What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%annual interest, compounded monthly? Use the analytical solution to find the answer.

They way you can change the grouping of the addends. in $5.50+$7.83+$3.50 is;  $5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

There are different algebraic properties such as;

Commutative Property

Associative Property

Distributive Property

Now, the commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product. For example;

a + b + c = c + a + b or a* b = b * a

Now, the associative property states that the way in which factors are grouped in a multiplication or addition problems does not change the product. For example; x + (y + z) = (x + z) + y

Now, to our question, one way to group the addends using associative property is;

$5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

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Answer:

( 3+ 4 + 5 ) °

=(3+9)°

=(12)°

C is the answer

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Write three solutions to the inequality that can be represented by the numbers x 26 + 24 n > 100.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,,, or indicate that the two expressions in an inequality are not always equal.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other

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The equation of inequality is [tex]26+ 24n > 100[/tex] .

Inequality, is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Make use of the following steps to solve an inequality:

Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.

Step 2: Simplify the inequality by merging like terms on each side.

Step 3: Add or subtract amounts to get the unknown and the numbers on either side.

In this question it is given that the farmer has 26 bushels of apples

Number of apples he can harvest each day is 24 bushels. This statement indicates that this is not constant.

Thus let us consider a variable say n to represent the inequality.

So we can write it as 24 n.

Also given that she has to sell more than 100 bushels.

The final equation becomes:

Apples present + Number of apples added each day > 100

⇒ 26+ 24n> 100 is the final answer.

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The required equation is 99 + 19 h = t  .

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

Given: Total cost = t

and the number of hours the vehicle is used = h hours

Since $99 is supposed to given that is, it is mandatory.

And $19 is supposed to be paid for per hour use.

Thus the equation is ;

99 + 19 h = t  ; where t is total cost and h is number of hours the vehicle is used

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The point (6,0) represent the length of time it takes for Ryan to use all the plant food

What is Time ?

Time is a continual and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

The location and value of x at which the function represented by f(x) equals zero are known as the x-intercept.

The height of the bean sprout and the quantity of plant food added were both measured, per the information given.

Given the observational aspect of the experiment, we know that the function of the variable y = f(x) is the height of the bean sprout, and the variable x, which may be chosen by the researcher, is the amount of the additional plant food.

As a result, the x-intercept, which represents the experiment's starting position (represented by the natural numbers of y = 0), shows how much plant food was initially added to the soil.

Hence, The point (6,0) represent the length of time

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The point (6, 0) represents the initial amount of plant food, which is 0 at this point.

When representing a point in the form (x, y), the x-coordinate typically represents a quantity or value on the horizontal axis, while the y-coordinate represents a quantity or value on the vertical axis.

The point (6,0) means that the x-coordinate is 6, which corresponds to a specific value or measurement along the horizontal axis.

Since the context of the question refers to plant food, the x-coordinate of 6 likely represents a measurement related to the amount of plant food.

The y-coordinate, in this case, is 0, indicating that there is no height or value represented on the vertical axis.

Therefore, (6, 0) represents the initial amount of plant food, which is 0 at this point.

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Since, Domain: 0≤d≤21 and Range: 0≤B(d)≤400, B(0)=200. On Day 0, the day Ebony opened her account, she made initial deposit of $200.

In mathematics, and more specifically in the graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to the mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in the diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are the one of the objects of study in discrete mathematics.

Edges may be directed or undirected. For example, if the vertices represent people at party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with person B only if B also shakes hands with A. In the contrast, if an edge from a person A to a person B means that A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated.

Graphs are basic subject studied by graph theory. J. J. Sylvester was the first to use the word "graph" in this context in 1878 due to the direct relation between mathematics and chemical structure (what he called a chemico-graphical image).

1) Domain: 0≤d≤21

Range: 0≤B(d)≤400

2) B(0)=200

On Day 0, the day Ebony opened her account, she made initial deposit of $200.

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A graph of the linear equation (2x - 4y = 0) is shown in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, the graph of any proportional relationship such as a linear equation is characterized by a straight line because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously as shown in the image attached below.

In conclusion, a graph which represents the linear equation (2x - 4y = 0) shows a proportional relationship between the value of x and y.

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Based on table shown above, we have that: A. Yes, the table describe a function.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Based on table shown above, we have the following parameters:

Input value       Output value

2001                         30

2002                        60

2003                        30

2004                        50

2005                        40

In conclusion, we can reasonably infer and logically deduce that this table is a function because it has the different input values (x-values) for different or the same output values (y-values).

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Explanations :

(a) (x;y) →(x-3 ; -y+2 ) ; this preserves the lengths of the side, with a reflection across the x -axis .

(b) (x;y) →(2x +1 ; y-5 ); this does not preserve the length of sides, because the 2 multiply by x will change the length by factor of 2 .

(c) (x;y) → (-x+6 ;-y -8 ), preserves the lengths of sides, with reflection of y = -x .

(d) (x;y) →(-x -5 ; y+10 ) preserves the lenghts of the sides , with a reflection in the y -axis .

The most appropriate choice for LCM will be given by

He can make 162 treat bags using all the candy.

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

Number of Snicker bars = 81

Number of kitkat bars = 54

Brown wants  to use all of the candy by making as many identical bags as possible.

Number of treat bags  he can make using all of the candy = LCM of 81, 54

81 = 3 x 3 x 3 x 3

54 = 2 x 3 x 3 x 3

LCM = 3 x 3 x 3 x 3 x 2

        = 162

He can make 162 treat bags using all the candy.

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Part (a)

[tex]C=\pi d \implies d=\frac{C}{\pi}[/tex]

Part (b)

[tex]d=\frac{8}{\pi}[/tex]

The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.

Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.

Here we  considering  the rate of the slow hiker  to be x, so the rate for the fast hiker will be x+2.2

Since we know that  distance = speed * time

therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km

As we are given the condition that it i they are  33 miles apart, So

=>5x + 5x+11 = 33

=>10x = 33-11

=>10x = 22

x =22/10 => 2.2

So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is   x+4.4= 4.4 mph.

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The function is decreasing.

The domain is the set of x-values.

The range is the set of y-values.

Answer:

70

Step-by-step explanation:

The  equation which represents the amount is p = 0.0625 t.

When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.

Sales tax rate = sales tax percent / 100.

Sales tax = list price * sales tax rate.

Total price including tax = list price + sales tax,

Total price including tax = list price + (list price * sales tax rate),

Total price including tax = list price * ( 1 + sales tax rate)

We have been given

sales tax rate = 6.25%.

The price of the item = p

The sales tax = t

We know that the amount of sales tax paid on a purchase is proportional to the price of the item.

p = 6.25% t

p = 6.25/100 t

p = 0.0625 t.

Hence , P = 0.0625 t is the equation used to represent the amount.

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Plug in 3 in the place of x and simplify

[tex]y=(3)^{2} \\y=3*3\\y=9[/tex]

y=9

Answer:

No, the reasoning is not correct.

Step-by-step explanation:

39.99 x .14 = 5.5986  Does it make sense that the sales price plus the tax would be $5.60?  Doesn't that seem really low?

39.99 x .3  = 11.997 is the amount that we are taking off of the original price.

39.99 - 12 (Rounded to the nearest cent) is 27.99.

Now we pay the tax on the discounted amount of the item.  

27.99 x .16 = 4.4784 or 4.48 rounded to the nearest cent.

The out the door cost of the item

is 27.99 + 4.48 = 32.48

Winston's total bill at the cash register is $1064.59

Sales tax for the items purchased is $80.59

Given,

The price for the items Winston purchased = $984

Sales tax in Winston's area = 8.19%

We have to find Winston's total bill at the cash register:

Total amount = Price of the items + sales tax amount

Sales tax amount = 8.19% of price of items

Sales tax amount = (8.19/100) × 984

Sales tax amount = $80.59

Now,

Total bill amount = Price of the items + sales tax amount

Total bill amount = 984 + 80.59

Total bill amount = 1064.59

Therefore, Winston's total bill at the cash register is $1064.59

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Based on the amount of time given, the number of degrees that the minute hand on the clock would have moved is  210 degrees

Based on the fact that the clock is a circle in shape, it means that when the minute hand moves around the clock for an hour, it would have moved 360 degrees.

If the time moved by 7/12 hours, the number of degrees it moved was then:

= Number of degrees x Number of hours

= 360 x 7/12

= 2,520 / 12

= 210 degrees

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Answer:

Step-by-step explanation:

5(1 − n) + 3n = 3(n − 1) – 5n

5 - 5n + 3n = 3n - 3 - 5n

5 + 3 = 5n - 3n + 3n - 5n

8 = 0

this equation is always false

The correct option a = 18 and b = 0, described the complex number 18.

For the given question.

Let R be the rational number.

All rational numbers can be written as complex numbers in the form;

R =  a +bi

Where 'a' is the real part and 'ib' is the imaginary part.

The number 18 can be written as;

18 + 0i = 18

As, in number 18 only real part is there.

Thus, a = 18 and b = 0 are correct expression for describing number 18.

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Every radical can be rewritten has an exponent .

Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).

1. Exponents that are written as fractions are referred to as rational exponents.

The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.

2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.

3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.

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The only possible answer that would match the simplified inequality is the first answer choice .i.e., -5c + 2 _< _27

An operation, often known as  "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by number of operands.

Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are operations that are most frequently studied. A constant is operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as ternary operation, is the mixed product.

The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to finiteary operations when infinitary operations are taken into consideration.

Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.

A closed or filled-in circle represents greater/lesser or equal to symbol (> or with the line at the bottom).

You must flip the inequality sign when multiplying or dividing when one of terms is negative on both sides. In inequality equations, this rule only holds when multiplying or dividing by negative value. This rule is very crucial.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

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The simple interest of the sum at the same rate and time is 2400

The interest that is paid on the principal and interest at regular intervals is known as compound interest.The difference between compound interest and simple interest starts to show after the first year, though.Beginning with the second year, interest is computed on both the principal amount and the interest from the prior year. As a result, interest on interest is another name for it.

Given that : Sum =8000 and time = [tex]\frac{3}{2} years[/tex] and rate is 20 %

When rate is calculate half yearly

R becomes [tex]\frac{R}{2}[/tex]

T becomes 2T

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

C.I = A-P

R = [tex]\frac{20}{2} = 10%[/tex]%

T = 2× [tex]\frac{3}{2} years[/tex] = 3years

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

A = 8000[tex]\frac{11}{10} ^{3}[/tex]

A = 8 ×1331

A = 10648

Now ,

C.I = A - P

C.I =10648 - 8000

C.I = 2468

The compound interest is 2468

Simple interest

A = P(1+rt)

A = 8000(1+0.2×1.5)

A =10400

S.I =A- P

= 10400 - 8000

=2400

The simple interest of the sum at the same rate and time is 2400

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Answer:

the answer to number 2 is: y=-4x-26

The answer to number 3 is y=5/2x+54

Step-by-step explanation:

Answer:

<CPB

Step-by-step explanation:

Because <APE= right angle

<APC= Obtuse angle

<CPE= Obtuse Angle.

Also, <CPB because its the only angle below 90 degrees and an acute angle must be below 90 degrees.

D

Step-by-step explanation:

....................

Answer:

102 squared in.

Step-by-step explanation:

the shaded area is the whole shape minus the unshaded shape.

calculating the whole shape area:

make sure you add all the width together and then all the height together before multiplying

(10+4) x (3+6) = 14 x 9 = 126 squared in.

calculating the unshaded shape area:

6 x 4 = 24 squared in.

based on the logic from my first sentence in this explanation:

126 - 24 = 102 squared in.

Answer:

c = 5

k = 3

Step-by-step explanation:

We have the expression:
(3+√c) (2√c - 3) = 1 + k √c

Expanding the LHS using the FOIL method =>
(3 + √c) (2√c -3)

= (3)(2√c) + 3(-3) + (√c)(2√c) -√c(3)

= 6√c -9 + 2(√c)² -3√c

= 3√c + 2c - 9                  [(√c)² = c]

Setting this equal to the RHS of 1 + k√c gives us

3√c + 2c - 9  = 1 + k √c

Since c and k are prime numbers, √c is irrational.

Therefore we match the irrational terms to get
3√c = k√c

=> k = 3      [divide both sides by √c]

Substitute k = 3 into 3√c + 2c - 9  = 1 + k √c

=> 3√c + 2c - 9 = 1 + 3√c

Add 9 to both sides
=> 3√c + 2c - 9 + 9 = 1 + 9 + 3√c

=> 3√c + 2c - 0 = 10 + 3√c

Subtract 3√c from both sides to eliminate this term on both sides
=> 3√c - 3√c + 2c - 0 = 10 + 3√c  3√c

=> 0 + 2c = 10 + 0

=> 2c = 10

Dividing by 2 on both sides gives us
c = 5

Answer: c = 5, k = 3