What type of breach discharges the nonbreaching party from his or her obligations under the contract

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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1. At atmospheric pressure, a sample of Cl2 gas has a volume of 3.45 L at 51.0ºC. What volume, in liters, will the Cl2 gas occupy if the temperature is decreased to -55.0ºC.

The gas laws state that the volume of a gas is directly proportional to its temperature, provided that the pressure and quantity of gas are constant. The equation for this is as follows:V1 / T1 = V2 / T2V1 = initial volume = 3.45 LT1 = initial temperature = 51.0ºCV2 = final volumeT2 = final temperature = -55.0ºCUsing the formula above and substituting the given values:V2 = (V1 x T2) / T1= (3.45 L x -55.0ºC) / 51.0ºC= -3.71 LThe volume of the Cl2 gas will occupy -3.71 L if the temperature is decreased to -55.0ºC.2. At constant temperature, a sample of 3.75 L of N2 at 775 mmHg pressure is compressed until the volume decreases to 3.15 L.

Follows:P1 x V1 = P2 x V2P1 = initial pressure = 775 mmHgV1 = initial volume = 3.75 LP2 = final pressureV2 = final volume = 3.15 LUsing the formula above and substituting the given values:P2 = (P1 x V1) / V2= (775 mmHg x 3.75 L) / 3.15 L= 922 mmHgThe new pressure of N2 is 922 mmHg, which can be converted to atmospheres using the conversion factor: 1 atm = 760 mmHgP2 = 922 mmHg x (1 atm / 760 mmHg) = 1.21 , the new pressure of N2 is 1.21 atm.

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Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.

His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.

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Therefore, the final answer with two significant digits is:Combined length = 110 cm

The combined length of the two rods can be found by adding the length of the first rod and the length of the second rod. The length of the first rod is given as 31.4 cm and the length of the second rod is given as 82.25 cm. Therefore, the combined length of the two rods can be found as follows:Combined length = length of first rod + length of second rod= 31.4 cm + 82.25 cm= 113.65 cm

However, we need to report our answer with the correct number of significant digits. The least number of significant digits in the given values is two, which is the number of significant digits in 31.4 cm. Therefore, we must round our answer to two significant digits. Since the digit in the hundredth place is 5, which is greater than or equal to 5, we must round up the digit in the tenth place.

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Yes, In order to determine the measure of EC, we need a proportion that relates the corresponding sides of similar triangles. we can use the proportion 9/10 = 8.75/EC to determine the measure of EC

The proportion is,

To solve for EC, we can cross-multiply and then solve for EC.

9/10 = 8.75/EC

9×EC=10×8.75

Simplifying we get,

EC = 9.72

Therefore, the measure of EC is approximately 9.72 units.

Please provide the correct proportion relating the corresponding sides of

ΔABC and ΔDEC, and I'll be happy to help you solve for EC.

Hence, the correct answer is:Yes, EC ≈ 9.7222.

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The required, Wallace performs graphic design work at the Computer Wholesale Warehouse.

Based on the description provided, Wallace performs visual design or graphic design work at the Computer Wholesale Warehouse. He develops visual impressions of products for advertisements and marketing materials. This involves creating visual elements, such as graphics, images, and layouts, to effectively convey messages and promote products.

Wallace's role at the Computer Wholesale Warehouse involves performing visual design work to create captivating visual impressions of products for advertisements and marketing materials, contributing to the overall effectiveness of their promotional efforts.

Thus, the required, Wallace performs graphic design work at the Computer Wholesale Warehouse.

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The quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.To determine the type of quadrilateral formed by the vertices W(-1,4), X(3,5), Y(4,1), and Z(0,0).

we can examine the properties and characteristics of the quadrilateral.

To identify the type of quadrilateral, we can consider its sides and angles.

1. Sides: We can calculate the lengths of the sides using the distance formula.

- Side WX = √[(3 - (-1))^2 + (5 - 4)^2] = √(16 + 1) = √17

- Side XY = √[(4 - 3)^2 + (1 - 5)^2] = √(1 + 16) = √17

- Side YZ = √[(0 - 4)^2 + (0 - 1)^2] = √(16 + 1) = √17

- Side ZW = √[(-1 - 0)^2 + (4 - 0)^2] = √(1 + 16) = √17

2. Angles: We can calculate the measures of the angles using the slopes of the sides.

- Angle WXY = arctan((5 - 4)/(3 - (-1))) ≈ 45.96°

- Angle XYZ = arctan((1 - 5)/(4 - 3)) ≈ -63.43° (Note: negative due to slope)

- Angle YZW = arctan((0 - 4)/(0 - (-1))) ≈ -75.96° (Note: negative due to slope)

- Angle ZWX = arctan((4 - 0)/(-1 - 0)) ≈ -90°

Based on the information above, we can conclude that the quadrilateral WXYZ is a parallelogram. This is because opposite sides are congruent (WX ≈ YZ and XY ≈ ZW), and opposite angles are congruent (WXY ≈ XYZ and YZW ≈ ZWX).

Therefore, the quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.

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The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.

The formula for a particular cylinder's total surface area is as follows:

TSA = 2πr (h + r)

Given that;

One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.

Hence, The plastic coating would be needed to coat the surface of the chain is,

2 × 3.14 × 2.5 × 22

= 345.4 cm²

So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

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Nadia has £5 to buy pencils and rulers. She says,"I will buy 15 pencils. Then I will buy as many rulers as possible. With my change, I will buy more pencils.

"Let the price of each pencil be p and the price of each ruler be r. Presenting the above scenario into the equation,15p + (x × r) = 5Here, x is the number of rulers to be bought. To minimize the number of pencils Nadia will buy with the change, we have to calculate the maximum number of rulers she can buy with the given £5.Let's assume Nadia buys a maximum of y rulers with all of her money, thus the number of pencils she will be left to buy will be,15p + (y × r) ≤ 5Therefore, Nadia can purchase 15 pencils and 2 rulers with £5 as shown below,15p + (2 × r) = 5Nadia can then buy more pencils with the remaining money, which is,£5 − [(15 × p) + (2 × r)] = Remaining money£5 − [(15 × 0.20) + (2 × 0.35)] = 0.40Hence, Nadia can buy 2 rulers and 15 pencils. She can buy only 2 rulers as many rulers she can buy with £5 is only 2.

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The distance that Benjamin travels in 100 seconds is 1400 meters.

Given that :

Benjamin is riding a unicycle.

Circumference of the tire = 2.8 meters

The number of times the tire revolves in 1 second = 5 times.

Distance travelled when revolved one time is :

Distance = 2.8 meters

Distance travelled in 1 second = 5 × 2.8 meters

                                                  = 14 meters

Distance travelled in 100 seconds is :

D = 14 × 100 = 1400 meters

Hence the distance is 1400 meters.

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The approximate radius of the bike wheel is 11.0 inches.

If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.

Circumference = 2piradius

where pi is approximately 3.14.

We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:

69.08 = 23.14radius

Dividing both sides by 2*pi, we get:

radius = 69.08 / (2*3.14) ≈ 11.0 inches

Therefore, the approximate radius of the bike wheel is 11.0 inches.

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Considering the ratio provided for cake pieces, the weight of the second piece of the cake is 2/7 kilograms.

Given that a one-kilogram cake is divided into 3 pieces whose weights are in the ratio 1:2:4.

We have to find the weight of the second piece.

Steps to find the weight of the second piece

Step 1: Let the three parts of the cake be x, 2x, and 4x respectively, where x is the weight of the first part of the cake.

Step 2: Find the total weight of the cake:

x + 2x + 4x = 7x

Total weight of cake = 7x

Total weight of cake = 1kg

Therefore,

7x = 1 kg

Or x = 1 / 7 kg.

Step 3: Find the weight of the second part of the cake (2x):

Weight of the second part of the cake = 2x

= 2 × (1 / 7)

= 2 / 7 kg.

Weight of the second part of the cake is 2/7 kilograms.

To conclude, the weight of the second piece of the cake is 2/7 kilograms.

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The cost of a call of m minutes duration, given the cost of the calls would be c = 0. 05 + 0. 99m

If you have $ 12 to spend, the time you can spend is 10.15 minutes.

The cost per minute would be :

= Difference between 5 and 10 minute call / Number of minutes

= ( 10. 86 - 5. 91 ) / 5

= $ 0.99

The cost per minute is therefore:

= 0. 99 x number of minutes

= 0. 99m

The initial cost is :

=  5 - 0. 99 x 5

= $ 0. 05

The number of minutes with $12 is:

= ( 12 - 0.05 ) / 0. 99

= 12. 1 minutes

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The graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.

The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.

The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.

Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:

X | Y | Ordered Pair

-- | -- | --

0 | 0 | (0, 0)

3 | 6 | (3, 6)

6 | 12 | (6, 12)

9 | 18 | (9, 18)

12 | 24 | (12, 24)

As you can see, the ordered pairs form a straight line.

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The solution to the linear system of equations in terms of a, b, and c is given by the values of x and y obtained from the determinants.

To solve the linear system of equations using determinants, we can use Cramer's Rule, which relies on the concept of determinants. The determinants involved in Cramer's Rule are the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy).

The general form of the linear system of equations is:

a1x + b1y = c1

a2x + b2y = c2

To find the solution using determinants, we first calculate the coefficient determinant (D):

D = | a1 b1 |

| a2 b2 |

The coefficient determinant D represents the determinant of the matrix formed by the coefficients of x and y.

Next, we calculate the x-determinant (Dx):

Dx = | c1 b1 |

| c2 b2 |

The x-determinant Dx is obtained by replacing the x-coefficients in the coefficient determinant D with the constants c1 and c2.

Similarly, we calculate the y-determinant (Dy):

Dy = | a1 c1 |

| a2 c2 |

The y-determinant Dy is obtained by replacing the y-coefficients in the coefficient determinant D with the constants c1 and c2.

Now, we can find the values of x and y using the determinants:

x = Dx / D

y = Dy / D

It's important to note that this method using determinants applies specifically to linear systems with two variables. For larger systems, the method becomes more complex and involves calculating determinants for higher-order matrices.

In summary, to find the solution using determinants, we calculate the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy) based on the given linear system of equations. Then, we find the values of x and y using the determinants. The solution is expressed in terms of a, b, and c.

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In 15 minutes, a water pump capable of pumping 13.2 gallons of water per minute will remove a total of 198 gallons of water from the pool.

If a water pump can pump 13.2 gallons of water in a pool every minute, we can calculate the amount of water it will remove in 15 minutes by multiplying the pumping rate by the duration. Therefore, 13.2 gallons/minute x 15 minutes = 198 gallons. During the 15-minute period, the water pump will continue to operate at a constant rate, removing water from the pool. Each minute, 13.2 gallons of water will be pumped out. When we multiply this rate by the duration of 15 minutes, we find that a total of 198 gallons of water will be removed from the pool. It's important to note that this calculation assumes a constant pumping rate without any interruptions or changes in efficiency.

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The correct representation of the equation "z minus 6 = 1.4" in words is "The difference of a number and z is the same as one and four-tenths."

The equation "z minus 6 = 1.4" can be represented in words as "The difference of a number and z is the same as one and four-tenths." This representation accurately conveys the meaning of the equation.

Let's break down the equation to understand its components. "z minus 6" represents the difference between the number z and 6. The equal sign indicates that this difference is equal to "1.4", which means one and four-tenths.

Now let's analyze the answer choices:

"The difference of a number and z is the same as one and four-tenths." This choice correctly represents the equation, expressing that the difference between a number and z is equal to 1.4.

"A number subtracted from one and four-tenths is equal to six." This choice represents a different equation, where a number is subtracted from 1.4, resulting in six. It does not match the original equation.

"Six less than a number is the same as one and four-tenths." This choice represents a different equation, where six is subtracted from a number, resulting in 1.4. It does not match the original equation.

"Six decreased by a number is equal to one and four-tenths." This choice represents a different equation, where six is decreased by a number, resulting in 1.4. It does not match the original equation.

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If we assume a normal distribution, we know that approximately 95% of the scores fall within 2 standard deviations of the mean. However, since we don't know the shape of the distribution.

To calculate the minimum proportion of scores that fall within 2.1 standard deviations on both sides of the mean, we need more information about the distribution, such as the shape (e.g., normal, skewed), mean, and standard deviation.

If we assume a normal distribution, we can use the empirical rule to estimate the minimum proportion. The empirical rule states that approximately 68% of the scores fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Therefore, if we assume a normal distribution, the minimum proportion of scores falling within 2.1 standard deviations on both sides of the mean would be slightly lower than 95%, but the exact proportion cannot be determined without more information about the distribution.

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The detail from the text that best supports the thesis is that over 3 million people visit Zion National Park every year, and the National Park Service works to accommodate them.

The thesis statement is not explicitly mentioned in the given text, but it can be inferred that the thesis is related to Zion National Park and its popularity.

The detail stating that over 3 million people visit Zion National Park every year supports this thesis by indicating the significant number of visitors the park attracts.

The fact that the National Park Service works to accommodate these visitors further strengthens the thesis.

This detail implies that the park's popularity requires the park service to take measures to ensure visitors have a positive experience and can enjoy the park's attractions.

By including this information, the text emphasizes the high visitation rate of Zion National Park, highlighting its appeal and significance as a tourist destination.

It suggests that the park's features, such as lush vegetation, deep canyons, towering sandstone cliffs, and a restless river, contribute to its popularity and the need for accommodations to manage the large number of visitors.

Overall, the detail about the park's annual visitation and the efforts made by the National Park Service to accommodate visitors provides strong support for the thesis statement related to Zion National Park's popularity and the measures taken to cater to the influx of tourists.

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The original price of one ticket is $37.50.

The original price of one ticket as x.

A coupon for $5 off the entire purchase, the price after the coupon is the total price minus $5. So the price after the coupon is $45.15 - $5 = $40.15.

The price after the coupon includes 7% sales tax, up the equation:

(1 + 7%) ×x = $40.15

To calculate the 7% sales tax,  $40.15 by 1.07:

$40.15 / 1.07 = $37.50

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Given,Number of moles of Aluminum fluoride = 12.52 mol AlF3The chemical equation of the reaction between aluminum oxide and fluorine is given by;

2Al2O3 + 6F2 → 4AlF3 + 3O2From the balanced equation above; 2 moles of Al2O3 will produce 4 moles of AlF3Hence, 1 mole of Al2O3 will produce 4/2 = 2 moles of AlF3Number of moles of Aluminum oxide needed to react with fluorine to produce 12.52 moles of aluminum fluoride = 12.52/2 = 6.26 moles Therefore, more than 250 moles of aluminum oxide are needed to react with fluorine to produce 12.52 moles of aluminum fluoride.

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The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.

We have the following functions to graph:f(x)=−32x and ​g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.

We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65

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The answer is C. 400 times more likely. The more likely is a manual filer to make an error than an electronic filer if 20% of all manually filed returns contain %-errors, and 0.05% of all electronically filed returns contain errors is 400 times using percentages.

It's important to note that percentages are ratios of numbers in relation to 100.

So, we must first convert 20% and 0.05% to decimals.

20% = 20/100

       = 0.200.0

5% = 0.05/100

     = 0.0005

Therefore, we know that if 20% of all manually filed returns contain errors, then 0.2 of every 1 return contains errors. Similarly, if 0.05% of all electronically filed returns contain errors, then 0.0005 of every 1 return contains errors.

To determine how much more likely a manual filer is to make an error than an electronic filer, we need to divide the probability of a manual filer making an error by the probability of an electronic filer making an error:(Probability of manual filer making an error) / (Probability of electronic filer making an error)= 0.2/0.0005= 400

Therefore, a manual filer is 400 times more likely to make an error than an electronic filer.

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The line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.

Let's consider a triangle ABC with median AD and midpoint M of AD. We want to prove that line BM trisects the side AC at point N.

To prove this, we can use the following steps:

Draw line BM and extend it to meet side AC at point N.

Since M is the midpoint of AD, we have AM = MD.

By the midpoint theorem, we also know that BM is half of AD, so BM = MD.

Therefore, we have AM = MD = BM.

We also know that triangles ABM and NBC are similar by angle-angle similarity, since they share angle B and have angles ABD and CBN that are alternate interior angles.

This means that the corresponding sides are proportional, so we have: AB/BM = BN/NC AB/MD = BN/NC (substituting BM=MD)

Multiplying both sides by 2, we get: AB/AD = 2BN/NC

Since AD is a median, we know that AB/AD = 1/2.

Substituting this into equation from step 7, we get: 1/2 = 2BN/NC

Solving for BN, we get: BN = NC/2.

This shows that line BM trisects side AC at point N.

Therefore, we have proved that the line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.

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

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

He also measures the angle DBK to be 55°. Therefore, ∠DBK = 55°.

To find the measure of the angle BDK, we can use the fact that the sum of the angles in a triangle is 180°.

∠BDK = 180° - ∠DBK - ∠BKD

Since DK ≅ BC, ∠BDK = ∠BCD.

∴ ∠BDK = ∠BCD = (125° - ∠BCD)

Simplifying the equation, we get:

2∠BCD = 125°

∠BCD = 62.5°

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

Hence, option D is correct.

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It is not possible to determine the area of the shape from the given information as the measurements of the sides and angles are not provided.

However, we can identify the shape as a trapezoid because it has one pair of parallel sides. A trapezoid is a quadrilateral with one pair of parallel sides. To calculate the area of a trapezoid, we can use the formula:Area of trapezoid = 1/2 × (sum of parallel sides) × (distance between parallel sides)If we have the measurements of the parallel sides and the distance between them, we can substitute them into the formula to find the area of the trapezoid.

If the measurements are not provided, we cannot find the area of the trapezoid. Thus, it is not possible to determine the area of the shape from the given information, which only tells us that it has one pair of parallel sides.

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The given figure has only one pair of parallel sides. The opposite sides of the trapezium are not parallel. The formula to calculate the area of the trapezium is given as:

A = (a+b)/2 * h, where 'a' and 'b' are the parallel sides of the trapezium and 'h' is the distance between these parallel sides.

We can clearly see that the parallel sides 'a' and 'b' are 6 cm and 10 cm, respectively, and the height 'h' of the trapezium is 4 cm.

Therefore, substituting these values in the above formula, we have:

A = (6 + 10)/2 * 4A = 16/2 * 4A = 8 * 4A

= 32The area of the trapezium is 32 sq cm.

Thus, the area of the given shape is 32 square centimeters.

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Morgan earns $378 for working 14 hours at the grocery store and 13 hours at the nursery. If she works gg hours at the grocery store and nn hours at the nursery, her calculated earnings would be $15gg + $19nn.

Morgan earns $15 per hour working at the grocery store and $19 per hour working at the nursery.

For the given scenario, if Morgan works 14 hours at the grocery store and 13 hours at the nursery, her earnings can be calculated as follows:

Earnings from grocery store job = $15 per hour * 14 hours = $210

Earnings from nursery job = $19 per hour * 13 hours = $247

Total earnings = Earnings from grocery store job + Earnings from nursery job

Total earnings = $210 + $247 = $457

Therefore, Morgan would earn $457 if she works 14 hours at the grocery store and 13 hours at the nursery.

For a general case where she works gg hours at the grocery store and nn hours at the nursery, her earnings can be calculated using the formula:

Total earnings = $15gg + $19nn

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In the function f(x) = 1/x, when x is close to zero, the value of f(x) approaches positive or negative infinity. As x approaches zero from the positive side (x → 0+).

The function f(x) = 1/x becomes increasingly large and approaches positive infinity. This is because dividing a positive number by a very small positive number yields a very large positive result.

On the other hand, as x approaches zero from the negative side (x → 0-), the function f(x) = 1/x also becomes increasingly large but in the negative direction, approaching negative infinity. Dividing a negative number by a very small negative number yields a very large negative result.

However, it is important to note that the function f(x) = 1/x is undefined at x = 0 since division by zero is undefined in mathematics. Therefore, we say that the function has a vertical asymptote at x = 0, meaning that the function gets arbitrarily close to positive or negative infinity as x approaches zero, but it never actually reaches zero. In conclusion, when x is close to zero in the function f(x) = 1/x, the value of f(x) could be positive or negative infinity depending on whether x approaches zero from the positive or negative side, respectively.

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The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.

After 60 turns, the fan will be rotating at 15 revolutions per second.

Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)

Final angular speed, ω₂ = 15 revolutions/sec

Angular acceleration, α = constant

Number of revolutions for the first part, n₁ = 60

Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions

Using the formula for the angular velocity, ω = ω₀ + αt

and the formula for the number of revolutions, n = ωt / 2π

We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α

The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁

We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0

Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α

The value of α can be found by equating the two formulas for t₂ obtained above:

20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²

We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s

Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.

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