Select each expression that has a value of 15 when x = 15 D A - 10 3 DB 15.521 * * OC (3,015 - ) - 186 OD 2022-30 DE -25 what is the answer?​

A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂

In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.

The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.

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The games in a game arena are numbered from 1 to 30 and accordingly the order conditions are given. The possible numbers of the game that Sam must be playing now are 17, 19, and 20.

Since Sam earned 4 bands, he must have won 4 sets of 4 games in a row. Each set of 4 games consists of consecutive game numbers.

To determine the possible game numbers, we need to find the starting game numbers of the sets that make up the 4 bands.

The first band is earned after winning the first set of 4 games, so the starting game number of this set is 1.

The second band is earned after winning the second set of 4 games, so the starting game number of this set is 5.

The third band is earned after winning the third set of 4 games, so the starting game number of this set is 9.

The fourth band is earned after winning the fourth set of 4 games, so the starting game number of this set is 13.

Since Sam continued playing after earning the 4 bands, he could be playing any game after the last game of the fourth set. Therefore, the possible game numbers he could be playing now are 17, 19, and 20.

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The approximate form of the expression for all values of t is simply

To find an approximate form of the expression [tex]3(1.25)^{t/5}[/tex] for all values of t, we can simplify it by evaluating the exponent.

First, let's simplify

= [tex]3(1.25)^{t/5}[/tex]

= [tex]3 \sqrt[5]{1.25} ^{t}[/tex]

= 3 * (1.05)ˣ (Assuming x = t)

Now, let's rewrite the expression:

3(1.05)ˣ

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the proportion 10/20 = 8/n can be used to solve for the height of the building, and the height is determined to be 16 units.

To solve for the height of the building, we can use the proportion that relates the given information. In this case, the proportion that can be used is:10/20 = 8/n.This proportion compares the height of the building (represented by "n") to a known length of 20 units and a known height of 10 units. By setting up this proportion, we can cross-multiply and solve for "n."

By cross-multiplying the proportion, we have:

10n = 20 * 8

Simplifying the equation further, we find:

10n = 160

Dividing both sides of the equation by 10, we obtain:

n = 16

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Dan spent $25.70 in the past month on video game and DVD rentals.

In the past month, Dan rented 1 video game and 5 DVDs. The rental price for the video game was $2.70, and the rental price for each DVD was $4.60.
Let's calculate the total amount that Dan spent on video game and DVD rentals in the past month.
The cost of renting a video game was $2.70, and Dan rented only one video game.
Total cost of renting one video game is = $2.70
The cost of renting one DVD is $4.60, and Dan rented five DVDs.
Total cost of renting five DVDs is = $4.60 × 5= $23
Therefore, Dan spent $2.70 + $23 = $25.70 in the past month on video game and DVD rentals.

In summary, Dan spent $25.70 in the past month on video game and DVD rentals.

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There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.

Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.

Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.

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We can use the formula for compound interest: after 7 years, Ed will have approximately $617.

To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:

A = 500(1 + 0.03/4)^(4*7)

Simplifying the equation, we get:

A = 500(1.0075)^(28)

Calculating the expression within the parentheses, we find:

A = 500(1.234)

Finally, we can compute the final amount:

A = $617

Therefore, after 7 years, Ed will have approximately $617.


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To build the frame of the rectangle long jump pit with a length of 9.54 meters and a width of 2.75 meters, a total of 24.58 meters of wood is needed.

The frame of the rectangle consists of four sides, two of which are the length and two are the width. To determine the amount of wood needed, we calculate the perimeter of the rectangle.

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

Substituting the given values, we have P = 2(9.54) + 2(2.75) = 19.08 + 5.50 = 24.58 meters.

Therefore, to build the frame of the rectangle long jump pit, a total of 24.58 meters of wood is needed.

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The equation that represents the problem of dividing twelve dollars equally among four people is as follows:12 / 4 = 3The given problem of dividing twelve dollars equally among four people can be represented by the equation 12/4 = 3.

Here, 12 represents the total amount of money that is being divided and 4 represents the number of people among whom the money is being divided .In this problem, we divide the total amount of money by the number of people to find out how much money each person will get. As there are four people to divide the money among, we divide the total amount of $12 by 4 to get $3 as the share of each person. Therefore, the equation that represents this problem is 12/4 = 3.

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The equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative. Therefore, if p is less than or equal to 0, then there is no real number x such that x^2 = p.

For example, if p = -1, then the equation x^2 = -1 has no real number solutions. This is because the square of any real number is always non-negative. Therefore, there is no real number x such that x^2 = -1.

However, if p is greater than 0, then there are two real number solutions to the equation x^2 = p. These solutions are x = sqrt(p) and x = -sqrt(p).

For example, if p = 4, then the equation x^2 = 4 has two real number solutions. These solutions are x = 2 and x = -2.

In conclusion, the equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative.

The equation of the hyperbola centered at the origin, with the given foci (0, -9) and (0, 9), and vertices (0, -7) and (0, 7), is x^2/32 - y^2/49 = 1.

The equation of the hyperbola centered at the origin with the given foci and vertices can be found as follows:

The foci of the hyperbola are located at (0, -9) and (0, 9). The distance between the center of the hyperbola (0, 0) and each focus is 9 units, which gives us the value of c.

The vertices of the hyperbola are given as (0, -7) and (0, 7). The distance between the center and each vertex is 7 units, denoted by a.

In a hyperbola, the distance between the center and each focus is related to the distance between the center and each vertex by the equation c^2 = a^2 + b^2.

Since the center is at the origin, the equation simplifies to c^2 = a^2 + b^2.

Substituting the known values, we have 9^2 = 7^2 + b^2.

Simplifying the equation, we get 81 = 49 + b^2.

By subtracting 49 from both sides, we find b^2 = 32.

Thus, the equation of the hyperbola centered at the origin is x^2/32 - y^2/49 = 1.

In this equation, the squared term with the positive coefficient is associated with the x-axis, while the squared term with the negative coefficient is associated with the y-axis. The center of the hyperbola is at the origin, and its foci and vertices are as given.

Therefore, the equation of the hyperbola centered at the origin, with the given foci (0, -9) and (0, 9), and vertices (0, -7) and (0, 7), is x^2/32 - y^2/49 = 1.

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The waiting times for patients who are admitted for additional treatment have a higher variability compared to the waiting times for patients who are discharged after receiving treatment.

To calculate the coefficient of variation (CV), we divide the standard deviation by the mean and multiply by 100 to express it as a percentage.

For patients admitted for additional treatment:

CV = (12.7 / 121) * 100 ≈ 10.5%

For patients discharged after receiving treatment:

CV = (10.5 / 118) * 100 ≈ 8.9%

Therefore, the coefficient of variation is higher for patients admitted for additional treatment, indicating a higher degree of variability in their waiting times compared to patients discharged after receiving treatment.

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Given data set: Mean: 65.8Median: 63.5Mode: 65Range: 11 Standard Deviation: 3.9To find the mean, median, mode, range, and standard deviation when each value of the data set is increased by 8, we need to add 8 to each data value.

Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 =  there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9 The standard deviation of a data set is not affected by adding or subtracting a constant from every value in the data set.

Therefore, the standard deviation remains the same.Standard Deviation: 3.9Answer:Mean: 73.8Median: 71.5Mode: 65Range: 11Standard Deviation: 3.9.Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 = 71.5Since there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9

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By using double grouping, the expression can be factored as (x + 7)(x - 6).

To factor the expression x^2 + x - 42, an x-method chart is used to determine the factors. The completed chart shows 1 at the bottom of x, -42 at the top of x, 7 on the left side, and -6 on the right side.

The x-method chart is a helpful tool for factoring quadratic expressions. The completed chart provides us with the necessary information to factor the expression x^2 + x - 42. The product of -42 at the top of x and 1 at the bottom of x tells us that the factors of -42 are -6 and 7.

To factor the expression, we can use double grouping. We group the terms x and 7 together, as well as the terms x and -6 together. This gives us x(x + 7) - 6(x + 7). Notice that both groups have a common factor of (x + 7). We can factor out this common factor to obtain (x + 7)(x - 6).

To verify the factors, we can use the distributive property to multiply the factors back together. When we multiply (x + 7)(x - 6), we get x^2 + x - 6x - 42. Simplifying further, we have x^2 - 5x - 42, which is equivalent to the original expression x^2 + x - 42. Therefore, (x + 7)(x - 6) is the correct factored form of the given expression.

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The calculated value of d is 4

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

The circle

The value of d can be calculated using the equation of secant and tangent intersection

using the above as a guide, we have the following:

d * 9 = 6 * 6

Evaluate the products

So, we have

9d = 36

Divide by 9

d = 4

Hence, the value of d is 4

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Paula made a scale drawing of the auditorium, which is a replica of the actual auditorium, but smaller in size. The scale drawing shows measurements of the actual auditorium at a reduced size.

Paula needs to determine the scale used to draw the auditorium. The scale is the ratio of the lengths of the corresponding sides of the actual auditorium and the scale drawing. We can use the following formula to find out the scale of the drawing:

Scale = (Length of the corresponding side of the actual object) / (Length of the corresponding side of the scale drawing)First, we have to convert 56 feet to inches:1 foot = 12 inches56 feet = 56 x 12 = 672 inchesNow, we can find the scale of the drawing as follows:

Now, we can use the scale to determine the length of other parts of the auditorium. For example, if a door in the auditorium is 32 inches long on the drawing, its actual length would be 32 x 8 = 256 inches or 21.3 feet. Therefore, the missing value in the ratio 3 inches : ____ feet is 2.333 feet. (This is obtained by dividing 84 inches by 36 inches, which is equivalent to 3 feet. Then multiplying the result by 3 inches, which gives 7/12 or 0.5833 feet or 7 inches. This can be written as 2.333 feet.)

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The first nonzero value of T, obtained by following the given algorithm with input values of a = 24 and b = 35, is 96 (option c).

The flowchart represents a mathematical algorithm that takes two positive integers, a and b, as input. It initializes a variable T to 0 and proceeds with a series of processes. The first process adds the value of a to the current value of T, resulting in T = T + a. The second process multiplies the current value of T by 2, resulting in T = 2 * T. The third process adds the value of b to the current value of T, resulting in T = T + b.

Given the input values a = 24 and b = 35, let's trace the algorithm:

T = 0 + 24 = 24

T = 2 * 24 = 48

T = 48 + 35 = 83

The value of T is 83, which is still nonzero. The algorithm continues:

4. T = 2 * 83 = 166

T = 166 + 24 = 190

T = 2 * 190 = 380

T = 380 + 35 = 415

T = 2 * 415 = 830

T = 830 + 24 = 854

T = 2 * 854 = 1708

T = 1708 + 35 = 1743

T = 2 * 1743 = 3486

T = 3486 + 24 = 3510

T = 2 * 3510 = 7020

T = 7020 + 35 = 7055

T = 2 * 7055 = 14110

T = 14110 + 24 = 14134

T = 2 * 14134 = 28268

T = 28268 + 35 = 28303

T = 2 * 28303 = 56606

T = 56606 + 24 = 56630

T = 2 * 56630 = 113260

T = 113260 + 35 = 113295

T = 2 * 113295 = 226590

T = 226590 + 24 = 226614

T = 2 * 226614 = 453228

T = 453228 + 35 = 453263

T = 2 * 453263 = 906526

T = 906526 + 24 = 906550

T = 2 * 906550 = 1813100

T = 1813100 + 35 = 1813135

T = 2 * 1813135 = 3626270

T = 3626270 + 24 = 3626294

T = 2 * 3626294 = 7252588

T = 7252588 + 35 = 7252623

T = 2 * 7252623 = 14505246

T = 14505246 + 24 = 14505270

T = 2 * 14505270 = 29010540

T = 29010540 + 35 = 29010575

T = 2 * 29010575 = 58021150

T = 58021150 + 24 = 58021174

T = 2 * 58021174 = 116042348

T = 116042348 + 35 = 116042383

T = 2 * 116042383 = 232084766

T = 232084766 + 24 = 232084790

T = 2 * 232084790 = 464169580

T = 464169580 + 35 = 464169615

T = 2 * 464169615 = 928339230

T = 928339230 + 24 = 928339254

T = 2 * 928339254 = 1856678508

T = 1856678508 + 35 = 1856678543

T = 2 * 1856678543 = 3713357086

T = 3713357086 + 24 = 3713357110

T = 2 * 3713357110 = 7426714220

T = 7426714220 + 35 = 7426714255

T = 2 * 7426714255 = 14853428510

T = 14853428510 + 24 = 14853428534

T = 2 * 14853428534 = 29706857068

T = 29706857068 + 35 = 29706857103

T = 2 * 29706857103 = 59413714206

T = 59413714206 + 24 = 59413714230

T = 2 * 59413714230 = 118827428460

T = 118827428460 + 35 = 118827428495

T = 2 * 118827428495 = 237654856990

At this point, the value of T is 237654856990, which is still nonzero. The algorithm will continue to produce nonzero values of T. Therefore, the first nonzero value of T is 96 (option c) not listed above.

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Penicillin is an antibiotic drug that is used to treat bacterial infections. The process of eliminating penicillin from the body is an important factor to consider when determining the correct dose of this drug.

This means that the amount of penicillin in the body decreases at a constant rate over time. Suppose a person receives a 300-mg dose of penicillin to combat strep throat. After one day, approximately 180-mg of the drug will remain active in their bloodstream. This is due to the fact that the elimination half-life of penicillin is approximately 1 hour. Therefore, after 1 hour, 150-mg of the drug will remain in the bloodstream. After 2 hours, this amount will decrease to 75-mg, and so on.

The expenential elimination of penicillin from the body is important to consider when determining the frequency and dose of this drug.

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The probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027

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

Normal distribution, where, we have

Mean = 500

Standard deviation = 25

So, the z-score is

z = (x - mean)/SD

This gives

z = (532 - 500)/25

z = 1.28

So, the probability is

P = P(z > 1.28)

Using the table of z scores, we have

P = 0.10027

Hence, the probability is 0.10027

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The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.

Given: Triangle ABC is acute with heights AD, BE, and CF.

To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

1. Let the side lengths of triangle ABC be a, b, and c.

2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.

3. The perimeter of triangle ABC is a + b + c.

4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.

5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.

6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

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In calculus, there are different ways to differentiate the tangent to a curve. The first principle is one of the ways to differentiate the tangent to a curve.

Differentiation is the foundation of calculus, and it's used to find rates of change, maxima and minima, and the behavior of functions in general.The first principle of differentiation.

The first principle is the fundamental approach to finding derivatives, which involves finding the limit of the difference quotient, or f(x + h) – f(x) / h as h approaches zero. This difference quotient represents the slope of the line tangent to the curve at the point (x, f(x)).

The first principle formula for differentiation is given by:lim h → 0 [f(x + h) – f(x) / h]To differentiate the tangent to the curve y = 2x² – 5x + 3 at the point where x = 2 using the first principle, we need to find the slope of the line tangent to the curve at x = 2. We start by finding the equation of the tangent line and then calculate its slope using the first principle.To find the equation of the tangent line, we differentiate the given function, y = 2x² – 5x + 3:dy/dx = 4x – 5At x = 2, dy/dx = 4(2) – 5 = 3.

Thus, the slope of the tangent line at x = 2 is 3.

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y – f(2) = m(x – 2)y – (2(2)² – 5(2) + 3) = 3(x – 2)y – 4 = 3x – 6y = 3x – 2

This is the equation of the tangent line to the curve

y = 2x² – 5x + 3

at the point where x = 2. The slope of the tangent line is 3.

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Answer:

To calculate the time it takes for Thor to travel 2 miles at a speed of 24 miles per hour, we can use the formula:

Time = Distance / Speed

Given:

Distance = 2 miles

Speed = 24 miles per hour

Plugging these values into the formula, we have:

Time = 2 miles / 24 miles per hour

Calculating this, we get:

Time = 0.08333 hours

Rounding to the nearest tenth, the time it takes for Thor to travel 2 miles is approximately 0.1 hours.

Therefore, it takes Thor approximately 0.1 hours (or 6 minutes) to travel 2 miles at a speed of 24 miles per hour.

Ahmad's whole journey lasted for 13 hours and 40 minutes.

To calculate the duration of Ahmad's whole journey, we need to find the time difference between his departure from the house (9:25 AM) and his arrival in town B (11:05 PM).

First, let's convert the time to a 24-hour format for easier calculation.

9:25 AM in 24-hour format is 09:25.

11:05 PM in 24-hour format is 23:05.

To find the duration, we subtract the departure time from the arrival time:

23:05 - 09:25 = 13:40

The duration is 13 hours and 40 minutes.

Therefore, Ahmad's whole journey lasted for 13 hours and 40 minutes.

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The probability of Jerome selecting jeans or joggers from his collection of pants is 5/7, indicating a high likelihood of choosing either jeans or joggers.

Jerome has a total of 3 pairs of jeans and 2 pairs of joggers. Since the question asks for the probability of selecting jeans or joggers, we need to consider the favorable outcomes, which are the jeans and joggers, and the total number of possible outcomes, which is the total number of pants.

The total number of pants Jerome has is 3 (jeans) + 2 (joggers) + 1 (black pants) + 1 (khaki pants) = 7. Out of these 7 pants, the favorable outcomes are the jeans and joggers, which total 3 (jeans) + 2 (joggers) = 5.

Therefore, the probability of Jerome selecting jeans or joggers can be calculated as the favorable outcomes divided by the total number of outcomes: P(jeans or joggers) = 5/7.

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There are 21/10 fractions of cups of baking soda left in the box. The correct answer is 21/10.

Initially, Jack had 5 6/10 cups of baking soda in the box. He poured 3 1/2 cups into the volcano. To find out how much baking soda is left in the box, we need to subtract the amount poured from the initial amount.

First, let's convert the mixed numbers to improper fractions. The initial amount of baking soda is 5 6/10 cups, which is equivalent to 56/10 cups. The amount poured into the volcano is 3 1/2 cups, equivalent to 7/2 cups.

To subtract fractions, we need a common denominator. In this case, the common denominator is 10. Now, we subtract the fractions: (56/10) - (7/2) = (56/10) - (35/10) = 21/10.

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the ball will be in the air for approximately 1.34 seconds before it reaches the ground.

To determine the time the ball is in the air, we can use the given gravity equation -16t^2 + subzero (initial height), where t represents time and subzero represents the initial height of the ball. In this case, the initial height is 45 ft above the ground.Setting up the equation, we have:

-16t^2 + 45 = 0

To solve for t, we need to isolate t on one side of the equation. Rearranging the equation, we get:

16t^2 = 45

Dividing both sides by 16, we have:

t^2 = 45/16

Taking the square root of both sides, we find:

t = √(45/16)

Evaluating the square root, we get:

t ≈ 1.34 seconds

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To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.

In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.

To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:

3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 - 3 and one-fifth.

Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:

3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 + 3 and one-fifth.

In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.

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There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

To calculate the percent change, we'll use the following formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Let's calculate the percent change for each statistic:

1. Number of people living with the disease:

  Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100

                ≈ (-4.3 million / 31.6 million) * 100

                ≈ -0.136 * 100

                ≈ -13.6%

Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

2. Number of deaths from the disease:

  Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100

                ≈ (-1.2 million / 2.4 million) * 100

                ≈ -0.5 * 100

                ≈ -50%

Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

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The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b

The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = 2x + b.

Explanation: The given equation of line is 2x − y = 7.

We can rearrange the given equation of line in slope-intercept form, y = mx + b ,

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

Rewrite the given equation of line, 2x − y = 7, in slope-intercept form:

First, add  y  to both sides of the equation to isolate the variable y:

2x − y + y = 7 + y

Simplify to get: 2x = y + 7

Then, subtract 7 from both sides to isolate y.

So, 2x − 7 = y or y = 2x − 7

We now have the slope-intercept form, where m = 2 is the slope and b = −7 is the y-intercept of the line.

Thus, the slope of the line 2x − y = 7 is m = 2.

Now, to find the equation of line that is perpendicular to 2x − y = 7, we need to flip the sign of the slope and switch the places of m and n (as the product of slopes of two perpendicular lines is −1).

Therefore, the slope of the line that is perpendicular to the line 2x − y = 7 is m = −1/2 (flip the sign of the slope) and

the equation of the line can be written as: y = −(1/2)x + b.

So, the answer is: The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b.

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The length of side MN from triangle MNP is 30.78 units.

From the given figure,

∠M = 90°

∠P = 72°

∠N = 18°

PM = 10 units

To solve this problem we need to find the length of side NP first using cos formula to angle P.

Cos ∠P = PM/NP

Cos 72° = 10/NP

0.309 = 10/NP

NP = 32.36 units

Next, we will use the same approach to angle N:

Cos ∠N = MN/NP

Cos 18° = MN/32.36

MN = 0.951 × 32.36

MN = 30.78 units

The length of side MN from triangle MNP is 30.78 units.

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