You are thinking about changing employment. Your goal is to work for three years and then return to university full-time, in pursuit of an advanced degree. A potential employer just offered you an annual salary of R55 000, R60 000, and R65 000 a year for the next three years, respectively. All salary payments will be made as lump sum payments at the end of each year. The offer also includes a starting bonus of R4 500, payable immediately. What is this offer worth to you today, at a discount rate of 8,25%?

So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

To find the greatest common factor (GCF) of the given terms, we need to factor out any common factors of the coefficients and variables.

-63x²y = (-1) × 3² × 7 × x² × y

9x³y³ = 3² × x³ × y³

90x³y = 2 × 3² × 5 × x² × y

The common factors among these terms are 3², x², and y. Therefore, the GCF of the given terms is:

GCF = 3² × x² × y

= 9x²y

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Answer:

2.75d+2t <= 40

Step-by-step explanation:

i may be wrong but I tried

The circles having an area less than 300 square centimeters are;

Option A: A circle with a radius of 9. 5 centimeters

Option D: A circle with a diameter of 15 centimeters

It is important to note the formula for calculating the area of a circle is expressed as;

A = πr²

Such that the parameters are;

From the information given, we have that;

radius = 9.5 centimeters

Substitute the value

Area = 3.14 × (9. 5)²

Area = 283. 4 cm²

For diameter of 15 centimeters

Radius = 7.5 centimeters

Substitute the values

Area = 3.14 × (7.5)²

Area = 176. 6 cm²

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answer is

512

Step-by-step explanation:

1.6x80=128

128x4=512

Answer:

The answer to this question is 391 points will be scored in 17 games. to find this answer you divide 94 by 4 to find the total points per single game, then multiply that by 17. in this case is is 92 divided by 4 = 23 then 23 X 17 = 391

Answer: 3. 35x + 15 = 155

Step-by-step explanation:

35 x 4 = 140

140 + 15 = 155

According to the solution we have come to find that, 48% of the teas served were caffeinated.

A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.

To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.

Total number of teas served = 36 + 39 = 75

Percentage of caffeinated teas served = (36/75) x 100%

                                                                = 48%

Therefore, 48% of the teas served were caffeinated.

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The distance from rock to tree is approximate 99.48 m.

The bearing in navigatiοn refers tο the path between twο pοints, calculated in clοckwise rοtatiοns arοund nοrth. It is frequently emplοyed tο indicate the directiοn οf travel between twο places οr the οrientatiοn οf a landmark with respect tο a ship οr aircraft.

The azimuth, which is the angle between a reference directiοn (οften nοrth) and the directiοn tο an οbject οr pοint, is distinct frοm the bearing.

A. check the attachment given.

B. Let the distance from rock to tree be = H meter

Now, [tex]$ \rm \frac{Sin(056^{\circ})}{1} = \frac{H}{120}[/tex]

H =  Sin(056°) × 120

H = 99.48 m

Thus, The distance from rock to tree is  99.48 m.

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Answer:

6 units the answer is C. just see it

Answer: Reflection in the y -axis:

Explanation: The rule for a reflection over the y -axis is (x,y)→(−x,y) .\

Answer:

Equation: y= -3/4x+15/2

Step-by-step explanation:

The points given: (-2,9) and (2,6)

Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)

slope ,m= -3/4

Equation: y-y1=m(x-x1)

Equation: y-6= -3/4(x-2)

y-6= -3/4x+3/2

y= -3/4x+3/2+6

y= -3/4x+15/2

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Answer:

B

Step-by-step explanation:

The correct answer is B. The total number of people on the field trip must be a multiple of 9 (1 adult and 8 students).

A is not true because if there were only 9 people, there could not be both an adult and 8 students, and the ratio would not be 1:8.

C is not necessarily true. It is possible that there were more adults than students on the field trip, or that the ratio was not an exact 1:8.

D is not true because if there were 8 times as many students as adults, the ratio would be 1:64, not 1:8

Therefore , the solution of the given problem of function comes out to be  y grows by 19/4 units for every unit increase in x.

There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.

Here,

The slope of the equation

=> y = 19/4x - 19 is 19/4.

This implies that y grows by 19/4 units for every unit increase in x.

You would need to be familiar with the expression or

graph of the other function in order to compare the rate of change with it.

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The perimeter of the decks is 120 feet

Perimeter is a mathematical term that refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

The property of circles states that "the tangents drawn from the same point on a circle are equal in length". It means that if two tangent lines are drawn from an external point to a circle, the length of both tangents will be equal.

Here we have

Tangents QR and QV from point Q

Tangents RS and ST from point S

Tangents VU and UT from point U

As we know,

The tangents drawn from the same point on a circle are equal in length  

=> Tangent QR = QV --- (1)  from point Q

=> Tangent RS = ST ----- (2) from point S

=> Tangent VU = UT ----- (3) from point U  

From the figure,

The perimeter of decks = QR + RS + ST + TU + UV + VQ  

From (1) (2) and (3)

=> QR + ST + ST + UV + UV + QR  

=> 2QR + 2UV + 2RS  

From the figure,

=> 2(24 ft) + 2(26 ft) + 2 (36 - 26)   [ ∵ ST = US - TU ]

=> 48 ft  + 52 ft + 20 ft

=> 120 ft  

Therefore,

The perimeter of the decks is 120 feet

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Answer:

64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100

Median= 92

Mode= 88, 97

Mean= 88.55

Range= 36

Quartile 1= 88

Quartile 2= 92

Quartile 3= 97

Interquartile range= 9

Minimum= 64

Maximum= 100

Not sure if this helped but I hope it did

By taking these factors into account, they can create a product that meets the needs of potential customers and is a success in the market. the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.

Triangular Pyramid Tent Design:

The triangular pyramid tent design is a unique shape that could potentially offer better stability against wind and other weather conditions. However, it may also require more complex construction and assembly than a traditional rectangular tent.

The design department should consult with engineers and experienced tentmakers to ensure that the triangular pyramid tent can be manufactured in a cost-effective and user-friendly manner.

Size options:

The design department has decided to make two sizes of the triangular pyramid tent. They should consider the intended use of the tents and the needs of potential customers when determining the size options.

For example, a smaller size might be suitable for backpackers or solo campers, while a larger size could accommodate families or groups.

Therefore, the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.

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Answer:

The given expression is:

3x + 2 / (x + 1)(x² + x + 2)

To simplify this expression, we need to factor the denominator first:

x² + x + 2 = (x + 2)(x + 1)

So the expression becomes:

3x + 2 / (x + 1)(x + 2)(x + 1)

Next, we can use partial fraction decomposition to express the expression in terms of simpler fractions. Let's assume:

3x + 2 / (x + 1)(x + 2)(x + 1) = A/(x + 1) + B/(x + 2) + C/(x + 1)²

Multiplying both sides by the common denominator, we get:

3x + 2 = A(x + 2)(x + 1) + B(x + 1)² + C(x + 2)(x + 1)

Expanding the right side, we get:

3x + 2 = Ax² + 3Ax + 2A + Bx² + 2Bx + B + Cx² + 3Cx + 2C

Combining like terms, we get:

3x + 2 = (A + B + C)x² + (3A + 2B + 3C)x + (2A + B + 2C)

Since this equation holds for all values of x, the coefficients of each power of x must be equal on both sides. We can equate the coefficients of x², x, and the constant term to get a system of three equations for A, B, and C:

A + B + C = 0

3A + 2B + 3C = 3

2A + B + 2C = 2

Solving this system, we get:

A = 2/3

B = -1/3

C = -1/3

Substituting these values back into the partial fraction decomposition equation, we get:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Therefore, the simplified expression is:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Answer:

3/4

Step-by-step explanation:

The angle is in the fourth quadrant.

What do you mean by quadrant?

The coordinate system's two axes (the x-axis and y-axis) constitute a region called a quadrant. The quadrants are the four areas generated when the x- and y-axes cross at a 90-degree angle.

                                Coordinate values, also known as x- and y-values, are present in both positive and negative directions in these locations.

What is a quadrant circle?

Any one of the four regions is a quadrant when a circle is uniformly divided into two perpendicular parts. In fact, anything that can be divided into four equal halves is said to be made up of quadrants. Hence, a quadrant of a circle is one-fourth of the entire circle.

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The terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.

Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.

The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.

These areas include coordinates or positive and negative values of the x- and y-axes.

The terminal ray falls at a rotational angle of 6 radians in the fourth quadrant.

Therefore, the terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.

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Answer:

11

Step-by-step explanation:

11 x 23 is 253

Answer:

Step-by-step explanation:

In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph

A graph is made up of vertices, or points, and edges, or lines connecting those vertices.

Graphs come in a wide variety of forms in discrete mathematics.

These are a few of them:

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The correct question is-

what are the different types of graph.

Answer:

Step-by-step explanation:

To convert the mixed angle measure 96° 29' 1" to decimal degrees, we can use the following formula:

decimal degrees = degrees + (minutes / 60) + (seconds / 3600)

Using this formula, we have:

decimal degrees = 96 + (29 / 60) + (1 / 3600)

decimal degrees = 96.4836111

Therefore, mHJ = 96.4836111 degrees (rounded to seven decimal places).

Step-by-step explanation:

I'd say the association is linear, based on the first 3 options you chose

Answer:

  D.  ∠EBF = 40°

Step-by-step explanation:

You want the measure of angle EBF in a diagram in which right angle EBD is split by ray BF to form angle FBD = 50°.

The angle addition postulate tells you ...

  ∠EBD = ∠EBF +∠FBD

  90° = ∠EBF +50° . . . . use the given values

  40° = ∠EBF . . . . . . . subtract 50°

It must be true that ∠EBF = 40°.

Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

Answer:

  336 feet

Step-by-step explanation:

You want the change in elevation as a result of driving 4813 feet up a road with a 4° incline.

The sine function relates an angle to the ratio of the opposite side and the hypotenuse in a right triangle:

  Sin = Opposite/Hypotenuse

In this application, we have ...

  sin(4°) = (elevation change)/(distance along the road)

  elevation change = (4813 ft)·sin(4°) ≈ 336 ft

The driver's increase in altitude is about 336 feet.