Jade is training for a marathon. During her first week of training, each run she completes is 90 minutes long. She increases the time she runs by 10% each week. Write the explicit formula to represent how many minutes she runs after n weeks.

If y/z = 0.7, then α can be determined using the trigonometric ratio "tan".

Since y/z = 0.7, we can let y = 7x and z = 10x. Thus, y + z = 7x + 10x = 17x.Also, we have tan α = y/x = (7/10)x/x = 7/10.So, we have tan α = 7/10.Thus, α = tan⁻¹(7/10).

Now, we can use a calculator to evaluate the angle to the nearest degree.

Using a scientific calculator, we can compute tan⁻¹(7/10) ≈ 35.54°.

Hence, the measure of α to the nearest degree is 36° (since we round up to the nearest degree).

That α measures 36° to the nearest degree.

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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 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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- Plane 1 travels at a speed of 225 mph.

- Plane 2 has an airspeed of 3 times faster than Plane 1, which is 3 * 225 mph = 675 mph.

- The wind speed is 500 mph.

Let's analyze the information provided:

Plane 1:

- Distance traveled: 450 miles

- Direction: South

- Time taken: 2 hours

Plane 2:

- Distance traveled: 525 miles

- Direction: North

- Time taken: 3 hours

- Airspeed: 3 times faster than Plane 1

We can calculate the speed of Plane 1 and the wind speed by dividing the distance traveled by the time taken.

Plane 1's speed = Distance / Time = 450 miles / 2 hours = 225 miles per hour (mph)

Let's assume the speed of the wind is W mph.

For Plane 2, since it is traveling against the wind, we need to consider the effect of the wind on its speed. The effective speed of Plane 2 against the wind can be calculated as the airspeed of Plane 2 minus the wind speed.

Effective speed of Plane 2 = Airspeed of Plane 2 - Wind speed = 3 * Plane 1's speed - W

Now we can use the formula: Speed = Distance / Time to calculate the wind speed.

For Plane 2:

Effective speed of Plane 2 = Distance / Time = 525 miles / 3 hours = 175 mph

175 mph = 3 * 225 mph - W

W = 3 * 225 mph - 175 mph

W = 675 mph - 175 mph

W = 500 mph

The wind speed is calculated to be 500 mph.

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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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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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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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To determine the height of the pole, we can use the concept of similar triangles. The ratios of corresponding sides of similar triangles are equal.The height of the pole is 24 meters.

By setting up a proportion between the height of the pole and the length of its shadow and the height of the observer and the length of their shadow, we can find the height of the pole.

Let's denote the height of the pole as h. We can set up a proportion between the height of the pole and the length of its shadow and the height of the observer and the length of their shadow:

h / 16 = 1.80 / 1.20

By cross-multiplying and solving for h, we get:

h = (16 * 1.80) / 1.20 = 24

Therefore, the height of the pole is 24 meters.

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The required answer is [tex][4x² + 36x + 85]/(x + 4)².[/tex]

Given [tex]f(x) = x² + 5x + 4[/tex]and g(x) = 1/(x + 4).

We are to find (f ∘ g)(x)

Formula used:

The composition of two functions f(x) and g(x) is given by (f ∘ g)(x) = f(g(x))

To solve the above problem, we substitute g(x) in place of x in f(x).

Hence,[tex](f ∘ g)(x) = f(g(x)) = f(1/(x + 4))f(g(x)) = g(x)² + 5g(x) + 4[/tex]

Putting the value of g(x) we get,

[tex]f(g(x)) = g(x)² + 5g(x) + 4= [1/(x + 4)]² + 5[1/(x + 4)] + 4= [1/(x + 4)][1/(x + 4)] + 5/(x + 4) + 4= (1/(x + 4))(1/(x + 4) + 5/(x + 4) + 4)= [1 + 5(x + 4) + 4(x + 4)²]/(x + 4)²= [4x² + 36x + 85]/(x + 4)²[/tex]

Therefore, [tex](f ∘ g)(x) = [4x² + 36x + 85]/(x + 4)².[/tex]

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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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option B is the correct answer.

The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b

Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².

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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 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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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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Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8

In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.

In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.

In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.

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The dimensions of one of the identical triangular pieces of the paper airplane are A. 2 cm base, 3 cm height

From the given information, the paper airplane is designed in the shape of a trapezoid when viewed from the top. The trapezoid has a base of 6 centimeters, a height of 3 centimeters, and a top side length of 2 centimeters.

When we divide the trapezoid along the height, we get two congruent triangles. These triangles have the same shape and size, making them identical. The height of the triangle corresponds to the same height as the trapezoid, which is 3 centimeters.

Therefore, the dimensions of one of the identical triangular pieces of the paper airplane are a base of 2 centimeters and a height of 3 centimeters.

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Full question is:

Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.

What are the dimensions of one of the identical triangular pieces of the plane?

2 cm base, 3 cm height

3 cm base, 3 cm height

3 cm base, 4 cm height

3 cm base, 6 cm height

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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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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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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Inequalities with absolute value need to be set up differently to solve based on whether it is an "and" situation or an "or" situation.

When dealing with an "and" situation, we use a compound inequality and solve two separate inequalities. For an "or" situation, we set up two separate inequalities and solve them independently.

The approach differs because the absolute value can result in both positive and negative solutions, which must be considered when determining the valid range of solutions.

When encountering an "and" situation in absolute value inequalities, we use a compound inequality to account for both the positive and negative solutions. For example, if we have |x - 3| ≤ 5 and need to find the valid range for x, we set up two separate inequalities: x - 3 ≤ 5 and -(x - 3) ≤ 5. Solving each inequality separately yields the range of valid solutions for x.

On the other hand, when dealing with an "or" situation, we set up two separate inequalities to handle the positive and negative solutions independently. For instance, if we have |x + 2| > 3 and need to find the valid range for x, we set up the inequalities: x + 2 > 3 and -(x + 2) > 3. Solving each inequality separately provides the distinct ranges of valid solutions for x in the given scenario.

The reason for this distinction lies in the absolute value's property of yielding both positive and negative solutions. By setting up separate inequalities for each case, we ensure that all possible valid solutions are considered and captured appropriately.

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The area under the probability density function to the left of the mean for the standard normal distribution is 0.5.

The standard normal distribution, also known as the Z-distribution, is a bell-shaped distribution with a mean of zero and a standard deviation of one. The area under the curve of a probability density function represents the probability of an event occurring. Since the mean of the standard normal distribution is at the center of the distribution, the area to the left of the mean is symmetrically equal to the area to the right of the mean. Therefore, the area under the probability density function to the left of the mean is 0.5 or 50%. This means that there is a 50% probability of observing a value less than the mean in a standard normal distribution.

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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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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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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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We know that the bottle contains 3 gallons of bleach. More than 250 quarts can be produced from 3 gallons. Let's find out how many quarts there are in a gallon.1 US gallon is equivalent to 4 US quarts.

So 3 gallons equal 12 quarts. Hence, More than 250 quarts can be obtained from 3 gallons, since more than 250 is greater than 12.Therefore, we can find the price per quart by dividing the total cost by the total number of quarts: Price per quart = Total cost ÷ Total number of quarts Since the cost of a 3-gallon bottle of bleach is $15.60, the cost of 1 gallon would be $15.60 ÷ 3 = $5.20.The cost of one quart is $5.20 ÷ 4 = $1.30.Therefore, the price per quart is $1.30.

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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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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 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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La opción que interpreta correctamente la razón entre los lápices azules y rojos en la caja de 3:1 es la opción B: "Hay tres lápices azules y 1 rojo".

Cuando se dice que la razón entre los lápices azules y los rojos en la caja es de 3:1, significa que por cada grupo de tres lápices azules, hay un lápiz rojo.
La opción A indica que hay tres lápices rojos y 1 azul, lo cual es incorrecto ya que la razón especifica que hay más lápices azules que rojos. La opción C sugiere que hay el triple de lápices rojos que de lápices azules, lo cual también es incorrecto según la razón proporcionada. La opción D indica que hay el triple de lápices azules que de lápices rojos, lo cual es contrario a la razón establecida de 3:1.
Por lo tanto, la opción que interpreta correctamente la razón 3:1 es la opción B: "Hay tres lápices azules y 1 rojo".

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