Answer:
84 paid with three 50p coins.
If $20,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
6 years
12 years
18 years
Answer:
6 years = $22,536.50
12 years = $25,394.69
18 years = $28,615.38
Step-by-step explanation:
The find the value of the investment after the given number of years, first create an equation for A in terms of t using the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\frac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal investment.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $20,000r = 2% = 0.02n = 2 (semi-annually)Substitute the given values into the formula to create an equation for the value of the investment, A, in terms of time in years, t:
[tex]\implies \sf A=20000\left(1+\dfrac{0.02}{2}\right)^{2t}[/tex]
[tex]\implies \sf A=20000\left(1+0.01\right)^{2t}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{2t}[/tex]
[tex]\hrulefill[/tex]
To find the value of the investment after 6 years, substitute t = 6 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 6}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{12}[/tex]
[tex]\implies \sf A=20000(1.12682503...)[/tex]
[tex]\implies \sf A=22536.5006026...[/tex]
Therefore, the value of the investment after 6 years is $22,536.50 rounded to the nearest cent.
[tex]\hrulefill[/tex]
To find the value of the investment after 12 years, substitute t = 12 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2 \cdot 12}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{24}[/tex]
[tex]\implies \sf A=20000\left(1.2697346...\right)[/tex]
[tex]\implies \sf A=25394.69297...[/tex]
Therefore, the value of the investment after 12 years is $25,394.69 rounded to the nearest cent.
[tex]\hrulefill[/tex]
To find the value of the investment after 18 years, substitute t = 18 into the equation:
[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 18}[/tex]
[tex]\implies \sf A=20000\left(1.01\right)^{36}[/tex]
[tex]\implies \sf A=20000\left(1.43076878...\right)[/tex]
[tex]\implies \sf A=28615.37567...[/tex]
Therefore, the value of the investment after 18 years is $28,615.38 rounded to the nearest cent.
Explain Why 387 is not a term of the sequence
Answer:
In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.
If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:
an = a1 + (n-1)d
where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.
If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:
a1 = 3
a2 = 8
a3 = 13
a4 = 18
and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:
a129 = a1 + (129-1)d
a129 = 3 + 128(5)
a129 = 643
Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.
Janna's health class measures the heart rates of students after they walked for five minutes. The heart rates, in beats
per minute, were as follows.
102, 74, 86, 74, 96, 95, 103, 102 Find the median of the data set. What does the median tell you? (Hint: If the data set has an even number of values,
the median is the mean of the two middle values.)
The median of the data set is: 95.5
What is median?
median is the number at the middle of the given data.
To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:
74, 74, 86, 95, 96, 102, 102, 103
Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.
Therefore, the median of the data set is: (95 + 96) / 2 = 95.5
To know more about median visit,
https://brainly.com/question/26177250
#SPJ1
Helppppppppppppppppppppp
differentiate x^5(2x+1)^5
Answer:
[tex]5x^4(2x+1)^4(4x+1)[/tex]
Step-by-step explanation:
Okay so we have to use the product rule for this i.e.
d/dx[uv] = u'v + uv'
d/dx[x^5(2x+1)^5] =
[tex]5x^4(2x+1)^5 + x^5 * 2 * 5(2x+1)^4\\\\= 5x^4(2x+1)^5 + 10x^5(2x+1)^4\\\\= (2x+1)^4[5x^4(2x+1) + 10x^5]\\\\= (2x+1)^4[10x^5 + 5x^4 + 10x^5]\\\\= (2x+1)^4(20x^5+5x^4)\\\\=5x^4(2x+1)^4(4x+1)[/tex]
Hope this helps and be sure to mark this as brainliest! :)
In triangle ABC, AB = 6, BC = 8, and angle ABC = 90 degrees. Find the area of triangle ABC.
Answer:
24
Step-by-step explanation:
The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.
6 x 8 = 48
48 / 2 = 24
Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 7, negative 2, W at negative 7, negative 4, Y at negative 1, negative 4, and Z at negative 1, negative 2. A second polygon V prime W prime Y prime Z prime with vertices V prime at 11, negative 2, W prime at 11, negative 4, Y prime at 5, negative 4, and Z prime at 5, negative 2.
Reflection across the x-axis
Reflection across the y-axis
Reflection across y = −2
Reflection across x = 2
An image of polygon VWYZ has a line of reflection across the x-axis. So option A is correct.
What is the line of reflection?In geometry, the line of reflection is the line over which a figure is reflected. When a point is reflected over a line, it moves the same distance on the opposite side of the line. The line of reflection is perpendicular to the figure at the point of reflection and is equidistant from the figure and its reflection.
What is a polygon?A polygon is a closed two-dimensional shape with straight sides. The sides are line segments that intersect only at their endpoints, called vertices. Polygons can have any number of sides, but they must have at least three. Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and octagons.
What is the formula for the line of reflection?The formula for the line of reflection in a Cartesian coordinate system is:
x = a
where a is the equation of the line of reflection.
This formula represents a vertical line that passes through the point (a, 0) and reflects points across the line of reflection to their corresponding images on the other side.
To know more about the line of reflection visit:
brainly.com/question/29248743
#SPJ1
Answer:
reflection across x=2
Step-by-step explanation:
the picture should be able to explain itself! :)))
answer these questions in detail
Answer:
5. x = 60
6. F' (1, 4)
Step-by-step explanation:
5. The angles shown are same side exterior angles, so they are supplementary (add to 180)
(x + 85) + 35 = 180
x + 120 = 180
x = 180 - 120 = 60
x = 60
6. The line x = 1 is a vertical line, passing through the x=axis at (1, 0). All x coordinates on this line equal 1.
The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)
Leon is building a square picture frame. The side of the frame is 335 millimeters long. If a meter of wood costs $8, how much will the wood he needs cost?
Answer: $9.66
Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380
We need 1380 millimeters which is equivalent to 1.38 meters.
We can multiply the number of meters by the cost of meters to find the total
Pedro wants to grow tomatoes and herbs so he can make his own fresh pizza sauce. Pedro's planter box is seven feet long and four feet wide on the inside. Pedro fills the planter box with soil to a height of two feet. What is the volume of soil in Pedro's planter box?
According to the question the volume of soil in Pedro's planter box is 56 cubic feet (ft³).
What is volume?Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is measured in units of cubic centimeters (cm3), cubic meters (m3) or liters. Volume is an important concept in many areas of mathematics, including geometry, calculus and physics. It is also a key concept in many other disciplines, including engineering, architecture and the sciences. Volume is an important property of a solid object, and it is often used to quantify the size or capacity of an object. Volume can be calculated by multiplying the length, width and height of an object. It can also be calculated using the formula for the volume of a cylinder, cone, sphere or other shapes.
To calculate this, we need to multiply the length of the planter box (7 ft) by the width (4 ft) by the height of the soil (2 ft). This gives us the following equation: 7 ft x 4 ft x 2 ft
= 56 ft³.
To learn more about volume
https://brainly.com/question/1972490
#SPJ1
There is a sale at khols, and tennis shoes are 30% off. How much are you saving if the shoes originally cost $62
Answer: $18.6
Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off
Antoni Gaudi purchased a bedroom set with an installment loan that has an APR of 12%. The bedroom set sells for $2,650. The store financing requires a 15% down payment and 42 monthly payments. What is the finance charge?
The finance charge for Antoni Gaudi's bedroom set purchase is $731.08.
What is an installment?An installment refers to a sum of money that is paid back in parts over a period of time, typically with interest.
Define loan?A loan is a financial agreement between a lender and a borrower, in which the lender provides the borrower with a specific amount of money or assets, which the borrower agrees to pay back with interest over a predetermined period of time. Loans can be used for a variety of purposes, such as purchasing a home, starting a business, or paying for education.
Based on the given information, the bedroom set sells for $2,650, and the financing requires a 15% down payment, which is $397.50 ($2,650 x 0.15).
Therefore, the amount financed is $2,252.50 ($2,650 - $397.50).
To calculate the finance charge, we need to know the total amount of payments Antoni Gaudi will make over the 42-month period. Each monthly payment can be calculated using the following formula:
Monthly Payment = (Amount Financed x (APR/12)) / (1 - (1 + APR/12)^-n)
Where:
APR is the annual percentage rate (12% in this case)
n is the total number of payments (42 in this case)
Plugging in the values, we get:
Monthly Payment = ($2,252.50 x (0.12/12)) / (1 - (1 + 0.12/12)^-42)
= $70.99 (rounded to the nearest cent)
Therefore, the total amount of payments Antoni Gaudi will make over the 42-month period is $2,983.58 ($70.99 x 42).
The finance charge can be calculated as follows:
Finance Charge = Total Payments - Amount Financed
= $2,983.58 - $2,252.50
= $731.08
Therefore, the finance charge for Antoni Gaudi's bedroom set purchase is $731.08.
Learn more about down payment here:
https://brainly.com/question/31293332
#SPJ1
What is 8% of 425 coins?
Answer: 34
Step-by-step explanation:
To find 8% of 425 coins, multiply 425 by 0.08 (which is the decimal equivalent of 8%).
425 * 0.08 = 34
So, 8% of 425 coins is 34 coins.
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
7 and 31 it asks
the 3rd and 6th is
The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.
How to find the Fibonacci sequence terms ?Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:
F(n) = F(n-1) + F(n-2)
We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:
F3 = F2 + F1 = 7
F6 = F5 + F4 = 31
We can also express F4 and F5 in terms of F1 and F2:
F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2
F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2
Now, let's substitute equation (4) into equation (2):
F6 = 2F1 + 3F2 + F1 + 2F2 = 31
3F1 + 5F2 = 31
By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:
F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)
F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)
The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.
Find out more on Fibonacci sequence at https://brainly.com/question/29764204
#SPJ1
The number of deer on an island is given by D=200+100sin( 2 π x), where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 150 ?
Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.
What are a leap year and a year?If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.
We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.
150=200+100sin(2πx)
Subtracting 200 from both sides, we get:
-50 = 100sin(2πx)
Dividing both sides by 100, we get:
-0.5 = sin(2πx)
To find the value of x that satisfies this equation, we can take the inverse sine of both sides:
sin⁻¹(-0.5) = 2πx
Using a calculator, we find that sin⁻¹(-0.5) = -π/6.
-π/6 = 2πx
Solving for x, we get:
x = -1/12
Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:
2000 + 1/12 ≈ 2000.1
To know more about Leap year visit:-
https://brainly.com/question/24068575
#SPJ1
In 1870, the French writer Jules Verne
In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.
Who is the French writer?The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.
Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.
To know more about French writer here:
https://brainly.com/question/17460800
#SPJ1
i don't understand this question please help me answer it :)
Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
Learn more about Discounts at
https://brainly.com/question/30814332
#SPJ9
In ΔHIJ, i = 550 inches, h = 460 inches and ∠H=159°. Find all possible values of ∠I, to the nearest degree.
What is
22.50 x 15 Steph by step
Answer: 337.5.
Step-by-step explanation:
Answer:
337.5
Step-by-step explanation:
yara said that the vertical distance between two points is -5 units how do you know that yara's statement is incorrect
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
Write the absolute value equation that has the following solutions.
One solution: x = 15
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
Learn more about absolute value:
https://brainly.com/question/1782403
#SPJ1
If $r=9$ and $4r+3s=75$, what is the value of $s$? asap answer i only have like 1 hour to answer 50 questions
Answer:
the value of $s$ is 13.
Step-by-step explanation:
We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.
Substituting $r=9$ into the second equation, we get:
$4(9) + 3s = 75$
Simplifying the left-hand side, we get:
$36 + 3s = 75$
Subtracting 36 from both sides, we get:
$3s = 39$
Dividing both sides by 3, we get:
$s = 13$
Therefore, the value of $s$ is 13.
What fractions are close to 1 than to 0
The answer of the given question based on the fraction is , a value that is greater than 1/2.
What is Fraction?A fraction is mathematical expression that represents part of whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.
Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.
So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:
2/3 is closer to 1 than to 0 because it is greater than 1/2
7/8 is closer to 1 than to 0 because it is greater than 1/2
3/4 is closer to 1 than to 0 because it is greater than 1/2
On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:
1/4 is closer to 0 than to 1 because it is less than 1/2
3/10 is closer to 0 than to 1 because it is less than 1/2
2/5 is closer to 0 than to 1 because it is less than 1/2
To know more about Expression visit:
https://brainly.com/question/1859113
#SPJ1
721.60 divided by 80
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.
Answer: 205.031(nearest thousandth)
or 205.03125
Step-by-step explanation:
Please help please show the step by step explanation:)
the decrease in emissions is due to the increase in alternative energy use. The alternative and nuclear energy use of the U.S. is given in the table below.
(Source: data.worldbank.org)
Year 2000 2003 2005 2008 2010 2011 2012
% of total
energy use 10.7696 10.6167 10.6213 11.1977 11.7184 11.9921 12.0645
Find a cubic model for this data and use it to predict the alternative energy use for 2016.
Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.
How to solveTo find a cubic model for the given data, we can use the method of least squares to fit the data points into a cubic polynomial of the form:
y = ax^3 + bx^2 + cx + d
where y represents the percentage of alternative and nuclear energy use, x represents the year, and a, b, c, and d are the coefficients to be determined.
Given the data points:
(2000, 10.7696)
(2003, 10.6167)
(2005, 10.6213)
(2008, 11.1977)
(2010, 11.7184)
(2011, 11.9921)
(2012, 12.0645)
Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.
Once you have the cubic model, you can plug in x = 2016 to predict the alternative energy use for 2016.
Read more about cubic models here:
https://brainly.com/question/28990074
#SPJ1
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.
His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.
x = 14.2
s²= 0.9867
s= 0.9933
t α2, n-1 = 3.7074
The margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).
(B) The right choice is Option B, which is Option II which is narrower.
Know more about the confidence interval here:
https://brainly.com/question/15712887
#SPJ1
Correct question:
Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot?
Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.
The nth term of an arithmetic sequence can be found using the formula:
an = a1 + (n-1)d.
The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:
(7/10) ÷ 7 = (7/10) × (1/7) = 1/10
Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.
To learn more about arithmetic sequence from the given link:
https://brainly.com/question/15412619
#SPJ1
Classify the following polynomial by its degree and the number of terms:
9x 3+4x 2 −7
We can classify the polynomial as a "trinomial" with a degree of 3.
How to Classify the following polynomial by its degreeThe given polynomial is:
9x^3 + 4x^2 - 7
The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the degree of the polynomial is 3, because the highest power of x in the polynomial is 3.
The number of terms in a polynomial is the number of individual expressions added or subtracted together. In this case, the polynomial has three terms: 9x^3, 4x^2, and -7.
Therefore, we can classify the polynomial as a "trinomial" with a degree of 3.
Learn more about polynomial at https://brainly.com/question/2833285
#SPJ1