The future value of this annuity would be approximately $20,461.96. The future value of the annuity due would be approximately $22,867.35. The future value of the cash flow mix stream would be approximately $1,886.32.
To calculate the future value of the annuity, we can use the formula for the future value of an ordinary annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
Where: FV = Future value of the annuity
P = Annual deposit amount
r = Interest rate per period
n = Number of periods
a. Using the given values:
P = $2,000 (annual deposit)
r = 12% per period (convert to decimal: 0.12)
n = 7 (number of years)
Plugging these values into the formula:
[tex]FV = 2000 * [(1 + 0.12)^7 - 1] / 0.12[/tex]
Calculating this expression: FV ≈ $20,461.96
Therefore, the future value of this annuity would be approximately $20,461.96.
b. If "part a" were a future value annuity due, we need to adjust the formula by multiplying it by (1 + r) to account for the additional period:
[tex]FV_{due}[/tex] = FV * (1 + r)
Plugging in the previously calculated future value (FV) and the interest rate (r):
[tex]FV_{due}[/tex] = $20,461.96 * (1 + 0.12)
Calculating this expression:
[tex]FV_{due}[/tex] ≈ $22,867.35
Therefore, the future value of the annuity due would be approximately $22,867.35.
c. To calculate the future value of the cash flow mix stream, we can sum up the future values of each individual deposit using the formula:
[tex]FV_{mix}[/tex] = FV1 + FV2 + FV3
Where: [tex]FV_{mix}[/tex] = Future value of the cash flow mix stream, FV1, FV2, FV3 = Future values of each deposit
Given: P1 = $400 (deposit in year 1)
P2 = $800 (deposit in year 2)
P3 = $500 (deposit in year 3)
r = 6% per period (convert to decimal: 0.06)
n1 = 1 (future value for year 1)
n2 = 2 (future value for year 2)
n3 = 3 (future value for year 3)
Using the formula, we calculate the future value of each deposit:
[tex]FV1 = P1 * (1 + r)^{n1} = 400 * (1 + 0.06)^1 = $424[/tex]
[tex]FV2 = P2 * (1 + r)^{n2 }= 800 * (1 + 0.06)^2 = $901.44[/tex]
[tex]FV3 = P3 * (1 + r)^{n3} = 500 * (1 + 0.06)^3 = $560.88[/tex]
Summing up the individual future values:
[tex]FV_{mix}[/tex] = $424 + $901.44 + $560.88 = $1,886.32
Therefore, the future value of the cash flow mix stream would be approximately $1,886.32.
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Which of the following sets of ordered pairs does not define a function?
{(1,2),(5,6),(6,7),(10,11),(13,14)}
{(−1,4),(0,4),(1,4),(2,4),(3,4)}
{(1,1),(2,2),(3,3),(4,4),(5,5)}
{(1,3),(5,2),(6,9),(1,12),(10,2)}
Answer: D
Step-by-step explanation: As we can see, D is the only one that has matching inputs, but those inputs have separate outputs. If they don't have the same output, it is not a function
Hope this helps :)
12 × (3 + 2²) ÷ 2 - 10
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
This should help
Solve for x.
PLEASE ANSWER I WILL GIVE BRAINLIEST!!
Answer:
16 + 5 =21 21 is your answer
Step-by-step explanation:
What is the equation of the line that passes through the point (7,-6) and has a slope of -2?
Answer:
y=-2+8
Step-by-step explanation:
The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!
[tex]2v^{2} +14=104[/tex]
Step-by-step explanation:
[tex]2 {v}^{2} + 14 = 104 \\ 2 {v}^{2} = 104 - 14 \\ 2 {v}^{2} = 90 \\ {v}^{2} = 90 \div 2 \\ {v}^{2} = 45 \\ v = \sqrt{45} [/tex]
I will leave the answer in square root form as i am not sure if you need to round your answer or not.
what differences can be found when contrasting the mood of third person acc with that of claudettes first person account?
Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.
Step-by-step explanation:
A structural steel rod 1-1/2 in. in diameter and 20 ft long supports a balcony and is subjected to an axial tensile load of 30,000 lb. Compute: (a) the total elongation (b) the diameter of the rod required if the total elongation must not exceed 0.10 in. A. a. Elongation = 0.2358in. b. Use a1-1/2" dia. Rod B. a. Elongation = 1.1358in. b. Use a 1-1/4" dia. Rod C. a. Elongation = 0.1358in. b. Use a 1-3/4" dia. Rod D. a. Elongation = 0.1458in. b. Use a 3/4" dia. Rod
The diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
(a) To compute the total elongation, we can use the formula:
Elongation = (P * L) / (A * E)
where P is the axial tensile load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity for the material.
Given:
P = 30,000 lb
L = 20 ft = 240 in
Diameter of the rod = 1-1/2 in
First, we need to calculate the cross-sectional area:
Area = π * (diameter/2)^2
Area = π * (1.5/2)^2
Area ≈ 1.767 in^2
Next, we need to determine the modulus of elasticity for the material. Assuming it's a standard structural steel, we can use a typical value of 29,000,000 psi.
Now we can plug the values into the formula:
Elongation = (30,000 * 240) / (1.767 * 29,000,000)
Elongation ≈ 0.2358 in
Therefore, the total elongation is approximately 0.2358 inches.
(b) If the total elongation must not exceed 0.10 inches, we need to determine the diameter of the rod that satisfies this requirement.
We can rearrange the formula for elongation to solve for the cross-sectional area:
A = (P * L) / (E * Elongation)
Using the given values:
A = (30,000 * 240) / (29,000,000 * 0.10)
A ≈ 2.069 in^2
To find the corresponding diameter, we use the formula:
Diameter = √(4 * A / π)
Diameter = √(4 * 2.069 / π)
Diameter ≈ 1.441 in
Therefore, the diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
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Consider the inequality x<1. Determine whether each value of x makes the inequality trueSelect Yes or No va Yes No 3/2 13/6
BRAINLY TO WHOEVER HELPS AND GET IT RIGHT
~no links pls~
Answer:
4 yards saved
Step-by-step explanation:
two adjacent sides: 6 + 8 = 14
diagonal: √(6² + 8²) = √100 = 10
14 - 10 = 4
PLEASE HELP
WILL GIVE BRAINLIEST
Identify the situation that each graph could represent.
A ray is graphed in the first quadrant. The horizontal axis is labeled Time. The ray starts at the bottom left and continues to the upper right.
A. the length of a necklace that you make at a rate of 10 cm per hour without taking a break
B. the height of a balloon as it rises, gets caught in a tree for a few minutes, and then continues to rise
C. the total distance you are from home if you ride your bicycle three miles per hour for one hour, and then stop and take a rest
D. The volume of water in a bath tub as it is draining.
Answer:
The answer your looking for is, C.
Make up any linear equation with two variables the solution to which will be these pairs of numbers. x=2, y=4.5 PLS HELP
Answer:
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
Step-by-step explanation:
Given
[tex]x = 2[/tex]
[tex]y = 4.5[/tex]
Required
Make up a linear function
A linear function is represented as:
[tex]y = mx + b[/tex]
Assume [tex]b = 4[/tex]
The equation becomes
[tex]y = mx + 4[/tex]
Substitute [tex]x = 2[/tex] and [tex]y = 4.5[/tex] to solve for m
[tex]4.5 = m*2 + 4[/tex]
[tex]4.5 = 2m + 4\\[/tex]
Solve for m
[tex]2m = 4.5 - 4[/tex]
[tex]2m = 0.5[/tex]
[tex]m = 0.5/2[/tex]
[tex]m = 0.25[/tex]
So, we have:
[tex]m = 0.25[/tex], [tex]b = 4[/tex], [tex]x = 2[/tex] and [tex]y = 4.5[/tex]
[tex]y = mx + b[/tex] becomes
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
In this class we considered a variety of problems, formulas, and theorems. For an extra credit problem, describe a concept that we covered in class in your own words. It can be a theorem or a question that we solved in class or in homework problems (please don't repeat problems above). State the concept, explain the details in your own words.
The Pythagorean Theorem is a concept in geometry that explains the relationship between the sides of a right-angled triangle. According to this theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its two legs. This can be represented in the form of an equation as c² = a² + b², where c is the hypotenuse and a and b are the legs of the triangle. This theorem is widely used in various fields, including architecture, engineering, and physics. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
In simpler words, the Pythagorean theorem is used to find the length of the missing side of a right-angled triangle. For example, if we know the lengths of two sides of a triangle, we can use this theorem to find the length of the third side. This theorem is based on the fact that the hypotenuse is the longest side of a right-angled triangle, and that the square of a number is the product of that number multiplied by itself. It is also used to prove whether a triangle is a right-angled triangle or not. The Pythagorean Theorem is a fundamental concept in geometry and is an essential tool for solving various mathematical problems.
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In the above figure, m∠AOC = 30° and m∠BOD = (2x + 39)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x? A. x = 69 B. x = -9 C. x = 34.5 D. x = -4.5
i need help asap
Answer:
bestie thats hard
Step-by-step explanation:
Answer:
D. x=-4.5
Step-by-step explanation:
Since they are both vertical angles, m∠BOD must also be equal to 30 degrees, and if you input -4.5 as x, (2 x -4.5x) + 39, that is rewritten as -9 and 39. 39 - 9 is 30 degrees.
What is the interquartile range The following data points represent the volume of gas in each race car driver's tank (in liters) Sort the data from least to greatest: 2.8 43 7.5 8.5 11.6 12 12.1 Find the interquartile range
The interquartile range of the data set is 4.7 liters.
To find the interquartile range, we first need to sort the data from least to greatest. This gives us the following data set:
2.8, 7.5, 8.5, 11.6, 12, 12.1
The first quartile (Q1) is the median of the lower half of the data set. In this case, the lower half of the data set is {2.8, 7.5, 8.5}. The median of this data set is 7.5. Therefore, Q1 = 7.5.
The third quartile (Q3) is the median of the upper half of the data set. In this case, the upper half of the data set is {11.6, 12, 12.1}. The median of this data set is 12. Therefore, Q3 = 12.
The interquartile range (IQR) is calculated by subtracting Q1 from Q3. In this case, IQR = 12 - 7.5 = 4.7 liters.
The interquartile range is a measure of the variability of the middle 50% of the data. In this case, the interquartile range tells us that the middle 50% of the race car drivers have between 7.5 and 12 liters of gas in their tanks.
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If an apple pie recipe calls for 3 pounds of candy apples then how many cups of canned apples required
Answer:
Seven cups of canned apples are required to make apple pie recipe
Step-by-step explanation:
The weight of one canned apple is 0.45 pounds
Weight of total canned apple required to make the apple pie recipe is 3 pounds.
Total number of cups of canned apples required
[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]
So approximately seven cups of canned apples are required to make apple pie recipe
It's been found that there is a 15% chance (3 out of 20) that you can
win a particular game. How many "wins” would you have if you
played 80 times?
PLEASE HELP:
The distance d, in kilometers, that a car travels at a speed of 80 km per hour, for t hours, is given by the equation d= 80t. What is the inverse to represent time, t as a function of distance, d?
Choices:
1. t= d/80
2.t= 80/d
3.t= 80d
Answer:
The car was traveling for 1.5 hours.
Step-by-step explanation:
Given that distance d, in kilometers, that a car travels at a speed of 80 km per hour , for t hours, is given by the equation d=80t.
Here wee need to find the time if the car has gone 120 kilometers.
That is
d = 120 km
we need to find t.
d=80t
120 = 80 x t
The car was traveling for 1.5 hours.
plllleeeasssw help scams are reporteddd
Consider the curve given by the parametric equations x=t(t2−192),y=8(t2−192) a.) Determine the point on the curve where the tangent is horizontal. t= b.) Determine the points t1,t2 where the tangent is vertical and t1
a) The point on the curve where the tangent is horizontal is at t = 0.
b) The points where the tangent is vertical are at t₁ = -5 and t₂ = 5.
To find the points on the curve where the tangent is horizontal, we need to find the values of t that satisfy dy/dt = 0.
a.) Differentiating y = 3(t² - 75) with respect to t, we get:
dy/dt = 6t
Setting dy/dt = 0, we have:
6t = 0
t = 0
Therefore, when t = 0, the tangent is horizontal.
b.) To find the points where the tangent is vertical, we need to find the values of t that satisfy dx/dt = 0.
Differentiating x = t(t² - 75) with respect to t, we get:
dx/dt = 3t² - 75
Setting dx/dt = 0, we have:
3t² - 75 = 0
t² = 25
t = ±5
Therefore, the points where the tangent is vertical are when t = -5 and t = 5, with t₁ = -5 and t₂ = 5.
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The question is -
Consider the curve given by the parametric equations
x = t (t²-75) , y = 3 (t²-75)
a.) Determine the point on the curve where the tangent is horizontal.
t=
b.) Determine the points t_1,t_2 where the tangent is vertical and t_1 < t_2.
t_1=
t_2=
please help anybody it would help alot
Mr. Frederick teaches 4 math classes. Which class period has the most students? Use the bar graph to answer the question.
Answer:
The class in the second and longest bar graph (the one labeled 3) has the most students.
Step-by-step explanation:
When looking for the largest amount of something in bar graphs, the largest bar graph is correct. In this case the second bar graph is the longest, and we can see it indicates the class contains 28 students.
16. You decide to drop a penny off the top of the Willis Tower (fromerly the Sears Tower) in Chicago, IL. The
height of the penny (in feet) can be represented by the equation h= -16t2 + 1451 where t is time (in seconds).
a) How long will it take for the penny to hit the ground? Show any work that leads to your answer.
Answer:
9.5 seconds.
Step-by-step explanation:
We know that the equation that represents the height of the penny as a function of time is:
h(t) = -16*t^2 + 1451
Where the height is in ft, and the time is in seconds.
a) We want to know how long takes the penny to hit the ground.
Well, the penny will hit the ground when its height is equal to zero.
Then we need to solve for t:
h(t) = 0 = -16*t^2 + 1451
0 = -16*t^2 + 1451
16*t^2 = 1451
t^2 = 1451/16 = 90.7
t = √90.7 = 9.5
This means that it takes 9.5 seconds to hit the ground.
Answer:9.5 seconds
Step-by-step explanation:you subtract
Correct Given the sample data, find the mean (round to 2 decimals): 23, 27, 35, 44 1.00 points out of 1.00 Flag question Answer: 32.25 Check Correct Marks for this submission: 1.00/1.00 Question 6 Incorrect 0.00 points out of 1.00 Given the data from problem 5 (sample data: 23, 27, 35, 44), find the sum of the squared deviations (the numerator of the fraction under the square root in the formula). In finding the number, round all calculations to 2 decimals (if you carry more or fewer your answer may be off enough to be marked incorrect on this system).
The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.
In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.
Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).
The mean turns out to be 32.25.Next, we subtract the mean from each data point:
(23 - 32.25) = -9.25
(27 - 32.25) = -5.25
(35 - 32.25) = 2.75
(44 - 32.25) = 11.75
Then, we square each of these differences:
(-9.25)² = 85.56
(-5.25)² = 27.56
(2.75)² = 7.56
(11.75)² = 138.06
Finally, we sum up these squared deviations:
85.56 + 27.56 + 7.56 + 138.06
= 212.00
Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).
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Jonah has two small bags of assorted doughnuts. Each bag contains exactly 8 powdered doughnuts.
Bag 1 contains 20 total doughnuts.
Bag 2 contains 24 total doughnuts.
What is the probability of Jonah grabbing
a powdered doughnut from
Bag 1?
Answer:
There is a 40% probability of Jonah grabbing a powdered doughnut from Bag 1.
Step-by-step explanation:
Total number of doughnuts in the bag 1 =20
Total powdered doughnuts in each bag = 8
Probability of selecting powdered doughnut from Bag 1 by Jonah =
[tex]\frac{8}{20} * 100\\40[/tex]%
Find the length of the diagonal of
rectangle whose length
is 12ft and whose
width 5 ft
Answer:
13 ft
Step-by-step explanation:
The formula to find the length of the diagonal of a rectangle =
Diagonal² = Length² + Width²
Diagonal = √Length² + Width²
Length = 12 ft
Width = 5ft
Diagonal = √12² + 5²
Diagonal = √144 + 25
Diagonal = √169
Diagonal = 13 ft
The length of the diagonal of the rectangle = 13 ft
Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.
(−10,1)
The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).
To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:
r = √(x² + y²)
θ = arctan(y / x)
We know that, the point is (-10, 1), we substitute the values into the formulas:
We get,
r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and
The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.
Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.
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number 8 please help me
Answer:
15.9??
Step-by-step explanation:
Least:
Greatest:.
Median
Lower Quartile Range:
Upper Quartile Range:
thx :)
Answer:
Below :)
Step-by-step explanation:
Least/Minimum: 0
Greatest/Maximum: 6
Median: 2
Lower Quartile Range: 1
Upper Quartile Range: 3
Find median:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6
Find Lower Quartile:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2
Find Upper Quartile:
2, 2, 3, 3, 3, 3, 4, 4, 4, 6
no links no links sssssdrerw
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
area = ___ square units
Answer:
9 square units
Step-by-step explanation:
Area of a square = base * height
= 3*3
= 9