Tracy puts $3,500 into an investment yielding 4.5% annual interest. She left the money in for 8 years and 3 months. How much interest does she get in that time

Answer:

[tex]20\ln(5)-16\approx16.18876[/tex]

Step-by-step explanation:

[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]

For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.

An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.

Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.

Let, n = 0.

Therefore,

7⁴ - 7⁰.

= 2401 - 1.

= 2400.

= 30×80, Divisible by 30.

Similarly for n = 1 we have,

7⁵ - 7¹.

= 16807 - 7.

= 16800.

= 30×560.

Hence by induction, the cycle will continue.

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The numeric value of the function d(t) = 12t + 20 at t = 4 is given as follows:

d(4) = 48.

The interpretation of this numeric value is that after a time of 4 hours, Joanna has cycled 68 miles.

The function for this problem is defined as follows:

d(t) = 12t + 20.

The meaning of each variable is given as follows:

The numeric value at t = 4 is obtained replacing the lone instance of t in the function by 4, as follows:

d(4) = 12(4) + 20

d(4) = 48 + 20

d(4) = 68 miles.

Meaning that after a time of 4 hours, the distance cycled by Joanna was of 68 miles.

The function for this problem is defined as follows:

d(t) = 12t + 20.

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Answer:

The length of the diagonal is 12.53

Step-by-step explanation:

Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.

a^2 + b^2 = c^2

We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.

See image.

Answer:

For the first function, F(pi:3) = sin(2 * pi:3) = sin(6 * pi / 3) = sin(2 * pi) = 0.

For the second function, f(-1) = 3 * -1 - (-1)^2 = -3 + 1 = -2.

Step-by-step explanation:

It looks like you are trying to find the value of two different functions at specific points.

For the first function, F(x) = sin(2x) and x0 = pi:3, we want to find the value of F(x) when x = pi:3. Plugging this value into the function gives us F(pi:3) = sin(2 * pi:3) = sin(6 * pi / 3) = sin(2 * pi) = 0.

For the second function, f(x) = 3x - x^2 and x0 = -1, we want to find the value of f(x) when x = -1. Plugging this value into the function gives us f(-1) = 3 * -1 - (-1)^2 = -3 + 1 = -2.

Answer:

she can fill 3 boxes completely and one book will be left over

Step-by-step explanation:

if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over

Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.

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Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either contingent equations or identities are categories for equations. An identity holds true for whatever value of the variables.

given

x+y=7

2x-y=-1

8x=20

x= 5/2

-4y = -8

y = 2

Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

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Answer:

12.57 ft

Step-by-step explanation:

First thing we need to find is the radius of the circular glass pane. We are given the information that the center of the glass plane is directly in the center of the triangle and that the closest distance from the center to the roof is 3 ft, including a metal border with a width of 1 ft.

Since the metal frame is the same width all the way around the window, we can safely conclude that the radius of the circular glass pane is 2 ft, as the 3ft measurement included the radius and the metal frame.

Now that we have our radius we can use the formula:

[tex]C=2\pi r[/tex] (Circumference = 2 x pi x radius)

Using 3.14 for pi we get:

[tex]C=2(3.14)(2)[/tex]

[tex]C=4 \pi[/tex] or 12.57 ft (2.d.p)

Answer: 7x+10

Step-by-step explanation:

combine like terms

x+3x+x+2x+2+5+3

7x+10

Answer:

Step-by-step explanation:

Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

First: find the (x) and collect them, put them in the bracket (to ensure the + or -)

(x + 3x + x + 2x) + 2 + 5 + 3

=  7x + 2 + 5 + 3

Then we add up the numbers

= 7x + 10

This is the end result.

x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

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The value of x is 18.

An equation is an expression that shows the relationship between two or more numbers and variables.

First, both angles shown are equal to each other.

5x + 5 = 95

Next, the opposite side of the equation to isolate x value (5x).

5x + 5 (-5) = 95 (-5)

5x = 90

Finally, we need to divide both sides of the equation by 5.

5x / 5 = 90 / 5

x = 18

The final answer: x = 18

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Answer:

point A

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be the distance of  the drone from the start point is  13feet.

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Height of drone  = 5 feet

and  distance of drone covered is 12 feet

Thus ,

to calculate the distance of  the drone from the start point

distance can be represented as H

Since it forms right triangle.

By using pythagoras theorem,

=> 5² + 12² = H²

=> H² = 169

=> H = √169

=> H = 13

Therefore , the solution of the given problem comes out to be the distance of  the drone from the start point is  13feet.

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a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.

b) Based on the above, the best interest rate the borrower could get is 8%.

Many factors are considered in determining the interest rate for a loan.

Some of the factors include:

We know that the longer the term of a loan, the higher the interest rate charged.  This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.

Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.

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The equation that justifies  ten to the one third power equals the cube root of ten is ten to the one third power all raised to the third power equals ten to the one third times three power equals ten. Option B

we are to find [tex]10^{\frac{1}{3} } = \sqrt[3]{10}[/tex]

The justification has to be done with the use of the properties of powers as well as roots.

[tex]a^\frac{m}{n} = \sqrt[n]{a^m}[/tex]

then we would have:

[tex]\sqrt[3]{10} = \sqrt[3]{10^1} =10^\frac{1}{3}[/tex]

then we would have

[tex](10^\frac{1}{3} )^3\\\\= 10^\frac{3}{3}[/tex]

= 10

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Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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Answer:

Step-by-step explanation:

As she is baking cookies = 3/20

she egave it to her neigbour = 7/20

Remaining = ?

R = 3/20 -7/20 = -1/5

Proportion of cars which are yellow -

= 1 - (0.24 + 0.20 + 0.15 + 0.12 + 0.15 + 0.10)

= 1 - 0.96

= 0.04

Answer:

A) 0.04

Step-by-step explanation:

edge 2023

Their Customer Acquisition cost was $10

Customer Acquisition Cost is the cost of winning a customer to purchase a product or service. As an important unit economic, customer acquisition costs are often related to customer lifetime value. Customer acquisition cost can also be referred as the fee associated with convincing a customer to buy your product or service.

To calculate customer acquisition cost

Customer Acquisition Cost (CAC) = Customer Acquisition Cost/total marketing cost

From the question,

The business gained 50+100+150= 300 new customers

Campaign budget = $30000

Customer Acquisition Cost (CAC) = $3000/300

=$10

Hence, it cost the business $10 to acquire a new customer

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Work Shown:

[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]

Answer:

  8.4

Step-by-step explanation:

You want to know the value of x that satisfies 1.2/4 = x/28.

The equation ...

  x/28 = 1.2/4

can be solved in one step by multiplying by 28.

  x = 28(1.2/4) = 8.4

The value of x is 8.4.

__

Additional comment

The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.

Often, you are told to "cross-multiply" a proportion. Doing that gives you ...

  4·x = 28·1.2

Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:

  x = 28·1.2/4 . . . . same as above.

That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.

Answer:

8.4

Step-by-step explanation:

[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]

cross multiply to solve for x:

(1.2)(28) = 4x

4x = 33.6

x = 33.6/4 = 8.4

Answer:

Step-by-step explanation:

Answer: This system of equations can be represented in matrix form as

| -1 | 650 | 175 |

| 75 | -120 | -25080 |

This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.

You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.

The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.

Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.

Step-by-step explanation:

On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.

If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

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Answer:

It is the first answer,

Step-by-step explanation:

The hypotenuse is always the longest side and opposite of the right angel.  Side b is the adjacent side to J and c is the opposite side of J.

Answer:

Monday??????

SteP-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:I believe it would be 5

Step-by-step explanation:

because if you do it on a table chart you reach five first as the same number

Answer:

Step-by-step explanation:use a calculator

Answer:

Step-by-step explanation:

-29.8+33.2=3.4