After graduating from college and earning a
degree, Edmond decided to move to Spain for
work and save €10,000 from his first year of work
for an emergency fund. Edmond's emergency
fund investment earns 6% per year and is
compounded annually.
PLS HELP
Answers
1) The expression that describes this scenario where Edmond decided to save €10,000 from his first year of work for an emergency fund, earning 6% per year and compounded annually is that the fund will grow to become equal to [tex]10,000 (1.06)^t[/tex] in t years.
2) After ten years of investing at 6%, compounded annually, the amount (future value) in the fund will be €17,908.
3) Given that the annual rate is 6%, the monthly rate will be 0.5%.
4) The exponent for the exponential function will be 120 with the 10 years in the scenario.
5) The complete expression that describes the scenario over 10 years is [tex]10,000(1.005)^{120}[/tex].
6) After ten years of investing at 6% APR compounded monthly, the amount (future value) in the fund will be €18,193.97.
7) There is more money with monthly compounding than annual compounding because the monthly interest is added and compounded more regularly, in this case, twelve times yearly than once a year.
Thus, more regular compounding increases the future value than periodic (annual, monthly, semiannual) compounding.
How the amounts are derived:The future values can be determined using an online finance calculator that compounds interest per period as follows:
We can also derive the future values using the FV formula given as [tex]PV(1+r)^t[/tex].
1) Principal investment = €10,000
Compound interest rate = 6% = 0.06 (6/100)
Compound factor = 1.06 (1 + 0.06)
Compounding period = annually
Investment period = t years
Expression: €10,000 x [tex]1.06^t[/tex]
= 10,000(1.06)^t
= [tex]10,000(1.06)^t[/tex]
2) After ten years, the amount in the account will be equal to [tex]10,000(1.06)^{10}[/tex]
= 10,000 x 1.7908
= 17,908
3) Annual rate of interest = 6%
Monthly rate = 0.5% (6%/12)
4) Exponent = 120 (10 years x 12)
5) Exponential function:
[tex]10,000(1.005)^{120}[/tex]
6) Future value after 10 years:
[tex]10,000(1.005)^{120}[/tex]
= 10,000 x 1.8193967
= €18,193.97
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Related Questions
A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 7% chance that it will not make any hires and a 10% chance that it will make all three hires.
a. What is the probability that the firm will make at least one hire? (Round your answer to 2 decimal places.)
b. Find the expected value and the standard deviation of the number of hires. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)
Answers
b. Let X be the number of hires. Then X can take on values 0, 1, 2, or 3. The expected value of X is E(X) = 2.1 and the standard deviation of X is σ = 0.7.
Find the quotient -7.3 1/2
Answers
Answer:
Step-by-step explanation: -3.655 hopefully that works
Which describes the correct order of steps to construct an angle bisector of ZJKL using only a straightedge and compass?
Answers
Answer:
First you draw the lines zjkl and then you make an archs to bisect the line using a compass and a pencil first you go to each point and it's corresponding letter you arch then draw a straight line which passes through the arch
27) Determine whether the graph can represent a normal curve. If it cannot, explain why.
A) The graph cannot represent a normal density function because it increases as x becomes very large
or very small.
B) The graph cannot represent a normal density function because it takes negative values for some
values of x.
C) The graph can represent a normal density function.
D) The graph cannot represent a normal density function because the area under the graph is greater
than 1.
Answers
The graph can represent a normal curve because it represent a normal density function. The Option C.
Can the graph represent a normal curve?The answer is yes. While these characteristics may deviate from the ideal properties of a normal distribution, they do not necessarily invalidate the possibility of the graph representing a normal density function.
A normal curve can have tails that extend indefinitely allowing for the graph to increase as x becomes very large or very small. Negative values can occur if the graph represents a standard normal distribution which is centered at zero.
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1. Solve the differential equation
(4+t²)dy/dt + 2ty = 4t
2. Find the general solution of the differential equation dy/dt + (1/2)y = (1/2)e^t/3 .
3. Solve the initial value problem .
ty' + 2y = 4t² , where y(1) = 2.
Answers
Answer:
1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.
2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.
3. The solution to the initial value problem is y = t^2 + 4/3.
Marie went golfing and tracked her golf cart's distance from the first hole over time. She stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours. She stopped to have lunch for 1 hour and then took 2 hours to drive back to the first hole.
Which of the following graphs could represent Marie's situation?
Answers
The graph that correctly represents Marie's situation is the graph B or the second graph.
How should the graph be?For the graph to correctly represent Marie's situation the followin elements are needed:
A step line that goes from 0 to 5 in the y-axis in the time of 2 hours, which represents her driving away for 2 hours.A horizontal line for 1 hour that represents Marie having lunch during that time.A negative step line that shows her driving back to the first hole, this line should go from 5 in the y-axis to 0.Note: This question is incomplete; below are the missing graphs:
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These tables of values represent continuous functions. In which table do the
values represent an exponential function?
Answers
The fourth table of values represents an exponential function (Correct choice: D).
Which table of value does represent an exponential function?
Herein we find four tables of values, three representing a linear function and one representing an exponential function. Each function is introduced below:
Linear equation:
n = m + r · n
Exponential function
n = m · rⁿ
Where:
m - Inputn - Outputr - Common rate.Common rate is the most appropriate criterion to distinguish linear equations of exponential equations. Now we proceed to summarize the results of each table of values:
Case A: Linear equation, r = 8.
Case B: Linear equation, r = 1.
Case C: Linear equation, r = 5.
Case D: Exponential equation: r = 2.
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Part B
Use the distance formula to find BC. Show your work.
Answers
Answer:
5 units------------------------
Use coordinates of endpoints, taken from the diagram, B(6, 2) and C(2, - 1) and the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute BC for d and given coordinates to find the radius:
[tex]BC=\sqrt{(2-6)^2+(-1-2)^2} =\sqrt{16+9} =\sqrt{25} =5[/tex]Hence the segment BC is 5 units long.
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
Answers
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
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winta and lensa invest birr 21000 and 17500 respectively in a business.at the end of the year, they make profit birr 24600. what is the the share of winta in the profit?
Answers
Answer:
Step-by-step explanation:
To determine the share of Winta in the profit, we need to calculate the ratio of her initial investment to the total initial investment and then apply that ratio to the total profit.
Winta's initial investment: Birr 21,000
Lensa's initial investment: Birr 17,500
Total initial investment: Birr 21,000 + Birr 17,500 = Birr 38,500
To find the share of Winta in the profit, we calculate:
Winta's share = (Winta's initial investment / Total initial investment) * Total profit
Winta's share = (Birr 21,000 / Birr 38,500) * Birr 24,600
Simplifying the calculation:
Winta's share = (0.5455) * Birr 24,600
Winta's share ≈ Birr 13,414.55
Therefore, Winta's share in the profit is approximately Birr 13,414.55.
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
Answers
Answer:
0.5(x)(x + 2) = 24
x² + 2x - 48 = 0
x² + (x + 2)² = 100
A dairy farmer wants to mix a 75% protein supplement and a standard 25% protein ration to make 1100 pounds of a high-grade 55% protein ration how many pounds of each should he use?
Answers
The farmer should use 660 pounds of the 75% protein supplement and 440 pounds of the 25% protein ration to make 1100 pounds of a high-grade 55% protein ration.
Let 75% protein supplement be x and 25% protein ration be y
The total weight of the mixture is x + y = 1100
The second equation related to the protein in the mixture is 0.75x + 0.25y = 0.55 × 1100
= 0.75x + 0.25y = 605
By using the elimination method multiply the first equation by 0.25 to match the coefficients of y:
0.25x + 0.25y = 0.25 × 1100
0.25x + 0.25y = 275
by subtracting this equation from the second equation:
0.75 x + 0.25 y - {0.25 x + 0.25y} = 605 - 275
0.75 x - 0.25 x = 330
0.5x = 330
x = 660
by substituting this in the first equation:
660 + y = 1100
y = 440
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find a and b find a and b find a and b find a and b find a and b find a and b find a and b find a and b find a and b vfind a and b
Answers
Answer
a=93
b=74
Step-by-step explanation:
a=180-87=93 b=180-106=74
Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit.
(Hint: Assume that the central point of each arc is its corresponding vertex.)
Answers
The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.
To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.
First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.
In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.
Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.
Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.
Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.
Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.
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Which is the standard equation of the parabola in the graph?
Graph of parabola opening to the right with vertex at 0 comma 4, focus at 4 comma 4, p equals 4, vertical dotted line going through negative 4 on x axis is labeled directrix, and horizontal dotted line going through 4 on y axis is labeled axis
x2 = 16(y – 4)
x2 = –16(y + 4)
(y – 4)2 = 16x
(y + 4)2 = –16x
Answers
The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].
The standard equation of the parabola in the graph can be determined based on its characteristics.
Given:
Vertex: (0, 4)
Focus: (4, 4)
P (the distance from the vertex to the focus or directrix): 4
We can conclude that the parabola opens to the right because the axis is horizontal.
The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:
[tex](x - h)^2 = 4p(y - k)[/tex]
In this case, the vertex is (0, 4), so the equation becomes:
[tex](x - 0)^2 = 4p(y - 4)[/tex]
Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.
Therefore, the standard equation of the parabola in the graph is:
[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]
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Given an isosceles triangle ABC (AB = AC) and a point M that does not belong to it, but belongs to angle ABC. Find the angle BAM if ∠ABC = 50°, ∠BMC = 40°, ∠BMA = 10°.
The answer is 160°. After numerous attempts I couldn't solve it anyway.
Give all my points away.
IMPORTANT: It's not a college problem, this problem is from an 8th grade textbook, the matter is "Inscribed and circumscribed circles". So it must be solved within this topic.
Answers
The angle BAM is 40°. as the correct angle based on the given values is not 160°, but rather 40°.
To solve this problem within the topic of inscribed and circumscribed circles, we can utilize the property of angles subtended by the same arc on a circle.
Let's consider triangle ABC and point M within angle ABC. Since triangle ABC is isosceles with AB = AC, we can draw the circumcircle passing through points A, B, and C. Let O be the center of this circumcircle.
Based on the property mentioned earlier, angle BAM will be equal to half the measure of arc BC on the circumcircle, subtended by chord BM.
Given that ∠ABC = 50° and ∠BMC = 40°, we can deduce that arc BC on the circumcircle will have a measure of 2 * ∠BMC = 2 * 40° = 80°.
Since angle BAM is half the measure of arc BC, we have:
∠BAM = 0.5 * 80° = 40°
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I need help answering this, I don’t remember how to do this
Answers
Answer:
37.5
Step-by-step explanation:
the therom of a parallelogram is width*height
so 7.5*5
=37.5
If you found this helpful, please consider giving a brainliest!
Answer:
A = 37.5
Step-by-step explanation:
The area of a parallelogram is:
Area = base × height
In your picture the base is 7.5 and the height is 5.
So multiply 7.5×5 and you get 37.5.
The area is 37.5cm^2
. A plastic marker buoy floating on the sea consisting of a cone attached to a hemispherica base is shown above. The radius of the hemispherical base is 0.95cm and height of the cone is 1.2m. Calculate the volume of the buoy.
Answers
Answer:
The volume of the buoy can be calculated by finding the volumes of the cone and hemisphere separately and then adding them together.
The volume of the cone is given by:
Vcone = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
Substituting the given values, we get:
Vcone = (1/3)π(0.95)^2(1.2) = 1.08 m^3 (rounded to two decimal places)
The volume of the hemisphere is given by:
Vhemisphere = (2/3)πr^3
where r is the radius of the hemisphere.
Substituting the given value, we get:
Vhemisphere = (2/3)π(0.95)^3 = 1.05 × 10^-3 m^3 (rounded to two decimal places)
Therefore, the total volume of the buoy is:
Vbuoy = Vcone + Vhemisphere = 1.08 + 1.05 × 10^-3 = 1.08 m^3 (rounded to two decimal places)
solve the equation…………….
Answers
Answer:
18
Step-by-step explanation:
[tex]\sqrt{x-2} =4\\x-2=16\\x=18[/tex]
Given equation :
[tex] \sqrt{x - 2} = 4[/tex]
Squaring both sides
[tex]( { \sqrt{x - 2} })^{2} = {(4)}^{2} [/tex]
[tex]x - 2 = 16[/tex]
Move all terms containing x to the left, all other terms to the right.
[tex]x = 16 + 2[/tex]
[tex]x = 18[/tex]
Verification:
Put value the x in the given equation.
[tex] \sqrt{x - 2} = 4[/tex]
[tex] \sqrt{18 - 2} = 4[/tex]
[tex] \sqrt {16} = 4[/tex]
[tex] \sqrt {4 \times 4 } = 4[/tex]
[tex]4 = 4[/tex]
Hence, The answer is 18.
Probability of dice and frequency
Answers
Probabilities are:
Even number = 0.5
Odd Number = 0.5
Number 1 face up = 1/6
Number 2 face up = 1/6
Number 3 face up = 1/6
Number 4 face up = 1/6
Number 5 face up = 1/6
Number 6 face up = 1/6
Mrs.Li's classroom is 34 feet wide and 42 feet long.
How much area is taken up by the objects in the classroom? How much area is left for the student's desks? Write and solve equations to find the area.
Mrs.Li's desk is 8 sq ft, Fish tank 6 sq ft, Math Center 100 sq ft, Reading Center 120 sq ft
PLEASE HELP THIS IS REALLY IMPORTANT
Answers
Answer:
1428
Step-by-step explanation:
Area=L×B/W
34×42
=1428
Which is a correct step when using the median-fit method for modeling data?
Answers
The correct step when using the median-fit method for modeling data is to fit a function to the median of the data.
The median-fit method can be used to model data by following these steps:
1. Arrange the data set in ascending order.
2. Find the median of the data set.
3. Divide the data set into two groups: one group that is below the median, and another group that is above the median.
4. Compute the median of each group.
5. Fit a function to the median of the data.
6. Use the fitted function to estimate values for the original data set.
The median-fit method is a statistical method used to model data. It involves fitting a function to the median of the data. This method is often used when the data set is skewed or has outliers.
The median-fit method is more robust to outliers than the mean-fit method. It is also less sensitive to the shape of the data distribution than other methods.
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Two friends wash cars to make extra money. The profit P(x) of one friend after x days can be represented by the function P(x) = −x2 + 5x + 12. The second friend's profit can be determined by the function Q(x) = 6x. Solve the system of equations. What solution is a viable answer to the question, "After how many days will the two students earn the same profit?" and which solution is a nonviable answer? Show your work and justify your answer.
Answers
After 3 days, the two friends will earn the same profit.
To find the number of days after which the two friends will earn the same profit, we need to set the profit functions P(x) and Q(x) equal to each other and solve for x.
P(x) = Q(x)
−x^2 + 5x + 12 = 6x
Rearranging the equation:
−x^2 + 5x + 12 - 6x = 0
Combining like terms:
−x^2 - x + 12 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:
-(x - 3)(x + 4) = 0
Setting each factor equal to zero:
x - 3 = 0 or x + 4 = 0
Solving for x:
x = 3 or x = -4
Both x = 3 and x = -4 are solutions to the equation. However, we need to determine which one is a viable answer and which one is a nonviable answer.
The question asks for the number of days, which cannot be negative. Therefore, x = -4 is a nonviable answer since it represents a negative number of days. The viable answer is x = 3.
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find the volume of the pyramid that has a square base.
picture provided down below.
PLEASE HELP THIS IS THE LAST DAY IM ABLE TO TURN THIS IN!!!!
Answers
Answer:
324 cm³
Step-by-step explanation:
Square based pyramid volume formula:
[tex]V=a^2\frac{h}{3}[/tex]
with a being the base length and h being the height
We can substitute in our values:
[tex]V=a^2\frac{h}{3} \\V=9^2\frac{12}{3}\\V=81(4)\\V=324[/tex]
So, the volume is 324 cm³.
Hope this helps! :)
need help ,plss like rn
Answers
Answer:
3 units to the left of the y-axis
Step-by-step explanation:
Since all answers involve 3, I believe we are looking at the x-axis. To answer your question, a negative x value means that it is to the left of the origin. Therefore the answer would be 3 units to the left of the y-axis.
Perform the following Sequence of Transformations on △ABC and provide the (x,y) coordinates for the image of each point after each transformation.
First, translate four units to the left and five units down
Next, reflect across the line y = x
Last, dilate with scale factor = 2
Answers
The (x, y) coordinates for the image of each point after each transformation include the following:
A' (-3, -4) A" (1, 1) A'" (2, 2).
B' (1, -4) B" (1, 5) B'" (10, 2).
C' (-1, -1) C" (4, 3) C''' (6, 8).
How to perform the sequence of transformations on triangle ABC?In order to apply a translation of four units to the left and five units down to triangle ABC, we would use this transformation rule;
(x, y) → (x - 4, y - 5)
A (1, 1) → A' (-3, -4).
B (5, 1) → B' (1, -4).
C (3, 4) → C' (-1, -1).
Next, we would reflect triangle ABC across the line y = x;
(x, y) → (y, x)
A (1, 1) → A" (1, 1).
B (5, 1) → B" (1, 5).
C (3, 4) → C" (4, 3).
Lastly, we would dilate triangle ABC with scale factor of 2;
(x, y) → (2x, 2y)
A (1, 1) → A'" (2, 2).
B (5, 1) → B'" (10, 2).
C (3, 4) → C''' (6, 8).
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Esmerelda simplified a complex fraction. Her work is shown below.
Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4
What errors did Esmerelda make? Select three options.
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda added the denominators.
Esmerelda did not divide –24 by 6 correctly.
Esmerelda did not use the reciprocal of the divisor
Answers
The correct options are:
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda did not divide –24 by 6 correctly.
The errors made by Esmerelda are as follows:
1. Esmerelda converted the mixed number to the wrong improper fraction.
2. Esmerelda added the numerators.
3. Esmerelda did not divide –24 by 6 correctly.
Let's go through each error:
1. Esmerelda converted the mixed number to the wrong improper fraction:
Esmerelda incorrectly converted "Negative 5 and one-fourth" to "Negative StartFraction 21 over 4 EndFraction." The correct conversion would be "Negative StartFraction 5 over 4 EndFraction" since the mixed number -5 1/4 can be expressed as -5 + 1/4 = -5 (1/4) = -5 (4/4) + (1/4) = -5 (4 + 1)/4 = -5 (5/4) = -5 (5 over 4).
2. Esmerelda added the numerators:
Esmerelda incorrectly added the numerators of the fractions, resulting in "Negative StartFraction 21 over 4 EndFraction" instead of the correct numerator of -5 * 4 = -20.
3. Esmerelda did not divide –24 by 6 correctly:
Esmerelda made an error in dividing -24 by 6, resulting in "StartFraction 24 over 6 EndFraction" instead of the correct value of -24 divided by 6, which is -4.
Therefore, the correct options are:
- Esmerelda converted the mixed number to the wrong improper fraction.
- Esmerelda added the numerators.
- Esmerelda did not divide –24 by 6 correctly.
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Now, at the animal shelter 4/6 of the animals are cats. Of the cats ½ are male. What fraction of the animals at the shelter are male cats?
Answers
In x=5. Solve for the equation c
Answers
Answer:
What is the equation?
Step-by-step explanation:
Can't solve it without knowing where c is in the equation
Shan scored 7 out of 10 for his maths test and 15 out of 20 for his science test. Which test did he achieve better results?
Answers
Shan performed better in his science test than in his math test based on the respective scores of 15 out of 20 and 7 out of 10.
To determine which test Shan achieved better results in, we need to compare the scores he obtained in both the math and science tests.
Shan scored 7 out of 10 in his math test, which can be written as a fraction 7/10. This fraction can also be converted to a decimal by dividing 7 by 10, resulting in 0.7.
Similarly, Shan scored 15 out of 20 in his science test, which can be written as a fraction 15/20. This fraction can also be simplified by dividing both the numerator and denominator by 5, resulting in 3/4. Converting this fraction to a decimal by dividing 3 by 4 yields 0.75.
Comparing the decimal values, we can see that 0.75 (science test) is greater than 0.7 (math test). Therefore, Shan achieved better results in his science test compared to his math test.
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