3

Step-by-step explanation:

the answer is 3 because 3*12=36 and 4*12=48

When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.

Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.

The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.

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The individual events are overlapping. The probability of the combined event is 11/26.

The individual events are overlapping because there are face cards that are also spades (i.e., the Jack, Queen, and King of Spades). To find the probability of the combined event, we need to add the probability of drawing a face card and the probability of drawing a spade, and then subtract the probability of drawing the Jack, Queen, or King of Spades (since we would be double-counting these cards otherwise).

The probability of drawing a face card is 12/52, since there are 12 face cards in the deck (4 Jacks, 4 Queens, and 4 Kings) out of a total of 52 cards.

The probability of drawing a spade is 13/52, since there are 13 spades in the deck (including the Jack, Queen, and King of Spades) out of a total of 52 cards.

The probability of drawing the Jack, Queen, or King of Spades is 3/52, since there are 3 such cards in the deck out of a total of 52 cards.

Therefore, the probability of the combined event is:

P(face card or spade) = P(face card) + P(spade) - P(Jack, Queen, or King of Spades)

P(face card or spade) = 12/52 + 13/52 - 3/52

P(face card or spade) = 22/52

P(face card or spade) = 11/26

So the probability of the combined event is 11/26 or approximately 0.42 when rounded to two decimal places.

This shows the individual events are overlapping and the probability is 11/26

The individual events are overlapping. The probability of the combined event is 11/26.

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The force exerted by the prism on the floor 245 N.

The physical force applied to an object is referred to as pressure. Per unit area, a perpendicular force is delivered to the surface of the objects. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa).

Given:

height = 4 m, volume = 28 m³

Pressure = 75 N/m²

Now, Volume of prism = Area of base x height

                              28     = Аrеа х 4

                                Area = 28/4 = 7 m²

Also, Pressure = force / Area

35 = force / 7

Force = 35 x 7

Force = 245 N

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Answer:208 mi

 Step-by-step explanation:

If David rents the car for four days,

that's an up-front costof 4 × 23.95 = $95.80.

The other cost depends on the distance (d) he drives.

The equation for his total cost (C) isC = 0.26d + 95.80If David has needs a budget

of $150, then

150 = 0.26d + 95.80- 95.80 from each side54.20 =

0.26d ÷ 0.26d = 208.5

David can't drive that extra 0.5 mi without going over his budget.He can drive 208 whole miles.

The required angle 1 between the side and diagonal of a square is approximately 45 degrees.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
Let's assume that the length of one side of the square is 'a'.

Then the length of the diagonal of the square is given by the Pythagorean theorem:

d² = a² + a² = 2a²

d = a * √(2)

To find the angle between the side and the diagonal, we can use the cosine function:

cos(Ф) = adjacent/hypotenuse = a / (a * √(2))

cos(Ф) = 1 / √(2)

Ф= cos⁻¹(1/√(2))

Ф≈ 45°

Therefore, the angle between the side and diagonal of a square is approximately 45 degrees.

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The equations; T = 2c + 43 and T = 3c + 33 for the total cost for the cakes indicates;

Part 1

The number of cupcakes for which the cost would be the same is the option;

In the solution, the x-value represents the A number of cupcakes and the y-value represents the B total cost

An equation is an statement of equivalence between two expression or values by joining them with an '=' sign.

Dolphin Bake Shop charges

Amount charged for each cup cake = $2

Amount charged for the large cake = $43

Total charge, T = 2·c + 43

Make A Splash Bakery

Amount charged for the large cake = $33

Amount charged for each cup cake = $3

Charges total, T = 3·c + 33

Part 1

The number of cupcakes that makes cost for the two options to be the same is found as follows;

The equivalent cost is the point where the equations for the total cost are also equivalent, therefore;

When the cost are the same; T = T and 2·c + 43 = 3·c + 33

2·c + 43 = 3·c + 33

3·c - 2·c = 43 - 33 = 10

c = 10

The number of cupcakes that makes the cost the same is 10 cup cakes

When the costs are the same; T = 2·c + 43, c = 10, therefore;

T = 2 × 10 + 43= 63

The charges at each store when the cost are the same is $63

The point on the graph of both equations at which the charges are the same is therefore the point (x, y) = (10, 63), which is the solution of the system of equations.

x-value is 10, which is the number of cupcakes

y-value is 63, which is the total cost

The correct option is therefore;

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The value of s-r is 2

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

each term is equal to the sum of the two terms after it.

=> ar^n = ar^(n+1) +  ar^(n+2)

On dividing both the sides by ar^n and simplfying we get

r= 0.618

 sum of the series is:

s= a/(1-r) , a=first term

=> s= 1/(1-0.618 )

=> s= 2.618

s-r = 2.618  -  0.618  = 2

The value of s-r is 2

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The set of values that we are permitted to enter into our function is referred to as the domain of a function. The x values for a function f make up this collection (x). A function's range is the range of values that it can accept as input. When we enter an x value, the function outputs this set of outcomes.

(a) f - {1 2 3 4 5} -> {1 2 1 2 1}

This function is neither injective nor surjective. It is not injective because f(1) = f(3) = f(5) = 1, and it is not surjective because 2 is not in the range.

(b) f - {1 2 3 4 5} -> {1 2 3 1 2}

This function is neither injective nor surjective. It is not injective because f(1) = f(4) and it is not surjective because 3 is not in the range.

(c) f(x) = { x if x < 3, x - 3 if x > 3}

This function is both injective and surjective, and hence bijective. It is injective because each element in the domain maps to a unique element in the codomain, and it is surjective because every element in the codomain is mapped to by at least one element in the domain. Hence, this function is bijective.

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Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

In mathematics, a functiοn definitiοn is a statement that defines a relatiοnship between input values (called the dοmain) and οutput values (called the cοdοmain οr range). A functiοn takes an input value and prοduces a unique οutput value based οn a certain rule οr algοrithm.

(a) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(b) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο the οutput 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(c) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 3 and 4 are mapped tο the οutput 0, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 1 is never used.

Hence,

Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

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The correctly matched pairs are mentioned below.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to match the correct pairs given below.

{ 1 } -

47, 41, 35, 29, 23   →   a{n} = a{1} + (n- 1)d

{ 2 } -

7, -21, 63, -189, 567   →   a{n} = a{1}rⁿ⁻¹

{ 3 } -

[tex]$A = P(1 + 0.025/12)^{12t}[/tex]   →   A = [tex]$P(1 + r/n)^{nt}[/tex]

{ 4 } -

An 18 - month invest on $10 at 5%.   →   A = P[tex]$e^{rt}[/tex]

{ 5 } -

Investments and loans -

Therefore, the correctly matched pairs are mentioned above.

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