A person places $479 in an investment account earning an annual rate of 8.2%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 12 years.
Answers
The amount of money to the nearest cent, in the account after 12 years will be $1281.39.
What is Compound Interest?Compound interest is the interest found with respect to the principal value and then interest is accumulated over the previous period.
Interest can be compounded monthly, quarterly, half yearly, yearly or continuously.
If the interest is compounded continuously, the formula will be,
V = P e^rt
where, V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.
P = $479
r = 8.2% = 0.082
t = 12 years
V = 479 × e^(0.082 × 12)
= 479 × e^(0.984)
= 479 × 2.67514
= 1281.38986 ≈ 1281.39
Hence the amount of money the person get after 12 years will be $1281.39.
To learn more about Compound Interest, click:
https://brainly.com/question/14295570
#SPJ1
Related Questions
which transformation is shown here?
Answers
It is a Rotation.
find the y - intercept of the graph
Answers
Answer:
Step-by-step explanation:
yes that is correct!-2
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
$$
Answers
The y-intercept of the line representing Beatrice's monthly music is 20
How to determine the y-intercept of the lineFrom the question, we have the following parameters that can be used in our computation:
y = -.95x + 20
To calculate the y-intercept of the line, we set x = 0
So, we have
y = -.95 * 0 + 20
Evaluate
y = 20
Hence, the y-intercept of the line representing Beatrice's monthly music is 20
Read more about intercept at
https://brainly.com/question/24363347
#SPJ9
Question
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
The equation is y = -.95x + 20
Question 11
A rectangle with a perimeter of 12 inches is enlarged by a scale factor of 3. What is the perimeter of the enlarged
rectangle?
Answers
Answer:
The perimeter of the enlarged rectangle is 36 inches.
Step-by-step explanation:
Perimeter of an enlarged figure:
To find the perimeter of an enlarged figure, we multiply the perimeter of the original figure by the scale factor.
In this question:
Perimeter of the original rectangle: 12 inches
Scale factor: 3
Perimeter of the enlarged rectange:
12*3 = 36 inches
Need answers please help
Answers
Answer
Yes, zero is contained in the interval
15. Kate has 63 pens. She gives all the pens to her 9 friends. Each friend gets
the same number of pens.
Kate said that when she divided the number of pens that each friend got by 9,
the answer was equal to 63. Her friend Margo said that when the number of
pens each friend got was multiplied by 9, the answer was equal to 63.
Which girl is correct? Explain your answer. I will mark as brainlist and vote if you answer
Answers
The girl which is correct between kate and her friend Margo is Margo.
The correct answer option is option B
How to multiply?Number of pens Kate has = 63Number of Kate's friends = 9If each friend gets the same number of pens;
Number of pens each friend get = Number of pens Kate has / Number of Kate's friends
= 63 / 9
= 7
Check:
Number of pens each friend get × Number of Kate's friends = Number of pens Kate has
7 × 9 = 63
Therefore, Kate's friend, Margo is correct.
Read more on multiplication:
https://brainly.com/question/10873737
#SPJ1
Help me please will be appreciated thx
Answers
Answer:
-6 +8d -2c
Step-by-step explanation:
\(\frac{-2}{5} (15 -20d +5c) = \frac{-2}{5} \times 15 - \frac{-2}{5}\times20d +\frac{-2}{5}\times5c = -6 + 8d -2c\)
Amanda is going to build some large wooden storage boxes. The boxes are shaped like rectangular prisms, as shown below. She wants to cover all the sides of each box with special wallpaper. If she has a total of of wallpaper, how many boxes can she cover?
Answers
The number of boxes that Amanda can cover with W square inches of wallpaper will be equal to W/2(lw + lh + wh).
Let's assume that Amanda wants to build n wooden storage boxes. All of these boxes are shaped like rectangular prisms, as shown in the image below.
She wants to cover all the sides of each box with special wallpaper. If she has a total of W square inches of wallpaper, we need to find out how many boxes she can cover. Let's solve this problem mathematically.
Mathematical Solution:
Each rectangular prism has six sides (faces). If we want to cover all the six sides of a rectangular prism with special wallpaper, we need to find the total surface area of that rectangular prism. Therefore, the surface area of each rectangular prism can be calculated by the formula:
Surface Area = 2lw + 2lh + 2wh,
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
We know that Amanda has W square inches of wallpaper to cover all the boxes. Therefore, the total surface area of n boxes will be:
n × Surface Area = W.
Substituting the value of the Surface Area, we have:
n × (2lw + 2lh + 2wh) = W
2n(lw + lh + wh) = W
n(lw + lh + wh) = W/2
n = W/2(lw + lh + wh).
To learn more about : number
https://brainly.com/question/24644930
#SPJ8
A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
Answers
The frequency of the A allele is 82.7%.
The frequency of the B allele is 17.3%.
We know that :
10,000 individuals
6,840 individuals have blood type AA
2,860 individuals have blood type AB
300 individuals have blood type BB
AA genotype frequency: 68.4%
AB genotype frequency: 28.6%
BB genotype frequency: 3%
The A allele occurs 6,840 * 2 + 2,860 * 1 = 16,540 times, which is a frequency of 82.7%, meaning the B allele occurs 3,460 times, which is a frequency of 17.3%. In the next generation, 3%, or 750, individuals would have blood type BB.
Read more about genotype frequency:
https://brainly.com/question/20039242
#SPJ4
The complete question is:
A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB, and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
What does the frequency of the A allele?
What is the frequency of the B allele?
The time it takes to completely clean an office building follows an exponential distribution with a mean of 135 minutes. What is the probability of cleaning an office building in 135 minutes or less?
Answers
Answer:
0.63212
Step-by-step explanation:
Given that :
Mean cleaning time (μ) = 135
Probability of cleaning the office is 135 minutes or less
Using an exponential distribution probability calculator :
P(X ≤ 135) = 0.63212
Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83
Answers
Answer:
S₂₇ = 1188
Step-by-step explanation:
using the given formula for \(S_{n}\) , that is
\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )
with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then
S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188
A city has a population of 370,000 people. Suppose that each year the population grows by 6.25%. What will the population be after 8 years?
Use the calculator provided and round your answer to the nearest whole number.
people
Answers
Answer:
600943 people-----------------------------
Current population is 370000 people.
Growth rate is 6.25%.
The population after 8 years will be:
370000*(1 + 6.25/100)⁸ = 370000*1.0625⁸ = 600943 (rounded)Given the linear function of 3x-7y=14, determine the ordered pair where the line crosses the y axis. Remember to write your answer in form (x,y)
Answers
Answer:
(0, -2)
Step-by-step explanation:
The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.
3x - 7y = 14
3*0 - 7y = 14
-7y = 14
y = -2
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answers
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
on saturday, it rained six sevenths of an inch. On Monday it rained an additional one fifth of an inch. what was the total rainfall on saturday and monday
Answers
Rewrite the fractions so they have a common denominator:
6/7 = 30/35
1/5 = 7/35
Now add:
30/35 + 7/35 = 37/35
37/35 = 1 and 2/35 inches of rain
5x(3/5+1/2)= _ _/_ while number and fraction already tried 4 2/3 said it was wrong help
Answers
9514 1404 393
Answer:
5 1/2
Step-by-step explanation:
You can use the distributive property to eliminate parentheses, then add the terms that result.
5(3/5 +1/2) = 5(3/5) +5(1/2) = 3 + 5/2 = 3 + 2 1/2 = 5 1/2
__
Or, you can add the numbers, then multiply by 5. This is the way the evaluation should be done according to the Order of Operations.
5(3/5 +1/2) = 5(6/10 + 5/10) = 5(11/10) = 11/2 = 5 1/2
Answer:
5 1/2.
Step-by-step explanation:
5*(3/5+1/2)
= 5 * (6/10 + 5/10)
= 5 * 11/10
= 55/10
= 5 1/2.
If the 10 letters are {aa,aa,aa,aa,bb,bb,cc,cc RR,RR} are available and all 10 of them are to be selected without replacement,what is the number of different permutations?
Answers
In order to calculate the number of permutations, first we start with the factorial of the number of letters.
There are 10 letters, so we start with the factorial of 10.
Then, we need to check the number of repetitions. Each repetition will be a factorial in the denominator:
\(x=\frac{10!}{a!\cdot b!\operatorname{\cdot}...}\)We have four repetitions of aa, two repetitions of bb, two repetitions of cc and two repetitions of RR, therefore the final expression for the number of permutations is:
\(x=\frac{10!}{4!2!2!2!}\)Calculating this expression, we have:
\(x=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5\operatorname{\cdot}4!}{4!\operatorname{\cdot}2\operatorname{\cdot}2\operatorname{\cdot}2}=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5}{8}=18900\)Therefore there are 18900 permutations.
Find the equation of a line perpendicular to y=-1/2x+4 that passes through the point (-2,8)
Answers
Answer:
y = 2x + 12.
Step-by-step explanation:
To find the equation of a line perpendicular to y=-1/2x+4 and passing through the point (-2,8), we can first determine the slope of the perpendicular line.
Recall that two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, the slope of the line we want to find is the negative reciprocal of the slope of y=-1/2x+4.
The slope of y=-1/2x+4 is -1/2, so the slope of the line perpendicular to it is 2 (since the negative reciprocal of -1/2 is 2).
Next, we can use the point-slope form of the equation of a line to write the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8):
y - 8 = 2(x + 2)
Simplifying and putting the equation in slope-intercept form, we get:
y = 2x + 12
Therefore, the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8) is y = 2x + 12.
\(\sf y =2x+12.\)
Step-by-step explanation:1. Find the slope of the given equation.The slope of any linear equation can be found just by taking a look at the equation when it's solved for "y".
\(\sf y=-\dfrac{1}{2} x+4\)
Looking at the given equation, we can clearly tell that the value of slope is \(-\dfrac{1}{2}\).
2. Find the slope of the perpendicular line.The slope of any linear equation that is perpendicular to another can be found by writting the multiplicative reciprocal of the original equation's slope, and changing the sign on it.
Let's do it step by step:
a) Write the slope of the original equation.
\(-\dfrac{1}{2}\)
b) Write the multiplicative reciprocal.
For this, you just need to change the order in the fraction. In other words, switch places between the numerator and denominator.
\(-\dfrac{1}{2}\Longrightarrow-\dfrac{2}{1}=-2\)
c) Change the symbol of the number.\(\sf -2\Longrightarrow2\)
Therefore, the slope of the new equation will be 2, and it is perpendicular to the original equation (\(\sf y=-\dfrac{1}{2} x+4\)).
3. Identify the values.With the given ordered pair (-2, 8) and the slope (2) we can calculate the formula of the new equation.
Formula to use: \(\sf y-y_{1} =m(x-x_{1} )\)
\(\sf x_{1} =-2\\ \\\sf y_{1} =8\\ \\m=2\)
4. Calculate.Now we substitute the variables in the equation by the identified values in step 3.
\(\sf y-(8) =(2)(x-(-2))\\ \\y-8 =(2)(x+2)\\ \\\)
Use the distributive property of multiplication on the right side of the equation (check the attached image).
\(\sf y-8 =(2)(x)+(2)(2)\\\\y-8 =2x+4\\ \\y-8+8 =2x+4+8\\ \\y =2x+12\)
5. Verify.a) Is it perpendicular?
According to the theory explained in step 2, it is, because the slope is 2.
b) Does it pass through point (-2, 8)?.
For this, simply substitute "x" by "-2" in the calculated equation. If y= 8, then the function also meets this requirement.
\(\sf y =2(-2)+12\\ \\y=-4+12\\ \\y=8\)
That's correct. We have found the correct answer.
-------------------------------------------------------------------------------------------------------
Learn more about linear equations here:https://brainly.com/question/30346638
https://brainly.com/question/28262883
https://brainly.com/question/28339006
https://brainly.com/question/28339255
https://brainly.com/question/28282032
Hit 96 must play 3minutes of commercials for every 30 minutes of music played how many minutes of commercials must be played for 210 minutes of music
Answers
Answer:
21
Step-by-step explanation:
Answer:
21 minutes
Step-by-step explanation:
I'll show you two way of solving:
1) Using division and multiplication with the given information
We can find out how many times 210 minutes is more than 30 minutes.
210/30 = 7
210 minutes is 7 times 30 minutes.
If for 30 minutes of music it needs 3 minutes of commercials, then for 7 times as much music played it needs 7 times the time of commercials.
7 * 3 minutes = 21 minutes
Answer: 21 minutes
2) Proportion
3 minutes of commercials is to 30 minute of music as x minutes of commercials is to 210 minutes of music
3/30 = x/210
Cross multiply.
30x = 3 * 210
Divide both sides by 30.
x = 3 * 210/7
x = 3 * 7
x = 21
Answer: 21 minutes
a girl attaches a rock to a string, which she then swings counterclockwise in a horizontal circle. the string breaks at point p on the sketch, which shows a bird's-eye view (as seen from at at the right). what path will the rock follow?
Answers
The correct option B. Path B: since velocity v is tangent to a circular path.
Explain the term tangential velocity?Any linear component of an object's motion that travels a circular path is called tangential velocity.
A vector is a quantity with both magnitude and direction, according to the definition of physics. As an illustration, velocity is indeed a vector whose magnitude is speed. Distance divided by the time equals speed.The direction anywhere at given location on the circle is always following the tangent line when speaking of tangential velocity, which describes motion along a circle's periphery. We refer to the speed in our equation as "tangential velocity" since we grasp the concept of tangential direction.Thus, the rock will follow path B since velocity v is tangent towards the circular path.
To know more about the tangential velocity, here
https://brainly.com/question/19660334
#SPJ4
The complete question is
A girl attaches a rock to a string, which she then swings counter-clockwise in a horizontal circle. The string breaks at point P in the figure, which shows a bird's-eye view (as seen from above). Which path (A-E) will the rock follow?
A. Path A
B. Path B
C. Path C
D. Path D
E. Path E
A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour. The average speed for the round trip is closest to?
Answers
The average speed formula is given by:
\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is \(\displaystyle\sf 2 \times 120 = 240\) miles.
Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula \(\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}\).
For the journey from A to B:
\(\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4\) hours
For the return journey from B to A:
\(\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3\) hours
The total time for the round trip is the sum of the individual times:
\(\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7\) hours
Now, we can calculate the average speed:
\(\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29\) miles per hour.
Therefore, the average speed for the round trip is closest to 34.29 miles per hour.
Find the value of x and y. If necessary, round your answer to the nearest tenth. *
Answers
Answer:
Step-by-step explanation:
"y" is geometric mean ⇒ y² = 5 × 12
y = √60 ≈ 7.7
x² = 5² + ( √60 )²
x = √85 ≈ 9.2
Please help, thank you!
Answers
Answer:
En español pliss y te ayudoo jajjaa
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
What is a Parabola:A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).
The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.
Here we have
The quadratic function f(x) = x²/5 – 5x + 12
Now check each option as follows
1. The value of f(–10) = 82
To check this find f(-10) as follows
f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82
Hence, The value of f(–10) is equal to 82
2. The graph of the function is a parabola.
As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c
Hence, the quadratic function represents a parabola
3. The graph of the function opens down.
In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.
Hence, The graph of the function opens down is false
4. The graph contains the point (20, –8).
To check this substitute the point in f(x)
=> –8 = 1/5(20)²– 5(20) + 12
=> –8 = 80 – 100 + 12
=> –8 = –8 [ Which is true ]
Hence, The graph contains the point (20, –8).
5. The graph contains the point (0, 0).
=> 0 = (0)²– 5(0) + 12
=> 0 = 12 [ which is not true ]
Hence, The graph doesn't contain the point (0, 0).
Therefore,
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
Learn more about Parabola at
https://brainly.com/question/21685473
#SPJ9
Need help answering question 5
Answers
Answer:
Step-by-step explanation:
4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?
Answers
Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.
This shows, with dots, the number of times that each of the measures appears in a data set.
For finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4
= 6.25 inches.
The tallest conifer measures 9.5 inches.
The difference is:
9.5 - 6.25 = 3.25 inches.
Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.
More can be learned about a dot plot at;
brainly.com/question/24912483
#SPJ1
What is an equivalent way to write the expression without grouping symbols?
7(4−x)
Answers
Answer:
28 - 7x
Step-by-step explanation:
You do the number 7 times each item in the brackets.
7 × 4 = 28
7 × x = 7x
At the end, you join the answers together with the minus '-' symbol.
Answer:
28 -7x
Step-by-step explanation:
7(4−x)
Distribute
7*4 - 7*x
28 -7x
Which equation best represents the curve of best fit for this data?
Answers
Answer:yes
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST THANK YOU
Answers
Answer:
6? I'm not sure honestly
Answer:
the legth is 6 and the weigh is 10
Step-by-step explanation:
because it is twice as big
Select an expression that is equivalent to to 5√6^3 5 √6^4
Answers
Answer:
5400 square root of 6
Step-by-step explanation: