2. $6500 principal earning 2.8% compounded monthly ... after 2 years

The dimensions of this rectangular swimming pool include the following:

Width = 10 meters.

Length = 21 meters.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

From the information about the width, we have:

Width, W = L - 11

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

62 = 2(L + L - 11)

62 = 4L - 22

4L = 84

Length, L = 21 meters.

For the width, we have:

Width, W = L - 11

Width, W = 21 - 11

Width, W = 10 meters.

Read more on perimeter of a rectangle here: brainly.com/question/17360327

#SPJ1

Answer:

Hopefully this is the answer you are looking for.

a) we are 95 percent confident the proportion of households in its county that own at least one dog lies in the interval (0.298,0.536)

b) it does not provide evidence that p is different from 39% .

c)   66   households were selected in the humane society's sample

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

a)

95 percent confidence level  = 0.417 ± 0.119 =(0.298,0.536)

we are 95 percent confident the proportion of households in its county that own at least one dog lies in the interval (0.298,0.536)

b)  it does not provide evidence that p is different from 39% .

Since 0.39 is included in the interval (0.298,0.536)  

c) margin of error = ( 0.536 - 0.298)/2

z√(pq)/n  = 0.119

=> 1.96 ( √((0.417(1-0.417)/n) ) = 0.119

=> 65.95 = n

=> n= 66

To Learn more about the percentage form the link:

https://brainly.com/question/24304697

#SPJ1

The value of x in the line segment is - 7 / 3.

A line segment is a section of a line bounded by two points or connecting two points. The value of x if U is between T and V can be found as follows:

TU = 7x + 35

UV = 4(x + 7)

TU ≅ UV

Therefore, let's find x as follows:

7x + 35 = 4(x + 7)

7x + 35 = 4x + 28

7x - 4x = 28 - 35

3x = - 7

x = -7  /3

Therefore,

x = - 7 / 3

learn more on line segment here: https://brainly.com/question/30072605

#SPJ1

The required real diameter of the tin is 250 mm.

Diameter is a measurement of the length of a straight line that passes through the center of a circular object, such as a circle or a sphere. It is the distance between two points on the object's edge that are furthest from each other and that pass through the center of the object.

Here,
If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:

Actual Diameter = 2.5 x Picture Diameter
Actual Diameter = 2.5 x 10 cm
Actual Diameter = 25 cm

To convert the actual diameter to millimeters (mm), we can multiply by 10:

Actual Diameter in mm = Actual Diameter x 10
Actual Diameter in mm = 25 cm x 10
Actual Diameter in mm = 250 mm

Therefore, the real diameter of the tin is 250 mm.

Learn more about diameter here:

https://brainly.com/question/5501950
#SPJ1

Answer:

⁷

Step-by-step explanation:

questions 1 and

The possible ratios of dogs to cats that could be made is

12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.

What is ratio in math?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.

                             As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

Given ,

If there are 12 dogs and 48 cats at a pet daycare,

So, we have to fill out all of the possible ratios of dogs to cats that could be made.

ratio could be  = 12 : 48

12 : 48  = 1 : 4

6 : 24 = 1 : 4

3 : 12 = 1 : 4

1 : 4 = 1 : 4

Therefore, The possible ratios of dogs to cats that could be made is

12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.

Learn more about ratio

brainly.com/question/1504221

#SPJ1

In formally proving that lim (x² + x) = 42

m = ⌈√ε⌉ - 1

It is shown that for any ε > 0, there exists a δ > 0 such that if 0 < |x - c| < δ, then |(x^2 + x) - 42| < ε.

|(x^2 + x) - 42| = |x^2 + x - 42| = |(x - 6)(x + 7)|

Since |x - c| < δ, we have:

|x - 6| < δ + 6 < δ(m+2)

|x + 7| < δ + 7 < δ(m+2)

Since δ = ε/(m+1), we can solve for m:

m+1 = ε/δ

m+1 = ε/ (ε/(m+1) )

(m+1)^2 = ε

m^2 + 2m + 1 = ε

m^2 + 2m + (1-ε) = 0

Using the quadratic formula, we get:

m = (-2 ±  ⌈√ε⌉ - 1 (4 - 4(1-ε)))/2 = -1 ± √(ε)

Therefore, in conclusion  m =  ⌈√ε⌉ - 1

Learn more about quadratic formula at: https://brainly.com/question/30164833

#SPJ1

The Segment Addition Postulate states that if C is between D and E, then DC + CE = DE. In this case, we can use this postulate to solve for T by substituting the given values into the equation and solving for T.

First, we will repeat the question in our answer: Let C be between D and E. Use the Segment Addition Postulate to solve for T.

Next, we will substitute the given values into the equation: DC + CE = DE

Since we are solving for T, we will rearrange the equation to isolate T on one side of the equation: T = DE - DC - CE

Finally, we will substitute the given values for DE, DC, and CE into the equation and solve for T: T = (DE) - (DC) - (CE)

T = (T + DC + CE) - (DC) - (CE)

T = T

Therefore, the value of T is equal to itself, and the Segment Addition Postulate has been used to solve for T.

https://brainly.com/question/14957499

#SPJ1

Answer:

12 teams means 6 games each match day. Each team can play all the 11 other teams so 11 match days. So 66 games.

The approximate area between the x-axis and the graph of f(x) =x² +3

over the interval [0, 2] is 9.75.

introducing intervals, bounded collections of numerical values that are highly helpful in explaining domain and range. To demonstrate where a value lies in relation to two endpoints, we can use interval notation.

To approximate the area between the x-axis and the graph of

 f(x) = x² + 3 over the interval [0, 2].

The heights of the rectangles in the right rectangle method are determined by the function's value at the right endpoint of each subinterval. The right endpoints of each subinterval would be 0.5, 1, 1.5, and 2 if the range [0, 2] were divided into 4 equal subintervals, each of width 0.5.

The height of the first rectangle

f(0.5) = 0.5² + 3

f(0.5) = 3.25

and, the height of the second rectangle

f(1) = 1² + 3

f(1) = 4

and, the height of the third rectangle

f(1.5) = 1.5² + 3

f(1.5) = 5.25

and, the height of the fourth rectangle

f(2) = 2² + 3

f(2) = 7

So, sum of the areas of the rectangles

= (0.5) × (3.25+4+5.25+7)

= (0.5) × 19.5

= 9.75

Learn more about Interval here:

https://brainly.com/question/29674711

#SPJ1

Answer:

Diameter: 17

Circumference: 53.58

Area: 226.865

Step-by-step explanation:

How to solve for diameter of a circle:

(The radius is half of the diameter.)

How to solve for a circumference of a circle:

How to solve for the area of a circle:

Hope it helped!

The terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

A terminal point is a point at which a line or curve ends. An example of a terminal point is the point where the line x=5 ends. This point is 5 on the x-axis and has no y-value because the line does not extend beyond that point.

Another example of a terminal point is the point where the circle x2 + y2 = 25 ends. This point is (5,0), where x=5 and y=0. This means that the circle has a radius of 5 and the point (5,0) is the end of the circle.

The unit circle is centered at the origin (0, 0) and has a radius of 1. To find the terminal point with an angle of 9π/2, use the trigonometric functions sine (sin) and cosine (cos).

By calculating the x-coordinate of the point. This can be done using cosine:

x = cos(9π/2)

Since cosine of an angle of 9π/2 is equal to 0, the x-coordinate of the point is 0.

Calculate the y-coordinate of the point. This can be done using sine:

y = sin(9π/2)

Since sine of an angle of 9π/2 is equal to -1, the y-coordinate of the point is -1.

Therefore, the terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

To know more about Terminal point, visit:

https://brainly.com/question/14435471

#SPJ1

By using the greatest common factor of 84 and 48, the sum 84+48 can be written as the product 12 x (7 + 4).

To write the sum 84+48 as a product using their greatest common factor, we need to factor both numbers and find the largest common factor.

The prime factorization of 84 is 2 x 2 x 3 x 7, while the prime factorization of 48 is 2 x 2 x 2 x 2 x 3.

To find the greatest common factor, we need to identify the factors that both 84 and 48 have in common. We see that both numbers have two factors of 2 and one factor of 3 in common. So, the greatest common factor of 84 and 48 is 2 x 2 x 3 = 12.

Now, we can rewrite the sum 84+48 as a product of 12 and another sum, using the distributive property of multiplication:

84 + 48 = 12 x (7 + 4)

So, the sum 84+48 can be written as the product 12 x (7 + 4).

To know more about greatest common factor, visit:https://brainly.com/question/11221202

#SPJ1

Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

A function,

f(x) = 3 sec 2θ - 2.

The standard form of the function is,

a sec(bx - c) + d.

Here, c is a phase shift and d is a vertical shift.

So, by comparison, we get,

Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Therefore, the graph is given in the attached image.

To learn more about the transformation on the graphs;

https://brainly.com/question/19040905

#SPJ1

Answer:

5 or -2

Step-by-step explanation:

|2x-3| can equal either (2x-3) or -(2x-3) thus

(2x-3) = 7

2x = 10

x = 5

-(2x-3) = 7

-2x = 4

x = -2

Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2

Step-by-step explanation: hope this helps0^0

Using Standard normal distribution, The probability that a family spends between $175 and $255 in playing video games every year is approximately 0.4821 or 48.21%.

Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is defined as the measure of the likelihood of an event happening, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a 3 on a fair six-sided die is 1/6 because there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

There are two types of probability: theoretical probability and experimental probability. Theoretical probability is based on mathematical analysis and assumes that all possible outcomes are equally likely to occur. Experimental probability, on the other hand, is based on actual observations and measurements of events and their outcomes.

Probability theory has many practical applications in fields such as statistics, economics, engineering, and physics. It can be used to model and predict the behavior of complex systems, such as stock prices, weather patterns, and the spread of diseases. Additionally, probability theory is used in decision-making processes to determine the most favorable course of action based on the likelihood of different outcomes.

(a) To find the probability that a family spends over $290 in playing video games every year, we need to standardize the value using the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

So, z = (290 - 238.92) / 31.38 = 1.63

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score greater than 1.63 is 0.0516.

Therefore, the probability that a family spends over $290 in playing video games every year is approximately 0.0516 or 5.16%.

(b) To find the probability that a family spends less than $150 in playing video games every year, we again need to standardize the value using the z-score formula:

z = (x - μ) / σ

So, z = (150 - 238.92) / 31.38 = -2.83

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than -2.83 is 0.0023.

Therefore, the probability that a family spends less than $150 in playing video games every year is approximately 0.0023 or 0.23%.

(c) To find the probability that a family spends between $175 and $255 in playing video games every year, we need to standardize the values of both $175 and $255 using the z-score formula:

z1 = (175 - 238.92) / 31.38 = -2.03

z2 = (255 - 238.92) / 31.38 = 0.51

Using a standard normal distribution table or a calculator, we can find the probability of a z-score between -2.03 and 0.51 is 0.4821.

Therefore, the probability that a family spends between $175 and $255 in playing video games every year is approximately 0.4821 or 48.21%.

To know more about distribution visit:

brainly.com/question/303666

#SPJ1

Answer:

The efficiency of the transmission and drive mechanism is 57.5%, rounded to two decimal places.

Step-by-step explanation:

We can use the following formula to calculate the efficiency of the transmission and drive mechanism:

Efficiency = (Power output / Power input) x 100%

where "Power output" refers to the amount of power delivered to the driving wheels, and "Power input" refers to the amount of power produced by the engine.

Determine the power input: The problem states that the automobile engine produces 120 horsepower, so this is our power input.

Power input = 120 hp

Determine the power output: The problem states that only 69 horsepower is delivered to the driving wheels of the car, so this is our power output.

Power output = 69 hp

Calculate the efficiency using the formula:

Efficiency = (Power output / Power input) x 100%

Substituting the values we found in steps 1 and 2, we get:

Efficiency = (69 / 120) x 100%

Simplifying this expression, we get:

Efficiency = 0.575 x 100%

Efficiency = 57.5%

Therefore, the efficiency of the transmission and drive mechanism is 57.5%, rounded to two decimal places.

The solution is, the answer is: The color is blue (D).

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Our matrix C is the encoder.  Let X be our secret message and let B be our encoded message.  Therefore the relationship between the 3 can be represented as:

CX = B

So we want to solve for X (our secret message). So using matrix algebra:

X = C^-1*B

where C^-1 is the inverse of C.

C^-1 = | 3 -2 |

          |4 -3 |

So we take C^-1 and multiply it by matrix B to get X.  Matrix B is already given to us.  So just multiply those two.  I used a calculator to get:

X = | 20 8 5 3 15 12 15 |

     | 18 9 19 2 12 21 5 |

And since A = 1, B = 2, C = 3, etc....

We decode our message and it says:

X = | T H E C O L O |

     | R I S B L U E |

So the answer is: The color is blue (D)

To learn more on matrix click:

brainly.com/question/28180105

#SPJ1

Answer: D

Step-by-step explanation:

1)

Area of a = 25 m²
2)

Length b = 5 m

3)

Length c = 7.94 m

4)

Area of d = 35.75 m²

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

1)

Figure a is a square:

Side = b

Area = b²

From (1),

Side = 5 m

Area of a = 5² = 25 m²

2)

Length b is in a triangle:

Using the Pythagorean theorem.

b² = 3² + 4²

b² = 9 + 16

b² = 25

b = 5 m _____(1)

3)

Length b is in a square:

From (2),

c = 7.94 m

4)

Figure d is a triangle.

Using the Pythagorean theorem.

c² + 9² = 12²

c² = 144 - 81

c² = 63

c = 3√7 m

c = 7.94 m _____(2)

Area = 1/2 x 9 x 7.94

Area =  35.73 m²

Thus,

Area of a = 25 m²
Length of b = 5 m

Length of c = 7.94 m

Area of d = 35.75 m²

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ1

Answer:

Sophie's pyramid is approximately 4.8 inches.

Step-by-step explanation:

The formula for the volume of a square pyramid is given by:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

We are given that the volume of Sophie's pyramid is 90 cubic inches, and the base has a side length of 7.5 inches. The area of the base is:

B = (7.5)^2 = 56.25 square inches

Substituting these values into the formula for the volume, we get:

90 = (1/3) * 56.25 * h

Multiplying both sides by 3, we get:

270 = 56.25 * h

Dividing both sides by 56.25, we get:

h = 4.8 inches (rounded to one decimal place)

Therefore, the height of Sophie's pyramid is approximately 4.8 inches.

For x = 4.1:

Slope of PQ =5.1

For x = 4.01:

Slope of PQ =6.01

For x = 3.9:

Slope of PQ =15.1

For x = 3.99:

Slope of PQ =105.99

From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

To find the slope of the secant line PQ, we need to first find the coordinates of point Q in terms of x:

Q = (x, x² + x + 8)

Then, the slope of the secant line PQ is given by:

(yQ - yP) / (xQ - xP)

where yP = 28 and xP = 4, and yQ and xQ depend on the value of x.

For x = 4.1:

Q = (4.1, 4.1² + 4.1 + 8) = (4.1, 28.51)

Slope of PQ = (28.51 - 28) / (4.1 - 4)

= 0.51 / 0.1

= 5.1

For x = 4.01:

Q = (4.01, 4.01² + 4.01 + 8) = (4.01, 28.0601)

Slope of PQ = (28.0601 - 28) / (4.01 - 4)

= 0.0601 / 0.01

= 6.01

For x = 3.9:

Q = (3.9, 3.9² + 3.9 + 8) = (3.9, 26.49)

Slope of PQ = (26.49 - 28) / (3.9 - 4)

= -1.51 / -0.1

= 15.1

For x = 3.99:

Q = (3.99, 3.99² + 3.99 + 8) = (3.99, 26.9401)

Slope of PQ = (26.9401 - 28) / (3.99 - 4)

= -1.0599 / -0.01

= 105.99

As x approaches 4 from both sides, the x-coordinate of Q approaches 4, and the slope of PQ approaches the slope of the tangent line to the curve at P(4,28). From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

Learn more on calculating slopes of tangent here https://brainly.com/question/6353432

#SPJ1

For the given function f(x) = cos x,  f '(x) = -sin x.

By the definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.

What is meant by the derivative of a function?

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. It is described as the fluctuating rate at which a function changes in relation to an independent variable. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The sensitivity of the dependent variable to the independent variable is assessed using the derivative. Calculus's core tool is derivative.

We are given the function f(x) = cos x

The derivative of cos x is -sin x.

That is, f '(x) = -sin x

Therefore, by definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.

To learn more about derivatives, follow the link.

https://brainly.com/question/12047216

#SPJ1

The length of river C and river D are 2005miles and 2505miles.

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted into mathematical equation or expression

represent the length of river C by x and the length of river D by y

x = 500+y

x+y = 5510

substitute 500+y for x

500+y+y = 5510

2y =5510-500

2y = 5010

divide both sides by 2

y = 5010/2

y = 2505miles

x = 500+y

x= 500+2505

x= 3050miles

therefore the length of river C and D are 3005miles and 2505miles respectively

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

The measurement of x, in the given circle, is 5 cm.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle with a tangent of 6 cm and a secant of length 4+x, we need to find the measurement of x,

Using properties of circle,

6² = 4·(4+x)

36/4 = 4+x

9 = 4+x

x = 5

Hence, the measurement of x, in the given circle, is 5 cm.

Learn more about circle, click;

https://brainly.com/question/29142813

#SPJ1

The last number in Row 8 is 56.

The number in Row 12 and column 3 is 80.

The row and column that will contain the number 400 is Row 58 Column 1

The figure shown in the image represents the multiplication table 7.

Each column contains 7 numbers.

Beginning with the first Row and column, 7 numbers are added until the next row. At the end of each row is a multiple of 7.

The last number in Row 8 will be the product of 7 and 8 = 56

The number in Row 12 and Column 3 will be:

7 * 11 + 3 = 80

The row and column that will contain the number 400 will be:

400/7 = 77 remainder 1

Hence, it will be Row 58 Column 1.

Learn more about multiplication tables at: https://brainly.com/question/29069569

#SPJ1

Answer:

The geometric mean of 16 and 36 is 24

The values are given below:

Given :  S is a geometric sequence

(√x + 1) , 1 and (√x -1) are first three terms of the sequence

To Find : Value of x

Recall that a geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.

a , ar , ar² , ... , arⁿ⁻¹

The nth term of a geometric sequence with the first term a and the common ratio r is given by:   aₙ = arⁿ⁻¹

(√x + 1) , 1 and (√x -1) are first three terms of the sequence

=> r =  1/(√x + 1) = (√x -1) /1

1/(√x + 1) = (√x -1) /1

=> 1 = (√x + 1)  (√x -1)

=> 1 = x - 1

=> x = 2

Hence x =2

a = (√2 + 1)

r = 1/(√2 + 1)

5th term of the sequence = ar⁴

=  (√2 + 1)  (1/(√2 + 1))⁴

=  (√2 + 1) /(3 + 2√2)²

=  (√2 + 1) /(17 + 12√2)

= (√2 + 1)(17 - 12√2)  /(17 + 12√2) (17 - 12√2)

=   -7 + 5√2

a = 5 , b = - 7

Read more about geometric sequence here:

https://brainly.com/question/1509142

#SPJ1

The solution of the equation is to the nearest ten-thousandth is x = 2.7712.

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459. Typically, the natural logarithm of x is expressed as ln x, loge x, or, if the base e is implicit, just log x.

The given equation is [tex]3^{x-1} = 7[/tex].

Take natural log on both sides of the equation:

[tex]\ln (3^{x-1} )=\ln( 7)[/tex]

(x - 1) ln(3) = ln(7)

x - 1 = ln(7) / ln(3)

x = 1 +  ln(7) / ln(3)

x = 2.7712

Hence, the solution of the equation is to the nearest ten-thousandth is x = 2.7712.

Learn more about logarithm here:

https://brainly.com/question/30085872

#SPJ1

Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.

Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.

Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.

Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:

     |          /

     |        /

     |      /

     |    /  

     |  /    

     |/      

---------------

The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:

y = x - 7

y = (-1/2)x + 5/2

Substituting the first equation into the second, we get:

x - 7 = (-1/2)x + 5/2

Simplifying this equation, we get:

(3/2)x = 19/2

x = 19/3

Substituting this value of x into either of the original equations, we get:

y = 19/3 - 7 = 2/3

So the point that represents a solution to the system is (19/3, 2/3).

Step-by-step explanation:

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.

To know more about domain visit:

https://brainly.com/question/28135761

#SPJ1

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.

To learn more about the functions, visit:

https://brainly.com/question/25638609

#SPJ1