You decide to work fewer hours per week, which results in an 8% decrease in your pay. what percentage increase in pay would you have to receive in order to gain your original salary again?

Answer: -403

Step-by-step explanation:

The circumference of a circle is the distance around the edge or perimeter of the circle.

1) Radius = 5cm/2 = 2.5 cm

2) Radius = 28 mm/2 = 14 mm

3) Radius = 3 1/2 m * 1/2 = 3/4 m

4) diameter = 2 * 6cm = 12 cm

5) diameter = 2 * 2m = 4 m

6) diameter = 2 * 0.8 ft = 1.6 ft

Circumference can be calculated using the formula:

C = 2πr

7) circumference = 2πr = 2 * 3.14 * 10/2 = 31.4 in

8) circumference = 2 * 7 * 3.14 = 43.96 in

9) Circumference = 2 * 3.14 * 18/2 = 56.52 in

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The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+

To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.

First, let's find the radius of the pool, which is half of the diameter:

radius = 11 feet / 2 = 5.5 feet

The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]

curved area = height * circumference

[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]

[tex]curved area = 68.2 square feet[/tex]

The top and bottom of the pool are two circles with a radius of 5.5 feet:

circle area = π * radius²

[tex]circle area = 3.14 * 5.5 square feet[/tex]

[tex]circle area = 95.0 square feet[/tex]

To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:

Total area = curved area + 2 * circle area

Total area = 68.2 square feet + 2 * 95.0 square feet

Total area = 258.2 square feet

The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.

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The answers to the questions on linear combination have been solved below

1. We can start by multiplying both sides by -2 to eliminate the x-term:

2x + 4y = 0

-2(2x + 4y) = -2(0)

-4x - 8y = 0

Now, we have:

-4x - 8y = 0

9x + 4y = 28

We can now use linear combination by adding these two equations to eliminate the y-term:

(-4x - 8y) + (9x + 4y) = 0 + 28

5x = 28

Dividing both sides by 5, we get:

x = 28/5

Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the second equation:

2x + 4y = 0

2(28/5) + 4y = 0

56/5 + 4y = 0

4y = -56/5

y = -14/5

Therefore, the solution to the system of equations is:

x = 28/5

y = -14/5

We can check that these values satisfy both equations:

9x4y = 28

9(28/5)(-14/5) = 28

-352/25 = 28/25 (true)

2x + 4y = 0

2(28/5) + 4(-14/5) = 0

56/5 - 56/5 = 0 (true)

Therefore, the solution is verified.

2. The system of equations is:

5x + 3y = 41

3x - 6y = 9

We can simplify the second equation by dividing both sides by 3:

3x - 6y = 9

x - 2y = 3

Now we can use linear combination by multiplying the first equation by 2 to eliminate the y-term:

2(5x + 3y) = 2(41)

10x + 6y = 82

(x - 2y) + (10x + 6y) = 3 + 82

11x = 85

Dividing both sides by 11, we get:

x = 85/11

Now we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:

5x + 3y = 41

5(85/11) + 3y = 41

425/11 + 3y = 41

3y = 41 - 425/11

3y = (451 - 425)/11

y = 26/33

Therefore, the solution to the system of equations is:

x = 85/11

y = 26/33

We can check that these values satisfy both equations:

5x + 3y = 41

5(85/11) + 3(26/33) = 41

425/11 + 26/11 = 41

451/11 = 41 (true)

3x - 6y = 9

3(85/11) - 6(26/33) = 9

255/11 - 52/11 = 9

203/11 = 9 (true)

Therefore, the solution is verified.

3.

3(x - 2y) = 3(-8)

3x - 6y = -24

3x - 6y = -12

3x - 6y = -24

Subtracting the second equation from the first equation, we get:

0 = 12

This is a contradiction, since 0 cannot equal 12. Therefore, there is no solution that satisfies both equations.

This means that the system is inconsistent, and there are no solutions.

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The length of the diagonal AC in square ABCD is approximately 9.899 units.

To find the length of the diagonal AC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our case, since ABCD is a square, angle ABC is a right angle. Therefore, triangle ABC is a right-angled triangle with sides AB and BC both equal to 7 units. We can apply the Pythagorean theorem to find the length of diagonal AC (the hypotenuse):

AC² = AB² + BC²

Plugging in the side lengths:

AC² = 7² + 7² = 49 + 49 = 98

Now, we take the square root of both sides to find the length of AC:

AC = √98 ≈ 9.899

So, the length of the diagonal AC in square ABCD is approximately 9.899 units.

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The temperature are the times  indicated are:

T( 0) =   5.800°

T( 0.22) = -4.9094 °

T (0.44) = -2.6792 °

T(0.66) = 2.3244°

T(0.88)  = 4.8184°

T(1.1) = -4.1686 °

To solve the above, we need to use the formuala that we given which is T(x) = 5.8cos(3.8πx)

Entering the various values of x, can can obtain

T(0) = 5.8 cos (3.8π  (0) )  = 5.8cos(0) = 5.800

T(0.22) = 5.8 cos (3.8  π(0.22)) ≈ -4.9094

T(0.44) = 5.8cos (3.8π (0.44) ) ≈ -  2.6792

T(0.66) = 5.8cos(3.8π (0.66)) ≈ 2.3244

T(0.88) = 5.8cos(3.8π(0.88)) ≈ 4.8184

T(1.1) = 5.8 cos(3.8π(1.1  )) ≈ -4.1686

So the above answers are correct.

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We can use the given point P(3, 4) to find the values of sin(theta) and cos(theta) as follows:

[tex]sin(theta) = opposite/hypotenuse = 4/5[/tex]

[tex]cos(theta) = adjacent/hypotenuse = 3/5[/tex]

Since theta is a first-quadrant angle, we know that tan(theta) = sin(theta)/cos(theta).

Using the half-angle formula for tangent, we have:

[tex]tan(1/2 * theta) = ±√((1 - cos(theta))/2) / (1 + √((1 - cos(theta))/2))[/tex]

We can substitute the values of sin(theta) and cos(theta) that we found earlier:

[tex]tan(1/2 * theta) = ±√((1 - 3/5)/2) / (1 + √((1 - 3/5)/2))[/tex]

[tex]tan(1/2 * theta) = ±√(1/5) / (1 + √(1/5))[/tex]

[tex]tan(1/2 * theta) = ±√5 - 1[/tex]

Since theta is in the first quadrant, tan(1/2 * theta) is positive. Therefore:

[tex]tan(1/2 * theta) = √5 - 1[/tex]

We can simplify this expression by rationalizing the denominator:

[tex]tan(1/2 * theta) = (√5 - 1) / (√5 + 1) * (√5 - 1) / (√5 - 1)[/tex]

[tex]tan(1/2 * theta) = (5 - 2√5)[/tex]

So the answer is (5 - 2√5), which is approximately 0.382. Therefore, the answer is not one of the choices given.

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The minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

To find the minimum and maximum measurements of Joshua's model airplane, we need to subtract and add 0.5 inches to the given length of 45 inches, respectively.

Minimum measurement:

45 - 0.5 = 44.5 inches

Maximum measurement:

45 + 0.5 = 45.5 inches

Therefore, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

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Answer:

48

Step-by-step explanation:

can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48

The remaining part of the given shape was drawn about to its symmetry. The complete shape obtained is similar to the Hexagon shape.

Given half shape has the following points,

The points which are missing to complete the other symmetry are:

By joining the above missing points, we can obtain the full symmetry of the shape.

To rotate the obtained shape of the Hexagon to 180° about the origin, we have to inverse the above complete symmetry points. It simply means if the above points are having positive values, we can inverse it to negative and vice-versa.

By rotating the obtained shape to 180° about the origin, we can obtain the below following points,

The images are attached below for the complete symmetry shape.

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Given question is not having enough required information, so I am attaching the image of the shape which we have to work on,

If Susan stands 300 m away from the lighthouse and looks up at it with an angle of elevation of 5 degrees, the height of the lighthouse is approximately 26 meters. This calculation is important for navigation and other purposes.

To determine the height of the lighthouse, we can use trigonometry. We know that the angle of elevation, which is the angle between Susan's line of sight and the ground, is 5'. We also know the distance between Susan and the lighthouse, which is 300 m.

We can use the tangent function to find the height of the lighthouse:

tan(5') = height/300

To solve for height, we can cross-multiply and simplify:

height = 300 x tan(5')

Using a calculator, we get that the height of the lighthouse is approximately 26.2 m.

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So, depending on the original coordinates, moving down 9 units and left 2 units will end up in either the third or fourth quadrant of the coordinate plane.

A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In a two-dimensional space, such as the Cartesian plane, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal position (or abscissa) of the point and y represents the vertical position (or ordinate) of the point.

Here,

Starting from an arbitrary point (x, y), if we move down 9 units and left 2 units, we will end up at the point with coordinates (x - 2, y - 9). The new x-coordinate is obtained by subtracting 2 from the original x-coordinate, since we moved 2 units to the left. The new y-coordinate is obtained by subtracting 9 from the original y-coordinate, since we moved 9 units down.

The quadrant we end up in depends on the original coordinates (x, y) and the direction of the movement. If we start in the first quadrant (x > 0, y > 0) and move down and left, we will end up in the third quadrant (x < 0, y < 0).

If we start in the second quadrant (x < 0, y > 0) and move down and left, we will also end up in the third quadrant (x < 0, y < 0).

If we start in the third quadrant (x < 0, y < 0) and move down and left, we will end up in the fourth quadrant (x > 0, y < 0).

If we start in the fourth quadrant (x > 0, y < 0) and move down and left, we will still end up in the fourth quadrant (x > 0, y < 0).

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Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

Answer:

1/6

Step-by-step explanation:

Therefore, the simplified expression is 24.

To simplify the expression (-8)(10+(-5)+(-8)), you first need to solve the parentheses, following the order of operations, which requires solving the addition and subtraction within the parentheses before multiplying.

So, you have (-8)(10-5-8), which becomes (-8)(-3) after solving the parentheses. Finally, you can solve the multiplication by multiplying -8 by -3, resulting in 24.

It's important to remember the order of operations when simplifying expressions, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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Answer:

Step-by-step explanation:

Given cos(θ) = 5/9, you want the six trig functions of θ.

The relevant identities are ...

The sine of θ is ...

  sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9

  sin(θ) = (2/9)√14

Then the cosecant is ...

  csc(θ) = 1/sin(θ) = (9/2)/√14

  csc(θ) = (9√14)/28

The tangent of θ is ...

  tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)

  tan(θ) = (2/5)√14

Then the cotangent is ...

  cot(θ) = 1/tan(θ) = (5/2)/√14

  cot(θ) = (5√14)/28

The secant of θ is ...

  sec(θ) = 1/cos(θ) = 1/(5/9)

  sec(θ) = 9/5

The cosine is given in the problem statement.

Here are 98,280 ways to lay off 12 employees from the company.

What is combination?

In mathematics, a combination is a way of selecting objects from a set, where the order in which the objects are selected does not matter. Combinations are used in various areas of mathematics and statistics, as well as in real-world applications such as probability theory, genetics, and computer science.

We can solve this problem using combinations. We need to choose 12 employees out of a total of 14+8+6=28 employees. The number of ways to do this is:

[tex]{28 \choose 12} \\= \frac{28!}{12!16!} = 98,!280[/tex]

Therefore, there are 98,280 ways to lay off 12 employees from the company.

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Answer:

Step-by-step explanation:

Geographers use satellites primarily to capture detailed images of a location from space (option A). These images can provide valuable information about the landscape, climate, and natural resources of an area, among other things. Additionally, satellites can be used in combination with other technologies to collect and store digital information about a location (option B), such as mapping the distribution of vegetation or tracking changes in land use over time. While satellites can be used to track the location of moving objects on Earth (option C), this is not typically their primary function. Finally, organizing and representing data for a location (option D) is more closely associated with Geographic Information Systems (GIS) than with satellite technology specifically.

Answer:

A. Capture detailed images of a location from space.

Step-by-step explanation:

Geographers use satellites to capture high-resolution images of the Earth's surface from space. This enables them to study and analyze different aspects of the Earth, such as its topography, land use patterns, and weather systems. These images are also used in cartography, the science of map-making, to create accurate and up-to-date maps of the Earth's surface.

Answer:

B

Step-by-step explanation:

0.4 inches = 2 miles

x    inches = 8 miles

Cross multiplication:

0.4 * 8 = 2 * x

3.2 = 2x

x = 1.6''

The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.

To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.

For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches

Volume of large box = 8 × 2.5 × 10 = 200 cubic inches

For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches

The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches

Volume of small box = 6 × 2.5 × 10 = 150 cubic inches

The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches

So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.

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The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .

You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.

We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67

Now we can solve this system of linear equations to find the values of x and y.

We can start by adding both equations:

(x + y) + (x - y) = 191 + 67

2x = 258

Then we'll divide by 2 to find the value of x:

x = 129

Now, we can plug x into Equation 1 to find the value of y:

129 + y = 191

y = 191 - 129

y = 62

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The circumference of the tank is is 125.66m and the percentage of the circumference that is visible to the person is 10.24%.

a) To calculate the circumference of the cylindrical tank, using the formula C = 2πr, where C is the circumference and r is the radius of the tank. In this case, r = 20 m, so:

C = 2π(20 m) ≈ 125.66 m

b) To determine the percentage of the circumference visible to the person, we first need to calculate the angle (in degrees) that subtends the visible arc. This can be done using the inverse tangent function:

angle = atan(opposite/adjacent) = atan(20 m/60 m)

angle ≈ 18.43°

Since the visible arc is symmetrical on both sides, the total angle of the visible arc is twice the calculated angle:

total angle ≈ 36.86°

Now, calculate the percentage of the circumference that is visible by dividing the total angle by 360° and multiplying by 100%:

percentage = (36.86°/360°) × 100% ≈ 10.24%

So, the visible percentage of the circumference to the person is approximately 10.24%.

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The overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.

Let's assume the original value of Alec's house as $100. After the first year, the value of the house increased by 1%, which means the new value of the house is $101.

Now, in the second year, the value of the house decreased by 10% of its value at the end of the first year. Therefore, the new value of the house at the end of the second year can be calculated as $101 - (10/100)*$101 = $90.90.

To find the overall percentage decrease in the value of Alec's house for the two-year period, we can use the formula:

Overall percentage decrease = [(Original value - Final value)/Original value] * 100%

Substituting the values, we get,

Overall percentage decrease = [($100 - $90.90)/$100] * 100% = 9.9%

Therefore, the overall percentage decrease in the value of Alec's house for the two-year period is 9.9%.

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The scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.

What is measurement?

Measurement is the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others.

It depends on the actual weight of the peaches. If the weight of the peaches is closer to 4.158 pounds, then the scale would show 4.158 pounds. Similarly, if the weight of the peaches is closer to 4.168 pounds, then the scale would show 4.168 pounds.

Since the scale can measure weight to the nearest thousandth of a pound, it can differentiate between weights that differ by one-thousandth of a pound.

Therefore, the scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.

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The expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

We have been given the expression

a⁻¹³/a⁻⁶

We know that whenever there is a minus sign in the power, we need to consider a reciprocal of the number

Hence,

a⁻¹³ will become 1/a¹ and a⁻⁶ will become 1/a⁶

Hence the numerator and denominator will interchange to get

a⁶/a¹³

Now, we know that when a number is broght from denominator to the numerator, there is a minus sign added to the power. Hence we will get

a⁶ X a⁻¹³

Since the two numbers have the same base- a, we can add the powers up as there is multiplication sign in between to get

a⁶ ⁺ ⁽⁻¹³⁾

= a⁶ ⁻ ¹³

= a⁻⁷

Hence, the expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.

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Answer:

Billy can buy 19 or less than 19 stickers.

Step-by-step explanation:

  Let the unknown variable - number of stickers be 'x'.

   Cost of one sticker = $1.34

   Cost of 'x' stickers = 1.34 * x = 1.34x

   Maximum amount that can be spent for buying stickers = 80 - 54.50

                                                                                                 = $25.50

   Inequality:

          1.34x ≤ 25.50

 Solving:

         Divide both sides by 1.34,

            [tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]

            x ≤ 19.03

            x ≤ 19

Billy can buy 19 or less than 19 stickers.

OD. M = log(I/10,000)

How can the magnitude of an earthquake be calculated when its intensity is 10,000 times that of the reference earthquake?

The correct equation that calculates the magnitude, M, of an earthquake with an intensity 10,000 times that of the reference earthquake is option B: M = log(10,000/Io).

In the given equation M = log(I/IO), I represents the intensity of the earthquake being measured, and IO represents the intensity of the reference earthquake. Since the intensity of the earthquake in question is 10,000 times that of the reference earthquake, we substitute I with 10,000 times IO.

Therefore, the equation becomes M = log(10,000/Io), which is option B. This equation allows us to calculate the magnitude of the earthquake based on the relative intensity compared to the reference earthquake.

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Limiting space heating would help decrease the greatest carbon-releasing activity in US homes.

From the table, we can see that space heating accounts for the largest percentage of energy use in US homes at 45%. Therefore, by limiting space heating, we can significantly reduce the amount of carbon released into the atmosphere, thus decreasing our carbon footprint.

Other activities like limiting time in hot showers, wearing layers of clothing, and turning off lights and electronics when not in use can also help reduce our carbon footprint, but they are not as effective as limiting space heating.

Additionally, we can consider using energy-efficient heating systems, improving insulation, and reducing air leaks to further reduce our energy use and carbon footprint.

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