a. The initial amount of money deposited into the account is $1575.
b. The annual interest rate being paid on the account is 4.5%.
c. The amount of money in the account after 15 years is approximately $2946.27.
d. It will take approximately 20 years for the account to reach a balance of at least $4000.
To answer these questions, let's analyze the given equation:
A(1) = 1575 * (1.045)^t
a. The initial amount of money deposited into the account is $1575. This is evident from the equation, where A(1) represents the amount of money after 1 year.
b. To determine the annual interest rate, we can compare the given equation with the general formula for compound interest:
A = P * (1 + r)^t
Comparing the two equations, we can see that the interest rate in the given equation is 4.5% (0.045) since (1 + r) is equal to 1.045.
c. To find the amount of money in the account after 15 years, we can substitute t = 15 into the equation and calculate the result:
A(15) = 1575 * (1.045)^15 ≈ $2946.27 (rounded to the nearest dollar)
Therefore, after 15 years, the amount of money in the account will be approximately $2946.
d. To find the number of years it will take for the account to have at least $4000, we need to solve the equation for t. Let's set up the equation and solve for t:
4000 = 1575 * (1.045)^t
To solve this equation, we can take the logarithm of both sides (with base 1.045):
log(4000) = log(1575 * (1.045)^t)
Using logarithm properties, we can simplify the equation:
log(4000) = log(1575) + log((1.045)^t)
log(4000) = log(1575) + t * log(1.045)
Now, we can isolate t by subtracting log(1575) from both sides and then dividing by log(1.045):
t = (log(4000) - log(1575)) / log(1.045)
Calculating this expression, we find:
t ≈ 19.56 (rounded to two decimal places)
Therefore, it will take approximately 20 years (rounded to the nearest whole year) for the account to have at least $4000.
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An arithmetic sequence has first term (a) and the common difference (d). The sum of the first 25 terms is 15 times the sum of the first 4 terms. Find (a)
Answer:
a = 12.
Step-by-step explanation:
Sum of n terms = n/2[2a + d(n-1)]
For 25 terms
S25 = 12.5(2a + 24d)
S25 = 25a + 300d
For 4 terms
S4 = 2(2a + 3d)
So:
S25 = 15*2(2a + 3d)
S25 = 60a + 90d
25a + 300d = 60a + 90d
35a = 210d
a = 6d
Take a to be 12 and d to be 2:
25th term = 12.5(2*12 + 24 * 2) = 900
4th term = 2(24 + 6) = 60
900 = 15 * 60 so a = 12.
On their first dive researchers Explorer part of the ocean that is 60 ft below sea level is that can be responded by the integer on their first dive researchers Explorer part of the ocean that is 60 ft below sea level is that can be responded by the integer 60 on their second dive research to explore a deeper depth
Complete question :
On their first dive, researchers explore a part of the ocean floor that is 60 feet below sea level. This depth can be represented by the integer -60. On their second dive, researchers explore a deeper depth. Write an inequality that represents the possible depth, d, of the researchers' second dive.
Answer:
d < - 60
Step-by-step explanation:
Depth explored during first dive = 60 feets below sea level = - 60 feets
The depth, d explored during second dive is deeper Than that explored during first dive
The inequality representing depth on second,
This means they the depth exceeds 60 feets below sea level. And hence. Deeper than - 60
Therefore, the depth will be values less Than - 60
Hence, d < - 60
81.3 x 47.5 = i am lost............
Answer:
3861.75
Step-by-step explanation:
i hope its the good answer
Need help due in 30 mins Find the area of each. Round to the nearest tenth. Do not include units in your answer (ie. ft, in, km, etc)(triangle-FR)
Your answer
Answer:
1)
Triangle formula:
A = 1/2bh
A = 1/2(3)(5.9)
A = 8.85
2)
Parallelogram Area:
A = bh
A = (8.9)(6)
A = 53.4
Drag the operations signs to make the number sentence true. Use each operation sign once. +–×÷ 4 (3 2) 6 1 = 14
Answer: its 4x(3+2)-6÷ 1=14
Step-by-step explanation: in the picture
the area of a rhombus is 24 square inches. What is the are of a similar rhombus that is 7 times as big?
Answer:
324
...................
Portfolio Benchmark 22.00% 17.88% 16.00% 21.25% -7.50% -9.63% -2.30% -3.88% 8.63% 3.25% 9.15% 9.63% 11.21% 15.25% 6.25% 5.75% -37.00% -42.00% 15.00% 13.75% An analyst is trying to understand the variation of portfolio returns shown in the left column by analyzing the variation of benchmark returns in the right column. Here, the analyst uses the benchmark returns as the explanatory variable, i.e., the x-variable, to explain the variation of portfolio returns, the y-variable. The analyst performs a regression analysis between the x and y variables. The y-intercept and slope coefficient of the x-variable are 0.013 and .892, respectively. If the benchmark return is 14%, the regression model will estimate the portfolio return closest to O 0% O 89.2% 1.3% O 13.79%
The regression model estimates the portfolio return closest to 13.79% when the benchmark return is 14%.
The analyst performed a regression analysis using the benchmark returns as the explanatory variable and the portfolio returns as the dependent variable. The y-intercept of the regression line is 0.013, indicating that when the benchmark return is zero, the estimated portfolio return is 0.013%. The slope coefficient of the benchmark returns is 0.892, meaning that for every 1% increase in the benchmark return, the estimated portfolio return increases by 0.892%.
To estimate the portfolio return when the benchmark return is 14%, we plug the value of 14 into the regression model. The estimated portfolio return is calculated as follows: 0.013 + 0.892 * 14 = 13.79%.
Therefore, based on the regression analysis, the model estimates that the portfolio return would be closest to 13.79% when the benchmark return is 14%.
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I need help with this question can you guys help me
Answer:
$18.5
Step-by-step explanation:
You just add up all the costs and divide them by two and then you would get your answer
Right answer gets brainlist !!
Robert takes out a loan for $7200 at a 4.3% rate for 2 years. What is the loan future value?
Answer: 7,833
Step-by-step explanation:
dba algebra 2 module 2 flvs what's on it
Answer:
Uh i dont really get it
Step-by-step explanation:
best of luck though
on a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong?
On a 7-question multiple-choice test, with 4 answer choices for each question, we need to determine the probability of getting at least one question wrong.
To calculate the probability of getting at least one question wrong, we can consider the complementary probability, which is the probability of getting all questions correct and subtract it from 1.
The probability of getting a single question correct is 1/4, since there are 4 answer choices for each question. Therefore, the probability of getting all 7 questions correct is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = [tex](1/4)^7[/tex].
To find the probability of getting at least one question wrong, we subtract the probability of getting all questions correct from 1:
P(at least one question wrong) = 1 - P(all questions correct).
Substituting the probability of getting all questions correct, we have:
P(at least one question wrong) = 1 - [tex](1/4)^7[/tex]
Calculating this expression, the probability of getting at least one question wrong is approximately 0.99999, which is essentially equal to 1
Therefore, on a 7-question multiple-choice test with 4 answer choices for each question, the probability of getting at least one question wrong is extremely high, nearly 1. This means that it is highly likely that a test taker will get at least one question wrong on such a test.
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PLEASE ANSWER ASAP
At a carry-out burger restaurant, an order of 4 burgers, 2 orders of French fries and 3 fountain drinks cost $32.25. A second order of 6
burgers, 3 orders of French fries, and 6 fountain drinks costs $51.15. If three burgers and two fountain drink cost $13.05 more than two
orders of French fries, what is the cost of each
Answer:
hmmm I think u need to talk to ur teacher
A culture started with 1,000 bacteria. After 7 hours, it grew to 1.200 bacteria. Predict how many bacteria will be present after 14 hours. Round your answer to the nearest whole number.
P= Ae^kt
Answer:
8
Step-by-step explanation:
Because i wanted extra points.
The width of a table is 2 feet less than the length. The area is 20 square feet. Find the dimensions. Show and explain all work using mathematical concepts in this module. (use quadratic equation)
Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.
The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:
Length × Width = Area
x(x - 2) = 20
Expanding the equation, we get:
x^2 - 2x = 20
Rearranging the equation in quadratic form:
x^2 - 2x - 20 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))
Simplifying further:
x = (2 ± √(4 + 80)) / 2
x = (2 ± √84) / 2
x = (2 ± 2√21) / 2
Simplifying the expression inside the square root:
x = (1 ± √21)
So the possible values for x are 1 + √21 and 1 - √21.
Since the length cannot be negative, we take the positive value:
x = 1 + √21
Now we can find the width by substituting this value of x into the expression for width:
Width = x - 2
Width = (1 + √21) - 2
Width = -1 + √21
Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.
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Which of the following sets of numbers could not represent the three sides of a right
triangle?
Answer:
{48, 64, 81}
Step-by-step explanation:
The number of dandelions at the beginning of the summer was 2,000. The population of dandelions is expected to grow at a rate of 2.5% each day. How many dandelions should we expect after 30 days?
Answer:
3500 dandelions
Step-by-step explanation:
To start you must multiply the number of dandelions by the growth rate to find the number of dandelions grown each day:
2,000 * 0.025 = 50
Then you multiply the number of dandelions by 30 for each day:
50 * 30= 1500
Lastly, you add the dandelions grown in 30 days to the original for your answer.
Find the profit function if cost and revenue are given by C(x) = 150 +5.8x and R(x) = 9x -0.01x?
The profit function is; P(x) = -0.01·x² + 3.2·x + 150
What is a profit?
Profit is the amount gained following a business transaction, which is the difference between the amount received as payment for doing a business transaction, within a specified period, known as the revenue and the amount amount spent or invested in doing the business, including the fixed and variable expenses, which is the cost of the business.
Therefore; Profit = Revenue - CostThe cost and the revenue functions, obtained from a similar question on the internet are;
The cost function is; C(x) = 150 + 5.8·x
The profit function is; R(x) = 9·x - 0.01·x²
The profit function, P(x), is therefore; P(x) = 9·x - 0.01·x² - (150 + 5.8·x) = -0.01·x² + 3.2·x + 150
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An asteroid is heading for the planet Zorgon (diameter of 2600 miles). When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact. What is the probability that Astronaut Joe, who is on Zorgon currently, will be affected by this impact?
The probability that Astronaut Joe, who is currently on Zorgon, will be affected by the impact is 0.667%.
To determine the probability that Astronaut Joe will be affected by the impact of the asteroid on planet Zorgon, we need to consider the area of the blast zone in relation to the total area of the planet.
An asteroid is heading for the planet Zorgon with a diameter of 2600 miles. When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact.
What is the probability that Astronaut Joe, who is currently on Zorgon, will be affected by this impact?
The total surface area of Zorgon is given by:2 * 3.14 * (1,300 miles)2 = 10.6 million sq Miles
The blast zone covers an area of:3.14 * (150 miles)2 = 70,685 sq Miles
To calculate the probability that Astronaut Joe will be affected by the impact, we divide the area of the blast zone by the total surface area of the planet.
That is,70,685 / 10.6 million = 0.00667 = 0.667%.
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Find slops ;
3y=9x+18
To find the slope of the line, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Divide both sides of the equation by 3 to get y by itself on one side of the equation.
3y = 9x + 18
y = 3x + 6
Step 2: Compare the equation to the slope-intercept form y = mx + b, and we can see that the slope is 3.
Therefore, the slope of the line is 3.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
What is the greatest number of obtuse angles that a triangle can have?
Answer:
1
Step-by-step explanation:
Water treatment plant receives a 5% polymer solution. Calculate how much polymer should be mixed with water to produce 350 gallons of a 0.5% solution.
Answer:
Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is 1.75 gallons.
Step-by-step explanation:
Solution weight-age 100% = 350 gallons
Polymer weight-age = 0.5 % = ?
Water weight-age = 99.5 % = ?
100 =99.5 w + 0.5 p
350 = ? + ?
Using ratios
100 350
0.5 p
Applying the cross product rule
p = 350 *0.5/100= 1.75 gallons
Polymer to be mixed with water to produce 350 gallons of a 0.5% solution is 1.75 gallons
Using ratios
100 350
99.5 w
Applying the cross product rule
w = 350*99.5 /100= 348.25 gallons
Water to be mixed with water to produce 350 gallons of a 0.5% solution is 348.25 gallons
Margaret's garden is 36 feet long and has a perimeter of feet. She is wanting to plant flowers along the diagonal of the garden. How long in the diagonal of her
Answer: Where is the rest of the question?
Step-by-step explanation:
Given v = 4i - j, and w = 3i + 2j, find the angle between v and w. (Type your answer in degrees. Do not round until the final answer. Then round to the nearest tenth as necessary.)
Given [tex]v=4i-j[/tex], and [tex]w=3i+2j\\[/tex], the angle between v and w is 47.7°.
To find the angle between vectors v and w, we can use the dot product formula:
v · w = |v| |w| cos(θ)
where v · w represents the dot product of v and w, |v| and |w| represent the magnitudes of vectors v and w, and θ represents the angle between the vectors.
First, let's calculate the magnitudes of vectors v and w:
|v| = √(4² + (-1)²) = √(16 + 1) = √17
|w| = √(3² + 2²) = √(9 + 4) = √13
Next, let's calculate the dot product of v and w:
v · w = (4)(3) + (-1)(2) = 12 - 2 = 10
Now, we can substitute the values into the dot product formula to find the angle θ:
10 = (√17)(√13) cos(θ)
cos(θ) = 10 / (√17)(√13)
cos(θ) = 10 / (√(17 * 13))
cos(θ) = 10 / (√221)
θ = cos⁻¹ (0.6717)
θ = 47.7°.
Therefore, the angle between vectors v and w is approximately 47.7° .
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b) Abigail (A) and Balan (B) want to share a pizza of size 1. Suppose both agents have the same utility function u(x) = 2 for pizza, Abigail discounts with 8A = 1/2 and Balan discounts with 88 1/2. Abi- gail moves first. Calculate the Rubinstein solution of the bargaining problem. c) Why does Abigail get a larger share of the pizza?.
Solution: Given, Abigail (A) and Balan (B) want to share a pizza of size
1. Both agents have the same utility function u(x) = 2 for pizza, Abigail discounts with 8A = 1/2. Balan discounts with 88 1/2 Abigail moves first.
We have to calculate the Rubinstein solution of the bargaining problem. Bargaining Solution Using Rubinstein's alternating offers model, the bargaining solution is:
Take x as the size of the pizza that Abigail gets.
Hence, Balan gets 1 - x.
The possible utility that they get are:
Abigail: 2x(1/2) + 0(1/2) = x
Balan: 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x The minimum utility that they both need to be satisfied is:
minimum value = 2 x 177/2 = 177
The bargaining range is [0,1], thus there are infinite pairs that satisfy the minimum utility requirement. However, Rubinstein assumes that the final solution should be somewhere between both parties' ideal points, so we can restrict the bargaining range to [1/2, 1]. Abigail gets x and Balan gets 1 - x. Now, we have to see what happens if Balan rejects this offer.
When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range,
Abigail's ideal point is 2x(1/2) + 0(1/2) = x and
Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.
The bargaining range is again restricted to [1/2, 1]. When Balan rejects, the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(88 1/2) + 0(11 1/2) = 177 - 177x.The bargaining range is again restricted to [1/2, x) and (x, 1].
Now, if Abigail rejects, then the bargaining range is (0, x) for Abigail and [x, 1] for Balan. In this range, Abigail's ideal point is 2x(88 1/2) + 0(11 1/2) = 177x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to (1/2, x) and (x, 1/2 + 1/176). In the next step, if Balan rejects, then the bargaining range is [0, x) for Abigail and (x, 1] for Balan. In this range, Abigail's ideal point is 2x(1/2) + 0(1/2) = x and Balan's ideal point is 2(1 - x)(1/2) + 0(1/2) = 1 - x. The bargaining range is again restricted to [1/2, x) and (x, 1/2 + 1/176).
Repeating the steps,
the solution is: x = 2/3, 177 - 177x = 59.
After calculating the Rubinstein solution of the bargaining problem, we can see that Abigail gets 2/3 of the pizza and Balan gets 1/3 of the pizza. There are two reasons why Abigail gets a larger share of the pizza: Abigail moves first, so she has an advantage because she can propose a deal that is more favorable to her. This is why the bargaining range is initially restricted to [1/2, 1]. Abigail has a lower discount rate than Balan, so she is willing to wait longer for a deal. This means that Abigail can drive a harder bargain because she has a higher reservation utility.
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i get alot of these please help
Answer:
18 is 3 more than 9- false
18 is 3 times as much as 6 - true
9 is 3 times as much as 27- false
9 is 3 more than 6 - true
Plsss helppp ASAP
Will mark brainleist
Answer:
B
Step-by-step explanation:
The average rate of change in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a , b ] = [ 15, 35 ]
and f(b) = f(35) = 400 ← from graph
f(a) = f(15) = 200 ← from graph
Then average rate of change is
[tex]\frac{400-200}{35-15}[/tex] = [tex]\frac{200}{20}[/tex] = 10 m/ s → B
The sum of two numbers is 18 and their difference is 6.
What are the two numbers?
Larger number
Smaller number
Answer:
Large number=12
Smaller number=6
Step-by-step explanation:
Let the two numbers be x and y
x+y=18
x-y=6
Guys i need help!!!!
Answer:
1/6
Step-by-step explanation:
1 out of the 6 cards is 4
Solve for the values of x and y.
Answer:
x = 20
y = 7.2
Step-by-step explanation:
12/x = 9/15
9x = 180
x = 20
12/x= y/12
12/20 = y/12
144 = 20y
y = 7.2
y = 20
46 people are going to the beach. Nine people can ride in each van. How many vans are needed?
Answer:
6
Step-by-step explanation:
No. of people going to beach = 46 .
Using Unitary Method ,
9 people can go in one van .
1 person can go in 1/9
46 people can go in 1/9 * 46 = 5.1
Since vans can't be in fraction , 1 extra van for 1 person is need that is for 46th person .
So total number of vans = 5 + 1 = 6