the area of a rectangle is 1,056 square inches. its length is 4 inches longer than 2 times its width. which equation can you use to find the width of the rectangle, w?

The planet will travel a distance of 17.088 x 106 miles in 8 days.

Distance is a numerical measurement of how far apart two or more objects, people, or locations are from one another. It is a fundamental concept in geometry, physics, and mathematics. Distance can be measured in a variety of ways, such as kilometers, miles, feet, inches, and light years. Distance can also refer to the physical separation between two points, such as the length of a line or the circumference of a circle. Distance can also refer to the emotional or psychological divide between two people. Distance can be both positive and negative, as it can bring people together or drive them apart.

To calculate how far the planet will travel in 8 days, we must first calculate the distance the planet will travel in one day. To do this, we must multiply the speed of the planet (8.9 x 104 mph) by 24 hours, which represents one day:

Distance in 1 day = 8.9 x 104 mph x 24 hours
Distance in 1 day = 2.136 x 106 miles

Now that we know the distance in one day, we can calculate the distance the planet will travel in 8 days. To do this, we must multiply the distance in one day (2.136 x 106 miles) by 8 days:

Distance in 8 days = 2.136 x 106 miles x 8 days
Distance in 8 days = 17.088 x 106 miles

Therefore, the planet will travel a distance of 17.088 x 106 miles in 8 days.

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Step-by-step explanation:

The three internal angles of a triangle sum to 180 °

x + 23      +      4x+17     +   80    = 180

5x + 120 = 180

5x = 60

x = 12 °

The value of x that makes the equation true is -1.

To obtain the value of x, we must first express the equation as seen in the diagram. This gives us:

5x + 6 = 1

Five x was obtained by counting the number of x's that we have in the boxes and the sum of figure 1.

Now, when we solve this, we will have

5x = 1 - 6

5x = -5

x = -1.

This then means that if we are to sum -1 five times and add 6 to it, the final value that we will have is 1.

Complete Question:

The diagram shows five boxes with the x initials and 6 boxes with figure 1. All of these are represented on the left-hand side and equated to 1.

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Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.

Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.

The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.

The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.

Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.

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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:

The term used for discovery sampling is statistical random sampling.

What is statistical random sampling?

A simple random sample is a subset of individuals chosen at random, all with the same probability, from a larger set of individuals. It is a method of choosing a sample at random.

Here,

We have to find another term for discovery sampling.

We concluded that another term that is used for discovery sampling is statistical random sampling.

Hence, the term used for discovery sampling is statistical random sampling.

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If Person A and Person B are playing archery together. the probability that A gets more targets than B is 0.5, or 50%.

The number of targets hit by A and B follows a binomial distribution with parameters n = 201 and n = 200, respectively, and p = 0.5.

To find the probability that A gets more targets than B, we need to find the probability that A hits more than 100 targets (since 100 is the average number of targets hit by each player). We can use the normal approximation to the binomial distribution to do this.

The mean of the difference in the number of targets hit by A and B is:

E(A - B) = E(A) - E(B) = np - np = 0

The variance of the difference in the number of targets hit by A and B is:

Var(A - B) = Var(A) + Var(B) = np(1-p) + np(1-p) = 100

The standard deviation of the difference is then:

SD(A - B) = sqrt(Var(A - B)) = 10

Using the normal distribution approximation, we can standardize the difference in number of targets:

Z = (X - E(A - B)) / SD(A - B)

where X is the number of targets that A hits.

P(A hits more targets than B) = P(A - B > 0)

= P(Z > (0 - 0) / 10)

= P(Z > 0)

= 0.5

Therefore, the probability that A gets more targets than B is 0.5, or 50%. This means that there is an equal chance that A will hit more targets than B as there is that B will hit more targets than A.

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Answer:

The area of the figure is 286 cm^2

Area of upper triangle = (1/2) base X height

= (1/2) 12 X 10

= 60

The middle portion is square so

area = l^2

= 100

the base of bottom triangle = 4 + 10 + 4 = 18

height of bottom triangle = 14

so area = (1/2) base X height

= 126

total area = area of upper triangle + area of square +area of bottom triangle

= 60 + 100 + 126

= 286 cm^2

Answer:

Let the fraction be represented by "a/b".

According to the problem statement, we can create two equations:

Equation 1: (a-1)/(b+2) = 1/2

Equation 2: (a+3)/(b-2) = 1 1/4 = 5/4

We can simplify Equation 1 by cross-multiplying to get:

2(a-1) = b+2

2a - 4 = b + 2

2a = b + 6 --- (Equation A)

Similarly, we can simplify Equation 2 by converting 1 1/4 to an improper fraction:

5/4 = 1 + 1/4 = 4/4 + 1/4 = (4+1)/4 = 5/4

So, Equation 2 becomes:

5(a+3) = 4(b-2)

5a + 15 = 4b - 8

5a = 4b - 23 --- (Equation B)

Now, we have two equations (Equation A and B) with two unknowns (a and b). We can solve for one variable in terms of the other and substitute in either equation to find the value of the other variable. Here, we will solve for 'b' in Equation A:

2a = b + 6

b = 2a - 6

Substitute this value of 'b' in Equation B:

5a = 4b - 23

5a = 4(2a - 6) - 23

5a = 8a - 47

3a = 47

a = 47/3

Substitute this value of 'a' in Equation A to find 'b':

2a = b + 6

2(47/3) = b + 6

94/3 - 6 = b

b = 76/3

Therefore, the fraction is (a/b) = 47/76.

Answer:

6. closed

7. open

8. open

Step-by-step explanation:

im so sorry if its wrong im not entirely sure

The volume of the sphere is 1372 cubic cm for the given radius.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Many forms have various volumes. We have examined the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these forms.

The volume of the sphere is given by the formula:

V = 4/3πr³

Substituting the value of π = 3 and r = 7 we have:

V = 4/3(3)(7)³

V = 1372 cubic cm.

Hence, the volume of the sphere is 1372 cubic cm for the given radius.

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The relative frequency is 8/25.

Relative frequency is a statistical concept that refers to the proportion of times that an event occurs in a given sample or population. It is calculated by dividing the number of times the event occurs by the total number of observations in the sample or population.

Relative frequency is an important concept in probability theory and statistics because it provides a way to estimate the probability of an event occurring based on the observed data. As the sample size increases, the relative frequency becomes a more accurate estimate of the true probability of the event.

Relative frequency is also used in hypothesis testing, where it is used to test whether a particular hypothesis is supported by the data. In this case, the observed relative frequency is compared to the expected relative frequency under the null hypothesis to determine whether the difference between the two is statistically significant.

The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

Therefore, the relative frequency for the event "spin a 3" is:

24/75 = 8/25

So, the relative frequency is 8/25.

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The total number of spins is 75 and the number of times the spinner landed on 3 is 24.

The "spin a 3" occurrence has a relative frequency of [tex]\frac{8}{25}[/tex].

A statistical concept known as "relative frequency" describes the percentage of times an event happens in a given sample or population. It is calculated by dividing the total number of observations in the sample or group by the frequency of the event.

Because it offers a method to calculate the probability of an event occurring based on the observed data, relative frequency is a crucial concept in probability theory and statistics. The relative frequency becomes a more precise indicator of the actual probability of the event as sample size rises.

In order to determine whether a specific hypothesis is backed by the data, relative frequency is also used in hypothesis testing. To determine

whether the difference between the two is statistically significant, the observed relative frequency is in this instance compared to the expected relative frequency under the null hypothesis.

There were 75 total spins, and 3 appeared 24 times during those rotations.

As a consequence, the proportional frequency of "spin a 3" is as follows:

[tex]\frac{24}{75} =\frac{8}{25}[/tex]

So, the relative frequency is [tex]\frac{8}{25}[/tex].

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The scale factor after dilation is 2 in.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here in the given figure QRST , the length of QT = 2in.

Now after dilation the figure Q'R'S'T' , the length of Q'T'= 4in

Then scale factor is,

=> Q'T'/QT = 4/2 = 2in.

Hence the scale factor after dilation is 2 in.

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The area of the shape given above which is the addition of area of semi circle and the area of the triangle prism =660.48 ft²

To calculate the area of a triangular prism the formula given below is used:

Area of a triangular prism = ab+ 3bh

where;

a = side = 20ft

b= base = 10 ft

h = height = 12 ft

Area = 20×10 + 3×10×12

= 200 + 360

= 560ft²

The area is semi circle = πr²/2

π = 3.14

R = 16/2 = 8ft

area = 3.14× 8²/2

= 200.96/2

= 100.48 ft²

Area of the shape = 560+100.48 = 660.48 ft²

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Answer & Step-by-step explanation:

We can make y the subject first

y = [tex]\frac{1}{5}[/tex](x + 8) - 7

Substitute values of x into the equation to find their corresponding y value

For example, when x is 0

[tex]\frac{1}{5}[/tex](0 + 6) - 7 = -5.8

When x is 1, y = -5.6

Repeat for other values of x

Here is an example of me plotting the points for x from -2 to 2:

Answer:

see attachment.

Step-by-step explanation:

To find:-

Answer:-

We need to find out the graph of the following line,

[tex]:\sf\implies y + 7 = \dfrac{1}{5}(x+6)\\[/tex]

For graphing this line we need to find at least two coordinates through which the graph passes . We can find out the third point to check if the other coordinates are correct.If all the three points do not come in a straight line , then there is some mistake .

Now solve out for any of the variables , i am solving out for "y" .

For that subtract 7 on both the sides,

[tex]:\sf\implies y =\dfrac{1}{5}(x+6)-7 \\[/tex]

Substitute x = 4 :-

[tex]:\sf\implies y =\dfrac{1}{5}(4+6)-7 \\[/tex]

[tex]:\sf\implies y = \dfrac{10}{5}-7 = 2-7 \\[/tex]

[tex]:\sf\implies \pink{ y =-5} \\[/tex]

Therefore one of the coordinate to mark on the graph is (4,-5) .

Again, substitute x = -6 ,

[tex]:\sf\implies y =\dfrac{1}{5}(-6+6)-7\\[/tex]

[tex]:\sf\implies y = 0 - 7 \\[/tex]

[tex]:\sf\implies \pink{ y = -7} \\[/tex]

Therefore the second coordinate to mark on the graph is (-6,-7) .

After marking these two points join the points by drawing a line. The line will represent the graph of the given equation.

You can see attachment for the graph for the same .

(2x10^n)+(4.02x10^5), what is n?

Step-by-step explanation:

To determine the value of n, we need to rewrite the expression as a number in scientific notation, in the form a x 10^n, where 1 ≤ a < 10.

We can start by factoring out 10^n from both terms:

(2 x 10^n) + (4.02 x 10^5) = 10^n (2 + 4.02 x 10^-5)

Now we need to divide both sides of the equation by (2 + 4.02 x 10^-5):

(2 x 10^n) + (4.02 x 10^5) / (2 + 4.02 x 10^-5) = 10^n

We can simplify the expression on the left side by multiplying the numerator and denominator by 10^5:

(2 x 10^n x 10^5 + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Simplifying the numerator:

(2 x 10^(n+5) + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Now we can cross-multiply to eliminate the fraction:

(2 x 10^(n+5) + 4.02 x 10^5) = 10^n (2 x 10^5 + 4.02)

Expanding both sides:

2 x 10^(n+5) + 4.02 x 10^5 = 2 x 10^(n+5) + 4.02 x 10^n

Subtracting 2 x 10^(n+5) from both sides:

4.02 x 10^5 = 4.02 x 10^n

Dividing both sides by 4.02:

10^5 = 10^n

Therefore, n = 5.

Here's a visual representation of the lines connecting each value to 10.56:

In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.

by the question.

sure, I can help you with that!

To join 10.56 to all the equivalent values, you can draw lines connecting each value to 10.56. Here's how:

105 tenths and 6 hundredths:

To convert 105 tenths and 6 hundredths to a decimal, you can add the two values together: 105/10 + 6/100 = 10.56.

Draw a line connecting "105 tenths and 6 hundredths" to "10.56".

10 ones and 56 tenths:

To convert 10 ones and 56 tenths to a decimal, you can add the two values together: 10 + 56/10 = 10.56.

Draw a line connecting "10 ones and 56 tenths" to "10.56".

1 ten and 56 hundredths:

To convert 1 ten and 56 hundredths to a decimal, you can add the two values together: 10 + 56/100 = 10.56.

Draw a line connecting "1 ten and 56 hundredths" to "10.56".

156 hundredths:

To convert 156 hundredths to a decimal, you can divide the value by 100: 156/100 = 1.56.

Add 1 to the whole number part to get 10.56: 1 + 0.56 = 10.56.

Draw a line connecting "156 hundredths" to "10.56".

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Answer: 55 min

Step-by-step explanation:

10:40 + 1 hr = 11:40

11:40 - 5min= 11:35

1hr - 5min= 55min

The given ratio of 0.42 to 1 means that for every 1 active subscription, there are 0.42 expired subscriptions.

What is a ratio?

The ratio is a comparison of two quantities that is expressed as a fraction. It is used to compare two values in mathematics. It is possible to write the ratio between a and b as:

a : b or a/b.

What does a ratio of 0.42 to 1 mean? The ratio of 0.42 to 1 means that there are 0.42 expired subscriptions for every 1 active subscription. It is worth noting that the ratio is less than 1, indicating that there are fewer expired subscriptions than active subscriptions.

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To accumulate $100,000 over 20 years at a 10% annual interest rate compound annually, you would need to make annual payments of $8,218.64.

You can use the formula for the future value of an annuity to accumulate $100,000 over 20 years at a 10% annual interest rate compound on a yearly basis:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

Where:

FV is future value, which is $100,000 in that case

Pmt: annual payment

r: annual interest rate, which is 10%

n: number of payment periods, which is 20

By plugging in values:

[tex]$100,000 = Pmt * [(1 + 0.1)^(20) - 1] / 0.1[/tex]

Solving for Pmt, we get:

[tex]Pmt = $100,000 / [(1 + 0.1)^(20) - 1] / 0.1\\Pmt = $100,000 / 12.167\\Pmt = $8,218.64[/tex]

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Answer:

4

Step-by-step explanation:

the distance around the field is the perimeter, which is 2(length) + 2(width)

2(150) + 2(100) = 500

2 kilometres = 2000 metres, and 2000/500 = 4

Answer: 4 times

Step-by-step explanation:

Step 1: find the Perimeter

Perimeter = 2L + 2W

= 2(150 meters) + 2(100 meters)

= 500 meters.

Step 2: find how many times the runner would have to run around the perimeter.

2 kilometers = 2000 meters

2000/500=4

The runner would need to go around the field 4 times to run 2km.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using this formula, we can find the distance between (16, 0) and (0, 12) as:

d = sqrt((0 - 16)^2 + (12 - 0)^2)

d = sqrt((-16)^2 + 12^2)

d = sqrt(256 + 144)

d = sqrt(400)

d = 20

Therefore, the distance between (16, 0) and (0, 12) is 20 units.

Answer:

Step-by-step explanation:

You want to know if the binomial 2x³ -10x can be factored further than 2x(x² -5) and how you can tell.

Usually, when we say "factor p(x)", where p(x) is a polynomial, we mean we want it factored to factors that have integer coefficients. In many cases, the result will be a product of linear and/or quadratic factors. Here, ...

  2x³ -10x = 2x(x² -5) . . . . . is factored to integers

When we want the polynomial "factored completely", or "factored to linear factors" the restriction that coefficients be integers or real numbers is removed. The difference of squares can be factored further, but irrational values are required:

  = 2x(x -√5)(x +√5) . . . . . factored completely to linear factors

You can tell if further factoring is possible by looking at the roots of the non-linear factors in question. If those roots are rational, you can continue factoring. If they are irrational or complex, then the problem statement will tell you whether further factoring is desired.

__

Additional comment

Of course, you need to be familiar with methods of factoring and of determining the possible rational roots of a polynomial. (A good graphing calculator can help.)

The horizontal distance covered by Viola is approximately 1282.6 meters.

The height of the plane is approximately 461.7 meters

The height of the pole is approximately 159.8 feet.

The perimeter is 44.2.

The horizontal distance covered by Viola can be calculated by using trigonometry. The angle of inclination is 9°, and the distance traveled up the hill is 200 meters.

Let x be the horizontal distance covered. Then we have:

tan(9°) = 200/x

x = 200/tan(9°) ≈ 1282.6 meters

Therefore, the horizontal distance covered by Viola is approximately 1282.6 meters.

We can use trigonometry to find the height of the plane. Let h be the height of the plane above the atoll, and let d be the horizontal distance from the airplane to the atoll. Then we have:

tan(7°) = h/d

h = d * tan(7°) ≈ 461.7 meters

Therefore, the height of the plane is approximately 461.7 meters.

We can use trigonometry to find the height of the pole. Let h be the height of the pole, and let d be the distance from the surveyor to the base of the pole. Then we have:

tan(44°) = h/(d + 4)

h = (d + 4) * tan(44°)

h = (140 + 4) * tan(44°) ≈ 159.8 feet

Therefore, the height of the pole is approximately 159.8 feet.

In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg and √3 times as long as the longer leg. Therefore, the shorter leg has length 18/2 = 9, and the longer leg has length 18√3/2 = 9√3.

The perimeter of the triangle is the sum of the lengths of the three sides, which are 9, 9√3, and 18. Therefore, the perimeter is:

9 + 9√3 + 18 = 27 + 9√3 ≈ 44.2

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After 2013 "changesums", the list {20, 1, 3} becomes {x, x, x}. The maximum difference between two numbers is 0 since all numbers are equal.

We can start by applying the "changesum" procedure to the list {20, 1, 3} repeatedly, until we have done it 2013 times.

After the first application, we get the list {4, 23, 21}. After the second application, we get {44, 25, 27}. We can continue applying the procedure to get the following list of values:

{44, 25, 27}

{69, 71, 52}

{142, 120, 140}

{262, 282, 262}

{524, 524, 544}

{1048, 1068, 1048}

{2116, 2096, 2116}

{4212, 4232, 4212}

After 2013 consecutive "changesums", the list will have the form {x, x, x} for some value x. The maximum difference between two numbers in the list will be 0 in this case, since all the numbers are equal.

Therefore, the maximum difference between two numbers of the list after 2013 consecutive "changesums" is 0.

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The coordinates of the final image for S' are (0, -7). The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the rotation, reflection, and translation of forms on a coordinate plane. Any line can be reflected, any point can be rotated, and every vector can be translated.

We are given a triangle QRS whose vertices are Q(-6, 6), R(-6, 0),and S(0, 0). The triangle is translated 7 units right, then rotated 90° clockwise about the origin.

So, from this we get the another triangle as Q'R'S' whose vertices become as follows after translation:

Q' = (-6 + 7, 6) = (1, 6)

R' = (-6 + 7, 0) = (1, 0)

S' = (0 + 7, 0) = (7, 0)

Now, we know that the rule for 90° clockwise rotation is that (x, y) becomes (y, -x).

So, we get the coordinates as:

Q' = (6, -1)

R' = (0, -1)

S' = (0, -7)

Hence, the coordinates of the final image for S' are (0, -7).

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Answer:

[tex]\large\boxed{\mathtt{x=8}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to solve for x.}[/tex]

[tex]\textsf{Note that our equation is in word form, let's change it into numerical form.}[/tex]

[tex]\large \tt { {4 \ plus \ 3 \ eighths \ x \ equals \ seven. } \atop {4+ \frac{3}{8} x = 7. } }[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Our goal is to find x. We should isolate x where its alone on the left side.}[/tex]

[tex]\underline{\textsf{How?}}[/tex]

[tex]\textsf{Simply subtract 4 from both sides to isolate x.}[/tex]

[tex]\large\underline{\textsf{Isolating x;}}[/tex]

[tex]\tt 4 - 4 + \frac{3}{8} x = 7 - 4[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt \frac{3}{8} x = 3[/tex]

[tex]\textsf{We don't know the value of x yet. We only know 3/8 of x.}[/tex]

[tex]\textsf{For x to equal 1, multiply both sides of the equation by the \underline{reciprocal} of the fraction.}[/tex]

[tex]\large\underline{\textsf{What is a Reciprocal?}}[/tex]

[tex]\textsf{A Reciprocal is a \underline{fraction} where the Numerator and the Denominator \underline{flip}.}[/tex]

[tex]\underline{\textsf{For example;}}[/tex]

[tex]\large \tt {Flip \ the \ Numerator \ and \ the \ Denominator.} \atop {The \ Reciprocal \ of \ \frac{5}{4} \ is \ \frac{4}{5}.}[/tex]

[tex]\large\underline{\textsf{Find the Reciprocal of} \ \frac{3}{8};}[/tex]

[tex]\tt{ The \ Reciprocal \ of \ \frac{3}{8} \ is \ \frac{8}{3}.}[/tex]

[tex]\underline{\textsf{Multiply;}}[/tex]

[tex]\tt \frac{8}{3} \times \frac{3}{8} x = 3 \times \frac{8}{3}[/tex]

[tex]\large\boxed{\mathtt{x=8}}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textsf{Four plus three eighths x equals seven}[/tex]

[tex]\huge\textbf{Equation should look like:}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\huge\textbf{How will we solve for it?}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4= 7}[/tex]

[tex]\large\text{SUBTRACT 4 to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4 - 4 = 7 - 4}[/tex]

[tex]\large\text{CANCEL out: 4 } \rm{-}\large\text{ 4 because it gives you 0.}[/tex]

[tex]\large\text{KEEP: 7 }\rm{-}\large\text{ 4 because it help us solve for the x}-\large\text{value.}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 7 - 4}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 3}[/tex]

[tex]\large\text{MULTIPLY }\rm{\dfrac{8}{3}\large\text{ to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x\times\dfrac{8}{3} = 3\times\dfrac{8}{3}}[/tex]

[tex]\large\text{CANCEL out: }\rm{\dfrac{3}{8}\times\dfrac{8}{3}\large\text{ because it gives you 1.}[/tex]

[tex]\large\text{KEEP: }\rm{3\times\dfrac{8}{3}\large\text{ because it gives the x}\rm{-}\large\text{value.}[/tex]

[tex]\mathtt{x= 3\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x= \dfrac{3}{1}\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x = \dfrac{3\times8}{1\times3}}[/tex]

[tex]\mathtt{x = \dfrac{24}{3}}[/tex]

[tex]\mathtt{x = 24\div3}[/tex]

[tex]\mathtt{x = 8}[/tex]

[tex]\huge\textbf{What is the overall answer?}[/tex]

[tex]\huge\boxed{\mathtt{x = 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. Equations are used in many disciplines, including physics, engineering, economics, and finance, to describe connections between quantities and to solve problems. For instance, the formula "2x + 5 = 11" states that the number 11 is equal to the sum of the two variables x and 5. We can determine that x equals 3 by finding a solution for x. On the basis of mathematical relationships, equations enable us to locate unknown values and create predictions.

given

We must evaluate the supplied data and search for trends to ascertain which machine generates parts at a steady rate. Calculating the ratio of parts produced for each machine over time and checking to see if the ratios are stable are two methods for achieving this.

The ratios for machine Q are:

9/1 = 9

18/3 = 6

72/9 = 8

Machine Q doesn't create parts at a constant rate since the ratios are inconsistent.

The ratios for machine R are:

8/1 = 8

24/3 = 8

72/9 = 8

As a result of the constant ratios, machine R consistently produces parts.

The ratios for machine S are:

6/1 = 6

18/3 = 6

52/9 ≈ 5.78

Machine S does not generate parts at a constant rate because the ratios are inconsistent.

As a result, we may formulate the following equation to represent the components made by machine R:

Y = kX

where k represents the machine R's constant rate of production and Y represents the quantity of components produced in minutes. Any of the ratios calculated above can be used to determine the value of k:

8 pieces per minute equals k.

Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

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The value of the given integral by converting it into polar coordinates is [a⁴ / 4] (1 - (-1)) = [a⁴ / 2].Hence, the correct option is (d) [a⁴ / 2].

To evaluate the iterated integral by converting to polar coordinates,

we need to change the limits of the integral into polar coordinates.

So the given integral in polar form is ∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0)[tex]4r^3cos(θ)sin(θ)dr dθ.[/tex]

The polar coordinate conversion is given by x = r cos(θ) and y = r sin(θ).Given integral ∫a0∫0−√a2−y24x2y dx dy can be expressed in the form of polar coordinates as follows:

∫(from θ = 0 to θ = π/2) ∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr dθ

Where, x = r cos(θ) and y = r sin(θ)

Now, we can evaluate this integral using the polar coordinate conversion.

∫(from θ = 0 to θ = π/2)

∫(from r = a to r = 0) 4r³cos(θ)sin(θ) dr

dθ=∫(from θ = 0 to θ = π/2) [cos(θ)sin(θ) ∫(from r = a to r = 0) 4r³ dr ]

dθ= ∫(from θ = 0 to θ = π/2) [ cos(θ) sin(θ) (r⁴) / 4] (from r = a to r = 0)

dθ=∫(from θ = 0 to θ = π/2) [cos(θ) sin(θ) (a⁴) / 4]

dθ= [a⁴ / 4] ∫(from θ = 0 to θ = π/2) sin(2θ)

dθ= [a⁴ / 4] ([- cos(2θ)] from θ = 0 to θ = π/2)

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Yes we can say that Liam's interpretation of the algebraic expression is correct because it has two variables, coefficients of 6 and 3, and two terms.

In Mathematics, an algebraic expression is defined as an expression that is normally made up of variables, constants, coefficients, and then arithmetic operations. These mentioned items are the different parts that make up the algebraic expression.

Let us consider an expression, 3x + 5y - 8

Here, the parts of the expression are:

Coefficients are 3 and 5

Constant is 8

Variables are x and y

Terms are 3x, 5y

Mathematical operators used are plus (+) and minus (-).

We are given the algebraic equation 6x + (-4) = 3y

Thus, it has:

Two coefficients which are 6 and 3

Two variables which are x and y

Two terms which are 6x and 3y

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