The total amount money after thirteen years of savings will be $5030.63
To calculate the amount of money in the account today, we need to calculate the future value of each contribution separately and then add them together.
Let's start by calculating the future value of the initial deposit of $2400 over the first five years at an interest rate of 8% compounded annually.
Using the formula for compound interest:
Future Value = [tex]Principal[/tex] * [tex](1 + Interest Rate)^{Time}[/tex]
Future Value = $2400 * (1 + 0.08)⁽⁵⁾
Future Value = $2400 * (1.08)⁵
Future Value = $2400 * 1.46933
Future Value = $3526.40
So, after five years, the initial deposit will grow to $3526.40.
Now, let's calculate the future value of the additional deposit of $1000 over the last eight years at an interest rate of 5.5% compounded annually.
Future Value = $1000 * (1 + 0.055)⁸
Future Value = $1000 * (1.055)⁸
Future Value = $1000 * 1.50423
Future Value = $1504.23
So, after eight years, the additional deposit will grow to $1504.23.
Now, let's add the two amounts together to find the total amount in the account today:
Total Amount = $3526.40 + $1504.23
Total Amount = $5030.63
So, the total amount money after thirteen years of saving will be $5030.63
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Complete question:
Thirteen years ago, you deposited $2400 into a superannuation fund. Eight years ago, you added an additional $1000 to this account. You earned 8%, compounded annually, for the first five years, and 5.5%, compounded annually, for the last eight years. How much money do you have in your account today?
show directly from the definition that if (xn) and (yn) are cauchy sequences, then (xn) (yn) and (xnyn) are cauchy sequences.
Given that (xn) and (yn) are Cauchy sequences, then for any ε > 0, there exist N1 and N2 such that |xn - xm| < ε/2, for all n, m ≥ N1 and |yn - ym| < ε/2, for all n, m ≥ N2. Then, for all n, m ≥ max{N1, N2},
we have: |xnyn - xmym| = |xnym - xmym + xmym - xnym| ≤ |xn - xm||ym| + |ym - yn||xm| ≤ |xn - xm|ε/2 + |ym - yn|ε/2 < εThis shows that (xnyn) is a Cauchy sequence.
Moreover, for any ε > 0, there exists N such that |xn - xm| < ε/2 and |yn - ym| < ε/(2max{|x1|, |x2|, . . . , |y1|, |y2|, . . . , |yn|}) for all n, m ≥ N. Then, for all n, m ≥ N,
we have: |xnyn - xmym| = |xnym - xmym + xmym - xnym| ≤ |xn - xm||ym| + |ym - yn||xm| + |ym - yn||yn| ≤ |xn - xm|ε/(2max{|x1|, |x2|, . . . , |yn|}) + |ym - yn|ε/(2max{|x1|, |x2|, . . . , |yn|}) + |yn|ε/(2max{|x1|, |x2|, . . . , |yn|}) < ε.
This shows that (xn)(yn) is also a Cauchy sequence.
Therefore, from the given definition, it has been shown that if (xn) and (yn) are Cauchy sequences, then (xn) (yn) and (xnyn) are Cauchy sequences.
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Elena is graduating from high school. She will attend a private, 4-year university and study to become a Certified Public Accountant. The annual cost for her tuition, room and board, and books is $22,255. Elena's parents have a college fund with $ 54,000 to help with the costs. Elena received a scholarship for $500 per semester for four years .
Answer:
Reminder to eat drink and take care. :)
Step-by-step explanation:
Answer:
8,255 reminder to eat today
1. The small bag of potting soil weighs 3 1/4 pounds. The large bag weighs 3 2/3 times more than the small bag. How much does the large bag weigh?
Answer:
11 11/12 lb
Step-by-step explanation:
"3 2/3 times more than the small bag" comes out to:
(3 2/3)*(3 1/4) lb.
Convert both mixed numbers to improper fractions:
11 13 143
--- * ---- = ----------- = 11.917
3 4 12
The large bag weighs 11.917 lb, which may be converted to the mixed number 11 11/12 lb
An 18-foot ladder leaning against a wall makes an angle of elevation of 70° with the ground. How far up the wall is the ladder, to the nearest foot?
Answer:
17 ft
Step-by-step explanation:
An 18-foot ladder leaning against a wall makes an angle of elevation of 70° with the ground. How far up the wall is the ladder, to the nearest foot?
We solve the above question using the Trigonometric function of Sine
sine theta = Opposite/Hypotenuse
theta = Angle of elevation = 70°
Hypotenuse =Length of the ladder = 18ft
Opposite = Height of the wall = x
Therefore
sin 70 = x/ 18 ft
Cross Multiply
x = sin 70 × 18 ft
x = 16.914467174 ft
Approximately = 17 ft
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
Answer: $1,800
Step-by-step explanation:
600x3=1,800
Answer:
1800 is the cost.
Step-by-step explanation:
Each hoop costs 600 dollars and their are 3 hoops so multiply 600 times 3 or you can do 6 times 3 and add the zeros at the end which is 1800 dollars and btw you got this!!! don't give up. I believe in you :)
Select all the equations that represent functions that are non-linear.
A. y = x
B. 2y = 1/2x
C. y = 8 + x
D. y - 6 = x^2
E. y= 1/3-5x
F. y= 2x^2 + 5 - 3x^2
Answer:
D, F.
Step-by-step explanation:
D and F contain x^2.
Determine the measure of arc BC
Answer:
arc BC = 132°
Step-by-step explanation:
The central angle is equal to the arc that subtends it , then
arc BC = ∠ BOC = 132°
Alternate Sources of Fuel Seventy-five percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 140 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels. Round your answers to three decimal places.
Part: 0/2 ______
Part 1 of 2
(a) Find the mean.
Mean: μ= _____
The mean number of Americans who favor government spending for alternative fuels can be calculated by multiplying the percentage of Americans who favor such spending by the total sample size. In this case, 75% of Americans favor government spending, and the sample size is 140.
Mean = (Percentage of Americans who favor government spending) * (Sample size)
= 0.75 * 140
= 105
Therefore, the mean number of Americans who favor government spending for alternative fuels is 105.
The mean represents the average or central tendency of the data. In this context, it indicates the average number of Americans in the sample who support government spending for alternative fuels. It is obtained by multiplying the percentage of Americans who favor such spending by the sample size.
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Find the value of the variables in the simplest form
Answer:
x = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + x² = (2[tex]\sqrt{2}[/tex] )² , that is
2x² = 8 ( divide both sides by 2 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
Find all eigenvalues of the given matrix. (Enter your answers as a comma-separated list.) 1 0 0 00-4 A = 04 0 a = =
The eigenvalues of the given matrix A are 1, 2, and -2.
To find the eigenvalues of the matrix A:
A = [1 0 0]
[0 -4]
[0 4]
To find the eigenvalues, we need to solve the characteristic equation |A - λI| = 0, where λ is the eigenvalue and I is the identity matrix.
The matrix A - λI is:
A - λI = [1 - λ 0]
[0 -4]
[0 4 - λ]
Taking the determinant of A - λI:
|A - λI| = (1 - λ)(-4 - λ(4 - λ))
Expanding the determinant and setting it equal to zero:
(1 - λ)(-4 - λ(4 - λ)) = 0
Simplifying the equation:
(1 - λ)(-4 - 4λ + λ²) = 0
Now, we can solve for λ by setting each factor equal to zero:
1 - λ = 0 or -4 - 4λ + λ² = 0
Solving the first equation, we get:
λ = 1
Solving the second equation, we can factorize it:
(λ - 2)(λ + 2) = 0
From this equation, we get two additional eigenvalues:
λ = 2 or λ = -2
Therefore, the eigenvalues are 1, 2, and -2.
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Sam needs a new jacket. Use the information
below to decide where Sam should buy the
jacket. The one he wants costs $84 dollars at
Coats 'R Us, but is 20% off. The same jacket
costs $95 at Coat Barn, but is 25% off. Where
should he buy the jacket and why?
A. Sam should buy the jacket at Coats 'R Us
because it is cheaper before the discount.
B. Sam should buy the jacket at Coats 'R Us
because it is cheaper after the discount.
C. Sam should buy the jacket at Coat Barn
because it is cheaper there after the discount.
D. Sam should buy the jacket at Coat Barn
because it has a bigger discount.
Answer:
B. Sam should buy the jacket at Coats 'R Us because it is cheaper after the discount
Answer:
I suggest that sum should buy the jacket at coats 'R us because it is still cheaper after the discount even when you've not counted the discount in it is still cheaper than the other one and the other one even when it has such a high discount it is still not cheap so I suggest that the answer is choice B
how can you find the diameter of this circke
Answer:
10cm
Step-by-step explanation:
pretty sure the diameter is measured by multiplying the radius twice :)
Answer:
Diameter = 10 cm
Circumference = 31.43 cm
Area = 78.57 cm²
Instructions:type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). Consider the parabola represented by the equation -2y2 = 4x. This parabola will open to the. The equation of the directrix of the parabola is. The focus of the parabola is
The given parabola is a downward-opening parabola, its directrix is y = -1/2, and its focus is located at (0, -1/2).
The parabola represented by the equation [tex]-2y^2 = 4x[/tex] is a downward-opening parabola.
To understand the direction of the parabola, we can look at the coefficient of the [tex]y^2[/tex] term in the equation. Since it is negative (-2), the parabola opens downwards. If the coefficient were positive, the parabola would open upwards.
The equation of the directrix of a parabola can be determined by rearranging the given equation to the standard form, which is [tex](y - k)^2 = 4p(x - h)[/tex], where (h, k) represents the vertex of the parabola and p represents the distance between the vertex and the focus.
In the given equation, [tex]-2y^2 = 4x[/tex], we can divide both sides by -2 to obtain [tex]y^2 = -2x[/tex]. Comparing this to the standard form, we can see that the vertex is at (0, 0) since h = 0 and k = 0.
The coefficient of x in the standard form equation is 4p. Therefore, in our equation, 4p = -2, which implies p = -1/2.
Since p is negative, the directrix will be a horizontal line parallel to the x-axis and situated below the vertex. The equation of the directrix can be written as y = -1/2.
The focus of the parabola can be found by adding p to the y-coordinate of the vertex. In this case, since the vertex is at (0, 0) and p = -1/2, the focus will be at (0, -1/2).
In summary, the parabola represented by [tex]-2y^2 = 4x[/tex] is a downward-opening parabola. The equation of the directrix is y = -1/2, and the focus is located at (0, -1/2).
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"Write a cost function for each of the given scenarios. Identify all variables used. (See Example 1.) 1.) A chain-saw rental firm charges $25, plus $5 per hour. 2.) A trailer hauling service charge $95 plus $ 8 per mile
The cost function for each of the given scenarios are as follows:
1) Cost function for chain-saw rental firm = $25 + $5h
2) Cost function for trailer hauling service = $95 + $8m
1.)
Cost function for chain-saw rental firm = $25 + $5h
Where, h is the number of hours the chainsaw is rented
Variables used in this scenario are:
Cost = C ($), Renting time = h (hours),
Charge per hour = c ($)
2.)
Cost function for trailer hauling service = $95 + $8m
Where, m is the number of miles the trailer has traveled.
Variables used in this scenario are:
Cost = C ($),
Distance traveled = m (miles),
Charge per mile = c ($)
Therefore the two cost functions are:
1) Cost function for chain-saw rental firm = $25 + $5h
2) Cost function for trailer hauling service = $95 + $8m
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Ann prefers ice cream cups. Ben and Clay prefer ice cream sandwiches. The cafeteria manager puts one coupon for an ice cream cup and two coupons for ice cream sandwiches in a bag. Ann, Ben, and Clay each draw, without looking, one coupon from the bag. Each keeps the coupon he or she drew. What is the probability that all three get their preference?
a. 1/2
b. 1/3
c. 1/6
d. 2/3
URGENT!!!!HELP!!!!PLS!!!NOW!!!!!!HURRY!!!
Answer:
I'm guessing it's 4 i think but sorry if it's wrong
Step-by-step explanation:
A set of dolls is made so that the volume,V of each of them varies directly as the cube of its height h. The doll with a height of 3cm has a volume of 6.75 cm³.
A) find an equation for V in terms of H.
B) find the volume of a doll with a height of 2.5cm
Answer:
A v=2.25 H=1
b. 5.625
Step-by-step explanation:
Answer:
V = 3.90625 cm³
Step-by-step explanation:
Given that V varies directly as h³ then the equation relating them is
V = kh³ ← k is the constant of variation
To find k use the condition
V = 6.75 when h = 3 , then
6.75 = k × 3³ = 27k ( divide both sides by 27 )
0.25 = k
V = 0.25h³ ← equation of variation
(b)
When h = 2.5 , then
V = 0.25 × 2.5³ = 3.90625 cm³
what is the y-intercept of the graph of 4y - 1= 3
Answer:Using the slope-intercept form, the y-intercept is 1
A dog trainer compared mean numbers of lessons for two
groups of dogs to learn a new trick.
Mean number of lessons Mean Absolute Deviation (MAD)
Group A 15
3
Group B 9
3
Which statement about the data is true?
A. The MAD for group A is more than the MAD for group B.
B. The mean number of lessons for group A is greater than the mean
for group B by 6 MADs.
C. The mean number of lessons for group A is greater than the mean
for group B by 2 MADs.
D. On average, the dogs in group B required more lessons than the
dogs in group A.
Answer:
C. The mean number of lessons for group A is greater than the mean for group B by 2 MADs.
Step-by-step explanation:
Mean of Group A is greater than the mean of group B. The mean absolute deviation for the group A and B is 3. The different between the mean is 6 (15 - 9)
Number of mean absolute deviations is :
Difference between mean of two groups / MAD
6 / 3 = 2.
What is the sign of −9⋅( 0/-3)
Answer:
hi
Step-by-step explanation:
sorry
Answer:
0
Step-by-step explanation:
The sine function of 0 is 0.
We got 0 because you multiplied -9 by 0 divided by -3. DIviding by 0 really doesn't have an answer, but it'd most logically be 0.
uh someone help D:
ill make the points high
Answer:
m = 18/4 = 9/2 = 4.5
Step-by-step explanation:
Notice that the line passes through (0, 0) and (4, 18). Thus, its 'rise' is 18 - 0, or 18, and its 'run' is 4 - 0, or 4, and the slope (which is the desired constant of proportionality) is m = 18/4 = 9/2 = 4.5 This is Answer B
Ms Carr made a mistake in her checkbook. she wrote a check for $8.98 to rent a video but mistakenly recoreded it in her checkbook as an $8.98 deposit on the blank slide represent each transaction with a rational number and explain the difference between the transactions
what does this equal??
Answer:
I think 3
Step-by-step explanation:
determine the mode of the set of data in the stem and leaf plot below
Answer:
51
Step-by-step explanation:
mode is the value which appears the most than other values. In this case 51 will appear 3 times.
Answer:
5.1
Step-by-step explanation:
dont forget the decimal
A flowerpot has a diameter of 15 centimeters. Which expression can be used to find its circumference, C, in centimeters?
A
C = 7.5 × π
B
C = 15 × π
C
C = 2 × 15 × π
D
C = 15 × 15 × π
the base of the cylinder? Use 3.14 for n and round the answer
to the nearest hundredth.
h-13 in
r =
in.
Answer:
r = 7
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
Given:
V = 2000
h = 13
Work:
V = πr²h
r² = V/(πh)
r² = 2000/(3.14 * 13)
r² = 2000/40.82
r² ≈ 49
[tex]\sqrt{r^2} =\sqrt{49}[/tex]
r = 7
Find the circumference of the pizza to the nearest hundredth.
18 in.
be
RE
circumference: about
GLASE
SHELIN
HALL
Complete Question
Find the circumference of the pizza to the nearest hundredth.
When Diameter = 18 in.
Answer:
56.55 inches
Step-by-step explanation:
A pizza is circular in shape.
The formula for the circumference of a circle is given as:
πD
Where D = Diameter
From the above question,
Diameter = 18 inches
Hence,
Circumference of the circular pizza = π × 18 inches
= 56.548667765 inches
Approximately = 56.55 inches
A racing car is one of the many toys manufactured by Mack Corporation. The assembly time for this toy follows a normal distribution with a mean of 50 minutes and a standard deviation of 5 minutes. If one worker starts assembling a racing car, what is the probability that she will finish this job in more than 60 minutes? Find the z score? QUESTION 2 1 pol 1b. What do you get from Table A? QUESTION 3 3 point 10. What is the probability that she will finish this job in more than 60 minutos? (round to a percent with two decimals)
The probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.1587. The z-score corresponding to 60 minutes is 2. The probability of completing the job in more than 60 minutes is 15.87%.
To find the probability that the worker will finish assembling the racing car in more than 60 minutes, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
where x is the given time (60 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (60 - 50) / 5
z = 2
Next, we look up the probability corresponding to a z-score of 2 in Table A (standard normal distribution table). The value in the table represents the probability of a random variable being less than the given z-score. To find the probability of the worker finishing in more than 60 minutes, we subtract this value from 1.
From Table A, the probability corresponding to a z-score of 2 is approximately 0.9772.
Probability = 1 - 0.9772
Probability ≈ 0.0228
Therefore, the probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.0228 or 2.28% (rounded to two decimal places).
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XXX
X
х
3
4
? 11 14 1 13
Worm Length (inches)
?
inch
?
DONE
AZ
539 Complete
Answer:
I can't able to understand this question plz check this question if it is right or not
What is the perimeter
___ miles
I think the anwser for this is 60 in miles
Answer:
23
Step-by-step explanation: