The value of the summation expression given in the task content is; 16.
What is the value of the summation expression given?It follows from the task content that the value of the summation expression given is to be determined.
Since the given expression is; 2x - 3,
On this note;
When x = 2; 2(2) - 3 = 1When x = 3; 2(3) - 3 = 3When x = 4; 2(4) - 3 = 5When x = 5; 2(5) - 3 = 7On this note, the sum of all of the results above is the correct Evaluation of the given expression; 1 + 3 + 5 + 7 = 16.
On this note, the result of the evaluation is; 16.
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Question 2
For this problem, let's assume the Earth is a perfect sphere of radius 6371 km. Calculate the
volume of the Earth in cubic kilometers (km³). Which of these comes closest to your answer?
Hint: the volume of a sphere is given by (4/3) π R³, where R is the radius. If you specify the radius
in km, the volume will come out in km³. You can use the approximate value π = 3.14.
A 6371
B 27,000
C 170 million
D 1 trilion
Volume of earth in shape of a sphere is 1 Trillion km^3 i.e. D.
What is a sphere?
A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.
The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.
Volume of sphere=4/3πr^3. where r=radius.
Surface area=4πr^2.
Now,
Given radius for earth=6371 km
so, Volume of earth=4/3*3.14*6371^3≈1Trillion km^3.
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Select the correct answer from each drop-down menu.
Identify the type of chart described and complete the sentence.
A
chart shows open and close prices and highs and lows, but over a long time period it can also show pricing
.
A particular sort of bar chart known as an OHLC chart displays the open, high, low, and final prices with each period.
What does "open-high-low-close chart" mean?It is obvious from the information provided that the chart being discussed is the Continuously compounded chart.It should be mentioned that an expansive chart (OHLC) is just a term used to describe a sort of chart that is used to depict price changes in a financial instrument over a specific time period.
Here,
The chart's vertical line depicts the price range as a function of time. Since it displays the entire price range for the time period, it is helpful in gauging volatility.
The four main data points throughout a period are displayed on OHLC charts, which are helpful since many traders believe the closing price to be the most significant of the four.
In addition to displaying the opening and closing values of the market for the same time period, open-high-low-close charts also display the high and low price that a stock achieved during that time.
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Please help thank you!
g(0)=-4x^2-3x+2
g(2)=-4^2-3x+2
The simplified value for the function at g(0) and g(2) are 2 and -20 respectively.
What is simplification?To simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given a function g(x) = -4x² - 3x + 2
to find the values of g(0)
and g(2)
for g(0)
substitute x = 0 in the equation,
g(x) = -4x² - 3x + 2
g(0) = -4(0)² - 3(0) + 2
g(0) = 2
for g(2), substitute x = 2 in the equation,
g(x) = -4x² - 3x + 2
g(2) = -4(2)² -3(2) + 2
g(2) = -4(4) - 6 + 2
g(2) = -16 - 6 +2
g(2) = -20
Hence the values for g(0) is 2 and for g(2) is -20.
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How many square feet of outdoor carpet will we need for this hole?
Answer:30
Step-by-step explanation:2*5 + 2*4 + 2*2 + 2*4
=10+8+8+4
=30
During a spring clearance sale, Sears advertise 1/4 off the list of Model II microwave ovens and an additional 1/5 off the sale price for ovens that are scratched or dented. If the list price of a Model II is $240, what is the sale price? What is the price of a scratched one?
Answer:
$180.00 sales price
$144.00 for a scratched one
Step-by-step explanation:
240 x .75 = 180
1/4 is 25% (100% - 25% = 75% which is .75 as a decimal)
180 x .80 = 144
1/5 is 20% (100% -20% = 80% which is .8 as a decimal)
Add one-fourth of two subtracted from thrice a number to twice the same number.
The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.
The expression can be written as,
E = (1/4)( 2 - 3x ) / ( 2x ).
Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).
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Geneva treated her parents to dinner at their favorite restaurant. The bill was $73.25. She wants to leave 24% of the total bill as a tip. How much should the tip be, in dollars?
Answer:
To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).
Tip = 0.24 * 73.25
= 17.58
Therefore, the tip should be $17.58 in dollars.
please help meeee :)
Answer:
9 students
Step-by-step explanation:
34 -25
Select all of the expressions equivalent to (0.5p + 7) + (0.3p-6).
A.1 +0.8p
B.-6.5p+7.3
C.7.5p - 5.7
D.0.8p + 1
E.7.3 -6.5p
Kimi Skuban deposits $2,000 at the beginning of each year into an Individual Retirement Account at
Boise Bank. The account pays 7% compounded annually. How much will be in the account in 25 years?
Total amount in the account after 25 years is, $5,500.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
Kimi Skuban deposits $2,000 at the beginning of each year.
The account pays 7% compounded annually.
Now, We know that;
⇒ Interest = PRT / 100
Where, P is principal amount, R is interest rate and T is time in years.
Substitute all the values, we get;
⇒ Interest = PRT / 100
⇒ Interest = 2000 × 7 × 25/ 100
⇒ Interest = $3,500
Hence, Total amount in the account after 25 years is,
⇒ $2,000 + $3,500
⇒ $5,500
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Please help me with this question.
The matrix products are given as follows:
a. AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
b. BA = [32 -26]
[10 56]
The addition A + B is not possible to obtain, the matrices have different dimensions.
How to multiply the matrices?The dimensions of each matrix are given as follows:
A = 3 x 2.B = 2 x 3.Hence the dimensions of each product are given as follows:
AB = 3 x 3.BA = 2 x 2.To multiply matrices, the rows of the first are multiplied by the columns of the second, hence matrix AB is obtained as follows:
Row 1, column 1: -7(-6) + 4(4) = 58.Row 1, column 2: -7(-2) + 4(-5) = -6.Row 1, column 3: -7(-4) + 4(-1) = 24.Row 2, column 1: -9(-6) - 9(4) = 18.Row 2, column 2: -9(-2) - 9(-5) = 63.Row 2, column 3: -9(-4) - 9(-1) = 45.Row 3, column 1: 7(-6) + 5(4) = -22.Row 3, column 2: 7(-2) + 5(-5) = -39.Row 3, column 3: 7(-4) + 5(-1) = -33.Hence the matrix AB is given as follows:
AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
Matrix BA is obtained as follows:
Row 1, Column 1: -6(-7) - 2(-9) - 4(7) = 32.Row 1, Column 2: -6(4) - 2(-9) - 4(5) = -26.Row 1, Column 1: 4(-7) - 5(-9) - 1(7) = 10.Row 1, Column 2: 4(4) - 5(-9) - 1(5) = 56.Hence the matrix BA is given as follows:
BA = [32 -26]
[10 56]
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Math expression work
The given expression is equivalent to the expression -x² + x + 30.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given expression,
= (5 + x)(6 - x)
Simplifying the expression using distributive property,
= 5 [6 - x] + x [6 - x]
= 30 - 5x + 6x - x²
= -x² + x + 30
Thus, the given expression is equivalent to the expression -x² + x + 30.
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Seats for Sale
State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?
Answer:
a. To determine how many seats should be reserved for premium ticket holders, Frank can use revenue management techniques. One common method is to use the expected revenue per seat, which is calculated by multiplying the number of seats by the expected price per seat and then multiplying that by the probability of that number of seats being sold. Frank can then compare the expected revenues for different numbers of premium seats and choose the number of seats that maximizes the expected revenue.
b. If the number of premium seats is 1,000, then the expected revenue is:
(1,000 x $200 x 0.10) + (75,000 - 1,000) x $40 x 1 = $200,000 + $3,000,000 = $3,200,000
If the number of premium seats is 5,000, then the expected revenue is:
(5,000 x $200 x 0.30) + (75,000 - 5,000) x $40 x 0.7 = $3,000,000 + $2,330,000 = $5,330,000
If the number of premium seats is 10,000, then the expected revenue is:
(10,000 x $200 x 0.24) + (75,000 - 10,000) x $40 x 0.76 = $4,800,000 + $3,768,000 = $8,568,000
and so on for the rest of the numbers.
From the above calculations, we see that the expected revenue is maximized at 10,000 premium seats, which is expected to generate $8,568,000.
c. Using the expected value of the number of premium seats would be calculated by multiplying the number of seats by its probability. The expected value of the number of premium seats is:
1,000 x 0.10 + 5,000 x 0.30 + 10,000 x 0.24 + 15,000 x 0.15 + 20,000 x 0.10 + 25,000 x 0.06 + 30,000 x 0.05 = 10,000.
Comparing this with the number of seats obtained by maximizing the expected revenue (10,000), we see that both approaches yield the same number of premium seats. This means that both approaches would yield the same potential revenue.
19. The speed, s, in feet per second, of an object dropped from a
height, h, in feet, is given by the formula s (h) = √64h. Evaluate
the function for heights of 0 feet to 25 feet by calculating points
every 5 feet.
The plotted graph is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
s (h) = √64h
now, when h=0
s(0) = √64h = 0
and, when h= 5
s(5) = √64h
= √64 x 5
= 8 x 2.25
= 17.88
and, when h= 10
s(25) = √64h
= √64 x 10
= 8 x 3.162
= 25.29
and, when h= 15
s(25) = √64h
= √64 x 15
= 30.98
and, when h= 20
s(25) = √64h
= √64 x 20
= 35.77
and, when h= 25
s(25) = √64h
= √64 x 25
= 8 x 5
= 40
The plotted graph is shown below.
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Suppose I deposit $500 into my bank account that earns 3% interest per year. Is the total amount in my bank account per year a linear relationship? Hint: use a table of values and look at the rate of change. Also, keep in mind that once you earn interest, the next year you will earn interest not only on your original investment but on the new amount.
Answer:
The total amount in your bank account per year is not a linear relationship, it's compound interest.
Step-by-step explanation:
The total amount in your bank account per year is not a linear relationship because it is not a straight line. Linear relationships are defined by an equation in the form of y = mx + b, where m is the slope of the line, x is the independent variable and y is the dependent variable, and b is the y-intercept.
In this case, the total amount in your bank account per year is not a straight line, it is a curve. The total amount in your bank account will increase as a function of time, but the rate of increase is not constant as it is with linear relationships.
The amount of money in your account will increase over time as the interest is compounded. The interest is calculated on the principal + accumulated interest, so the growth rate of the account is not constant, it increases as the balance grows.
For example, the first year you will earn $5000.03 = $15 in interest, and the second year you will earn $5150.03 = $15.45 in interest, the next year the interest will be $530.45*0.03 = $15.91 and so on.
PLEASE HELP AGAIN!!!!!!!!!!
The constant of proportionality from the graph is 5.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
The proportional relationship between x and y can be written symbolically as
[tex]x \propto y[/tex]
That middle sign is called sign of proportionality.
To find the constant of proportionality:
We can see that for every 1 unit we move to the right on the x- axis (positive), the line moves up 5 units.
Divide the change on y by that change on x:
5/1=5
For the next point;
10/2=5
Therefore, the proportionality constant will be 5
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Topic - n-th term
If x + 1 and -x + 17 are the second and sixth terms of a sequence with a common difference
of 5, find the value of x.
Answer: -2
Step-by-step explanation:
So, the arithmetic sequence formula for the nth term is as follows.
Tₙ = a + (n-1)d
So,
2nd term or (x + 1) = a + d
x + 1 = a + 5 (d = 5). - 1
6th term or (-x + 17) = a + 5d
- x + 17 = a + 25. - 2
Subtract 2 from 1, we get,
2x - 16 = -20
2x = -4
x = -2
You can check it if you want,
Second term = - 1
Sixth term will be - 1 + 5 + 5 + 5 + 5 = 19
There you go.
Help me with this question please!
Answer:
Line B slope = 9
Step-by-step explanation:
When dealing with perpendicular lines, we can let the slope we know represent m1, while the slope we don't know represents m2.
Thus, to find m2, we use the formula:
[tex]m_{2}=\frac{-1}{m_{1} }[/tex]
If we plug in -1/9 for m1, we have:
[tex]m_{2}=-\frac{1}{(-1/9)} \\m_{2}=9[/tex]
If f(x)= |a³-31 |. then f(-1) is equivalent to
The value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.
We substitute -1 for x in the function: f(-1) = |a³ - 31| To find the value of f(-1), we need to find the value of a³ - 31. If a³ - 31 is positive, then |a³ - 31| will be equal to a³ - 31. If a³ - 31 is negative, then |a³ - 31| will be equal to the absolute value of a³ - 31 (which is the positive value of a³ - 31).So, the value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.It is not possible to find the exact value of f(-1) without knowing the value of a.
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How would you solve question 12b?
The line y = 3 is shown in the diagram of the graph of y = (x + 1)² for -4 ≤ x ≤ 2.
By using the graph, the solutions of (x + 1)² = 3 to 1 decimal place include the following:
x = -2.7 or x = 0.7.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Next, we would use an online graphing calculator to plot the above quadratic equation with points of intersection at (-2.732, 3) and (0.732, 3) as shown in the graph attached below.
By critically observing graph of the given quadratic equation, we can logically deduce that the solutions of (x + 1)² = 3 on the x-coordinate are x is equal to -2.7 or x is equal to 0.7.
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Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her
13
character unlocking the treasure chest is
Find the odds in favor of her character unlocking the treasure chest.
The odds in favor of Amanda unlocking the treasure chest is 1/5.
We have to find the odds in favor of Amanda's character unlocking the treasure chest. Odds in favor is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
[tex]P (A) = \frac{no.of favorable outcomes}{no. of unfavorable oucomes}[/tex]
P(A), is used to denote the probability of the event A.
Before finding out the odds in favor, we need to find the probability of her unlocking the treasure chest {P(T)}
Total no. of outcomes = 6 (as a dice has 6 sides)
Number of outcomes desired = 1 (that unlocks the treasure chest)
Therefore, the probability of unlocking the treasure chest
P(T) = Number of outcomes desired/ Total no. of outcomes = 1/6
P(T) is our favorable outcome.
Any other outcome would be unfavorable,
Therefore, the number of unfavorable outcomes would be
= Total no. of outcomes - number of the desired outcomes = 6-1 = 5
Thus, applying the formula for P(A)
P(A) = no. of favorable outcomes/ no. of unfavorable outcomes
= 1 / 5 (Ans)
Thus, the odds in favor of Amanda unlocking the treasure chest is 1/5.
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Factorise the following
a. x square - 16
b. 8m square - 50n square.
Answer:
(i) (x+4)(x-4)
Step-by-step explanation:
(ii)64m² - 800mn +2500n²
Tell whether b = 12 is a solution of b - 7 = 5
Answer:
Yeah, [tex] \sf b = 12 [/tex]
Step-by-step explanation:
Given equation,
→ b - 7 = 5
Now the value of b will be,
→ b - 7 = 5
→ b = 7 + 5
→ [ b = 12 ]
Hence, the value of b is 12.
Answer: Yes
Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.
Try solving 12-7. It is 5.
Make me brainliest! Have a nice day :)
ON = MN, find MN.
A.4
B.5
C. 4// 2
D.4 // 30
The value of x for the given figure is 4√2.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
ΔMNO is a right triangle.
Applying the Pythagorean theorem.
MO² = ON² + MN²
8² = x² + x²
64 = 2x²
2x² = 64
x² = 32
x = √32
x = √(16 x 2)
x = √(4² x 2)
x = 4√2
Thus,
The value of x is 4√2.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2 Mark this and return
The following equations which are equivalent are:
2 + x = 5 x + 1 = 4 Negative 5 + x = negative 2How to determine equivalent equation?2 + x = 5
collect like terms
x = 5 - 2
x = 3
x + 1 = 4
Subtract 1 from both sides
x = 4 - 1
x = 3
9 + x = 6
Subtract 9 from both sides
x = 6 - 9
x = -3
x + (negative 4) = 7
x +(-4) = 7
Open parenthesis
x - 4 = 7
x = 7 + 4
x = 11
Negative 5 + x = negative 2
-5 + x = - 2
x = -2 + 5
x = 3
Therefore, 2 + x = 5; x + 1 = 4; Negative 5 + x = negative 2 are equivalent to each other.
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Convert the following [ Use exchange rate 1CAD 0.82 USD]
1.45 CAD = ? USD
45.50 USD = ? CAD
2.50 CAD = ? USD
1,500 CAD = ? USD
Answer: For converting Canadian Dollars to US Dollars divide 1 by 0.82 to give you an answer of around 1.2195(repeating). Then multiply that number by each of the Canadian Dollar amounts. US Dollars to Canadian Dollars is much simpler, as you just multiply the amount by 0.82 to find the answer.
$1.45 CAD x 1.2195 = $1.77 USD
$45.5 USD x 0.82 = $38.31 CAD
$2.50 CAD x 1.2195 = $3.05 USD
$1,500 CAD x 1.2195 = $1,829.27 USD
Hope this helped, and have a great day!
Help pleaseeee I can’t figure this out
Answer: B. Exponential decay
Step-by-step explanation:
An exponential function is a function of the form f(x) = ab^x where a and b are constants, x is the independent variable, and b is a positive number not equal to 1. In this case, f(x) = -3(4^x). The base of the exponential function is 4, and it is a common base of exponential decay, because the base is less than 1, and the exponent is positive, this means that the output of the function will decrease as the input increases. Therefore, the function represented by f(x) = -3(4^x) is an exponential decay function.
Answer:
Exponential Decay
Step-by-step explanation:
In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed
Substitute the given value into the function and evaluate.
f(x)= -3⋅4^x/8
Calculate each year-end balance using the simple
interest rates listed.
Principal
$100.00
$550.00
$1,200.00
$5,000.00
Annual interest
rate
5%
2%
7%
11%
End of year
balance
The year-end balance interest rate for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00.
What is the interest rate?Interest is the cost of borrowing money or the amount of money that is earned on an investment. It is the amount of money paid by a borrower to a lender or earned by an investment, in exchange for the use of the lender's or investor's money.
Here,
To calculate the year-end balance for each principal using the given annual interest rates, we can use the formula:
End of year balance = Principal + (Principal x Interest rate x Number of years)
For a principal of $100.00, the annual interest rate is 5%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $100.00 + ($100.00 x 0.05 x 1) = $100.00 + $5.00 = $105.00
For a principal of $550.00, the annual interest rate is 2%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $550.00 + ($550.00 x 0.02 x 1) = $550.00 + $11.00 = $561.00
For a principal of $1,200.00, the annual interest rate is 7%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $1,200.00 + ($1,200.00 x 0.07 x 1) = $1,200.00 + $84.00 = $1,284.00
For a principal of $5,000.00, the annual interest rate is 11%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $5,000.00 + ($5,000.00 x 0.11 x 1) = $5,000.00 + $550.00 = $5,550.00
Hence, the year-end balance for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00, and for a principal of $5,000.00 is $5,550.00
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Write the quotient 25/4+3i in the form a + bi.
Answer:
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