Write an explicit formula for � � a n ​ , the � th n th term of the sequence 36 , 32 , 28

Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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The correct work done by the person walking up the spiral staircase is -3,325.89 ft-lb, indicating that the person did work against gravity while climbing up the stairs.

The force required to lift a person of weight 195 lb against gravity is F = mg,

where g is the acceleration due to gravity and

m is the mass of the person.

We can convert the weight in pounds to mass in pounds by dividing by the gravitational acceleration, g = 32.2 ft/s²:

m = 195 lb / 32.2 ft/s²= 6.05 slugs

The work done by a force F over a distance d is given by the dot product of the force and displacement vectors:

W = F · d

In this case, the force is the weight of the person, F = mg, and the displacement vector is the difference between the initial and final positions, d = r(1) - r(0),

where r(t) is the position vector parameterized by t.

We can compute the displacement vector as follows:

r(1) = ⟨4cos(2π), 4sin(2π), 18⟩ = ⟨4, 0, 18⟩

r(0) = ⟨4cos(0), 4sin(0), 0⟩ = ⟨4, 0, 0⟩

d = r(1) - r(0) = ⟨0, 0, 18⟩

The work done is therefore:

W = F · d = (6.05 slugs) · (32.2 ft/s^2) · ⟨0, 0, 18⟩

= 0 · 0 + 0 · 0 + (6.05 slugs) · (32.2 ft/s^2) · 18 ft

= 3,325.89 ft-lb

Therefore, the work done by the person walking one revolution up the spiral staircase is 3,325.89 ft-lb.

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The survey questiοn is What is yοur favοrite brand οf sοda?

In mathematics, a survey is a technique fοr gathering data that invοlves pοsing a series οf questiοns tο participants in οrder tο learn mοre abοut their attitudes and behaviοrs. It is the mοst typical and affοrdable methοd οf data cοllectiοn. A sample size can change depending οn the situatiοn.

What dο yοu like and dοn’t like abοut the CEO? It is nοt a survey questiοn. In a survey questiοn, there shοuld be an οbject, nοt a  persοn.

Dο yοu οwn a car οr a truck? It is nοt a survey questiοn.  The survey is dοne οn a particular prοduct. But in the questiοn, nο band is mentiοned.

Hοw much credit card debt dο yοu οwe? It is nοt a survey questiοn. It is a persοnal questiοn.

What is yοur favοrite brand οf sοda? It is a survey questiοn. The survey is dοne οn a sοda brand.

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After addressing the issue at hand, we can state that As a result, decimal midfielders make up around 36.36% of the players on the pitch

The decimal number system is frequently used to express both integer and non-integer quantities. Non-integer values have been added to the Hindu-Arabic numeral system. The technique used to represent numbers in the decimal system is known as decimal notation. A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers. The full number and the fractional part of a decimal number are separated by a decimal point. The decimal point is the little dot that appears between whole numbers and fractions. An example of a decimal number is 25.5. In this case, 25 is the total number, and 5 is the minimum.

The following formula can be used to determine the percentage of midfielders on the field:

Overall number of players on the field / Total number of midfielders

In this situation, the total number of midfielders is 4, and the total number of players on the pitch is 11.

As a result, the percentage of midfielders on the field is:

4 / 11

This can be expressed in decimal or percentage form as follows:

0.3636 (rounded to four decimal places) (rounded to four decimal places)

36.36% (rounded to two decimal places) (rounded to two decimal places)

As a result, midfielders make up around 36.36% of the players on the pitch.

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The height of the tower is 25.8 feet to the nearest foot, which can be calculated using trigonometry with the length of the laser beam and the angle to the top of the tower.

A. The length of each laser beam is 30 feet. Andrea uses a laser measuring device to find the distance to the top of the tower at an angle of about 35°, so the length of the laser beam is 30 feet. Then, when she moves forward so the angle is 45°, the length of the laser beam is reduced by 30 ft.

B. The height of the tower can be calculated using trigonometry. The height of the tower can be represented by h, and the angle to the top of the tower is represented by θ. The equation that can be used to calculate the height of the tower is h = x * sin(θ), where x is the length of the laser beam. Therefore, the height of the tower when the angle is 35° is (30 ft) * sin(35°) = 25.8 ft. The height of the tower when the angle is 45° is (30 ft) * sin(45°) = 21.2 ft. Therefore, the height of the tower is 25.8 ft to the nearest foot.

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The maximum number of hikers who walked between 8 and 19 miles is 17 and the minimum number is 13.

Maximum and minimum are terms used to describe the highest and lowest values, quantities, and a set of variables.

The maximum value is the highest value that a variable or set of variables can take within a given context or range.

Conversely, the minimum value is the lowest value that a variable or set of variables can take within a given context or range.

Here we have a table

The table shows the distance walked by the walkers

From the table,

Between intervals 5 ≤ x < 10 there are 4 hikers

Between intervals 10 ≤ x < 15 there are 7 hikers

Between intervals 15 ≤ x < 20 there are 6 hikers  

Maximum number of hikers who walked between 8 and 19 miles

= 4 + 7 + 6 = 17

Minimum number of hikers who walked between 8 and 19 miles  

= 7 + 6 = 13

Therefore,

The maximum number of hikers who walked between 8 and 19 miles is 17 and the minimum number is 13.

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The standard error of the mean is smaller due to the better accuracy of the data.

Standard deviations are a measure of how spread out a dataset is. It is calculated by taking the square root of the variance of the data. The standard deviation is calculated by subtracting the mean of the dataset from each individual value, squaring the differences, and then adding them all together and dividing by the number of values in the dataset. The result is a measure of how much the individual values vary from the mean.

The average of means for a sample of size 10 is 5.0. Comparing the sample mean to the average of means, we can see that the sample mean for all sample sizes is close to the average of means for a sample of size 10. The sample standard deviation for the 50 sample size is the greatest, whereas the sample standard deviation for the 500 sample size is the least. Additionally, the standard error of the mean decreases as the sample size increases. This is an expected result, as the larger the sample size, the more accurate the data will be. Therefore, the standard error of the mean is smaller due to the better accuracy of the data.

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The slope of the line is 2, which was calculated using the slope-intercept form of a linear equation and the given point (5,8) and y-intercept of -2.

To calculate the slope, we need to use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the point (5, 8) lies on the line, so we can substitute x = 5 and y = 8 into the equation:

8 = 5m + b

We are also given that the y-intercept is -2, which means that when x = 0, y = -2. We can use this information to find b:

-2 = 0m + b

b = -2

Substituting this value into the equation above, we have:

8 = 5m - 2

Solving for m, we get:

5m = 10

m = 2

Therefore, the slope of the line is 2.

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well, we know that a year has 12 months, so 6 months is really just 6/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2588\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}[/tex]

[tex]2588 = 2500[1+(\frac{r}{100})(\frac{1}{2})] \implies \cfrac{2588}{2500}=1+\cfrac{r}{200}\implies \cfrac{647}{625}=\cfrac{200+r}{200} \\\\\\ \cfrac{(200)(647)}{625}=200+r\implies \cfrac{(200)(647)}{625}-200=r\implies \boxed{7.04=r}[/tex]

Answer:

A. 63

Step-by-step explanation:

in triangle TRS, it is an isosceles triangle with TS congruent to RS. So, angle T congruent to angle r. So, the angle is 63.

Answer:

0.8

Step-by-step explanation:

8 divided by 0.8= 10

10 times 0.8= 8

:)

The average rate of change is the slope of the line between the points

     ( -4, f(-4) ) and ( 4, f(4) )

f(-4) = 16 + 40 + 5 = 61

f(4) = 16 - 40 + 5 = 19

The slope (AKA average rate of change) is then

    [tex]m =\dfrac{19-61}{4-(-4)}=\dfrac{-42}{8} = -\dfrac{21}{4}[/tex]

If Ahmed is given a 15% discount of the total price, discounted price that ahmed pays is $1134. 75, the price of the computer before the discount was $335.14.

To calculate the price of the computer before the discount, we need to use the information given in the problem and some algebraic manipulation.

Let's start by setting up an equation. We can let x be the price of the computer before the discount. We know that Ahmed received a 15% discount off the total price, so the total price would be:

Total price = x + 375 + 70

Then, we can use the fact that the discounted price that Ahmed paid was $1134.75 to set up an equation:

Discounted price = Total price - 15% of Total price

$1134.75 = (x + 375 + 70) - 0.15(x + 375 + 70)

Simplifying this equation by combining like terms, we get:

$1134.75 = 1.85x + 513.75

To solve for x, we can subtract 513.75 from both sides of the equation:

$621 = 1.85x

Finally, we can divide both sides of the equation by 1.85 to get the price of the computer before the discount:

x = $335.14

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Complete question is:

Ahmed buys a new monitor, keyboard and computer.

He is given a 15% discount off the total price.

The discounted price that Ahmed pays is $1134.75.

The price of the monitor before the discount was $375.

The price of the keyboard before the discount was $70.

Calculate the price of the computer before the discount?

The percentage value that represents what percent of 64 is 4? is (b) 6 1/4%

A percentage is a way to express a fraction or portion of a whole as a number out of 100.

From the question, we have the following parameters that can be used in our computation:

What percent of 64 is 4?

Represent the percentage with x

So, we have

x percent of 64 is 4

Express as product expression

x% * 64 = 4

Multiply through by 100

x * 64 = 400

Divide by 64

x = 6.25 or 6 1/4

Hence, the percentage is 6 1/4%

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Answer:

Step-by-step explanation:

To find this answer you need to find the vertex of the parabola. Do this by using the formulas for h and k as follows:

[tex]h=\frac{-b}{a}[/tex]    and    [tex]k=c-\frac{b^2}{4a}[/tex], where a, b, and c come from the quadratic equation.

Filling in for h:

[tex]h=\frac{10}{2(.2)}=25[/tex]

Filling in for k:

[tex]k=650-\frac{100}{4(.2)} =525[/tex]

Thus, the coordinates for the vertex are (25, 525). The h value interprets the number of bowls that should be produced to minimize the cost of production (25) and the minimum production cost is the k value (525).

Answer:The ratio of the area of the small circle to that of the bigger circle is 25:36.

Step-by-step explanation:

Based οn the simulatiοn yοu shοuld switch, because prοbability οf winning a car if yοu dο is 0.8 which is greater than 0.5.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here prοbability οf winning a car when yοu stick tο dοοr 1 is ,

=>P(stick)=2/10

=>0.2

If yοu switch, prοbability οf winning a car is,

=>P(switch)=1-P(stick)

=>1-0.2=0.8

Sο, based οn the simulatiοn yοu shοuld switch, because prοbability οf winning a car if yοu dο is 0.8 which is greater than 0.5.

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Answer:

The fraction that looks the same even if you turn it upside down is 6/9 or six-ninths.

Step-by-step explanation:

Using the remainder theorem, the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is Ox²+2x+3

What exactly is the remainder theorem?

The Remainder Theorem is an approach to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder.

Given Data

x³ +3x² +5x +3 / x+1 = x² +2x +3

x³ +x²

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

0   2x² +5x

  2x² +2x

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

    0      3x +3

            3x+3

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

            0    0  

The quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is x² +2x+3 using remainder theorem.

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The distance around the track along the inside edge of each lane is 614.44 yd for lane 1, 634.88 yd for lane 2, 655.32 yd for lane 3, 675.76 yd for lane 4, 696.20 yd for lane 5, 716.64 yd for lane 6, 737.08 yd for lane 7 and 757.52 yd for lane 8.

The distance around the track along the inside edge of each lane can be calculated using the following formula:

Distance = (2 × 44 yd) + (2 × π × radius)

where the radius is equal to 44 yd + (lane number × 10 yd).

For lane 1, the radius is equal to 44 yd + (1 × 10 yd) = 54 yd. Therefore, the distance around the track along the inside edge of lane 1 is (2 × 44 yd) + (2 × π × 54 yd) = 614.44 yd.

The same calculation can be done for the other lanes, with the radius increasing by 10 yd for each lane. The radius for lane 2 is 64 yd, for lane 3 is 74 yd, for lane 4 is 84 yd, for lane 5 is 94 yd, for lane 6 is 104 yd, for lane 7 is 114 yd and for lane 8 is 124 yd.

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Therefore , the solution of the given problem of probability comes out to be the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the schemes inside a practise known as criteria. Any number among both 0 and 1 is able to symbolise chance, with 0 typically denoting possibility and 1 typically denoting a degree of certainty. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Only one of the wheel's seven equally sized regions, which there are a total of seven of, correlates to the number 6.

The likelihood of spinning a 6 on a single rotation is thus:

=> P(six) = 1/7

=>  P(six) = 0.143

Therefore, the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

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There are 27 different ways to choose a lunch special combination.

To determine how many different ways there are to choose a lunch special combination:

At a pizza parlor, the lunch special comes with your choice of a pizza slice, a salad and a drink.

There are pizza slice options, salad options, and soda options.

Therefore, there are three options for each category, which are pizza slice, salad, and drink.

Then, we can use the multiplication principle to determine how many different ways there are to choose a lunch special combination:

3 options for pizza × 3 options for salad × 3 options for drink

= 27 different ways to choose a lunch special combination.

Therefore, there are 27 different ways to choose a lunch special combination.

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Answer: Voluntary Response

Step-by-step explanation:

The question was, "Mrs. Finn had a terrible experience at a hotel last weekend. The water was cold, the bathroom wasn't cleaned, and it smelled really bad. She decided to write a horrible review on travel.com about the experience."

And we're asked to evaluate whether this is

A) Statistic

B) Random Sampling

C) Voluntary Response

A statistic is "any quantity computed from values in a sample which is considered for a statistical purpose."

Random sampling is "a method of data collection and analysis designed to select a representative sample of respondents out of a larger population."

Finally, we have voluntary response which is "a deliberately chosen reaction to a stimulus that may require a complex coordination of excitatory and inhibitory impulses with feedback from visual, motor, and other systems."

Out of all of the following definitions, voluntary response is what fits this scenario best. Voluntary response usually includes the response of people with very strong opinions, and recalling how Mrs. Finn reacted to her hotel, I'd say it fits.

The total weight of the 4 small jars of coffee is W = 400 grams

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the weight of large jar be x

Let the weight of small jar be y

5 large jars of coffee have a total weight of 1250 grams.

So , 5x = 1250

Divide by 5 on both sides , we get

x = 250 grams

And , 2 large jars of coffee and 7 small jars of coffee have a total weight of 1200 grams.

So , 2x + 7y = 1200

2 ( 250 ) + 7y = 1200

Subtracting 500 on both sides , we get

7y = 1200 - 500

7y = 700

Divide by 7 on both sides , we get

y = 100 grams

On simplifying the equation , we get

So , the weight of 4 small jars is 4y = 400 grams

Hence , the weight of 4 small jars is y = 400 grams

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Answer:

We can substitute m = 2.5 and n = 5 into the expression:

m + (7*9)/n = 2.5 + (7*9)/5

We can simplify the second term:

(7*9)/5 = 63/5

Substituting back into the expression:

m + (7*9)/n = 2.5 + 63/5

We can find a common denominator and add the terms:

2.5 + 63/5 = 12.5/5 + 63/5 = 75/5 = 15

Therefore, the value of the expression is 15, which corresponds to option (b) as the correct answer.

The probability of selecting a boy from the class is 15/25, or 3/5, since there are 15 boys in a class of 25 students.

When selecting two students randomly without replacement, the probability of selecting a boy on the first draw is 15/25, and the probability of selecting another boy on the second draw (assuming the first student selected was a boy) is 14/24, since there will be 14 boys left out of 24 students remaining.

So the probability of selecting two boys in a row is:

(15/25) * (14/24) = 7/20

Therefore, the probability that both students chosen for the presentation are boys is 7/20, or approximately 0.35.

The surface area of building with the skyview is found as 331.625 sq. yd.

A solid shape having six square faces is called a cube. Because every square face shares a comparable side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.

Total area = TSA of cuboid + CSA of hemisphere - area of circle

Total area = 2(lb + bh + hl) + 2πr² - πr²

Total area = 2(6*10 + 10*6 + 6*6) + 2*3.14*2.5² - 3.14*2.5²

On simplification:

Total area = 331.625

Thus, surface area of the building with the skyview is found as 331.625 sq. yd.

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The solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0. Therefore the solution is of trapezoidal method.

The model problem (4.3) with a real constant a < 0 is given by:
[tex]y' = ay, y(0) = 1[/tex]
The trapezoidal method is given by:
[tex]yn+1 = yn + (h/2)(f(tn, yn) + f(tn+1, yn+1))[/tex]
where h is the step size, tn and yn are the current time and solution values, and  [tex]f(t, y) = ay[/tex]  is the right-hand side of the model problem.

To show that the solution of the trapezoidal method is stable for a < 0, we can substitute the right-hand side into the trapezoidal method and solve for yn+1:
[tex]yn+1 = yn + (h/2)(ayn + ayn+1)yn+1 - (h/2)ayn+1 = yn + (h/2)aynyn+1(1 - (h/2)a) = yn(1 + (h/2)a)yn+1 = yn(1 + (h/2)a)/(1 - (h/2)a)[/tex]

Since a < 0, the denominator [tex](1 - (h/2)a)[/tex] is always positive, and the numerator [tex](1 + (h/2)a)[/tex] is always less than or equal to 1. Therefore, the solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0.

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Answer:

12x - 8x^2 - 8.

Step-by-step explanation:

To find the sum of the two expressions, we add the corresponding coefficients of each term:

(x - 5x^2 - 12) + (4 + 11x - 3x^2)

= x + 11x - 5x^2 - 3x^2 - 12 + 4

= 12x - 8x^2 - 8

Therefore, the ladder touches the house at a height of 28 feet above the ground.

A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.

Here,

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side, which is opposite the right angle). In this problem, the ladder, the side of the house, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the house to the ladder is one leg, and the height we want to find is the other leg.

Let x be the height above the ground where the ladder touches the house. Then, using the Pythagorean theorem, we have:

x² + 21² = 35²

Simplifying and solving for x, we get:

x² + 441 = 1225

x² = 784

x = 28

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