A manager wants to rearrange the shelves into 3 identical rows of short and tall shelves in each row

Answer

there's 120 members in total

84 not pensioners

Explaination

36÷30% = 120

70% are not pensioners

so 70% × 120 = 84

or you could minus the pensioners from the total 120-36=84

To solve the given problem we have to add the quantities of blue and yellow paint that were used by Gunther to make the mural.We are given that:Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.To add these two quantities we need to find a common denominator.

Here, the common denominator is 10.As such, we have to convert the mixed numbers to improper fractions.3 3/5 = (3 × 5 + 3)/5 = 18/5 2 1/10 = (2 × 10 + 1)/10 = 21/10Now, we can add the two fractions to get the total amount of paint used:18/5 + 21/10 = (36 + 21)/10 = 57/10 Therefore, Gunther used a total of 57/10 pints of paint to make the mural.Now, let's simplify this answer.

We can simplify the fraction by dividing both the numerator and denominator by the greatest common factor of 57 and 10, which is 1.57/10 = 5.7Thus, Gunther used 5.7 pints of paint to make the mural.In conclusion, Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint, or a total of 5.7 pints of paint to make the mural.

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The surface area of the cuboid is 324 cm2, the volume of the cuboid is 360 cm3. And the Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Solution: Length of cuboid = l = 12cmWidth of cuboid = b = 6cmHeight of cuboid = h = 5cmSurface area of cuboid = 2 (lb + bh + lh)

By substituting the given values of l, b and h, we get:

Surface area of cuboid = 2 (12 × 6 + 6 × 5 + 12 × 5) = 2 (72 + 30 + 60) = 2 × 162 = 324 cm2∴ The surface area of the cuboid is 324 cm2.Length of diagonal of cuboid, d =√l2 + b2 + h2By substituting the given values of l, b and h, we get:d =√12² + 6² + 5²=√144 + 36 + 25=√205=14.317 cm (approx)∴

The length of diagonal of the cuboid is 14.317 cm.

Volume of cuboid = lbh

By substituting the given values of l, b and h, we get:

Volume of cuboid = 12 × 6 × 5 = 360 cm3∴

The volume of the cuboid is 360 cm3.

(2b) Calculation of the area of a kite when its sides are 8cm and 6cm, and its vertical diagonal is 5cm.Given, sides of the kite are 8cm and 6cm respectively. Vertical diagonal of kite = 5cmArea of kite = (Product of diagonals)/2By using Pythagoras theorem on a kite, we have:

Horizontal diagonal of kite, d =√(52 + 42)=√41 = 6.403 cm

Area of kite = (Product of diagonals)/2

By substituting the given values of vertical diagonal and horizontal diagonal, we get:

Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Surface area of cuboid = 2 (lb + bh + lh)

Length of diagonal of cuboid, d =√l2 + b2 + h2Volume of cuboid = lbh2b) Area of kite = (Product of diagonals)/2.

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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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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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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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Emma is using x fence panels along the width of her garden. We need to find expressions for f(x), the width of her garden in feet, and g(x), the length of her garden in feet.

To find an expression for f(x), the width of Emma's garden, we need to determine how the number of fence panels (x) relates to the width. Assuming each fence panel has a fixed width, we can express f(x) as:

f(x) = x * width of each fence panel

The width of each fence panel may vary depending on the specific measurements provided. For example, if each fence panel has a width of 4 feet, then the expression for f(x) becomes:

f(x) = 4x

To find an expression for g(x), the length of Emma's garden, we need additional information or assumptions. The given information does not specify how the number of fence panels along the width relates to the length of the garden. Without this information, we cannot determine a specific expression for g(x).

In summary, we can express the width of Emma's garden, f(x), by multiplying the number of fence panels (x) by the width of each fence panel. However, we cannot determine a specific expression for the length of her garden, g(x), without additional information or assumptions.

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Complete question:

Emma wants to enclose her rectangular garden with fence panels. If she uses x fence panels along the width of her garden, find an expression for f(x), the width of her garden in feet.

f(x) = ?

"Next, find an expression for g(x), the length of her garden, in feet.

g(x) = ?

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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.

To calculate the number of cones that need to be sold in order to break even, we need to use the formula, Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit).

Here, the fixed cost is the cost of the freezer which is $200. The variable cost per unit is the cost of making each single-scoop ice cream cone which is $0.45. The selling price per unit is $1.25.Substituting the values in the formula, we get, Break-even point = $200 / ($1.25 - $0.45) = $200 / $0.8 = 250 cones Therefore, 250 cones need to be sold in order to break even.

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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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The mean absolute deviation (MAD) of the data set, rounded to the nearest tenth, is 5.4 bags of caramel corn.

To calculate the mean absolute deviation, we first find the mean of the data set by adding up all the values and dividing by the total number of nights: (16 + 23 + 32 + 24 + 19 + 27 + 18) / 7 = 19.7 bags.

Next, we find the absolute deviation for each night by subtracting the mean from each data point and taking the absolute value of the difference: |16 - 19.7| = 3.7, |23 - 19.7| = 3.3, |32 - 19.7| = 12.3, |24 - 19.7| = 4.3, |19 - 19.7| = 0.7, |27 - 19.7| = 7.3, |18 - 19.7| = 1.7.

We then calculate the average of these absolute deviations by adding them up and dividing by the total number of nights: (3.7 + 3.3 + 12.3 + 4.3 + 0.7 + 7.3 + 1.7) / 7 = 5.4 bags.

Therefore, the mean absolute deviation of this data set is 5.4 bags of caramel corn. This value represents the average distance between each data point and the mean, providing an indication of the variability or dispersion in the number of bags sold each night at the concession stand.

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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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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 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.

To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.

Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

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The area of the figure is given by 34cm²

The figure is made up of  triangle and a square.

The area of the figure is given by area of the square + area of the triangle

The area of a triangle is the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 b h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle

area of triangle = 1/2bh

Area of triangle = 1/2*10*6

Area = 30 com²

But the area of the square is S²

Where s = side

Area of square = 2*2 = 4cm²

therefore area of the shape is( 4+30)cm² = 34cm²

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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 value of the given expression is approximately 71.31.

[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

[tex]$$20 ÷ 2.5 = 8$$[/tex]

Now, the given expression becomes:

[tex]$$75 - 12 × 8 ÷ 26$$[/tex]

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

[tex]$$75 - 96 ÷ 26$$[/tex]

Evaluating division, we get:

[tex]$$75 - 3.6923$$[/tex]

Now, we will add and subtract from left to right.

[tex]75 − 3.6923 ≈ 71.31[/tex]

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

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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 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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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 weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m=  mass, and g = the acceleration due to gravity.

a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.

b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg.  c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.

d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).

e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.

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To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².

The first step is to substitute the given values into the formula:

29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).

Next, we simplify the equation and distribute the terms:

29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).

After combining like terms, we have:

29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.

Combining similar terms further, we get:

29,946 = 34x² + 40x - 6.

Now, we can rearrange the equation and set it equal to zero:

34x² + 40x - 29,946 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.

After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.

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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 length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.

To find the length of the arc, denoted as s, on a circle with radius r intercepted by a central angle θ, we can use the formula:

s = (θ/360°) * 2πr

Given:

Radius, r = 5 feet

Central angle, θ = 230°

Substituting the values into the formula, we have:

s = (230°/360°) * 2π * 5

Simplifying the expression:

s = (23/36) * 2π * 5

s = (23/36) * 10π

s = (23/18)π

To round the answer to two decimal places, we can approximate the value of π as 3.14:

s ≈ (23/18) * 3.14

s ≈ 4.02 feet

Therefore, the length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.

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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 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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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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The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.

To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.

Let's represent the number of apples as 'a' and the number of bananas as 'b'.

We know that a + b = 30, as the total number of fruits is 30.

From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.

To find the values of 'a' and 'b', we can use the table provided:

Types of Fruit  | a | b | a + b |

-------------------------------

16 apples and 14 bananas

20 apples and 10 bananas

22 apples and 8 bananas

24 apples and 6 bananas

We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.

If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.

We can also verify that a = 4b: 16 = 4 * 14.

Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.

It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.

In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.

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The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.

To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.

1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.

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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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