an open rectangular box with volume 2 m3 has a square base. express the surface area of the box as a function of the length of a side of the base and its domain

The 18th term of the sequence is -83, the correct option is C.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n-1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given:

The sequence=19,13,7,1...

n=18

D= 13-19

D= 6, a= 19

Now,

=a + (n+1)d

=19+(18-1)x-6

=-83

Therefore, the 18th term of the sequence will be -83

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The amount of pure acid in the solution is 109.2ml. The solution has been obtained using the concept of proportion.

What is proportion?

When a ratio is expressed as a/b and two ratios are equal, the expression is a proportion. A and B can be any two integers in this case. Understanding many ideas in mathematics and science requires a solid understanding of ratios and proportions.

According to the direct proportion formula, we can state y = kx given a constant k if the quantity y is directly proportional to the quantity x. The direct proportion equation also has a generic form, which is y = kx.

Let 'x' ml be the quantity of pure acid in the solution.

We are given that we have 780 ml of a 14% solution

This means that 780ml is 100%.

So, using proportion:

⇒780/x= 100/14

⇒780*14/100=x

⇒109.2ml = x

Hence, the amount of pure acid in the solution is 109.2ml.

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The friction force on the 40 kg crate is the product of the coefficient of static friction, μs, and the normal force on the crate. Therefore, the friction force is 40 kg ×0.5 = 20 N.

The resultant normal force on the crate is the sum of the force P and the friction force, which is

300 N + 20 N = 320 N.

The position x, measured from point A, is determined by the direction of the force P. If the force P is acting to the right, then the normal force will have a position x that is to the right of point A. If the force P is acting to the left, then the normal force will have a position x that is to the left of point A.

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The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run.

A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.

The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in relation to other lines plotted on the same coordinate plane.

slope=rise/run.

The ratio of the change in the y-value to the change in the x-value can also be used to determine slope. For instance: Given two points on the line, P = (0, -1) and Q = (4,1), we may compute

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Answer:

x=54°

Explanation step by step

The sum of angles of a Pentagon is 5

from the question Pentagon is given an angles of

75°, 62°, 68°, and 101°

Let the other angle of Pentagon be x.

The measures of the last exterior

=x+75° +62° +68° +101° = 360°.

Note: the sum of exterior angle add up to 360°

306° + x = 360°

x = 360° - 306°

x = 54°.

Individuals basically use statistics to make decisions in financial planning and budgeting, while organizations are guided by statistics in financial policy decisions.

What exactly do you mean by statistics?

Given data :

Step 1 :

The statistics department at Brigham Young University (BYU) is doing research to contrast various teaching strategies.

For lengthy courses, two technological echelons are contrasted: standard and multimedia. Eight lecture parts with students are present. There are four teachers in all.

Step 2 :

Consider that we randomly select two professors to use standard technology and the other two to use multimedia technology. Various professors will have various teaching philosophies, which will eventually influence final grades. We won't be able to tell a teaching method from a piece of technology in this way. Regarding technological disparities, there is no assurance.

Step 3 :

The ideal plan would be to divide each teacher's lectures into two sections, one utilising normal technology and the other multimedia.

There are four blocks as a result, one for each teacher.

Variability would be reduced because they are all being taught by the same person.

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The vector is given by  (1,4) and (1,4) for the given 2 conditons

A vector is a mathematical object that has both magnitude and direction. In physics, vectors are used to represent quantities such as velocity, force, and acceleration. In mathematics, vectors can be represented by an ordered list of numbers (also known as components or coordinates) that specify the magnitudes of the vector in different directions. Vectors can be added, subtracted and multiplied by scalars. They also have properties such as dot and cross product. Vectors can be represented graphically as directed line segments. They are used in various fields like physics, engineering, computer science etc.

Part 1:

The vector is given by (final -initial)

=> (5-4 , 6-2)

=> (1 , 4)

Part : 2

The 2nd vector is given by (final - initial)

=> (3-2 , 8-4)

=> (1 , 4)

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The angles of rotation symmetry for the flower are:

B. 90 degrees  

D. 180 degrees  

F. 270 degrees

A shape with a rotation symmetry will look the same, after the rotation also.

The order of symmetry is the number of rotations that can be applied to a figure while maintaining its original appearance.

From the image of the flower (image attached at the end of solution), we can see that the lines that pass through the origin of the flower are perpendicular.

The perpendicular lines will form the degrees of 90.

This means that 90 degrees of rotation will produce symmetry for the flower.

Other angles that produce symmetry must be multiples [tex]90^{\circ}[/tex].

These angles are:

[tex]\theta=90^{\circ}, 180^{\circ}, 270^{\circ}, 360^{\circ}[/tex].

Here we have [tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex] options

Hence, (B),  (D), and (F) are the correct options.

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The seedlings grew by 7/6 inches in the first 2 weeks.

What is LCM ?

The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.

Let' assume the growth of seedling was 'nil' at the beginning.

According to the situation,

In the first week it grew by 1/3 inches and,

In the next week it grew by  5/6 inches.

So, we can say that the total growth will be the sum of growth in the first and second week.

Hence, total growth would be 7/6 inches (i.e. 1/3 + 5/6).

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This is the Law of Sines, which is one of the main formulas used in trigonometry to calculate the length of sides and angles of a triangle.

sin 15° 2 = bc = sin 105° c

2/sin 15° = bc/sin 105°

bc = (2/sin 15°)sin 105°

bc = 2.68 cm

bc ≈ 2.7 cm

sin A a/ac = sin B b/bc

sin(15°)2/2 = sin(105°)b/b

b = 2 sin(105°)

b = 2.99 cm

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The relationship between the plane and the cone is expressed by the statement that it is parallel to the base of the cone.

Given,

A circle is a closed, curved shape with two dimensions in geometry, alternatively we might say that a circle is a spherical form without borders or edges.

When a cone is cut by a plane that is parallel to the cone's base, a circle is the resultant cross-section.

The form that results from a plane cutting a cone at an angle such that it misses the base or the vertex is called an ellipse. (As in the figure.)

Hence When a plane cuts through a cone and the plane is parallel to the base of the cone, the result is a circle.

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The most obvious concern is those who chose to respond to the survey may have different eating habits from those who did not respond.

One of the major worries when conducting a survey is that people who choose to reply can differ from those who choose not to. The term for this is nonresponse bias. The representativeness of the sample may be impacted by the traits, opinions, or actions of respondents that differ from those of non-respondents.

In this given case, the chef issued a survey to 1000 families, but only 150 of them responded, or 15% of the households. It's probable that those who are very interested in food or cooking will respond to the poll more frequently than others who aren't. Due to the possibility that the eating patterns of individuals who replied may not be typical of the total population, this could cause the sample to be skewed. Thus, the chef would need to consider the nonresponse bias when interpreting the results of the survey.

Complete Question:

Before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. He randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, 150 are returned. Which of the following is the most obvious concern with how this information is gathered?

(A)Mailing questionnaires instead of conducting in-person interviews produce a convenience sample.

(B)Those who chose to respond to the survey may have different eating habits from those who did not respond.

(C)Only residents from the local area were polled.

(D)The chef must conduct a census in order to avoid all sources of bias.

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The volume of the cylinder is 769.3 cubic feet.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given a cylinder,

radius = 7 feet

height = 5 feet

volume of cylinder = πr²h

V = πr²h

V = 3.14*(7²)*5

V = 769.3 cubic feet

Hence the volume of a cylinder is 769.3 cubic feet.

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Answer: 57°

Step-by-step explanation:

Because the angle has a bisector ON, we should be able to add the angles together to collectively equal 106. This will help us to find c, so then we can solve <LOM.

(10c-23) + (-3c+73) = 106

Now combine like terms of the left side of the equation

7c + 50 = 106

get the variables alone on one side of the equation

7c = 56

c = 8

Now, plug in c to the equation for the degree of <LOM to solve

10(8) -23 = 80 - 23 = 57°

Hope this helps!

Someone might have arrived at the incorrect number by incorrectly counting frequencies or not accounting for every data point.

Table 1.35 should be as follows:

Number of Years in US | Frequency

2  | 3

5  | 4

7  | 2

10 | 2

12 | 2

15 | 2

20 | 2

b. This statement is incorrect because 47 percent does not equal the total number of people surveyed.

c. This statement can be fixed by saying "Four out of the nineteen people surveyed have lived in the U.S. for 5 years."

d. The fraction of people surveyed who have lived in the U.S. for five or seven years is 6/19, or 31.58%.

e. The fraction of people surveyed who have lived in the U.S. for at most 12 years is 10/19, or 52.63%.

f. The fraction of people surveyed who have lived in the U.S. for fewer than 12 years is 9/19, or 47.37%.

g. The fraction of people surveyed who have lived in the U.S. from five to 20 years, inclusive, is 12/19, or 63.16%. This can be calculated by subtracting the number of people who have lived in the U.S. fewer than five years (3) from the number of people who have lived in the U.S. 20 or more years (2), and dividing the result (12) by the total number of people surveyed (19).

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The length of the air strip is 451feet.

Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthened n sides).

Given in question;

Perimeter= 8876feet

Let the length be x;

and the width be y;

Now, length will be x= 10+35y

Perimeter of rectangle= 2l+2b

8876=2(10+35y)+y

8876=20+700y+y

y=12.6

x=10+35y

x=451;

Hence, the answer by the given perimeter will be 451feet.

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The surface area of the rectangular prism is: 312 ft².

The surface area of rectangular prism can be calculated using the formula that is given as:

Surface area (SA) = 2(w * l + h * l + h * w), where l is the length, w is the width, and h is the height of the rectangular prism.

Given the following dimensions of the rectangular prism as:

length (l) = 12 ft

width (w) =  3 ft

height (h) = 8 ft

Therefore:

Surface area of the rectangular prism = 2*(3 * 12 + 8 * 12 + 8 * 3) = 312 ft²

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Answer:

A = $8,725.58

P (principal) = $8,500.00

I (interest) = $225.58

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.25/100

r = 0.0525 rates per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,500.00(1 + 0.0525/12)(12)(0.5)

A = 8,500.00(1 + 0.004375)(6)

A = $8,725.58

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $8,500.00 at a rate of 5.25% per year compounded 12 times per year over 0.5 years is $8,725.58.

Hope it helps.

If you have any query, feel free to ask.

The particle's average acceleration between (1,3) and (3,3) is 0 m/s2.

The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections. Coordinates are a pair of numbers that are used to locate a point or shape in a two-dimensional plane. A point's position on a 2D plane is defined by two numbers called the x-coordinate and the y-coordinate.

Here,

A= velocity/time

Points: ( 1,3) (3,3)

Velocity: 3-3=0

Time: 3-1=2

0/2= 0 meters/seconds^2

The average acceleration of the particle over the interval (1,3) and (3,3) is 0 m/s^2.

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Complete question:

What is the average acceleration of the particle within the time interval 1 second to 3 seconds? A. -1 meter/second2 B. 0 meters/second2 C. 1 meter/second2 D. 1.5 meters/second2 E. 2 meters/second2

Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.

Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.

Thus, the two sets s and t have the same saturation since they yield the same localization.

If two multiplicative sets s and t yield localizations with the same primes, then the two sets s and t have the same saturation since they yield the same localization.

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The longest piece of same size that can be cut from 90 inches and 72 inches pieces of wood using HCF is of length 18 inches.

So, the correct option is (c) 18.

Given that,

   Jeremy has two pieces of  90 inches and the other is 72 inches wood. He wants to cut both pieces of wood into smaller pieces of same length and length as long as possible.

Therefore, the Highest Common Factor (H.C.F.) of both the lengths will gives the highest possible length i.e between both the wooden pieces.

To find Highest Common factor,

Prime factorizations of 90 and 72 :

90 = (2 x 3 x 3) x 5

72 = 2 x 2 x (2 x 3 x 3)

2 x 3 x 3 is common factor between 90 and 72

∴ The  Highest Common Factor of 90 and 72 = 2 x 3 x 3 = 18

The longest possible length that can be cut out from both the  pieces are of length = 18 inches

Number of pieces that can be cut from 90 inches long piece = 90/18 = 5

Number of pieces that can be cut from 72 inches long piece = 72/18 =  4

Therefore, the total number of pieces of lumber  = 5+4 = 9 pieces

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Positively Skewed: A positively skewed distribution is one that has a long tail in the positive direction (to the right).

The mean is usually greater than the median, and the data points are concentrated on the left side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is greater than the median, and the skewness is therefore positive.

Symmetric: A symmetric distribution is one that is perfectly centered around the mean and has equal amounts of data points on either side of the mean. In the histogram, the data points are not perfectly centered around the mean, so this term does not apply.

Uniform: A uniform distribution is one that has all the data points clustered around the same value. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Unimodal: A unimodal distribution is one that has a single peak. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Bimodal: A bimodal distribution is one that has two peaks. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.

Negatively Skewed: A negatively skewed distribution is one that has a long tail in the negative direction (to the left). The mean is usually less than the median, and the data points are concentrated on the right side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is less than the median, and the skewness is therefore negative.

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On solving the provided question, we can say that n this parallelograms (2x+1)+(x+5) =180 => x = 58

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

here,

in this parallelograms

2x = 1 and x+5

so, (2x+1)+(x+5) =180

3x + 6 = 180

3x = 174

x = 58

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The graph which represents the velocity of the free-falling rock that changes during the first four seconds is option L: Same as “J” except the line is going from top left corner to bottom right corner.

What is velocity?

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction.

The velocity of a free-falling rock can depicted by equation of motion.

The first equation of motion, v = u + it is referred to as the velocity-time relation. On the other hand, the second equation of motion is s = ut + 1 / 2at² can be called the position-time relation. Likewise, we call the third equation of motion, v² = u²+ 2as, position – velocity relation.

The laws are: (1) Every object moves in a straight line unless acted upon by a force. (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object's mass. (3) For every action, there is an equal and opposite reaction.

Since, the rock is falling freely it will form a straight line (first equation of motion) on the graph and not curved.

The rock will start to fall at an increasing speed with respect to time.

Therefore, option L is the correct answer.

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The interest earned by the investment of $8,000 at an annual simple interest rate of 4% for 10 years is $3,200.

The simple interest method is a system that does not accumulate interest on interest.d

The simple interest system is unlike the compound interest system.

The formula for computing the simple interest is principal x rate x time.

Initial deposit = $8,000

Interest rate = 4%

Investment period = 10 years

Interest system = simple interest

Simple interest = P x R x T

= $8,000 x 4% x 10

= $3,200

Thus, the investment will earn a total interest of $3,200.

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The two plans cost the same for 550 miles of driving  and $113.5 is the total cost.

This problem is about linear equations. We assume Maya drive X miles, and the total cost is $Y, then we can get like, the first plan has an initial fee of $53 and costs an additional $0.11 per mile driven

             For plan 1:  Y = 53 + 0.11 X

The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven,

              For Plan 2: Y= 42 + 0.13 X

When both plans cost the same, then

              Plan 1 = Plan 2

              53 + 0.11 X = 42 + 0.13 X

              0.13 X - 0.11 X = 53 - 42

               0.02 X = 11

[tex]$X=\frac{11}{0.02}=550$[/tex] miles

Put the value of X in equation of Plan 1, we get,

     Y = 53 + 0.11(550) = 53 + 60.5= $113.5

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Answer:

It means Progressing

In Progress

Step-by-step explanation:

The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.

The likelihood that an event will occur is measured by probability. It is difficult to make a complete prediction for many events. By using it, we are only able to forecast the likelihood of an event, or how likely it is, to occur. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probability. For students in class 10, probability is a crucial subject because it clarifies all of the fundamental ideas. In a sample space, there is a probability of 1 for each event.

a. Let there be 100 lights, 1/5th are faulty = 20

There is one faulty in first three, P = 3/100 × 20/100

                                                          = 0.006

                                                          = 0.60%

b. There are two faulty lights, P = 3/100 × 20/100 × 20/100

                                                          = 0.0012

                                                          = 0.12%

c. There is at least one faulty light = 3/100 ×1/5

                                                           = 0.006                                                                            

                                                           = 0.60%      

Thus, The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.

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Answer:

2

Step-by-step explanation:

26/13=2

Answer:

2

Step-by-step explanation:

26-13=13-13=0