P (-3,5), Q (1,7), R (8,1), and S (-4,-5) are connected to form a trapezoid. What is the length of SR? Round to the nearest hundredth.

To combine terms, we look for similarities or coefficients that can be added or subtracted. In the given expression, the terms that can be combined are 6 and Negative (m/5).

The given expression includes various terms: 6, 3.2m, two-fifths n, and Negative (m/5). To combine terms, we look for similarities or coefficients that can be added or subtracted.

Among the given terms, the terms 6 and Negative (m/5) can be combined. Since they both have numerical coefficients, we can add or subtract them.

Therefore, we can combine the terms 6 and Negative (m/5) to simplify the expression.

It's important to note that the combination of terms depends on the context of the expression and the desired simplification. Other combinations may be possible depending on the specific requirements of the problem.

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The wall area that needs to be painted, excluding the doorway, is 125 square feet.

The total area of the wall is obtained by multiplying its length and width:

Total area = 11 ft * 13 ft = 143 square feet.

The area of the doorway is given by multiplying its length and width:

Doorway area = 6 ft * 3 ft = 18 square feet.

To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:

Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.

Therefore, you will need 125 square feet of paint to cover the wall only.

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b is 10 times bigger than c. the ratio A:b is equivalent to the ratio a:c multiplied by 5: A:b = (a:c) * 5

To determine how many times b is bigger than c, we need to compare their respective ratios.

Given:

A:b = 1:5

a:c = 2:1

To make a comparison, we can find the relative sizes of b and c by considering the ratios they have with other variables.

From the ratio A:b = 1:5, we can rewrite it as A:b = 2:10 (multiplying both sides by 2).

Comparing the ratios A:b and a:c, we can see that the ratio A:b is equivalent to the ratio a:c multiplied by 5:

A:b = (a:c) * 5

Substituting the given ratios, we have:

2:10 = (2:1) * 5

Now, we can compare the values of b and c directly:

b = 10

c = 1

Therefore, b is 10 times bigger than c.

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To find the x-values that are solutions of the equation

[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3)[/tex], we first need to simplify the equation and find the zeros.

By subtracting x^2 + 6x + 3 from both sides of the equation, we get:

[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3) = 0[/tex]

[tex]x^3 + 5x^2 - x - 7 - x^2 - 6x - 3 = 0\\x^3 + 4x^2 - 7x - 10 = 0[/tex]

Now, to find the zeros of this polynomial, we set it equal to zero and factor it if possible:

[tex]x^3 + 4x^2 - 7x - 10 = 0[/tex]

By trying different values, we can find that x = -2 is a zero of the polynomial. Therefore, (x + 2) is a factor of the polynomial.

Using synthetic division or long division, we can divide the polynomial [tex]x^3 + 4x^2 - 7x - 10 = 0[/tex] by (x + 2):

[tex]| (x^3 + 4x^2 - 7x - 10) ÷ (x + 2) |= x^2 + 2x - 5[/tex]

Now, we can factor the quadratic equation x^2 + 2x - 5:

(x + 2)(x - 1) = 0

Setting each factor equal to zero and solving for x, we get:

x + 2 = 0 --> x = -2

x - 1 = 0 --> x = 1

Therefore, the x-values that are solutions to the equation x^3 + 5x^2 - x - 7 = x^2 + 6x + 3 are x = -2 and x = 1. The intersection points of the two polynomials occur at these x-values.

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The probability that a randomly selected male would have a higher SSHA test score than a randomly selected female is approximately 0.385.

To find the expected value of the difference (female minus male) between their SSHA test scores, we need to use the formula:

Expected value = E(female) - E(male)

where E(female) is the expected value of the SSHA test score for a female student, and E(male) is the expected value of the SSHA test score for a male student.

Using the given means and standard deviations, we can find the expected values:

E(female) = 120

E(male) = 105

Therefore, the expected value of the difference (female minus male) between their SSHA test scores is:

Expected value = E(female) - E(male) = 120 - 105 = 15

So we can expect that the female student will score, on average, 15 points higher than the male student.

To find the probability that a randomly selected male would have a higher SSHA test score than a randomly selected female, we need to use the formula for the standardized normal distribution:

z = (x - μ) / σ

where z is the standard score, x is the SSHA test score, μ is the mean, and σ is the standard deviation.

Using the given means and standard deviations, we can find the z-scores for the male and female students:

z_male = (x - 105) / 35

z_female = (x - 120) / 28

To find the probability that a randomly selected male would have a higher score than a randomly selected female, we need to find the probability that z_male is greater than z_female. This can be done using a standard normal distribution table or a calculator, and we find that the probability is approximately 0.385.

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In a ruby crystal with the composition (Al0.99Cr0.01)2O3, there are approximately 3.7 x 10^18 Cr3+ ions in a ruby of dimensions 1 cm^3. It is based on the molar mass and Avogadro's number.

To determine the number of Cr3+ ions in the ruby crystal, we need to consider the composition of the crystal and use some basic calculations. The composition (Al0.99Cr0.01)2O3 indicates that for every two formula units of the crystal, there is a total of 0.01 moles of Cr present.

First, we calculate the molar mass of Cr3+, which is 51.996 g/mol. Since the crystal has a composition of 0.01 moles of Cr, we can calculate the mass of Cr in the crystal as follows:

Mass of Cr = (0.01 moles) * (51.996 g/mol) = 0.52 g

Next, we convert the mass of Cr to the number of Cr3+ ions using Avogadro's number, which is approximately 6.022 x 10^23 ions/mol. The number of Cr3+ ions is given by:

Number of Cr3+ ions = (Mass of Cr) / (Molar mass of Cr3+) * Avogadro's number

Number of Cr3+ ions = (0.52 g) / (51.996 g/mol) * (6.022 x 10^23 ions/mol)

Calculating this expression gives us approximately 3.7 x 10^18 Cr3+ ions.

Therefore, in a ruby crystal with the given composition and dimensions of 1 cm^3, there are approximately 3.7 x 10^18 Cr3+ ions present.

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During the Cretaceous Period, Earth's air composition was similar to the present-day composition, consisting primarily of nitrogen (N2) and oxygen (O2).

The atmosphere contained approximately 78% nitrogen and 21% oxygen, with trace amounts of other gases such as carbon dioxide (CO2), water vapor (H2O), and noble gases.

However, the precise levels of these gases varied over time due to natural processes and geological events. The Cretaceous Period, which lasted from approximately 145 million to 66 million years ago, was characterized by high global temperatures and a lush environment, supporting a diverse range of plant and animal life.

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Let's assume the number of regular bouquets as "x" and the number of mini bouquets as "y".

According to the given information, each regular bouquet has 6 roses and 2 peonies, and each mini bouquet has 2 roses and 2 peonies.

Therefore, the total number of roses used in the regular bouquets would be 6x, and the total number of peonies used in the regular bouquets would be 2x.

Similarly, the total number of roses used in the mini bouquets would be 2y, and the total number of peonies used in the mini bouquets would be 2y.

We also know that the florist has a total of 60 peonies available.

So, the equation for the total number of peonies used in both types of bouquets would be:

2x + 2y = 60

Now, let's consider the total number of bouquets. The florist has a total of 100 bouquets.

So, the equation for the total number of bouquets would be:

x + y = 100

We have two equations:

2x + 2y = 60

x + y = 100

We can solve these equations to find the values of x and y, representing the number of regular and mini bouquets, respectively.

Using any suitable method for solving linear equations, we find that x = 30 and y = 70.

Therefore, the florist makes 30 regular bouquets and 70 mini bouquets.

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To open the mystery door, you need to input a 3-digit code. The code calculated using least common multiple to open the mystery door is 630.

Based on the given hints, let's determine the code.

Hint 1: The last two digits are the least common multiple of 5 and 6.

The least common multiple (LCM) of 5 and 6 is 30.

Hint 2: The hundreds digit is the greatest common factor of 12 and 18.

The greatest common factor (GCF) of 12 and 18 is 6.

Putting these hints together, we can construct the 3-digit code:

The hundreds digit is 6, and the last two digits are 30.

Therefore, the code to open the mystery door is 630.

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Juan earned $40 for mowing a yard and incurred expenses of $5.99 for lunch and $1.79 for water. Therefore, his total expenses amount to $5.99 + $1.79 = $7.78.

To calculate the amount of money he has left, we subtract his total expenses from his initial earnings: $40 - $7.78 = $32.22.

Juan's earnings of $40 are his starting point. From this, we deduct the expenses he incurred, which consist of the lunch cost of $5.99 and the water cost of $1.79.

Combining these expenses gives us a total of $7.78. By subtracting this total from his initial earnings, we find that Juan has $32.22 remaining. This represents the amount of money he has left after paying for his lunch and water. Juan can now inform his parents that he still has $32.22 available.

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The volume of the empty portion of Container B is given as follows:

34.6 ft³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

(the radius is half the diameter).

Hence the volume of Container A is given as follows:

V = π x 7² x 13

V = 2001.2 ft³.

The volume of container B is given as follows:

V = π x 6² x 18

V = 2035.8 ft³.

Then the volume of the empty portion of Container B is given as follows:

2035.8 - 2001.2 = 34.6 ft³.

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The range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.

The range of the function is a set of all possible values of a function. It is the set of all output values of a function. In the given function, h(x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Here is the solution;

As per the question, the given function is (x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.Now, let us find the range of the function; Let's find the value of the function at each of the domain points. x h(x)-2 h(-2) = -4-3 = -7 0 h(0) = -3/2 2 h(2) = -2 10 h(10) = 2

Therefore, the range of the function is {-7, -3/2, -2, 2}.Hence, the correct option is the last option.

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The statement that is true about this comparison is that they differ in the thousandths place, with 0.739 being greater than 0.7380.

The statement that is true about the comparison

0.739 > 0.7380

is that they differ in the thousandths place. The difference between the two numbers is

0.001 or 1/1000,

which is why we can say that they differ in the thousandths place. This difference is very small, but it is enough to make

0.739 greater than 0.7380.

The comparison between

0.739 and 0.7380

is true in that the former is greater than the latter by a small margin. The two numbers differ in the thousandths place, with 0.739 having a value of

0.739 and 0.7380

having a value of 0.738.

The difference between the two values is

0.001 or 1/1000,

which is very small.

However, this difference is enough to make 0.739 greater than 0.7380.

Therefore, the statement that is true about this comparison is that they differ in the thousandths place, with

0.739 being greater than 0.7380.

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fg(x) is 2x³ - 3x² + 2x - 3.To find fg(x), we need to multiply f(x) and g(x).

The given functions are f(x) = 2x - 3 and g(x) = x² + 1.

We know that (f · g)(x) = f(x) · g(x).

So, (f · g)(x) = (2x - 3)(x² + 1)

(f · g)(x) = 2x³ - 3x² + 2x - 3.

Hence, the value of fg(x) is 2x³ - 3x² + 2x - 3

Given f(x) = 2x - 3 and g(x) = x² + 1

We have to find fg(x) = f(x)g(x)

= (2x - 3)(x² + 1)

We will use the distributive law of multiplication to multiply the given two functions.

(2x - 3)(x² + 1)= 2x(x² + 1) - 3(x² + 1)

Expanding further, we get the following:

2x³ + 2x - 3x² - 3=2x³ - 3x² + 2x - 3

Therefore,

fg(x) = 2x³ - 3x² + 2x - 3.

So, we get the value of fg(x) as 2x³ - 3x² + 2x - 3.

We have found that fg(x) is 2x³ - 3x² + 2x - 3 by multiplying f(x) = 2x - 3 and g(x) = x² + 1.

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Now we know that;tan x = Opposite/Adjacent side of the angle x tan x = Opposite/Adjacent sideTherefore, the Opposite side = tan x * Adjacent sideHere, we have only the value of tan x.

Thus, we need the value of any one side to find the other side value. But, we don't have the value of any of the sides. So, we will take an arbitrary value of one of the sides, suppose 1.We know that tan x = Opposite/Adjacent sideNow, we have Adjacent side = 1Therefore, tan x = Opposite/1Opposite side = tan xNow, Opposite side = 0.2962 (from the given equation)

Therefore, the measure of the angle can be found using the tangent ratio formula.tan x = Opposite/Adjacenttan x = 0.2962/1tan x = 16.92°Thus, the measure of the angle x to the nearest tenth of a degree is 16.9°.Therefore, the answer is, the measure of angle x is 16.9° to the nearest tenth of a degree.

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The cost of a 12-minute phone call is $4.20.

The cost of a nine-minute phone call is $3.15. To find the cost of a 12-minute phone call, we must first determine the cost per minute. We can do this by dividing the cost of a nine-minute call by 9 minutes, which gives us the cost per minute.

3.15 ÷ 9 = $0.35 (cost per minute) Now that we know the cost per minute, we can find the cost of a 12-minute phone call by multiplying the cost per minute by the number of minutes. 12 × $0.35 = $4.20 Therefore, the price of a 12-minute phone call is $4.20.

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The correct answer is that the event you described is dependent.

When Yolanda grabs 2 red checkers and replaces them between each draw, the outcome of the first draw affects the probability of the second draw. This is because replacing the checkers means that the probability of drawing a red checker remains the same for each individual draw, but the overall probability changes after each draw.

Let's break it down:

In the first draw, Yolanda has a certain probability of drawing a red checker.

After the first draw, if Yolanda indeed drew a red checker, there is one less red checker in the pool and the total number of checkers has decreased.

In the second draw, Yolanda now has a different probability of drawing a red checker compared to the first draw because the pool of available checkers has changed.

Therefore, the outcome of the first draw affects the probability of the second draw, making the event dependent.

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Thus, the measure of the angle BDK is 62.5°.

Given that Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.

He also measures the angle DBK to be 55°. Therefore, [tex]∠DBK = 55°.[/tex]

Using these measurements, we need to find the measure of the angle BDK.

Step-by-step explanation:

Since DK ≅ BC, we know that [tex]∠BDK = ∠BCD[/tex].

We are given that ∠DBK = 55°.

The sum of the angles in a triangle is 180°. Therefore, we can find ∠BKD as follows:

[tex]∠BDK + ∠DBK + ∠BKD = 180°

∠BKD = 180° - ∠BDK - ∠BDK

∠BKD = 180° - 55° - ∠BDK

∠BKD = 125° - ∠BDK[/tex]

We know that ∠BDK = ∠BCD (because DK ≅ BC).

Therefore, ∠BCD = ∠BDK = 125° - ∠BDK.

Simplifying the equation, we get:

2[tex]∠BDK = 125°∠BDK = 125° / 2∠BDK = 62.5°[/tex]

Thus, the measure of the angle BDK is 62.5°.

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The area of the triangular park in square meters is given by (b * h) / 2, where "b" represents the base in meters and "h" represents the height in meters.

To find the area of the triangular park in square meters, we need the measurements of the triangular park in the scale drawing. Since the scale is 1 unit = 1 meter, the measurements in the scale drawing represent the actual measurements in meters.

To determine the area of the triangular park in square meters, we need the base and height of the triangle in meters.

Let's assume that in the scale drawing, the base of the triangular park is represented by a certain number of units, and the height is represented by another number of units.

If we denote the base of the triangular park as "b" units and the height as "h" units in the scale drawing, then the actual measurements in meters would also be "b" meters for the base and "h" meters for the height.

The formula for the area of a triangle is:

Area = (1/2) * base * height

Substituting the actual measurements in meters, we have:

Area = (1/2) * b meters * h meters

Area = (1/2) * b * h square meters

Area = (b * h) / 2 square meters

Therefore, the area of the triangular park in square meters is given by (b * h) / 2, where "b" represents the base in meters and "h" represents the height in meters.

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The true statements are: - (x × y) × z = x × (y × z) and - (x – y) – z = x – (y – z)

Let's evaluate each statement:

1. X y = y x:

  This statement is generally not true for complex numbers. Multiplication of complex numbers is not commutative, so in most cases, X y is not equal to y x.

2. (x × y) × z = x × (y × z):

  This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.

3. x – y = y – x:

  This statement is generally not true for complex numbers. Subtraction of complex numbers is not commutative, so in most cases, x - y is not equal to y - x.

4. (x y) z = x (y z):

  This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.

5. (x – y) – z = x – (y – z):

  This statement is true. The associative property holds for subtraction of complex numbers. The order of subtraction does not affect the final result.

To summarize, the true statements are:

- (x × y) × z = x × (y × z)

- (x – y) – z = x – (y – z)

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Devon should use motor 2 with body 1 to build the car with the greatest acceleration.

To determine which combination of motor and body would result in the greatest acceleration for the toy car, we need to calculate the force-to-mass ratio for each combination. The greater the force-to-mass ratio, the greater the acceleration.

For motor 1 and body 1:

Force-to-mass ratio = Force / Mass

= 10 N / 0.2 kg

= 50 N/kg.

For motor 1 and body 2:

Force-to-mass ratio = Force / Mass

= 10 N / 0.6 kg

= 16.67 N/kg.

For motor 2 and body 1:

Force-to-mass ratio = Force / Mass

= 15 N / 0.2 kg

= 75 N/kg.

For motor 2 and body 2:

Force-to-mass ratio = Force / Mass

= 15 N / 0.6 kg

= 25 N/kg.

Comparing the force-to-mass ratios, we can see that the combination with the greatest acceleration would be motor 2 with body 1, as it has a force-to-mass ratio of 75 N/kg. Therefore, Devon should use motor 2 with body 1 to build the car with the greatest acceleration.

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--The given question is incomplete, the complete question is given below " Devon has several toy car bodies and motors. The motors have the same mass, but they provide different amounts of force, as shown in this table.

The bodies have the masses shown in this table.

Which motor and body should Devon use to build the car with the greatest acceleration?

motor 1, with body 1

motor 1, with body 2

motor 2, with body 1

motor 2, with body 2"--

The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.

To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.

To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.

Converting the fractions to have a denominator of 12, we get:

James: 2/3 = 8/12

Gilbert: 11/12 (already in terms of 12)

Matthew: 5/6 = 10/12

Simon: 7/12 (already in terms of 12)

Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).

To find the difference between these two times, we subtract the slowest time from the fastest time:

8/12 - 11/12 = -3/12 = -1/4

Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.

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The average velocity of an airplane during its journey when it moves at a velocity of 200 km/hour for 45 minutes and changes its velocity to 240 km/hour for 35 minutes can be calculated as follows:The first step is to convert the time from minutes to hours.

We can do this by dividing the number of minutes by 60 (since there are 60 minutes in an hour).So, time taken to move at a velocity of 200 km/hr for 45 minutes = 45/60 = 0.75 hoursTime taken to move at a velocity of 240 km/hr for 35 minutes = 35/60 = 0.583 hoursNow we can find the total distance traveled by the airplane. We can do this by multiplying the velocity of the airplane with the time it traveled at that velocity.Distance traveled at 200 km/hr = 200 x 0.75 = 150 kmDistance traveled at 240 km/hr = 240 x 0.583 = 139.92 kmTotal distance traveled by the airplane = 150 + 139.92 = 289.92 km.

The average velocity of the airplane during its journey can now be found by dividing the total distance traveled by the total time taken to travel that distance. Total time taken = 0.75 + 0.583 = 1.333 hours Average velocity of the airplane = Total distance traveled.

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The slope of a line perpendicular to the line given by the equation 4x - 6y = -24 is -3/2.

To find the slope of a line perpendicular to the line given by the equation 4x - 6y = -24, we first need to put this equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the given equation, we get:

4x - 6y = -24

-6y = -4x - 24

y = (2/3)x + 4

So the slope of the original line is m = 2/3.

For a line that is perpendicular to this line, the slope will be the negative reciprocal of the original slope. That is, if the original slope is m, then the slope of the perpendicular line will be -1/m.

So for the line given by the equation 4x - 6y = -24, the slope of a line perpendicular to it is:

-1/m = -1/(2/3) = -3/2

Therefore, the slope of a line perpendicular to the line given by the equation 4x - 6y = -24 is -3/2.

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Therefore, at the equilibrium point, the number of DVDs will be 510.71 and the price per DVD will be $18.85 (rounded to the nearest cent).

The equilibrium point is the point at which supply and demand are equal. At this point, the price and quantity demanded will be stable. When a commodity's unit price increases, demand decreases, while the manufacturer usually increases the supply. The point at which supply and demand are equal is known as the equilibrium point. The quantity demanded and the price per DVD can be calculated when supply equals demand.

When supply is equal to demand, we can equate both equations as:

S = Dwhere S is supply and D is demand.

S = -0.05P + 600 ... equation 1

D = 0.3P - 60 ... equation 2

We will now solve the above equations for P, which is the price per DVD.

S = D-0.05P + 600 = 0.3

P - 60-0.05P - 0.3

P = -60 - 600-0.35

P = -660

P = 660/0.35

= 1885.71 cents

= 18.85 dollars (rounded to the nearest cent)

Now that we know the price per DVD, we can calculate the quantity demanded by inserting P into one of the above equations. Using equation 1:

S = -0.05(1885.71) + 600S

= 510.71

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The speed of the object, which is moving at 6 feet per day, can be expressed as approximately 0.00114 miles per year. To calculate this, we convert the feet to miles and the days to years.

To convert feet to miles, we divide the distance in feet by the number of feet in a mile. Since there are 5,280 feet in a mile, we divide 6 feet by 5,280 feet/mile, which gives us 0.00113636 miles.

Next, we convert the speed from per day to per year. Since there are approximately 365.25 days in a year (accounting for leap years), we multiply the speed in miles per day by 365.25 days/year. Multiplying 0.00113636 miles/day by 365.25 days/year gives us 0.41475 miles/year.

Rounding this answer to the nearest hundredth, we get approximately 0.41 miles per year.

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Answer:

[tex]\sf z - \dfrac{3}{4}[/tex]

Step-by-step explanation:

      Subtract 3/4 from z.

             [tex]\sf z - \dfrac{3}{4}[/tex]

To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.

Edgar's behavior is an example of a learning process known as operant conditioning. Operant conditioning is the concept that we learn to associate our behavior with its consequences, either positive or negative. We are motivated by rewards, such as praise, and punishments, such as criticism, that we experience as a result of our behavior.

In Edgar's case, his relief and ability to fall asleep after completing his research paper can be considered a reward. Thus, he has been conditioned to associate finishing his work before going to bed with positive consequences. This learning process is an example of positive reinforcement.

Positive reinforcement, in which a positive stimulus is used to encourage a desired behavior, is the most effective way to promote good behavior and discourage undesirable behavior. Positive reinforcement can take many forms, including praise, recognition, and tangible rewards.

By contrast, negative reinforcement, which involves removing an unpleasant stimulus, can also be used to encourage a desired behavior, but it is not as effective as positive reinforcement in the long term.

To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.

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The length of the third side of the isosceles triangle is 16x + 8.

Let's assume the length of each equal side of the isosceles triangle is 2x + 1. Therefore, the perimeter of the triangle can be calculated as follows:

Perimeter = 2(2x + 1) + third side

Given that the perimeter is 20x + 10, we can set up the equation:

20x + 10 = 2(2x + 1) + third side

Simplifying the equation:

20x + 10 = 4x + 2 + third side

To find the length of the third side, we isolate it on one side of the equation:

third side = 20x + 10 - 4x - 2

third side = 16x + 8

Hence, the length of the third side of the isosceles triangle is 16x + 8.

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The completed recursive function to describe the given sequence would be: f(n) = f(n-1) + 13, for n = 2, 3, 4, ...

The given sequence is: -34, -21, -8, 5, ...

To determine the recursive function, let's analyze the pattern in the sequence.

Starting with the first term, -34, if we add 13 to it, we get the second term, -21. Similarly, if we add 13 to the second term, we get the third term, -8. We can observe that each term is obtained by adding 13 to the previous term.

Based on this pattern, we can define the recursive function as follows:

f(1) = -34 (the first term)

f(n) = f(n-1) + 13 (for n = 2, 3, 4, ...)

This means that the nth term (where n is greater than 1) is obtained by adding 13 to the (n-1)th term.

For example, to find the fifth term of the sequence, we use the recursive formula:

f(5) = f(4) + 13

     = 5 + 13

     = 18

Therefore, the fifth term is 18.

Similarly, we can use the recursive formula to find any term in the sequence.

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