Mr. Remy Osta took earned leave for 50 days from February 10, 2008 onwards. When did he resume his duty?

The ratio of people who prefer streaming to the people surveyed is 25:50, or 1:2.

Ratio is a comparison of two or more numbers or quantities that indicates the relative size of the quantities. Ratios are expressed in the form of a fraction or decimal, and they are used in mathematics, statistics, and other sciences. Ratios can be used to compare the sizes of different objects or values, or to compare the relationships between different numbers. Ratios are often used to measure the efficiency of a process or the relationship between different variables.

This ratio indicates that half of the people surveyed prefer to stream movies, while the other half prefer to rent DVDs.

Of the 50 people surveyed, 5 had no preference, meaning that 45 out of the 50 people had a preference for either streaming or renting DVDs.

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On solving the provided question, we can say that Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

here,

we have a cuboid

Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

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Answer:

-3x^2 +3x +18

Step-by-step explanation:

Y= -3(x+2)(x-3)

= - 3 (x^2 - x - 16)

= - 3x^2 - 3(-x) - 3(-6)

= - 3x^2 +3x +18

n to the power of 6, also written as n⁶, is a mathematical operation that raises the number n to the sixth power. This means that n is multiplied by itself six times.

For example, if n = 2, then n⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.

Exponentiation is a mathematical operation that is used to represent repeated multiplication. The number that is being multiplied is called the base, and the number that represents how many times the base is being multiplied is called the exponent. In the case of n⁶, the base is n and the exponent is 6.

In general, when raising a number to a power, the result is the product of that number multiplied by itself the number of times represented by the exponent. For example, n³ = n × n × n and n⁴ = n × n × n × n.

In addition to being a mathematical operation, exponentiation also has practical applications in fields such as computer science, engineering, and physics.

For example, in computer science, exponentiation is used to perform fast computations, such as in the process of encryption and decryption. In engineering and physics, exponentiation is used to calculate rates of growth, such as in the case of compound interest and radioactive decay.

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On solving the provided question we can say that the value of trigonometry value is - [tex](sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin^6 x - cos^6x\\(sin^3x)^2 - (cos^3x)^2\\(sin x - cosx)(sinx + cosx)(1 + sinx cosx)(1 - sinx cosx)\\(sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

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Enlarging or contracting a figure's size is known as dilatation. In other words, a scale factor is used to either enlarge or diminish the image while maintaining similarity between the preimage and the image.

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Answer: 2 and 3

Step-by-step explanation:

Answer: x=1,y=3

Step-by-step explanation:

Given,

y - 1 =2x

y = 2x + 1-----(i)

Again,

We have,

y = 2x + 1

Now replacing the value of y from (i)

2x + 1= -x +

or, 2x + x= 3

or,3x= 3

So x=1

Now,

y=2x +1

or, y=2×1+1

so y=

Answer:

x=1, y=3. (1, 3).

Step-by-step explanation:

2y-2=4x

y=-x+4

----------

2y-2=4x implies 2(y-1)=2(2x), so y-1=2x.

(-x+4)-1=2x

-x+4-1=2x

-x+3=2x

3=2x-(-x)

3=2x+x

3=3x

x=3/3

x=1

y=-1+4=3

The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;

2x³ divided by x equals 2x²

x - 4 multiplied by 2x² equals 2x³ - 8x²

subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x

x² divided by x equals x

x - 4 multiplied by x equals x² - 4x

subtract x² - 4x from x² - 8x will give us -4x + 16

-4x divided by x equals -4

x - 4 multiplied by -4 equals -4x + 16

subtract -4x + 16 from -4x + 16 will result to a remainder of 0

Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.

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Answer:

c.

Step-by-step explanation:

Both triangles ABC and DEF are similar to each other based on angle angle similarity

Two triangles are said to be similar if the ratio of the corresponding sides of both triangles are proportional to each other. Also, all the three angles of one triangle are equal to that of the other triangle.

The angle angle (AA) similarity theorem states that two triangles are similar if two angles of one triangle is equal to that of the other triangle.

Both triangles ABC and DEF are similar to each other

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For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The given expression is - (x - 8)(x + 8)

Use the arithmetic operation of multiplication -

(x - 8)(x + 8)

x(x + 8) - 8(x + 8)

x² + 8x - 8x -64

Now, use the arithmetic operation of addition and subtraction -

x² + 8x - 8x -64

x² - 64

Now, collect the like terms on each side -

x² = 64

x = √64

Now, solve the radical form to get the value of x -

x = √64

x = 8

Therefore, the value of x is obtained as x = 8.

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The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ade and Ola share a sum of 4000.00 in a ratio of 3:5.

Let 'x' and 'y' be the number of shares that Ade and Ola have, respectively. Then the equations are given as,

x / y = 3 / 5            ...1

x + y = 4000        ...2

From equations 1 and 2, then we have

(3/5)y + y = 4000

(8/5) y = 4000

y = 2500

Then the value of the variable 'x' is calculated as,

x + 2500 = 4000

x = 1500

The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

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 Answer:

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.

Step-by-step explanation:

positive number to the power negative 1 is a number that is always less than 1.

Explanation: a-m = 1/am. when calculate have the result when a positive number is raised to the power of -1, we always get a number that is less than one; for example, 2-1 = 1/2 < 1.

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Answer:

7.5

Step-by-step explanation:

10 + ( 7 × 1.5) = 20.5

6 + ( 7 × 13 ) = 13

20.5 - 13 = 7.5

The trend line equation to estimate the hiker's elevation after 150 minutes is 2033 feet.

Given that,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

We must determine,

The trend line equation is used to calculate the hiker's elevation after 150 minutes.

In response to the question,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

Where x is the number of minutes and y is the elevation of the hiker in feet.

Substitute the value of x = 150minute in the given equation to find the trend line to estimate the hiker's elevation after 150minutes.

Therefore,

y = 9.16x + 659

x = 150

y = 9.16(150) + 659

y = 1374 + 659

y = 2033

As a result, the trend line equation for estimating the hiker's elevation after 150 minutes is 2033 feet.

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It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

10.2 + 5.8 > 4.5

16 > 4.5

Now we add 10.2 and 4.5

10.2 + 4.5 > 5.8

14.7 > 5.8

Now we add 5.8 and 4.5

5.8 + 4.5 > 10.2

10.3 > 10.2

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

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Answer:

y = 7

Step-by-step explanation:

The equation of a horizontal line is worth memorizing. It is:

y = anumber

(and just in case for future reference the equation of a vertical line is

x= anumber)

Well, you are given one point (3,7).That is in the form (x,y). So x is 3 and y is 7.

y is 7

y = 7

(if it helps...horizontal lines have 0 slope. So m = 0. The equation in point-intercept form is

y = mx + b

y = 0x + b

y = b this is the y= anumber) originally mentioned here)

The midpoint formula is a mathematical formula used to find the midpoint of a line segment, given the coordinates of the two endpoints of the segment. In class 11, it is defined as:

Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )

Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint of the segment.

For example, if the two endpoints of a line segment are (5,6) and (9,11)

Midpoint = ( (5 + 9)/2 , (6 + 11)/2 )

Midpoint = (7,8.5)

The midpoint of the line segment with endpoints (5,6) and (9,11) is (7,8.5)

It's worth noting that this formula can be adapted for three-dimensional points, where the midpoint formula would be

((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

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The exponential equation that matches the number of bacteria after 3 hours is given as follows:

y = 50(4)^3.

An exponential function is used to model this situation as the output is multiplied for each unit of the input.

The general format of an exponential function is given as follows:

y = a(b)^x.

In which:

In a lab experiment, a population of 50 bacteria is able to quadruple every hour, hence the parameters a and b are given as follows:

a = 50, b = 4.

Thus the exponential function that gives the population after x hours is of:

y = 50(4)^x.

After three hours, we have that x = 3, hence the population is given as follows:

y = 50(4)^3.

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Based on the information, it can be inferred that Gustave gives 2,100 steps for every mile he walks.

To calculate the number of steps Gustave takes in a mile, we must take into account the information available about the ratio of steps to the distance he covers. In this case, we know that for every 3 miles, Gustave takes 6,300 steps.

To find how many steps he takes in a mile we must divide the number of steps into the number of miles he walked as shown below:

According to the above, Gustave takes 2,100 steps for every mile he walks.

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A. Without computing, the sum of 2, 3, and -2 is 3.

B. The explanation that supports the answer in Part A is (A) 2 and -2 are additive inverses and the sum of any number and its additive inverse is zero. The integer 3 is positive, so the sum with be positive.

An additive inverse of a number is the value that results in zero when added to the original number. It is the value that we add to a number in order to get zero. If an is the original number, then its additive inverse is minus a, i.e., -a, such that;

a+(-a) = a – a = 0

By changing the sign of a number, we can find its additive inverse. A positive number's additive inverse is negative, while a negative number's additive inverse is positive. Except for the sign, the numerical value will not change. The additive inverse of 8 is -8, for example, while the additive inverse of -6 is 6.

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The formula for a triangle is the area of a triangle = ½ × base × height. The formula for a square is the area of a square = side2.

This formula is used to calculate the area of any triangle when the base and height are known. For example, if the base of a triangle is 10 cm and the height is 5 cm, the area of the triangle is 25 cm2.

The formula for a square is the area of a square = side2. This formula is used to calculate the area of any square when the side length is known. For example, if the side of a square is 10 cm, the area of the square is 100 cm2. To calculate this, we can use the formula by squaring 10 (102 = 100).

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Answer:

Step-by-step explanation:

so basically Use the Triangle Sum Theorem to find the measure of each angle. Drag and drop the angle measures into the correct boxes to show the measure of each angle.

your welcome lol. -_-

The solution of (15 feet, 51.5 feet) represents the perimeter of a shape with a longest side of 15 feet.

Equation is a mathematical statement that express the equality of two expression use in equal sign.

The equation for this perimeter can be written as y = 2.5x + 14, where y is the perimeter of the shape and x is the longest side of the shape.

Thus, when x is 15 feet, the perimeter of the shape is 51.5 feet, as represented by the solution (15 feet, 51.5 feet).

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Answer:

The break even point is 380.

Step-by-step explanation:

36x + 200 = 76x

200 = 76x - 36x

200 = 40x

200/40 = x

5 = x

C = 36(5) + 200            R = 76(5)

C = 180 + 200              R = 380

C = 380

Answer:

The breakeven point is 5 units

Step-by-step explanation:

C is the cost ($) and R is the revenue ($).

We are told that :

R=76x

C=36x+200

Profit would be the Revenue minus the Cost:

Profit = R - C

The "breakeven point" is the situation in which there is neither a profit nor a loss.  That means that the total profit equals the total cost for x units. We want to find the value of x that would result in no profit or loss: Profit = 0.

0 = R-C

====

Profit = 76x - (36x+200)

Profit = 40x - 200

0 = 40x - 200         [The Breakeven Point]

-40x = -200

x = 5 units

5 units results in 76*5 or $380 in revenue.

5 units results in a cost of 36*(5)+200 or $380 in costs.

The result is breakeven (Profit = $390 - $380) of $0.00