Arisia puts $500.00 into a savings account with an annual simple interest rate of 4.5%
If the interest rate stayed the same, how much interest would Arisia’s account earn after 15 years?

[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (3-5z)^{14}~\hspace{4em} \begin{array}{clcl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(3)^{14 }(-5z)^0\\ 2&+14&(3)^{13}(-5z)^1\\ 3&+91&(3)^{12}(-5z)^2\\ 4&+364&(3)^{11}(-5z)^3\\ 5&+1001&(3)^{10}(-5z)^4 \end{array} \\\\[-0.35em] ~\dotfill\\\\ 3^{14}-14(3^{13})(5z)+91(3^{12})(5z)^2-364(3^{11})(5z)^3+1001(3^{10})(5z)^4 \\\\\\ 4782969-111602610z+1209028275z^2-8060188500z^3+13299311025z^4[/tex]

I find the key to binomial expansion is mainly to get coefficient that goes next as  you see in the middle of the table above.

now, if wonder how I get it sequentially, namely as I go, for example, how did I get 91?  

well, (14 * 13 )/ 2

the current coeffient times the exponent of the 1st term divided by the "exponent of the 2nd term plus 1"

how did I get 1001?

well, (364 * 11) / 4

and so on.

Answer:  120

120 x 0.85 = 102

Have a good day!

Answer: 120

Step-by-step explanation: (102 x 100) / 85

a. The fixed cost is 750 dollars. b. The cost of making 25 items is 1000 dollars. c. The domain of the cost function C'(x) is all non-negative real numbers and The range of the function is all real numbers greater than or equal to 750.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

a. The fixed cost is determined when zero items are produced, so we can substitute x = 0 into the function C'(x) = 10x + 750 to find the fixed cost:

C'(0) = 10 × 0 + 750 = 750

So the fixed cost is 750 dollars.

b. To find the cost of making 25 items, we substitute x = 25 into the function C'(x) = 10x + 750:

C'(25) = 10 × 25 + 750 = 750 + 250 = 1000

So the cost of making 25 items is 1000 dollars.

c. To find the maximum cost allowed, which is $1250, we can set the function equal to 1250 and solve for x:

C'(x) = 10x + 750 = 1250

10x = 1250 - 750 = 500

x = 500 / 10 = 50

So the maximum number of items that can be produced while staying under the cost limit of $1250 is 50.

Since x represents the number of items produced, the domain of the cost function C'(x) is all non-negative real numbers. The range of the function is all real numbers greater than or equal to 750 since this is the minimum value of the function (when x = 0).

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1.5 is not an integer.

We know that the integers are the numbers that include positive whole numbers, negative whole numbers, and zero.

The set of integers is denoted by I

From above definition of integers, I = W(-) ∪ {0} ∪ W(+)

where W is the set of whole numbers

The set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

and the set of integers I = {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}

A set of integers do not include fractions or decimals.

here we have been given a number 1.5 which is a decimal number.

By definition of integers, a number 1.5 can not be an integer.

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Answer:

No solutions.

The given expression at a = 9 and b = 8 is equivalent to 71.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the mathematical expression as -

{b + 7a}

Given is the expression as -

{b + 7a}

For a = 9 and b = 8, we can write -

{b + 7a}

{8 + 7 x 9}

{8 + 63}

71

Therefore, the given expression at a = 9 and b = 8 is equivalent to 71.

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{The complete question is -

evaluate the expression when a = 9 and b = 8 :

b + 7a}

Answer:

(-2,-3)

Step-by-step explanation:

The explanation in the photo

The Initial value is computed at: 190

The Growth Factor is computed at: 0.5

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

Given: Q = 190 / 2t

To compute: If [tex]Q = ab^t}[/tex]

Then,

→ 1 / aˣ = (1 / a)ˣ

Now we know that:

∵ (1 / aˣ) = (1 / a)ˣ

⇒ Q = 190 / 2t = 190 * (1 / 2t)

⇒ Q = 190 * (1 / 2)

[tex]Q = 190 * (\frac{1}{2})^{t}[/tex]

[tex]Q = 190 * (0.5)^{t}[/tex]

Comparing the aforementioned expression to:

[tex]Q = ab^{t}[/tex]

Initial Value, a = 190

Growth Factor, b = 0.5

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Answer:in 6 hours, she will make 30

Step-by-step explanation:

12min = 1 ring..

1min =1/12 ring..

6×60min = 1/12×360ring

=30 rings

Answer:

30

Step-by-step explanation:

12x5=60=1 hour

She can make 5 rings in one hour

5x6=30

Therefore she can make 30 in 6 hours

We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal.

The BODMAS rule dictates that in this situation, we should compute the operations that are indicated inside the brackets first (2 + 4 = 6), then the Orders (52 = 25), any Multiplication or Division (3 x 6 (the solution to the brackets) = 18), and any Addition or Subtraction (18 + 25 = 43).

The order of operations is a set of common principles that represent standards about which process to carry out first to assess a given numerical statement in logic-oriented courses like mathematics. Calculating the outcome of a simple sum that only uses two numbers and one operation, or sign, is simple.

Either division, multiplication, subtraction, or addition are performed. Incorrect calculations will result in an incorrect response. Therefore, systematically memorise the order. There is a bracket.

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Answer:

x=1 and y= -2

Step-by-step explanation:

4x-3y=10------------------------->eqn1

3x+5y=-7------------------------->eqn2

to eliminate, (eqn1 X 3) and (eqn2 X -4)

12x-9y=30------------------>eqn3

-12x-20y=28--------------->eqn4

eliminate the variable x (12x-12x)

Now,

-9y-20y=30+28

-29y=58

y=58/-29

 = -2

from eqn1,

4x-(-2 X 3)= 10

4x+6= 10

4x=10-6

    =4

x=4/4

 =1

Yes, the given equations are consistent. Both of the equations are linear equations with the same slope and can be written in the standard form of ax + by = c. Since both of the equations have the same values of a, b, and c, they are consistent and have a single solution.

The equations can be solved by elimination, substitution, or graphing. To solve by elimination, multiply the first equation by two and subtract it from the second equation. This yields the equation

0 + 3y - 18 = 0, which can be simplified to

3y = 18. Then, substitute

3y = 18 into the first equation to solve for x. The solution is

(x, y) = (6, 6).

The given equations are

2x+3y−9=0 and

4x+6y−18=0.

These equations are both linear equations that can be written in the standard form of ax + by = c. Since the values for a, b, and c are the same in both equations, they are consistent and have a single solution. The equations can be solved by elimination, substitution, or graphing. To solve by elimination, multiply the first equation by two and subtract it from the second equation. This yields the equation 0 + 3y - 18 = 0, which can be simplified to 3y = 18. Then, substitute 3y = 18 into the first equation to solve for x. The solution is (x, y) = (6, 6). This is the only solution to the given equations, thus proving that the equations are consistent.

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The complete question is

Which of the following is correct for given equations 2x+3y−9=0 and 4x+6y−18=0 consistent and dependent.

Answer: $2,704.00

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.04/1)(1)(2)

A = 2,500.00(1 + 0.04)(2)

A = $2,704.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,500.00 at a rate of 4% per year compounded 1 times per year over 2 years is $2,704.00.

Answer:

Step-by-step explanation:

Solve by Completing the SquareSolve for xSolve Using the Quadratic FormulaSolve by FactoringWrite in Standard FormFactorFind the Roots (Zeros)Find All Complex SolutionsFind the Discriminant

The volume of 3-dimensional shape is 5 cubic feet.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

3-D shape is a cuboid.

The volume of the cuboid,

= length x width x height.

Substituting the values,

The volume of the cuboid,

= 5/2 x 3/2 x 4/3.

= 60/12

= 5 cubic feet.

Therefore, the volume is 5 cubic feet.

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The x-coordinate of P is 5 and the y-coordinate of P is 3.333.

To find the x- and y-coordinates of point P on the directed line segment from point A to point B, such that P is two-thirds the length of the line segment from A to B, we can use the following formula:

P = A + (2/3)(B-A)

Where A and B are the coordinates of the starting and ending points of the line segment, and P is the point we are trying to find the coordinates for.

For example, if the coordinates of A are (3,4) and the coordinates of B are (6,8), then the coordinates of P would be:

P = (3,4) + (2/3)((6,8) - (3,4)) = (3,4) + (2/3)((3,4)) = (3,4) + (2/3)(3,4) = (3,4) + (2,8/3) = (3,4) + (2,8/3) = (5,10/3) = (5,3.333)

So the x-coordinate of P is 5 and the y-coordinate of P is 3.333.

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The required solutions to the given equation are x = 0, x = -3 +√41, and x = -3-√41.

The quadratic equation is defined as a function containing the highest power of a variable is two.

The equation is given in the question, as follows:

4x⁽⁴⁾ + 24x⁽³⁾- 128x⁽²⁾ = 0

Factor out 4x² from the equation,

4x²(x² + 6x - 32) = 0

Using the zero factor principle, then

4x² = 0 and (x² + 6x - 32) = 0

After solving the above quadratic equation, we get the values:

x = 0, x = -3 +√41, and x = -3-√41

Thus, the required solutions are x = 0, x = -3 +√41, and x = -3-√41.

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Answer:

A. Let x be the number of hours for which the companies charge the same amount.

Party Time: 100 + 50x = 175 + 25x

Let's Dance Company: 175 + 25x = 100 + 50x

B. To solve this system of equations, we can use substitution. We can start by isolating one of the variables on one side of the equation and then substitute that expression into the other equation.

x = 25

C. To show that the solution results in the same charge for both companies, we can substitute the value of x back into the equations for each company and see if they are equal.

Party Time: 100 + 50(25) = 100 + 1250 = 1350

Let's Dance Company: 175 + 25(25) = 175 + 625 = 800

1350 = 800

The two companies charge the same amount for 25 hours.

The company should prepare 23,000 packages of Italian style, 12,000 packages of French style, and 59,000 packages of Oriental style to use up existing supplies.

To determine how many packages of each style the company should prepare to use up existing supplies, we can set up a system of equations using the information provided. Let x be the number of packages of Italian style, y be the number of packages of French style, and z be the number of packages of Oriental style.

We know that the company has 21,000 kg of zucchini, 28,300 kg of broccoli, and 44,700 kg of carrots. Therefore, the total amount of zucchini, broccoli, and carrots used in each package of each style must be less than or equal to the total amount of each of these vegetables the company has in stock.

We can express this information in the following system of equations:

0.4x + 0y + 0.2z ≤ 21,000 (zucchini)

0.2x + 0.5y + 0.3z ≤ 28,300 (broccoli)

0.4x + 0.5y + 0.5z ≤ 44,700 (carrots)

We also know that x, y, and z are non-negative integers (since we are counting the number of packages)

x > 0

y > 0

z > 0

To find the solution to this system of equations, we can use a method such as substitution or elimination, or use a solver to get:

x = 23000, y = 12000, z = 59000

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Observations are the collection of measurements made for a specific element. Observations are typically collected from a sample of data, which are then used to measure particular variables. This information is then used to make inferences about a larger population, often referred to as a census.

A set of measurements collected for a particular element is called observations. Observations are typically generated from a sample of data which is then used to measure particular variables. Variables are measurable characteristics which can be observed and measured. For example, a variable can be a person’s age, height, or gender. The data collected from these variables are then used to make inferences about a larger population, such as a census. A census is a complete count of a population, which may be used to measure the characteristics of a population or to make estimates about a population. Observation data is used to make inferences about a larger population and is used to make decisions or draw conclusions about a particular element. This data is often used in research, policy making, and decision-making.

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Gerald read  ( 4 / 7 ) more of the book comparing to book read by Mary.

As given in the question,

Portion of book read by Gerald is equal to ( 6 / 7 ).

Portion of book read by Mary is equal to ( 2 / 7 ).

( 6 / 7 ) is greater than  ( 2 / 7 )

Gerald read more portion of the book comparing to Mary.

Difference between the portion read by Gerald and Mary is given by :

= ( 6 / 7 ) - ( 2 / 7 )

Both are like fractions Least common multiple is 7.

= ( 6 - 2 ) / 7

=  ( 4 / 7 )

Therefore, the Gerald read ( 4 / 7 ) more portion of the same book than Mary read.

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Yes, there are formulas in algebra. Algebra is a branch of mathematics that deals with mathematical equations and their properties. Some common formulas in algebra include the quadratic formula, the slope-intercept form of a linear equation, and the distance formula. These formulas can be used to solve a wide variety of mathematical problems involving equations and variables.

1.  (a + b)^2 = a^2 + 2ab + b^2

2.  (a - b)^2  = a^2 - 2ab + b^2

3.  (a + b) (a - b)  = a^2 - b2

4.  (x + a)(x + b)  = x^2 + (a + b)x + ab

5.  (x + a)(x - b)  = x^2 + (a - b)x - ab

6.  (x - a)(x + b)  = x^2 + (b - a)x - ab

7.  (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

8. a^3 + b^3 + c^3 - 3abc = (a + b + c ) ( a^2 + b^2 + c^2 – ab – bc – ca ) + 3abc

9. a^3 + b^3 + c^3 = 3abc   (if a + b + c = 0)

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems.

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The required rate of change of the surface area of the cube is 32.48sq,feet/second.

The rate of change, which is used to mathematically express the percentage change in value over a certain period of time, is a representation of the momentum of a variable. The general formula for determining the rate of change is R = (D2 - D1)/T.

According to question:

V/dt = 536 cubic feet per second

A = 66

Differentiate w, r, t

v/dt = 3a²da/dt

536 = 3(66)²da/dt

da/dt = 0.041

Now,

Surface area(S) = 6a²

Differentiate w, r, t

dS/dt = 12a(da/dt)

dS/dt = 12(66)(0.041)

dS/dt = 32.48 Sq.feet/second

Thus, required rate of change of the surface area of the cube is 32.48

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A simplified expression for the perimeter of the triangle would be = 2(2x +7)

The perimeter of a triangle is defined as the summation of the total sides of the triangle which is made up of three sides.

The length of the base of the triangle = X

The length of first side = 11 +2x

The length of the second side= 3 + X

The perimeter = X + 11 +2x + 3 + X

= 2x + 2x + 14

= 4x + 14

= 2(2x +7)

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Answer:

1000

Step-by-step explanation:

100/0.1=1000

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Answer:

  20 feet

Step-by-step explanation:

You want the distance between the zeros of the function y = -11/50(x -4)(x -24), where x and y are in feet.

The function value is zero when the factors are zero:

  x -4 = 0   ⇒   x = 4

  x -24 = 0   ⇒   x = 24

The distance between these values on the x-axis is ...

  24 -4 = 20

The width of the tunnel at ground level is 20 feet.

Answer: 5$ took test

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 is the answer

Answer:

sheep and goats fed with silphuim were said to produce more succulent meal

The amount owed in 20 years is $712.08.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P= $325

R= 4%

n= total years = 20 year

So, A = P [tex](1+ r)^n[/tex]

A = 325 [tex](1+ 4/100)^{20[/tex]

A = 325  [tex](1+ 0.04)^{20[/tex]

A = 325 x 2.191

A = 712.08

Hence, the amount is $712.08

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Cq = P [(1+r)4*n - 1]

From the compounding formula, the quarterly compounding formula is derived. The rate of interest is merely increased by 4*2 to reflect the quarterly interest calculation.

Cq = P [(1+r)4*n - 1]

Where:

Quarterly Compound Interest

Principal Amount

interest rate, r

N is the number of periods.

Example #1

25,000 as the principal

Interest Rate: 3.50 percent

Number of Years: 3

Cq = P [(1+r)4*n - 1]

Cq = $25,000 [ (1+3.5%/4)4*3 – 1 ]

Cq = $25,000 [ (1.00875)12 – 1 ]

Cq = $2,755.09.

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