Assume you wish to save money on a regular basis to finance an exotic vacation in Dubai in the next 7 years. You are confident that, with sacrifice and discipline, you can force yourself to deposit $2,000 annually at the end of each period for the next 7 years into a savings account.
If the savings account is paying 12%, calculate the future value of this annuity. (4 Marks)


b. What would be the value if "part a" above were a future value annuity due? (2 Marks)


c. Assume we want to determine the balance in an investment account earning 6% annual interest, giving the following three-year deposits:
$400 in year 1, $800 in year 2, and $500 in year 3.
Calculate the future value of the cash flow mix stream

The hydrogen emission spectrum provides strong evidence for energy levels in atoms.

The hydrogen emission spectrum refers to the set of wavelengths of light emitted by hydrogen atoms when excited by energy. These wavelengths are discrete and can be precisely measured. The unique set of wavelengths emitted by hydrogen can be explained by the Bohr model of the atom.

According to the Bohr model, the electrons in an atom occupy specific energy levels or shells. When an electron absorbs energy, it jumps to a higher energy level, or excited state. As it returns to its original energy level, it emits the excess energy in the form of light or radiation. The energy of the emitted light is directly related to the energy difference between the two levels.

The emission spectrum of hydrogen consists of several distinct lines of different wavelengths, each corresponding to the transition of an electron from a higher energy level to a lower energy level. The wavelengths of these lines are given by:

λ = R(1/n₁² - 1/n₂²)

where λ is the wavelength of the emitted light, R is the Rydberg constant (a physical constant), n₁ is the initial energy level, and n₂ is the final energy level.

This equation shows that the wavelengths of the emitted light are directly related to the energy difference between the two energy levels. Therefore, the hydrogen emission spectrum provides strong evidence for the existence of quantized energy levels in atoms.

In conclusion, the discrete wavelengths of light emitted by hydrogen can be explained by the quantized energy levels predicted by the Bohr model. This fundamental concept of quantization has far-reaching implications in modern physics, and its understanding is crucial in many areas of science and technology.

To know more about energy here.

https://brainly.com/question/1932868

#SPJ4

A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.

The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.

The action or process of inducting someone to a position or organization.

We have given that,

A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.

As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.

learn more about induction here:

brainly.com/question/24672369

#SPJ1

The true statement about angle x is determined as x + 30 = 180 .

option D.

Corresponding angles in geometry are defined as the angles which are formed at corresponding corners when two parallel lines are intersected by a transversal.

From the given two parallel lines m and n, we can conclude the following;

angle formed by the intersection of line a and m = x ( corresponding angles are equal).

the angle formed by the intersection of line b and m, above angle 30 = x ( corresponding angles are equal)

So the angle on the same straight line with 30 is angle x

x + 30 = 180 ( sum of angles on a straight line)

x = 180 - 30

x = 150⁰

Learn more about corresponding angles here: https://brainly.com/question/2009183

#SPJ1

Answer:

Scalene, isosceles,

Step-by-step explanation:

In order to divide these polynomials, let's use the following property:

So we have:

Add 1.50 to each time the price goes up

Step-by-step explanation: Multiply by two each time and you will have your answer 1 hot dog is 1.50 two are 3.00 use that method and you will have the correct answer

Answer:

Your answer is 6213.45! :)

The equation \(x^2 + y^2 + 10y + 20 = 0\) represents a circle with center (0, -5) and radius 5.

To determine if the equation represents a circle, we need to rewrite it in standard form. The standard form of a circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center of the circle and r represents the radius.

Completing the square for the y terms:

\(x^2 + y^2 + 10y + 20 = 0\\ x^2 + y^2 + 10y = -20\\ x^2 + y^2 + 10y + 25 = -20 + 25\\ x^2 + (y + 5)^2 = 5\)

Now the equation is in standard form, \((x - 0)^2 + (y + 5)^2 = 5^2\), which represents a circle.

By comparing the equation to the standard form, we can determine the center and radius of the circle. The center is given by the values (h, k), which in this case is (0, -5). Therefore, the center of the circle is (0, -5).

The radius is determined by the term \(r^2\), which in this case is \(5^2 = 25\). Therefore, the radius of the circle is 5.

In summary, the equation x^2 + y^2 + 10y + 20 = 0 represents a circle with center (0, -5) and radius 5. The completion of the square allowed us to rewrite the equation in standard form, making it evident that it represents a circle. The center of the circle is determined by the values of x and y, and the radius is determined by the value of r.

Learn more about circle equation here:

https://brainly.com/question/29104982

#SPJ11

Answer: 5 triangles

Step-by-step explanation:

we can take the circles out of the top scale and see that 2 triangles equal a square, so we see 2 squares on the bottom so that is 4 triangles plus one extra

The trigonometric substitution x = 2secθ simplifies the expression x^2 - 4x to (-4sin^2θ)/cosθ.

To make the indicated trigonometric substitution in the given algebraic expression and simplify, we can use the substitution x = 2secθ, where secθ = 1/cosθ.
First, we need to solve for x in terms of θ:
x = 2secθ
x = 2/(cosθ)
Now, we can substitute this expression for x in the original expression:
x^2 - 4x = (2/(cosθ))^2 - 4(2/(cosθ))
Simplifying, we get:
x^2 - 4x = 4/cos^2θ - 8/cosθ
To further simplify, we can use the identity cos^2θ = 1 - sin^2θ:
x^2 - 4x = 4/(1-sin^2θ) - 8/cosθ
We can then combine the two fractions by finding a common denominator:
x^2 - 4x = (4cosθ - 8(1-sin^2θ))/((1-sin^2θ)cosθ)
Simplifying further, we get:
x^2 - 4x = (-4sin^2θ)/cosθ
Therefore, the trigonometric substitution x = 2secθ simplifies the expression x^2 - 4x to (-4sin^2θ)/cosθ.
To know more about trigonometric visit:

https://brainly.com/question/29156330

#SPJ11

An average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

To determine the number of people who are stepping onto the roller coaster per minute at peak time, you need to divide the number of people on the roller coaster by the duration of the ride. Hence, the correct option is B) 6.

To be more specific, this means that at peak time, an average of 3 people is getting on the ride per minute. This is how you calculate it:

Number of people per minute = Number of people on the roller coaster / Duration of the ride

Number of people on the roller coaster = 24

Duration of the ride = 8 minutes

Number of people per minute = 24 / 8 = 3

Therefore, an average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

Learn more about average visit:

brainly.com/question/24057012

#SPJ11

First we need the whole garden:

16 x 5 = 80

Now we need to fountain:

5 x 9 = 45

Now to find our answer:

80 - 45 = 35

So our answer is B. 35ft²

Answer:

25 used games

Step-by-step explanation:

Divide his money by the price for one used game

300/12

25

Answer:

y=0

12x=300

X=300/12

X=25

he can buy 25 used games .

Step-by-step explanation:

10 performances must the company put on in order to break even.

To determine the number of performances needed for the production company to break even, we need to find the point of intersection between the expenses and income lines.

The expense line can be represented by the equation: y = 2900 + 110x, where y represents the total expenses and x represents the number of performances.

The income line can be represented by the equation: y = 400x, where y represents the total income earned.

To find the break-even point, we set the total expenses equal to the total income:

2900 + 110x = 400x

Now we solve for x:

2900 = 400x - 110x

2900 = 290x

x = 10

Therefore, the production company must put on 10 performances in order to break even. At this point, the total income earned from the performances will be equal to the total expenses incurred, resulting in a break-even situation.

It's important to note that this calculation assumes all other factors remain constant and that the income from each performance is $400.

Know more about equation here:

https://brainly.com/question/29174899

#SPJ8

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

Learn more about: Equations,

brainly.com/question/29657983

#SPJ11

Answer:

$11.25 was the tip

Step-by-step explanation:

I subtracted 75.00 by 15% and got 63.75 (what they paid) and subtracted 75.00 by 63.75, which got me the tip= 11.25 dollars

The explanatory and response variables for each set of data:

a.  number of hours spent reading is response variable and page number on which you are reading is explanatory variable.

b. calories burned is response variable and number of minutes of exercising is explanatory variable.

c. amount paid as income tax is response variable and the amount of a paycheck is explanatory variable.

d. pounds of hamburger used to make a meatloaf is response variable and number of people that can be fed from the meatloaf is explanatory variable.

A variable in mathematics is a symbol that represents a mathematical object. A variable can be a number, a vector, a matrix, a function, its argument, a set, or an element of a set.

Here,

For each set of data, the explanatory and response variables are as follows:

a. the number of hours spent reading is the response variable, and the page number on which you are reading is the explanatory variable.

b. The response variable is calories burned, and the explanatory variable is the number of minutes spent exercising.

c. the amount of income tax paid is the response variable, and the amount of a paycheck is the explanatory variable.

The response variable is the number of pounds of hamburger used to make a meatloaf, and the explanatory variable is the number of people who can be fed from the meatloaf.

To know more about variable,

https://brainly.com/question/2466865

#SPJ1

Answer:

Spiders=8

Ants=12

Step-by-step explanation:

Spider(s)=8 legs

Ants(a)=6 legs

Total legs=136

Total heads=20

8s+6a=136 (1)

s+a=20 (2)

From (2)

s=20-a

Substitute 20-a into (1)

8s+6a=136

8(20-a)+6a=136

160-8a+6a=136

160-2a=136

-2a=136-160

-2a=-24

a= -24/-2

a=12

Substitute a=12 into (2)

s+a=20

s+12=20

s=20-12

s=8

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

Learn more about derivative

brainly.com/question/29144258

#SPJ11

Answer: \(\frac{3}{10}\)

Step-by-step explanation:

Given

Sean paints \(\frac{8}{15}\) of a fence in 1 hour

Sean paints \(\frac{3}{10}\) part less in the second hour

So, fraction he paints in the second hour = \(\frac{8}{15}-\frac{3}{10}=\frac{16-9}{30}=\frac{7}{30}\)

Paint in 2 hours = \(\frac{8}{15}+\frac{7}{30}=\frac{16-7}{30}=\frac{9}{30}\)

                          =\(\frac{3}{10}\)

No, he did not finish his job

Note: You will need to write the degree symbol for the arguments of these trigonometric functions.

As sin(x)=cos(90-x), this means sin10 = cos80 and cos75=15.

So,

LHS = (cos80)(sec80)(sin15)(cosec15)

LHS = (cos 80)(1/cos 80)(sin 15)(1/sin 15)

LHS = 1

Therefore, the identity is true.

Answer:

"Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks."

Answer:

"Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks."

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

In order to learn more about perpendicular lines visit link:

https://brainly.com/question/29582941

#SPJ4

Answer:

0.000752739974

by the way  i used a calculator

       I hope this helps :)

The percentage of tourists who do not know Huancayo or Cuzco is 6%.

In this scenario, we are given information about a group of tourists. Among them, 12% do not know Huancayo, 14% do not know Cuzco, and 80% know both cities. To determine the percentage of tourists who do not know Huancayo or Cuzco, we need to subtract the percentage of those who know both cities from 100%.

Let's calculate it step by step. First, we find the percentage of tourists who know at least one of the cities. Since 80% know both, the remaining percentage of tourists who know only one city is 100% - 80% = 20%.

Next, we find the percentage of tourists who do not know either city by subtracting the percentages of those who know each city individually from the percentage who know at least one city. From the given information, 12% do not know Huancayo and 14% do not know Cuzco. Therefore, the percentage of tourists who do not know either city is 20% - 12% - 14% = 6%.

In conclusion, 6% of the tourists do not know Huancayo or Cuzco.

By using the principle of set theory and subtraction, we can determine the percentage of tourists who are unfamiliar with specific cities based on the information given about overlapping knowledge. This approach allows us to analyze and understand the distribution of knowledge among the group of tourists. It is a valuable technique in various fields, such as market research, demographics, and social studies.

Learn more about tourists

brainly.com/question/27993350

#SPJ11

Answer:

620 cm2

Step-by-step explanation:

The base of the prism is a rectangle with 24 cm x 10 cm, so the base area is:

B = 24 * 10 = 240 cm2

The cross section is a triangle with base = 24 cm and height = 5 cm, so its area is:

C = 24 * 5 / 2 = 60 cm2

The sides are rectangles with 10 cm x 13 cm, so their area is:

D = 10 * 13 = 130 cm2

The total surface area is:

S = B + 2C + 2D = 240 + 2*60 + 2*130 = 620 cm2

Answer:

y=5

Step-by-step explanation:

The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.

-Hope this helped