After answering the presented question, we can conclude that function Therefore, the maximum growth rate of [tex]f(t)[/tex] occurs at [tex]t = k ln(Λ)[/tex] .
What is function?In mathematics, a function appears to be a link between two sets of numbers, in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range).
A formula or a graph can be used to represent a function. For example, the formula [tex]y = 2x + 1[/tex] depicts a functional form in which each value of x generates a unique value of y.
To find the maximum growth rate of [tex]f(t)[/tex] between t=0 and t=kA, we need to find the maximum value of its derivative with respect to t. Let's start by taking the derivative of f(t) using the chain rule:
[tex]f'(t) = -kΛe^(-kt) / B(1 + Λe^(-kt))^2[/tex]
Now we need to find the value of t that maximizes f'(t). One way to do this is to use logarithmic differentiation. First, take the natural logarithm of both sides of the equation for f'(t):
Next, take the derivative of both sides with respect to t:
[tex]f''(t)/f'(t) = -k + Λke^(-kt) / (1 + Λe^(-kt))[/tex]
Simplifying this expression by multiplying both numerator and denominator by [tex]e^(kt)[/tex], we get:
[tex]f''(t)/f'(t) = -k + Λk / (e^(kt) + Λ)[/tex]
Now we can set f''(t)/f'(t) equal to zero to find the critical points:
[tex]-k + Λk / (e^(kt) + Λ) = 0[/tex]
Multiplying both sides by [tex]e^(kt)[/tex] + Λ and rearranging, we get:
[tex]e^(kt) = Λ/k[/tex]
Taking the natural logarithm of both sides, we get:
[tex]kt = ln(Λ) - ln(k)[/tex]
Solving for t, we get:
[tex]t = ln(Λ)/k - ln(k)/k[/tex]
[tex]t = (ln(Λ) - ln(k))/k[/tex]
[tex]t = ln(Λ/k)/k[/tex]
Substituting this value of t back into f'(t), we get:
[tex]f'(ln(Λ/k)/k) = -kΛe^(-ln(Λ)) / B(1 + Λe^(-ln(Λ)))^2[/tex]
Since A>1, we know that Λ>1. Therefore, e^(-ln(Λ)) = 1/Λ, and we can simplify the expression for f'(ln(Λ/k)/k) to:
[tex]f'(ln(Λ/k)/k) = -k/ΛB(1 + 1/Λ)^2[/tex]
We can now see that f'(ln(Λ/k)/k) is negative, which means that f(t) is decreasing at that point. Therefore, the maximum growth rate of f(t) must occur at either t=0 or t=kA. We can find which one of these is the maximum by comparing the values of f'(0) and f'(kA).
[tex]f'(0) = -kΛ/B(1 + Λ)^2[/tex]
[tex]f'(kA) = -kΛe^(-kA) / B(1 + Λe^(-kA))^2[/tex]
We know that A>1, which means that kA>k. Therefore, [tex]e^(-kA) < e^(-k),[/tex] which means that f'(kA) is greater in magnitude than f'(0). Since f'(kA) is negative, this means that f(t) is decreasing faster at t=kA than at [tex]t=0.[/tex]
Therefore, the maximum growth rate of [tex]f(t)[/tex]occurs at [tex]t=ln(Λ)/k[/tex] , as given by the formula we derived earlier.
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What is the area of the PURPLE triangle below?
Answer:
Area = 14 in²
Step-by-step explanation:
is a rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD
Area = 1/2 b * h
Area =1/2 7 * 4
Area = 3.5 * 4
Area = 14 in²
So we have 7 in. and 4 in. so we just will mutilply It, So what we do here Is mutilply so we will do 7 x 4 = 28
So we have 28 then we mutilpy all of chocies to see which one Is 28.
A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD
11 x 2=22 ❌ Not 28
14 x 2 = 28 ✅ Is 28
22 x 2 = 44 ❌ Not 28
28 x 2 = 56 ❌ Not 28
Step 2:A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD
Area = 1/2 b * h ❌
Area = 3.5 * 4 ❌
Area = 3.5 * 4 ❌
Area = 14 in² ✅
dose 2+2=4?.............................
Answer:
[tex]yeah \: 2 + 2 = 4[/tex]
Please help me!!!
Suppose the proportion p of a school’s students who oppose a change to the school’s dress code is 73%. Nicole surveys a random sample of 56 students to find the percent of students who oppose the change. What are the values of p that she is likely to obtain?
Make an expression with 4 terms where 3 of them are like terms.
2. Rewrite the expression by combining like terms. How many terms are there?
please help
Answer:
Step-by-step explanation:
An example of an expression with 4 terms where 3 of them are like terms is:
$5x^2 + 7x - 2x^2 + 3x$
To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:
$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$
The resulting expression has 2 terms.
1 The table below shows the cost of an attorney as a function of the number o
hours worked.
A C=355h
3 C= _—_h+355°
Number of
Hours, h
1
255
4
7
8
Based on the table, which function models this situation?
Total Cost, C
с
$355
$1120
$1885
$2140
D
C=255h+100
C=765h-410
All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.
What does a function look like in math?A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".
The following function represents this circumstance:
C = -195h + 550
The first two data points can be used to create two equations:
355 = -195(1) + C
1120 = -195(3) + C
When we solve for C in each equation, we obtain:
C = 550
C = 550 + 585 = 1135
We can try utilising the first and third data points as the second equation doesn't quite match the third data point:
355 = -195(1) + C
1885 = -195(4) + C
Solving for C in each equation, we get:
C = 550
C = 550 + 975
= 1525
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mr. allen has a wife and three children. His monthly slary during the year 2007 was $7500. Calculate his annual salary
Mr. Allen's annual salary in the year 2007 was $90,000.
What is the annual salary of mr Allen?Given that, mr. Allen has a wife and three children. His monthly salary during the year 2007 was $7500.
To calculate Mr. Allen's annual salary, we need to multiply his monthly salary by the number of months in a year:
Annual salary = Monthly salary × Number of months in a year
Since Mr. Allen's monthly salary in 2007 was $7500 and there are 12 months in a year, his annual salary can be calculated as:
Annual salary = Monthly salary × Number of months in a year
Annual salary = $7500 × 12 months
Annual salary = $90,000
Therefore, his annual salary was $90,000.
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could someone please help thank you
The number of runners who are expected to finish the race, given the probability of finishing and the number who registered is 1, 375 runners.
How to find the number of runners ?The probability of a runner finishing the race is 11/12. This means that out of every 12 runners, 11 are expected to finish the race.
We know that 11 out of 12 runners are expected to finish the race, so we can write:
11/12 = x/1,500
11 × 1,500 = 12 × x
16,500 = 12x
x ≈ 1,375
Therefore, approximately 1375 runners are expected to finish the race out of 1500 runners.
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While the earth’s orbit (path) about the sun is slightly elliptical, it can be approximated by a circle with a radius of
miles.
How far does the earth travel in one orbit about the sun? That is, what is the approximate circumference of the earth’s path?
Approximately how fast is the earth traveling in its orbit in space? Calculate your answer in miles per hour.
The radius of the Earth's orbit around the sun is approximately 93 million miles.
To calculate the circumference of the Earth's orbit, we can use the formula:
C = 2πr
where C is the circumference and r is the radius. Plugging in the value for the radius, we get:
C = 2π(93,000,000) = 584,336,000 miles
So the Earth travels approximately 584,336,000 miles in one orbit around the sun.
The speed of the Earth in its orbit around the sun can be calculated using the formula:
v = 2πr/T
where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.
Plugging in the values, we get:
v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour
So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.
Suppose a man is 25 years old and would like to retire at age 60. Furthermore, he would like to have a retirement fund from which he can draw an income of $50,000 per yearforever! How can he do it? Assume a constant APR of 8%.
Answer:
Step-by-step explanation:
0.08*X >= 100000, i.e. X >= 100000%2F0.08 = 1,250,000 dollars.
Then each year he will draw 100000, but the bank will return equal or even greater amount than 0.08*1250000 = 100000,
so his balance will only increase from year to year.
It is a rough estimation.
If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,
then the unknown starting amount X must satisfy inequality
0.08*(X-100000) >= 100000, which gives
0.08X - 0.08*100000 >= 100000,
0.08X > (1+0.08)*100000
x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.
Answer. Having $1,350,000 or more initially on the account provides the sough condition.
Answer:
$26421.76
Step-by-step explanation:
We have to calculate final value i.e. balance to earn $50,000 annually from interest.
[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]
Now, N = n × y = 12 × 25 = 300
I = 8% = APR = 0.08
PV = 0 = PMT = 0
FV = 625,000 = A
[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]
[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]
[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]
[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]
[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]
[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]
[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]
Monthly payment (PMT) = $26421.7591469 ≈ $26421.76
$26421.76 is required monthly payment in order to $50,000 interest.
You flip a coin 100 times and record that 48 are heads and 52 are tails. What is the relative frequency or experimental probability of landing on heads?
whats the percentage
As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.
The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:
Number of Heads / Total Number of Flips = Experimental Probability of Heads
The number of heads in this case is 48, and the total number of flips is 100. Therefore,
Heads Experimental Probability = 48 / 100 = 0.48
We can multiply this by 100 to get a percentage:
Heads Experimental Probability = 0.48 * 100 = 48%
As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.
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Is the triangle Acute, Right, or Obtuse?
side1 = [tex]5\sqrt{2}[/tex]
side2 = [tex]4\sqrt{5}[/tex]
side3 = [tex]2\sqrt{3}[/tex]
which is the longest side? 1, 2, or 3
value of a^2, b^2, and c^2
classify the triangle
1. The longest side is side 2 (4√5). 2. a² = 50, b² = 80, c² = 12.
3. Since a² + b² < c², the triangle is obtuse.
What is an Obtuse Triangle?An obtuse triangle is a triangle with one angle greater than 90 degrees.
To classify a triangle as acute, right, or obtuse, we need to compare the squares of the lengths of the sides.
In this case, a² = 50, b² = 80, and c² = 12.
If a² + b² < c², the triangle is obtuse.
If a² + b² = c², the triangle is right.
And if a² + b² > c², the triangle is acute.
In this triangle, a² + b² = 50 + 80 = 130, which is less than c² = 12. Therefore, the triangle is obtuse. This means that one of the angles in the triangle is greater than 90 degrees.
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13 Convert 20 to a percentage.
How many 50ml can be filled from 5L
At age , someone sets up an IRA (individual retirement account) with an APR of %. At the end of each month he deposits $ in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Question content area bottom
Part 1
After retirement the IRA will contain $
enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
We can compare the amount in the IRA at retirement to the total deposits made over the time period to determine if the interest earned has exceeded the amount deposited.
What is IRA?IRA is an acronym that stands for "Individual Retirement Account." It is a sort of investment account meant to assist individuals in saving for retirement. Individuals can deposit pre-tax income to an IRA, and the money in the account grows tax-free until taken in retirement.
Part 1: To calculate the amount that the IRA will contain when the person retires at age 65, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
In this situation, the individual establishes the IRA at age a, thus they have t = 65 - a years till retirement. Because the APR is expressed as a percentage, we must divide it by 100 to obtain the annual interest rate in decimal form. Because the individual deposits $d at the end of each month, n = 12 (monthly compounding) and the effective monthly interest rate is r/12.
Therefore, the amount of money in the IRA at retirement can be calculated as:
[tex]A = d * ((1 + r/12)^(12*(65-a)) - 1) / (r/12)[/tex]
Part 2 : We can compare the amount in the IRA at retirement to the total amount of deposits made over the time period. The total amount of deposits can be calculated as:
Total Deposits = 12 * (65-a) * d
The amount in the IRA upon retirement (estimated in Part 1) may then be compared to the total contributions made during the time period. If the amount in the IRA exceeds the total deposits, the interest generated has exceeded the entire deposits. If the amount in the IRA is less than the total deposits, the interest produced will not be sufficient to compensate for the amount contributed.
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The blueprint of a pool has 2inches that equals 7 feet, what is it
Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.
Part B: the cost of the cover for the pool would be $15.00.
What is dimension?Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.
Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.
The actual length of the pool is 20 ÷ 2 = 10 feet.
The actual width of the pool is 10 ÷ 2 = 5 feet.
Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.
Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.
Area = length x width
Area = 10 ft x 5 ft
Area = 50 ft²
Therefore, the cost of the cover for the pool would be
$0.30 x 50 ft² = $15.00.
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Question :
The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10
Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft
Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?
Shaq painted 21 portraits every 35 minutes. At that rate, how long, in minutes, will it take to paint 15 portraits?
Answer:
25 minutes
Step-by-step explanation:
To find how long each portrait takes divide 35/21. This equals about 1.67 minutes per painting. Multiply this by 15 to get the answer: 25 minutes.
Answer:
25 minutes
Step-by-step explanation:
We find the unit rate.
21 portraits per 35 minutes = 21/35 = 3/5 portraits per minute
15 portraits / (3/5 portrait/minute) = 25 minutes
please help!!
angle relationships in circles
Answer:60
Step-by-step explanation:
30x2=60
If i have a 97% grade and i get a 75% on a quiz that counts 7% of my grade, how much is my grade? (37 points)
Answer: 90.32%
Step-by-step explanation:
To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:
New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)
Plugging in your values, we get:
New grade = (97 * (100 - 7)) + (75 * 7)
New grade = (97 * 93) + (5.25)
New grade = 903.16
Therefore, your new grade is 90.32%.
Answer: The sum of the weight of all your coursework plus your final is equal to 14.00
Step-by-step explanation:
not sure
savvas realize topic 5 assesment
Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.
How to solve inequality?To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:
Determine the type of inequality: Is it a greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality?Simplify both sides of the inequality as much as possible using algebraic operations such as addition, subtraction, multiplication, and division. Remember to apply the same operation to both sides of the inequality.If you multiplied or divided both sides of the inequality by a negative number, you need to reverse the direction of the inequality. For example, if you multiplied both sides of x < 3 by -1, you would get -x > -3.If there are variables on both sides of the inequality, move them all to one side of the inequality and simplify.If there are absolute values in the inequality, you may need to split the inequality into two separate cases, one for when the quantity inside the absolute value is positive, and one for when it is negative.Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).
by the question.
a. x-3.5>6.9
x>6.9+3.5
x>10.4
b. 6.4>x+3.1
x[tex]\geq 32[/tex]
c. x/4≤8
x≤32
d. 2/3x≤-10
x≤-15
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The diameter of a circle is 19 inches what is the area in inches square
a bakery has 17 pounds of flour they want to put into 6 containers. They put the same amount of flour in each container. If they want to use up all the flour, how much flour should they put in each container?
Answer:
2.83333 pounds of flour in each container
please answer need help
Find the circumcenter of the triangle with the following vertices: P(-2,5) Q(5,1) R(-4,-5)
Answer:
(-0.5, -0.5)
Step-by-step explanation:
d = √ (a - ax)2 + (b - bx)2
plug in
Answer:
%......
............….
Find the mean of the data in the dot plot below. years A number line labeled from left to right 0 through five scaling by ones. The dot distribution is as follows: 1, 1; 2, 1; 3, 1; 4, 1.
Answer: The mean of 1 1 2 1 3 1 4 1 is 1.75.
Step-by-step explanation:
:D
solve for x and say if it’s complementary or supplementary
Answer: Supplementary x=2
Step-by-step explanation:
supplementary adds up to 180
complementary adds up to 90
On the bottom shelf there are 20 shirts . Three-fourths of them are red. Draw a picture to show the shirts.
Answer:
Step-by-step explanation:
Elon is purchasing materials for a gardening project. Mulch costs $ 33 $33dollar sign, 33 per cubic yard. Edge material costs $ 60 $60dollar sign, 60 for 5 55 yards. Elon needs 60 6060 yards worth of edge material. Let � vv be the volume, in cubic yards, of mulch that Elon buys; and let � cc be the total cost, in dollars, of his purchase. Which of the following equations correctly relates � vv and � cc?
The correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720
What is total cost?The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total.
The cost of the mulch depends on the volume purchased, so the equation relating the volume of mulch purchased (v) and the cost of the purchase (c) is:
c = 33v
The cost for 5 yards of edge material is $60, so the cost for 60 yards of edge material is:
60/5 x 60 = $720
Therefore, the total cost of the purchase is the sum of the cost of the mulch and the cost of the edge material:
total cost = cost of mulch + cost of edge material
c = 33v + 720
So the correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720
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1. The Osbournes bought a color television set for $736.70. The installment contract required 15% down and the remainder in 18 installments of $41.16. What is the amount of the finance charge on the account?
2. Which would be the smarter buy?
a. Samuel Evans wants to buy a piano for his daughter. He can borrow $1289 from his credit union at an annual rate of 15%. He would repay the credit union $44.69 per month for 36 months.
Or
b. Samuel can finance the $1289 through the music dealer at an annual rate for 21%. He would pay the dealer $84.09 per month for 18 months.
What is the cost for each plan? Which plan costs less?
3. A promissory note for $300 at 19% interest per year is due in 6 months. What is the total amount due?
4. Marion needs to borrow $5000. Plan A will allow her to repay the $5000 in 6 monthly payments of $954. Plan B requires 18 monthly payments of $325. Which plan costs less?
5. The unpaid balance on a credit account was $7500.00. The annual interest rate is 19%, or 1.58% per month. A $150.00 minimum payment is required. Calculate each monthly payment and balance including the interest by paying only the minimum payment. How long will it take to pay off the entire balance?
The amount of the finance charge on the account is $96.48.
Here's how to calculate it:
The total cost of the television set is $736.70.
The down payment is 15% of $736.70, which is $110.50.
So the amount to be financed is $626.20.
The total amount paid in installments is 18 x $41.16 = $740.88.
Therefore, the finance charge is $740.88 - $626.20 = $114.68.
However, this amount includes the first installment of $41.16, which is not part of the finance charge.
So the actual finance charge is $114.68 - $41.16 = $73.52.
Rounded to the nearest cent, the finance charge is $96.48.
Plan a would cost a total of $1608.84, and Plan b would cost a total of $1513.62. Plan b would be the smarter buy because it has a lower total cost.
Here's how to calculate the cost of each plan:
For Plan a, the total cost is 36 x $44.69 = $1608.84 ($1289 borrowed + $319.84 in interest).
For Plan b, the total cost is 18 x $84.09 = $1513.62 ($1289 borrowed + $224.62 in interest).
The total amount due is $313.50.
Here's how to calculate it:
The interest rate is 19% per year, or 0.095 per 6-month period.
So the interest on the $300 loan is $300 x 0.095 = $28.50.
Therefore, the total amount due is $300 + $28.50 = $328.50.
Rounded to the nearest cent, the total amount due is $313.50.
Plan B costs less.
Here's how to calculate it:
Plan A requires 6 monthly payments of $954, for a total cost of $5,724.
Plan B requires 18 monthly payments of $325, for a total cost of $5,850.
Therefore, Plan B costs less.
The minimum monthly payment is $150.
Here's how to calculate the payments and balance:
The interest rate is 1.58% per month.
So the monthly interest on the unpaid balance of $7500 is $7500 x 0.0158 = $118.50.
Therefore, the monthly payment of $150 only covers $31.50 of the balance ($150 - $118.50).
So the new balance is $7500 + $118.50 - $31.50 = $7587.
The next month, the interest on the unpaid balance of $7587 is $7587 x 0.0158 = $120.02.
So the monthly payment of $150 only covers $29.98 of the balance ($150 - $120.02).
So the new balance is $7587 + $120.02 - $29.98 = $7677.04.
This process continues until the entire balance is paid off.
It will take 91 months (7 years and 7 months) to pay off the entire balance.
You deposit $2000 in an account earning 2% interest compounded continuously. How much will you have in the account in 10 years? Use this formula and round to the nearest cent.
(Hint: A = Pet^rt)
The amount after 10 years will be obtained by continuous compounding is $2443.1.
Define about the continuous compounding?By continuously compounding for an endless amount of time, continuous compounding determines the upper limit that compounded interest can reach, thus raising the revenue component and the portfolio value of all investments.The calculation makes use of infinitely many periods with continuous compounding. The exponent aids in multiplying the existing investment because the time is endless. The current rate as well as time are multiplied by this.The formula for the continuous compounding:
A = P[tex]e^{rt}[/tex]
A = amount after compounding.
P = principal $2000
r = rate of interest 2%
t = time 10 years
Then,
A = 2000* [tex]2.72^{0.02*10}[/tex]
A = 2000* 1.22155
A = 2443.1
Thus, the amount after 10 years will be obtained by continuous compounding is $2443.1.
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What is the value of the angle?
The angle indicated by a green arc is 54 degrees.
What is the definition of a simple angle?A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.
The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.
To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.
So we have:
The blue arc angle is equal to the sum of the red and green arc angles.
We get the following equation when we plug in the given angle measurements:
98° = 44° + Green arc angle
We can simplify this equation as follows:
Green arc angle = 98° - 44° = 54°
The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.
We currently have:
Green arc angle + 70° + 56° = 180°
We get the following by substituting the value we found for the green arc angle:
54° + 70° + 56° = 180°
We can simplify this equation as follows:
180° - 70° - 56° = 54°
As a result, the angle indicated by a green arc has the value:
It is 54 degrees outside.
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