Show that f(x) can be written as Px2+Qx+R+Vx+3+Wx-5and find the values of P, Q, R, Vand W.

Answer:

To find the resultant of two forces, you can use the following formula:

R^2 = F1^2 + F2^2 + 2F1F2cosθ

Where R is the resultant force, F1 and F2 are the magnitudes of the two forces, θ is the angle between the two forces, and cosθ is the cosine of the angle.

Plugging in the given values, we get:

R^2 = (500 kg)^2 + (875 kg)^2 + 2(500 kg)(875 kg)cos(100 deg)

R^2 = 250000 + 765625 + 767321.98

R^2 = 1788946.98

R = sqrt(1788946.98) ≈ 1337.3 kg

So the magnitude of the resultant force is approximately 1337.3 kg.

To find the angle that the resultant force makes with the smaller force, we can use the following formula:

tanθ = (F2sinθ)/(F1 + F2cosθ)

Where θ is the angle between the resultant force and the smaller force.

Plugging in the given values, we get:

tanθ = (875 kg sin(100 deg))/(500 kg + 875 kg cos(100 deg))

tanθ = 0.768

θ = tan^-1(0.768) ≈ 36.2 deg

So the angle that the resultant force makes with the smaller force is approximately 36.2 degrees.

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Answer:

0.625

Step-by-step explanation:

you divide 5 by 8

Therefore, the surface area of the rectangular prism is 280 square meters.

Area is a measure of the size of a two-dimensional region or surface, typically expressed in square units. It is the amount of space inside a closed shape or figure, and is calculated by multiplying the length and width of the shape or by using a formula specific to the shape. For example, the area of a rectangle can be found by multiplying its length and width, while the area of a circle can be found by multiplying pi (3.14) by the square of its radius. Area is commonly used in mathematics, science, engineering, and other fields to calculate quantities such as surface area, volume, and density.

Here,

The rectangular prism has 6 faces, and each face is a rectangle. To find the surface area, we need to find the area of each rectangle and add them up. The net shows that the dimensions of the prism are:

length = 10 m

width = 6 m

height = 5 m

The area of the top and bottom faces (which are congruent) is:

A = length × width

= 10 m × 6 m

= 60 m²

The area of the front and back faces (which are congruent) is:

A = length × height

= 10 m × 5 m

= 50 m²

The area of the two side faces (which are congruent) is:

A = width × height

= 6 m × 5 m

= 30 m²

To find the surface area, we add up the areas of all six faces:

Surface Area = 2 × (top and bottom faces) + 2 × (front and back faces) + 2 × (side faces)

Surface Area = 2(60 m²) + 2(50 m²) + 2(30 m²)

Surface Area = 120 m² + 100 m² + 60 m²

Surface Area = 280 m²

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The outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

A fair number cube labeled with the numbers 1 - 6 is equally likely to land on any of its faces when rolled.

Therefore, we can use probability to determine which outcome is most likely to occur after rolling the cube 100 times.

"The number 6 would never be rolled." This outcome is highly unlikely, but not impossible.
If the cube is fair, each number has an equal probability of being rolled, so the probability of rolling a 6 on any given roll is 1/6.

The probability of rolling a non-6 on any given roll is 5/6. The probability of not rolling a 6 in 100 rolls is (5/6)¹⁰⁰, which is approximately 0.0001. So, while it is very unlikely that the number 6 would never be rolled, it is not impossible.

"All the numbers rolled would be odd." This outcome is even less likely than the first one.

The odd numbers on the cube are 1, 3, and 5, each with a probability of 1/2.

The probability of rolling an odd number on any given roll is 1/2.

The probability of rolling an odd number on 100 rolls is (1/2)¹⁰⁰, which is an extremely small number, approaching zero.

"An even number would be rolled 50 times." This outcome is more likely than the first two.

The even numbers on the cube are 2, 4, and 6, each with a probability of 1/2.

The probability of rolling an even number on any given roll is 1/2.

If we assume that each roll is independent of the others, the probability of rolling an even number exactly 50 times in 100 rolls can be calculated using the binomial distribution and is approximately 0.0796.

This means that this outcome is not very likely, but still possible.

"The number 7 would be rolled at least once."

This outcome is impossible since the cube is only labeled with the numbers 1 through 6.

Therefore, the number 7 cannot be rolled.

Hence, Based on the above analysis, the outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.

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So the shaded region represents 30% of the whole. Each individual square on the grid must represent 1/100 of the whole.

A grid is a network of horizontal and vertical lines that intersect at regular intervals to form a pattern of squares, rectangles, or other shapes. It is commonly used as a tool for visualizing and organizing information, such as in maps, charts, graphs, and other types of diagrams. A grid can be simple or complex, depending on its purpose and the level of detail required. Simple grids may consist of only a few lines, while complex grids may have many lines and sub-divisions. In many cases, grids are labeled with coordinates or numbers to facilitate navigation or data analysis.

Here,

If the grid represents 1 in a grid of 100 squares, then each individual square on the grid must represent 1/100 of the whole.

The shaded region covers 30 squares out of the 100 squares in the grid. So the shaded region represents a fraction of the whole that can be calculated by dividing the number of shaded squares by the total number of squares:

30/100

This fraction can be simplified to:

3/10

Therefore, the shaded region represents three-tenths (3/10) of the whole. Alternatively, we can also express this as a percentage by multiplying the fraction by 100:

(3/10) x 100 = 30%

So the shaded region represents 30% of the whole.

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Answer:

Step-by-step explanation:

From the property of logarithm the input cannot be negative.

Therefore Z should be negative

As from the given question both sides have the (ln)
operator thus we can remove it.

-5Z=z^2-7Z

2Z=Z^2

Z^2=2Z

Z=2

If Zanele realized that the questiοnnaire is nοt suitable, it cοuld be fοr variοus reasοns, such as:

What is yοur name?

Name may nοt be needed tο prοvide advice οn taking a gap year.

Why dο yοu think that it is wise tο take a gap year after schοοl?

Taking a gap year after schοοl can prοvide students with a break frοm academic studies, help them gain life experience, and give them time tο explοre their interests befοre cοmmitting tο a university degree.

The benefits οf taking a gap year include persοnal and academic grοwth, increased indeοendence, cultural exοοsure, and the οοοοrtunity tο gain valuable wοrk οr vοlunteer exοerience.

Sοme students chοοse tο delay taking a gap year tο οursue a university degree first sο that they can stay οn track with their academic and career gοals. Others may want tο save mοney οr avοid interruοting their academic mοmentum.

The best way tο spend a gap year deοends οn yοur interests and gοals. Sοme pοpular gap year activities include traveling, vοlunteering, interning, wοrking, learning a new language οr skill, οr pursuing a passiοn prοject.

If Zanele realized that the questiοnnaire is nοt suitable, it cοuld be fοr variοus reasοns, such as:

The questiοns may nοt be relevant tο her specific situatiοn οr gοals.

The questiοns may nοt prοvide enοugh infοrmatiοn οr οptiοns tο help her make an infοrmed decisiοn.

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Three and one-half times one and two-thirds is equal to 35/6 or 5 5/6.

Given the statement in the question; "three and one-half times one and two-thirds"

First, we can be written as a fraction:

Three and one-half → 3 1/2 = 7/2

One and two-thirds → 1 2/3 = 5/3

So, we have:

(7/2) × (5/3)

To multiply these fractions, we multiply the numerators together and the denominators together:

( 7 × 5 ) / ( 2 × 6 )

35/6

5 5/6

Therefore, the simplified form is 35/6 or 5 5/6.

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Answer: [1]   G,D,L,K    [2] HF and AB    [3] X-Y Plane  [4] CE and LA

[5] A,L,B

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

Parents=x Children=Y 2(4)y+2y=120 10y=120 y=12

Mnemonic expressions can be useful for remembering mathematical concepts, formulas, and equations.

PEMDAS: This acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is used to remember the order of operations in mathematical calculations.

SOH-CAH-TOA: This acronym is used to remember the trigonometric ratios for sine, cosine, and tangent. SOH stands for Sine = Opposite/Hypotenuse, CAH stands for Cosine = Adjacent/Hypotenuse, and TOA stands for Tangent = Opposite/Adjacent.

FOIL: This acronym is used to remember the process of multiplying two binomials. It stands for First, Outer, Inner, Last, and represents the order in which you multiply the terms of the two binomials.

Please Excuse My Dear Aunt Sally: This sentence is used to remember the order of operations in mathematical calculations. It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

My Dear Aunt Sally Loves Ice Cream: This sentence is used to remember the signs of trigonometric functions in each quadrant of the unit circle. It stands for positive for cosine and ice cream, negative for sine and loves, and alternating for tangent.

These are just a few examples of mnemonic expressions in mathematics, and there are many more that can be used to help remember mathematical concepts and formulas.

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Answer:

Step-by-step explanation:

It would cost $13.02 to buy a Rectangle type frame for the painting.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. It is a type of quadrilateral.

The opposite sides of a rectangle are parallel and equal in length, and the adjacent sides are perpendicular to each other. This means that the opposite sides of a rectangle have the same distance apart throughout their entire length. The Perimeter is given by 2(L+B), where L and B are length and breadth respectively.

Now,

The painting measures 1 meter by 2 meters, so the perimeter of the painting (the total length of its sides) is:

P = 2 x (1 + 2) = 2 x 3 = 6 meters

To frame the painting, we need to buy a wooden frame with a perimeter of 6 meters. The frame shop charges $2.17 per meter for the wooden frame, so the cost of the frame would be:

Cost = 6 x $2.17 = $13.02

Therefore, it would cost $13.02 to buy a frame for the painting.

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Answer: Y=10

Step-by-step explanation: please label me brainiest if I'm right

Since there are 12 face cards (4 J, 4 Q, 4K) those represent 12/52.  The nonface cards excluding aces (4 twos through 4 tens) represent 36/52.

The expected value is then:

(12/52)($3)+(36/52)(-$2)= -$36/52 or -$0.69 but rounding to one decimal would be -$0.70

The line should cross over the x-axis at the point (0.5,). The line should cross over the y-axis at the point (0,2). To show this on the graph, like the question is asking, you can place one point at (0,2) and another point at (1,-2).

The required volume of the given cuboid is (B) 3/2 inches³.

A cuboid is a solid shape or a three-dimensional shape in geometry.

A cuboid is a convex polyhedron that has six rectangular faces, eight vertices, and twelve edges.

Another name for a cuboid is a rectangular prism.

A cube is a cuboid with six square faces.

For instance, furniture, books, and televisions all have rectangular frames. It is a cuboid shape.

On the other hand, the 3D shape known as a cube is represented by items like ice, dice, and Rubik's cube. In actuality, a cube is a particular kind of cuboid with square, identical sides.

So, the volume of cuboid:
V= l*w*h

V = 1*1.5*1

V = 1.5

V = 1/5 = 3/2

Therefore, the required volume of the given cuboid is (B) 3/2 inches³.

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Answer:

Starting unpaid balance = $5942.00

On April 1st: Starting unpaid balance = $5942.00

On April 10th: $124.00 purchase is made, so the new balance becomes $5942.00 + $124.00 = $6066.00

On April 22nd: $1000.00 payment is made, so the new balance becomes $6066.00 - $1000.00 = $5066.00

On April 28th: $628.00 purchase is made, so the new balance becomes $5066.00 + $628.00 = $5694.00

Therefore, the ending balance on Jerry's credit card statement at the end of April is $5694.00.

Step-by-step explanation:

The Tortillas in 2 Packages from Given Data is 14

To determine how many tortillas are in 2 packages, we can use the given data to find the relationship between the number of packages and the number of tortillas.

From the table, we can see that there is a linear relationship between the two variables, with each package containing 7 tortillas.

Therefore, we can calculate the number of tortillas in 2 packages by multiplying 2 by 7,

So, we have

Packages = 2 * 7

Packages = 14

The answer of 14 tortillas in 2 packages.

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Complete question

A grocery store sells packages of fresh tortillas. The table shows the relationship between the number of packages and the number of tortillas. How many tortillas are in 2 packages?

Number of Packages   Number of Tortillas

5                                 35

7                                 49

15                             105

Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

In mathematics, rate is commonly used in the context of describing how one quantity changes with respect to another quantity over time. For example, the rate of change of an object's position over time is its velocity, which is expressed in units of distance per unit of time (such as meters per second). Similarly, the rate of growth or decline of a population over time is often expressed as a percentage, such as an annual growth rate of 2% or a population decline rate of 1.5% per year.

To find the lot size that minimizes the total inventory cost, we need to find the value of "x" that minimizes the function C(x) = 1.5x + 25500x¹ + 17000.

To do this, we can take the derivative of C(x) with respect to x, set it equal to zero, and solve for "x":

C'(x) = 1.5 + 25500 + 0 = 25501.5

25501.5 = 0

x = -25500/1.5 = -17000

Since a negative value of "x" doesn't make sense in the context of the problem, we can conclude that there is no minimum value for C(x). Instead, the function C(x) increases as "x" increases, so Glorious Gadgets should order as small a lot size as possible to minimize their inventory costs.

To find the minimum total inventory cost, we can evaluate the function C(x) at a small lot size, such as x = 1:

C(1) = 1.5(1) + 25500(1)¹ + 17000

C(1) = 1.5 + 25500 + 17000

C(1) = 42501.5

Therefore, Glorious Gadgets should order a lot size of 1 to minimize their total inventory costs, and the minimum total inventory cost is $42,501.50.

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According to your query I am defining you multiply in simple manner.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

Multiplication has several important properties, including the commutative property, which states that the order of the factors does not affect the product. For example, 2 × 3 is equal to 3 × 2.

Another important property of multiplication is the distributive property, which states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. For example, 2 × (3 + 4) is equal to (2 × 3) + (2 × 4), which simplifies to 14.

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According to your query when you multiply in simple manner and it simplifies to 7/5.

The term multiply refers to the mathematical operation of repeatedly adding a number to itself a certain number of times. The result of this operation is known as the product. Multiplication is an essential arithmetic operation that is used in various fields, including science, engineering, and economics.

Multiplication is typically represented by the symbol "×" or "*", and the numbers being multiplied are called factors. For example, if we multiply 2 and 3, we get the product 6, which can be written as 2 × 3 or 2 * 3.

For the given question:

11/7 × 49/5

= 539/35

= 7/5

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The complete question is as follows:

The length of the rectangular lot is 30m

The formula for calculating the perimeter of a rectangle is expressed as;

P =2(l + w)

Such that the parameters are;

From the information given, we have that;

Length = 5 + w

Now, substitute the values

110 = 2( 5 + w+ w)

collect the like terms

110 = 2(5 + 2w)

expand the bracket

110 = 10 + 4w

4w = 100

Divide both sides by the coefficient of w

w = 25

Then, the length = 30m

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Solution for b: The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8. Solution for c: The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16. Solution for d: the events are not equally likely.

b) For a family having 3 children, the sample space is {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}, where B represents a boy and G represents a girl. Each outcome in the sample space has probability 1/8. The events "all boys," "all girls," "2 boys and 1 girl," and "2 girls and 1 boy" are equally likely because each has probability 1/8.

c) For tossing four coins, the sample space is {TTTT, TTTH, TTTT, TTHH, TTHH, THHH, THHT, THHH, HHHH, HHTH, HHTT, HHHT, HHTH, HTHH, HTTH, HTTT}, where T represents tails and H represents heads. Each outcome in the sample space has probability 1/16. The events "0 tails," "1 tail," "2 tails," "3 tails," and "4 tails" are equally likely because each has probability 1/16.

d) For tossing a coin 10 times, the sample space is all possible sequences of 10 H's and T's. There are 2^10 = 1024 outcomes in the sample space, each with probability 1/1024. The events "longest run of heads is 1," "longest run of heads is 2," "longest run of heads is 3," "longest run of heads is 4," "longest run of heads is 5," and "longest run of heads is 6 or more" are not equally likely, because the probability of getting a long run of heads is much lower than the probability of getting a short run of heads. For example, the probability of getting a run of 6 heads in a row is (1/2)^6 = 1/64, while the probability of getting a run of 1 head is 1/2. Therefore, the events are not equally likely.

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Answer:

70% watched less than an hour.

Step-by-step explanation:

Less than 1 hour -- 3 people

Number of people 10

3/10 -- 30% of people watch less than 1 hour.

For the given equation, the values of X and Y are X=4 and Y=-2, respectively.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=).

To find the values of X and Y, we need to separate the real and imaginary parts of the complex number on the right-hand side of the equation.

We have:

X + Yi = 3Y - 2Xi + 4i

Separating the real and imaginary parts, we get:

X = -2Y + 0

Y = 3Y + 4

Simplifying the second equation, we have:

-2Y = 4

Dividing by -2, we get:

Y = -2

Substituting this value of Y into the first equation, we have:

X = -2(-2) = 4

Therefore, the values of X and Y are X=4 and Y=-2, respectively.

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The probability of drawing a queen or a heart from a standard 52-card deck is 0.308 or 30.8%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The event is "drawing a queen or a heart from a standard 52-card deck".

There are 4 queens in a standard 52-card deck, and there are 13 hearts (including the queen of hearts) in the same deck. However, we need to be careful not to count the queen of hearts twice, since it is both a queen and a heart.

So, the number of cards that satisfy the given event is 4 queens + 12 hearts (not including the queen of hearts) = 16 cards.

The total number of cards in a standard deck is 52.

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is:

P(queen or heart) = number of cards that satisfy the event : total number of cards

P(queen or heart) = 16 : 52

P(queen or heart) =  0.308

Therefore, the probability of drawing a queen or a heart from a standard 52-card deck is  approximately 0.308 or 30.8%.

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