the length of a regtangle is 3 times the width. the perimeter is 3 times the width. the perimeter is 96 cm. find the width and length

Thus, the obtained formula for the arithmetic sequence is found as:

f(n) = -42 + 10(n - 1).

A list of integers called an arithmetic sequence has a constant difference between terms. Any number may be the first in an arithmetic sequence, but the distance between succeeding terms must remain constant.

Unreal numbers can be used in a series. I believe that the next step in an equation should be an actual real number.

The nth term formula for the arithmetic sequence is:

f(n) = a1 + (n - 1)d

arithmetic sequence -

−42, −32, −22, −12, −2 …

a1 = -42

d = -32 - (-42) = -32 + 42 = 10

So, formula for the sequence:

f(n) = -42 + (n - 1)10

f(n) = -42 + 10(n - 1)

Thus, the obtained formula for the arithmetic sequence is found as:

f(n) = -42 + 10(n - 1).

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Answer:

12π feet

Step-by-step explanation:

The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area is 36π ft², so we can set up an equation:

36π = πr²

To solve for the radius, we can divide both sides by π:

36 = r²

Taking the square root of both sides, we get:

r = 6

Now that we know the radius is 6 feet, we can use the formula for the circumference of a circle, C = 2πr:

C = 2π(6)

Simplifying, we get:

C = 12π

Therefore, the circumference of the circle is 12π feet.

10-hole harmonicas, which can produce a wider range of notes and are more commonly used in professional music settings.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

The terms "6 holes and 1/2" and "10 holes" are often used to refer to harmonicas, which are small wind instruments that produce sounds when air is blown into or drawn out of them.

The main difference between a 6-hole harmonica and a 10-hole harmonica is the number of holes on the instrument. As the name suggests, a 6-hole harmonica has 6 holes, while a 10-hole harmonica has 10 holes.

In addition to the number of holes, the two types of harmonicas may also differ in their size, range, and the specific notes that they can produce. 6-hole harmonicas are typically smaller and produce a more limited range of notes compared

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The vertex form of the equation is:

y = a(x - h)² + k, where a = 1, h = 1, and k = -16

It should be noted that to rewrite the equation in vertex form by completing the square, we first need to factor out the coefficient of x²:

y = x² - 2x - 15

y = (x² - 2x + 1) - 16

y = (x - 1)² - 16

Here, the vertex form of the equation is:

y = a(x - h)² + k, where a = 1, h = 1, and k = -16

The key features revealed by both equations are:

Vertex: The vertex of the parabola is (1, -16).

Axis of symmetry: The axis of symmetry is the vertical line x = 1.

Minimum/Maximum: Since the coefficient of x² is positive, the parabola opens upwards, and the vertex represents the minimum point of the graph.

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The risk of owning a home in Randolph County based on the given sample can be calculated as:

Risk of owning a home = Number of residents who own a home / Total number of residents in the sample

Risk of owning a home = 59 / 90

Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.

The expression 75 + 1.45x represents the total cost of a training session with Terrell

Let x be the distance (in miles) that Terrell must drive to and from the training session.

Then the total cost C of the training session, in dollars, can be expressed as:

C = 75 + 1.45x

Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.

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Answer:

y = 10(3)^x

Step-by-step explanation:

The general form of an exponential function is

[tex]y=ab^x[/tex], where x and y are any coordinate in the exponential function, a is the initial value, and b is the base.

Currently, we only have xs and ys, which forces us to find a and b:

[tex]90=ab^2\\810=ab^4[/tex]

We can find b first by dividing the larger x and y (4, 810) by the smaller x and y (2, 90).  Thus, we must plug the xs and ys in and create a fraction:

[tex]\frac{810}{90}=\frac{ab^4}{ab^2}[/tex]

We know that a represents a value a number divided by itself is 1 and that 810/90 = 9 so we now have:

[tex]9=\frac{b^4}{b^2}[/tex]

According to quotient rule of exponents, when you divide bases with exponents, you subtract the exponent on the numerator from the base on the denominator:

[tex]9=b^4^-^2\\9=b^2\\3=b[/tex]

Now we can simply plug in our first coordinate and 3 for b to find a:

[tex]90=a(3)^2\\90=9a\\10=a[/tex]

Thus, the equation of the exponential function which contains the points (2,90) and (4,810) is

y = 10(3)^x

Answer: He needs 6 baskets

Step-by-step explanation: Its division 24 divided by 4 equals 6

Anderson traveled 15 mph to go to the restaurant and 12 mph to get home. Anderson went at 15 mph for 3 hours and at 12 mph for 6 hours. if the entire trip took 9 hours.

    The given speed Anderson, the total time taken, and asked to find the time traveled at each speed:

         Speed, [tex]S_1[/tex] = 15 mph

         Speed, [tex]S_2[/tex] = 12 mph

         Total time, [tex]t[/tex] = 9 hours

         Time traveled with speed 1,

         [tex]t_1[/tex] Time traveled with speed 2, [tex]t_2[/tex]

To solve the given problem, let's use the following formula:

         Total   [tex]t[/tex] (time) = [tex]t_1[/tex] ( time 1) + [tex]t_2[/tex] (time 2)

   Now, time 1 can be represented as

          [tex]t_1[/tex] (time 1) = [tex]d[/tex] (distance) /  [tex]S_1[/tex] (speed 1)

Similarly, time 2 can be represented as:

           [tex]t_2[/tex] (time 2) = [tex]d[/tex] (distance) /  [tex]S_2[/tex] (speed 2)

 Here, we need to find the time traveled at each speed. Let's use these equations to solve the given problem.

      Time traveled with speed 1, [tex]t_1[/tex]  = [tex]d[/tex] /  [tex]S_1[/tex]

      Time traveled with speed 2,  [tex]t_2[/tex] = [tex]d[/tex] /  [tex]S_2[/tex]

As we know the total time, we can find the value of d in terms of [tex]t[/tex].

        So, [tex]d[/tex] =  [tex]S_1[/tex] * [tex]t_1[/tex]  =  [tex]S_2[/tex]  *  [tex]t_2[/tex]

     From the above equation, we can write: [tex]t_1[/tex]  /  [tex]t_2[/tex] =  [tex]S_2[/tex]  /  [tex]S_1[/tex] [tex]t_2[/tex]

                                                                                    =  [tex]t[/tex]  - [tex]t_1[/tex]

     Substitute the value of  [tex]t_2[/tex]  in equation(1):

           [tex]t_1[/tex]  / ([tex]t[/tex] - [tex]t_1[/tex] ) =  [tex]S_2[/tex]  / [tex]S_1[/tex][tex]t_1[/tex]  [tex]S_1[/tex]

                            = ([tex]t[/tex] - [tex]t_1[/tex] ) [tex]S_2[/tex] .[tex]t_1[/tex] . [tex]S_1[/tex] + [tex]t_1[/tex]  [tex]S_2[/tex]

                            = [tex]tS_1[/tex][tex]t_1[/tex]  

                            = [tex]tS_1[/tex] / ( [tex]S_1[/tex] +  [tex]S_2[/tex] ) [tex]t_2[/tex]  

                            =  [tex]t[/tex]  - [tex]t_1[/tex]  

                            = [tex]tS_2[/tex] / ( [tex]S_1[/tex] +  [tex]S_2[/tex] )

   Therefore, Anderson traveled at 15 mph for 3 hours Anderson traveled at 12 mph for 6 hours.

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The area of the pie is approximately 113.0 square inches.

The ratio of a circle's circumference to its diameter is denoted by the mathematical constant pi . It is roughly equivalent to 3.14159 and is not repetitive or terminal. As pi is an irrational number, it cannot be written as an exact fraction of two integers and its decimal representation never ends. Pi is used to compute the characteristics of circles, spheres, cylinders, and other curved objects in many branches of mathematics and science, including geometry, trigonometry, calculus, physics, and engineering.

The area of the circle is given as:

A = πr²

Here, diameter = 12, thus radius is 6 inches.

Substituting the values:

area = 3.14 x (6)²

area = 113.04 square inches

Hence, the area of the pie is approximately 113.0 square inches.

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The value of the given lengths are as follows:

a.) KL = 11.1ft

LO = 5.7ft

b.) m<OMN = 45°

For Side LO ;

7/11 = 7√2/7√2+LO

7(7√2+LO) = 11×7√3

69.3+7LO = 108.9

7LO = 108.9-69.3

LO = 39.6/7

LO = 5.7 ft

For KL ;

This can be solved using the Pythagorean theorem;

c²= b²+a²

C = 5.7+7√2 = 15.6

b = 11

a²= 15.6²-11²

= 243.36 - 121

= 122.36

a= √122.36

a= 11.1ft

For angle OMN;

This can be solved using SOHCAHTOA.

Sin∅ = opposite/hypotenuse

opposite = 7

hypotenuse = 7√2

sin∅ = 7/7√2

sin∅ = 0.707106781

∅= sin-1 0.707106781

∅ = 45°

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Kathy's speed is 2 mph and Dennis's speed is 2+8 = 10 mph.

Let's assume that Kathy's speed is "x" mph. Since Dennis rides 8 mph faster than Kathy, his speed is "x+8" mph.

We know that Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Therefore, we can use the formula:

time = distance/speed

For Kathy: time = 2 miles / x mph

For Dennis: time = 10 miles / (x+8) mph

Since they both take the same amount of time, we can set these two equations equal to each other:

2 / x = 10 / (x+8)

We can then solve for "x" as follows:

2(x+8) = 10x

2x + 16 = 10x

16 = 8x

x = 2 mph

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The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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On social issues, progressives think people should be liberated from the ways of the past and able to decide for themselves about how to live.

Progressivism is a political and social philosophy that emphasizes individual liberty, equality of opportunity, and the role of government in protecting citizens from social and economic abuses.Progressives believe that people should be free to make their own choices about how to live their lives and that the government should not interfere with their decisions. They believe that individuals should have the right to make choices regarding their personal lives, including decisions about marriage, sexuality, and reproductive health.Progressives also advocate for the protection of the environment and the promotion of sustainable practices.

They believe that it is the government's responsibility to protect the natural world and to ensure that future generations have access to clean air, water, and food.In addition, progressives advocate for social justice and the elimination of discrimination on the basis of race, gender, sexuality, and religion. They believe that everyone should have equal access to education, healthcare, and other basic services, regardless of their background or socioeconomic status.Overall, progressives believe in the power of individuals to make positive changes in their own lives and in the world around them. They believe that by working together and advocating for social and economic justice, we can create a better future for ourselves and for future generations.

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The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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The function f(x) = sec(x) has no x-intercepts.

The y-intercept of the graph of f(x) = sec(x) is (0, 1).

From the question, we are to identify any x-intercepts and y-intercepts of the graph of f(x) = sec(x).

The function f(x) = sec(x) is defined as the reciprocal of the cosine function, that is:

f(x) = 1 / cos(x)

The cosine function has a zero at x = π/2 + nπ, where n is an integer.

At these values of x, the denominator of the secant function becomes zero, and the function becomes undefined.

Therefore, the function f(x) = sec(x) has no x-intercepts.

To find the y-intercept, we need to evaluate the function at x = 0, which gives:

f(0) = 1 / cos(0) = 1 / 1 = 1

Hence, the y-intercept of the graph of f(x) = sec(x) is (0, 1).

The graph of the function f(x) = sec(x) is shown below.

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The average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

What is amplitude ?

In mathematics, amplitude refers to the maximum displacement or distance from the equilibrium position of a periodic function, such as a sine or cosine wave. In other words, if a periodic function oscillates back and forth between two extreme values, the amplitude is the maximum distance from the average value or midpoint of the oscillation to one of the extreme values.

To calculate the average period of the trials that were conducted with an amplitude of 10 degrees, we simply add up all the periods and divide by the total number of trials.

10 degrees: 1.66 s, 1.700 s, 1.71 s, 1.68 s, 1.72 s

Average period = (1.66 + 1.700 + 1.71 + 1.68 + 1.72) / 5 = 1.694 seconds

Therefore, the average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.

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Answer:

Step-by-step explanation:

The total revenue from selling 300 tickets for £5 each is:

300 x £5 = £1500

The profit will be the difference between the total revenue and the cost of prizes:

£1500 - £400 = £1100

The amount of profit that goes to Charity A is:

55% x £1100 = £605

The amount of profit that goes to Charity B is:

45% x £1100 = £495

Therefore, Charity A receives £605 and Charity B receives £495.

The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.

P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.

Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.

Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

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Answer:

Step-by-step explanation:

Answer:

We can use the formula:

time = distance ÷ speed

where distance is in kilometers (km) and speed is in kilometers per hour (km/h).

Substituting the given values, we get:

time = 340 km ÷ 12 km/h

time = 28.33 hours (rounded to two decimal places)

Therefore, it takes approximately 28.33 hours for the car to travel a distance of 340 km at an average speed of 12 km/h.

Answer:28hrs and 20min

Step-by-step explanation:

rgrghwrt

The distance d between the train and the railroad marker can be expressed as:

d = 200 - 65h

where 200 represents the initial distance between the train and the marker, and 65h represents the distance the train has covered after h hours, assuming a constant speed of 65 miles per hour.

To find the time it will take for the distance between the train and the marker to be 4 miles apart, we can set d to 4 and solve for h:

4 = 200 - 65h

65h = 196

h = 196/65

So the equation to find the time it will take for the distance between the train and the railroad marker to be 4 miles apart is:

200 - 65h = 4

or

65h = 196

or

h = 196/65

Answer:

500 meters.

Step-by-step explanation:

Answer:

  4 pieces each

Step-by-step explanation:

You want to know the number of $0.10 candies each brother can buy with his equal share of Karla's $1.44.

Each column of the diagram represents $0.10, the cost of one piece of candy. Then 3 columns represent 3 pieces, or one for each brother.

We can divide the shaded area into four (4) groups of 3 columns, representing 4 pieces of candy that each brother can buy. The remaining $0.24 will be divided so that each brother will have $0.08 left over after buying 4 pieces of candy.

a) an = 3n-1 · 2

b) an = 2·n

c) an = 5·n + 8

d) an = 4n-1 · 1

Let's dive deeper into the details below.
(a) The sequence 2, 5, 10, 17, 26 is a geometric sequence with common ratio 3 and a1 = 2. Therefore, the closed formula is an = 3n-1 · 2.

(b) The sequence 0, 2, 5, 9, 14 is an arithmetic sequence with common difference 2 and a1 = 0. Therefore, the closed formula is an = 2·n.

(c) The sequence 8, 12, 17, 23 is an arithmetic sequence with common difference 5 and a1 = 8. Therefore, the closed formula is an = 5·n + 8.

(d) The sequence 1, 5, 23, 119 is a geometric sequence with common ratio 4 and a1 = 1. Therefore, the closed formula is an = 4n-1 · 1.

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Clark completed a self-administered questionnaire, which is also known as an online survey.

This type of survey is administered online and is completed by the participant (in this case, Clark) without the assistance of a researcher or interviewer. It can be delivered through an online form or through an email or online survey link.

The questionnaire typically includes multiple-choice questions, short-answer questions, and rating scales that the participant can answer with a click or tap. After the participant completes the survey, their answers are collected and analyzed by the researcher. This type of survey is a cost-effective and convenient way to collect data from a large number of people in a short amount of time.

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1.  Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ,  V(x) = 1275(1-0.165)ˣ

An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.

In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.

The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.

1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.

2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.

3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.

Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.

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Step-by-step explanation:

If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.

Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:

8x = 44, 44 being the area, and 8x being the width times the variable of the height.

You get 5.5. for the height of the rectangle.

Add 8+8 to 5.5+5.5
you get 27

The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.

This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).

Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.

Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.

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