grade 12 calculus Special Derivatives
4. You've invested $525 into a savings account that pays 4% annual interest compounded monthly. At what point will your investment be earning $200 a month? (C /3 A 2T (2)
Answers
It will take approximately 16.08 years for the investment to be earning $200 per month.
What is the method to calculate compound interest?Use the formula of compound interest to calculate the answer:
\(A = P(1 + r/n)^{nt\)
Where:
A = final amount.
P = principal amount.
r = annual interest rate.
n = number of times the total interest per year.
t = number of years.
We can first solve for the time it takes for the investment to reach a value of $200 per month, which is equivalent to $2400 per year:
$2400 = \($525(1 + 0.04/12)^{12t\)
4.5714 = \((1 + 0.04/12)^{12t\)
ln(4.5714) = ln[\((1 + 0.04/12)^{12t\)]
t = [ln(4.5714)]/(12 ln(1 + 0.04/12))
t ≈ 16.08 years
Therefore, it will take approximately 16.08 years for the investment to be earning $200 per month.
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Related Questions
An t-shirt was originally priced at 45, but was placed on sale for 10% off the original price. If a sales tax of 8% was added on to the sale price what did the t-shirt cost at the register, including the tax?
Answers
Answer:
$43.74
Step-by-step explanation:
10% off of 45 is $40.50
$40.50 with a sales tax of 8% is $43.74 (+$3.24)
I hope this is helpful :>
Caroline is considering two video game rental plans. Plan A can be modeled with the equation C = 2n, and Plan B can be modeled with the equation C = n + 6, where C represents the cost in dollars and n represents the number of games rented each month. Which statement would justify selecting Plan A instead of selecting Plan B?
Answers
Options
A. Caroline rents exactly 7 games each month.
B. Caroline rents exactly 6 games each month.
C. Caroline rents 6 or more games each month.
D. Caroline rents from 1 to 5 games each month.
Answer:
D. Caroline rents from 1 to 5 games each month.
Step-by-step explanation:
Given
Plan A:
\(C = 2n\)
Plan B:
\(C = n + 6\)
Required
Which options justifies A over B
The solution to this question is option (d).
In option d, n = 1,2,3,4,5
When any of the values of n is substituted in plan A and B, respectively; the cost of plan A is cheaper than plan B.
This is not so, for other options (A - C)
To show:
Substitute 1 for n in A and B
Plan A:
\(C = 2n\) \(= 2 * 1 = 2\)
Plan B:
\(C = n + 6\) \(= 1 + 6 = 7\)
Substitute 5 for n in A and B
Plan A:
\(C = 2n\) \(= 2 * 5 = 10\)
Plan B:
\(C = n + 6\) \(= 5 + 6 = 11\)
See that A < B
suppose the probability of a painter selling his art at his first art show is 16.26% . if he painted 26 pieces of art, what is the probability that he sells more than 2 of them? round your answer to four decimal places.
Answers
The probability that the painter sells more than 2 pieces of art is 0.8251.
What is the probability?The probability of the painter selling his art is P(S) = 16.26/100 = 0.1626
Since the painter painted 26 pieces of art, the number of trials, n = 26.
Let X be the random variable representing the number of pieces the painter sells. We need to find the probability that he sells more than 2 of them.
P(X > 2) = P(X = 3) + P(X = 4) + ... + P(X = 26)
Using the binomial probability formula, we have
P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ⁻ˣ⁾
where ⁿCₓ = n!/x!(n - x)!
p = probability of success
q = probability of failure = 1 - p
We can substitute n, p, and q to find P(X = x) for each x, and then add them up.
\(P(X > 2) = P(X = 3) + P(X = 4) + ... + P(X = 26)\\P(X > 2) = 1 - P(X = 0) - P(X = 1) - P(X = 2)\\P(X > 2) = 1 - P(X < 2)\\P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\\P(X \leq 2) = 0.0047104 + 0.0379791 + 0.1321676\\P(X \leq 2) = 0.1748571\\P(X > 2) = 1 - 0.1748571\\P(X > 2) = 0.8251429\)
Rounding this to four decimal places, we get: P(X > 2) ≈ 0.8251. Therefore, the probability that the painter sells more than 2 pieces of art is 0.8251.
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17. The points (0, b) and
(a, b) are graphed on a coordinate plane. What
is the distance between the points? Explain.
Answers
Therefore, the distance between the two points is simply the difference in their x-coordinates, this makes sense since both points lie on the same horizontal line, and so the vertical distance between them is zero.
What is distance?Distance is a numerical measurement of how far apart two objects or points are from each other. It is a scalar quantity that is usually expressed in units of length, such as meters, kilometers, miles, or feet. Distance is often used in physics, mathematics, and engineering to describe the spatial separation between two objects or points. It is also used in everyday language to describe how far away something is, such as the distance between two cities or the distance from a person's house to their workplace.
By the question.
The distance between two points on a coordinate plane can be found using the distance formula:
distance =\(\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-x_{1}^{2} ) }\)
In this case, the two points are (0, b) and (a, b). We can substitute these values into the distance formula:
distance = \(\sqrt{(a-0)^{2}+(b-b)^{2} }\)
distance = \(\sqrt{a^{2}+0 }\)
distance = a
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a statistical technique that would allow a researcher to cluster is called ____
Answers
Answer:
Factor analysis
Step-by-step explanation:
A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion.
The statistical technique that would allow a researcher to cluster is called Cluster Analysis. It is a statistical technique that enables researchers to cluster groups of objects that share certain similarities based on their attributes, observations, or characteristics.What is cluster analysis?Cluster analysis is a data-driven technique that helps in grouping similar objects based on the data provided. It is often used in many fields, including data mining, machine learning, and bioinformatics. Cluster analysis is used to find the natural groupings of objects, which have similar attributes or characteristics. For instance, it is used to group customers based on their behavior, cluster genetic markers in DNA, cluster galaxies in the universe, and much more. Cluster analysis helps in analyzing large datasets by grouping similar objects into smaller groups that are easier to understand.The Cluster analysis technique is a valuable tool in statistical analysis and it is used in different fields like market research, bioinformatics, genetics, etc. It is a method of statistical data analysis that helps researchers identify groups or clusters of data. It is a commonly used technique that is used to identify natural patterns within large datasets.
Two college students are standing in a room of the room could fit around ten students in the room how many does it have when thirty walk in?
Answers
10?and the rest of the 22 can't fit i think
2340, 3455,675,960 1350 . 1 . () () , ()
Answers
a) 8780
b) i) 1159 ii) 1990
c) 9611
a) The total number of workers at the beginning is 2340 + 3455 + 675 + 960 + 1350 = 8780 workers.
b)
i) The first two companies laid off 1 worker for every 5 workers, so for the first company (2340 workers) this means 2340/5 = 468 workers lost their job. For the second company (3455 workers) this means 3455/5 = 691 workers lost their job.
In total, 468 + 691 = 1159 workers lost their job.
ii) The other three companies recruited 2 new workers for every 3, so for the third company (675 workers) this means 6752/3 = 450 new workers were recruited. For the fourth company (960 workers) this means 9602/3 = 640 new workers were recruited. For the fifth company (1350 workers) this means 1350×(2/3) = 900 new workers were recruited.
In total, 450 + 640 + 900 = 1990 new workers were recruited.
c) The total number of workers finally is 8780 - 1159 + 1990 = 9611 workers.
The complete question is -
Five companies employed 2340, 3455, 675, 960, and 1350 workers. The first two companies laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for every 3.
a) What was the total number of workers at the beginning?
b) How many people: i) Lost job ii) Got a job?
c) What was the total number of workers finally?
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
One day at 3:00 a.m., the temperature was –13°F
in Kodiak, Alaska. At 10:00 a.m., the temperature was 22°F. What was the average change in temperature per hour?
Answers
Step-by-step explanation:
13 + 22 = 35 degree change. 10-3 = 7. 35/7 = 5 degrees per hour.
-0.8x+40-8x-35 need help asap
Answers
Answer:
-8.8x + 5
Step-by-step explanation:
Equation:
-0.8x + 40 - 8x - 35
-0.8x -8x + 5
-8.8x + 5
*This answer might be from a misunderstanding*
Answer:
-8.8x + 5
Step-by-step explanation:
See attached picture!!
Hope this helps!!
Robin can clean 727272 rooms in 666 days.
How many rooms can Robin clean in 999 days?
Answers
Answer:
1,090,908
Find the half of 727272,then when you find the half,add it to 727272
>727,272÷2=363,636
>727,272+363,636=1,090,908
Step-by-step explanation:
Answer:
1,090,908
Step-by-step explanation:
727,272 divided by 666=
1,092
999 - 666=
333
1,092 x 333=
363,636
727,272 + 363,636=
1,090,908
Summer Storme is analyzing an investment. The expected one-year return on the investment is 20 percent. The probability distribution of possible returns is approximately normal with a standard deviation of 15 percent. a. What are the chances that the investment will result in a negative return? b. What is the probability that the return will be greater than 10 percent? 20 percent? 30 percent? 40 percent? 50 percent?
Answers
Answer:
suchh harddb
Step-by-step explanation:
According to a study, 45% of Americans have type O blood. If a random number generator produces three-digit values from 000 to 999, which values would represent those having type O blood?
(1) between 000 and 045, inclusive
(2) between 000 and 444, inclusive
(3) between 000 and 449, inclusive
(4) between 000 and 450, inclusive
Answers
The values that would represent those having type O blood are between 000 and 449, inclusive (Option 3).
The given study states that 45% of Americans have type O blood. This means that out of 100 individuals, 45 would have type O blood. When using a random number generator producing three-digit values from 000 to 999, we can determine which values represent those having type O blood.
Since 45% of Americans have type O blood, it implies that the probability of an individual having type O blood is 0.45. The random number generator produces equally likely values from 000 to 999, where each value has a probability of 1/1000.
To find the values representing those having type O blood, we need to consider the range of values that corresponds to the 45% probability. The inclusive range between 000 and 449 (Option 3) represents the values that have a probability less than or equal to 0.45. Therefore, the values between 000 and 449, inclusive, would represent those having type O blood.
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out of 340 racers who started the marathon, 301 completed the race, 28 gave up, and 11 were disqualified. what percentage did not complete the marathon? round your answer to the nearest tenth of a percent.
Answers
Approximately 11.5% of the racers did not complete the marathon.
Step-by-step explanation:
To find the percentage of racers who did not complete the marathon, we need to add the number of racers who gave up and were disqualified:
28 + 11 = 39
So, out of the 340 racers who started the marathon, 39 did not complete it.
To find the percentage, we can use the formula:
percentage = (part/whole) x 100
In this case, the "part" is 39 and the "whole" is 340.
percentage = (39/340) x 100
percentage = 11.5
Rounding to the nearest tenth of a percent, we get:
percentage = 11.5%
Therefore, approximately 11.5% of the racers did not complete the marathon.
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rack heights vary from a few rack units to many rack units. the most common rack heights are 24u and 42u. how tall is a 24u rack?
Answers
A 24U rack is approximately 44.5 inches (113.03 cm) tall.
What is Expression in math ?
An expression is made up of one or more integers or variables, as well as one or more operations.
The "U" unit in a rack height refers to unit of measurement for the height of equipment in a standard 19-inch server rack.
1U is equal to 1.75 inches (4.45 cm)
so, 24U is equal to 24 * 1.75 inches = 42 inches (106.68 cm).
However, in practice, the height of a 24U rack is typically slightly taller to account for the height of the mounting brackets and other hardware.
Hence, A 24U rack is approximately 44.5 inches (113.03 cm) tall.
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I am a three digit number the digits total is nine when added together all of my digits are odd numbers the hundreds digit is less than the tens digit but more than the ones digit what is the mystery number
Answers
Answer:
The mystery number is 351.
Step-by-step explanation:
Let the numbers be xyz.
The digits total is 9; That is, x+y+z = 9All of the digits are odd numbers; That is, the digits will be 1,3,5,7 and / or 9.Since the digits total is 9, then '9' cannot be among since summing it with other digit(s) will be greater than 9. Hence, '9' cannot be among the digits.
Also, '7' cannot be among the three digit number, since adding 7 to any two of the remaining three digits (that is, 1, 3, and / or 5) will make the total greater than 9. Hence, '7' also cannot be among the digits.
The remaining digits are 1,3 and 5; which all sum up to 9. That 1 + 3 + 5 = 9.
The hundreds digit is less than the tens digit, that is, x is less than y. But it (hundreds digit) is more than the ones digit, that is, x is more than z. Hence, x is 3, since '3' is the only number which is less than one of the numbers and as well more than one of the numbers. If x is less than y, then y is 5 and then z is 1. Hence, xyz becomes 351.Hence the mystery number is 351.
Help asap plz! Ron has a budget of $1,500 to paint the walls in his office building. One gallon of paint will cost 200 square feet and will cost $29.98, including tax. Paint can be bought in only 1 gallon cans. Additional painting supplies will cost $49 , including tax what is the maximum number of square feet Ron can paint if he stays within budget when he buys the paint and supplies?
Answers
The maximum number of square feet Ron can paint if he stays within budget when he buys the paint and supplies is 22.7.
Calculation of the maximum no of squaresSince the remaining would be
= $1,500 - $200
= $1,300
Now per unit cost should be like
= \(1,300 \div 29.98\)
= 533
Now then the maximum no of squares should be
\(= 533 \div 49\)
= 22.7
Hence, The maximum number of square feet Ron can paint if he stays within budget when he buys the paint and supplies is 22.7.
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Multiply and rewrite the system: 16푥−10푦=10 −8푥−6푦=6 solving for elimination
Answers
Please read directions do number 1
Answers
=20m^2
Triangle:1/2*10*5
=25m^2
The lines r: x+3=0 and s: y-2=0 intersect at a point P.
a) Determine the coordinates of point P.
b)What is the distance of P from the origin?
Answers
Answer:
(-3,2)
Step-by-step explanation:
The given Equations of lines are ,
\(\implies x + 3 = 0 \)
\(\implies y -2 = 0 \)
On plotting the graph of the given two equations we will get that the two lines will intersect each other at a point and that point will be the solution of the system of equation. On drawing a graph ,
On looking at graph , Point P will be ,
\(\implies Solution = P(-3,2) \)
On a math test a student, Jake, has to identify all the coefficients and constants of the expression 9y+n+5. Jake says that 9 is a coefficient and 5 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?
Answers
However, Jake made an error when he said that 9 is a coefficient. In this expression, 9 is not a coefficient, but rather the coefficient of the variable y. The coefficient of a variable is a number that is multiplied by the variable, so it must be a number that is not associated with any other variables. In the expression 9y+n+5, the number 9 is associated with the variable y, so it is the coefficient of y, not a coefficient on its own.
333 years ago, the residents of Planet XXX found a black hole leading to another galaxy. Since then, they have been leaving Planet XXX at a rate of 120120120 residents per year.
The following equation describes this situation:
\\3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.
(Choice B)
B
360360360 residents left Planet XXX each year.
(Choice C)
C
None of the above
Answers
Answer:
Choice A
Step-by-step explanation:
It said it was right in Khan lol :)
Anyone who helps w this page gets brainliest
Answers
The required coordinates of point Q are (-46/13, 50/13) lie on line PR.
What is a line?A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
Let the coordinate of Q be (x, y)
Given PR with P(-6, -6) and R(-2, 10), it is on PR such that the ratio of PO to PR is 5:8,
Apply the Section formula.
x = mx₂ + nx₁ / m + n ; y = my₂ + ny₁ / m + n
m = 5 and n = 8
Put the values in the section formula along with points.
x = 5 × -6 + 8×-2 / 5 + 8 ; y = -6×5 + 8 × 10 / 8 + 5
x = -46/13 ; y = 50/13
Thus, the required coordinates of point Q is (-46/13, 50/13) lie on line PR.
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calculate the volume of a cylinder with a radius of 3cm and a height of 7.5 cm. use 3.14 for pi
Answers
Answer: 141.3
Step-by-step explanation:
This is 9th-grade math
Answers
An inequality for the graph above is y ≤ -3x + 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 6)/(3 - 0)
Slope (m) = -9/3
Slope (m) = -3
At data point (0, 6) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = -3(x - 0)
y = -3x + 6
y ≤ -3x + 6 (since the solid line is shaded below).
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PLS HELP ASAP...A triangle has side lengths of (10m-5) centimeters, (6m-2) centimeters, and (8n+4) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
1. 12n+16m−7
2. 16m+8n−3
3. 12n+5m+4
4. 12n+9m
Answers
Answer:
perimeter = 10m - 5 + 6m - 2 + 8n + 4
= 16m -7 + 8n + 4
16m + 8n -3
option 2
The expression represents the perimeter of the triangle will be 16m + 8n - 3. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The sum of all the sides of the triangle will be known as the perimeter of the triangle.
A triangle has side lengths of (10m - 5) centimeters, (6m - 2) centimeters, and (8n + 4) centimeters.
The expression represents the perimeter of the triangle will be
P = (10m - 5) + (8n + 4) + (6m - 2)
P = 16m + 8n - 3
The expression represents the perimeter of the triangle will be 16m + 8n - 3. Then the correct option is B.
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Rebecca is given two triangles, ABC and DEF. At first glance, she thinks
that the triangles are congruent. How can she use what she knows about
rotations and triangle congruence to prove the triangle congruence? I need it fast plz
Answers
Answer: Side Angle Side
Answer:
B.
She can rotate triangle DEF 180and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.
Step-by-step explanation:
2. Alexander and Anne had $3,000 to invest to help towards their son's college expenses. They wanted to
see how long it would take to grow this money into $5,000 if they invested it in an account earning 5%
interest. To figure this out, they used the formula FV = PV(1 + r), where FV represents the future
value, PV represents the present value, r represents the interest rate, and t represents the number of
years. How many months would it take for the account to have $5,000 in it? Round your answer to a
whole month, HINT: 1 year = 12 months
Answers
It will take t=18 months to take for the account to have $5000 in it.
What is meant by interest rate?The proportion charged for borrowing money by the lender is known as the interest rate. An actual cost of borrowing should be reflected by the APR, or annual percentage rate. Along with interest rate, the APR calculation also accounts for fees and discount points. In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate (called the principal sum).
An annual interest rate is a rate that is calculated over a year. Over different time frames, such a month, other interest rates are in effect.
FV=PV\((1+r)^{t}\)
Given,
FV=5000
PV=3000
r=5%
r=5/100
r=0.05
5000=3000\((1+0.05)^{t}\)
\((1+0.05)^{t}\)=1.667
t log(1.05)=log(1.667)
t=log(1.667)-log(0.05)
t=1.5 years
t=1.5×12
t=18 months
Therefore, It will take t=18 months to take for the account to have $5000 in it.
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control limits are based on multiples of the process standard deviation. question 11 options: true false
Answers
Control limits are based on multiples of the sample statistic's standard deviation, hence the assertion is false that "control limits are based on multiples of the process standard deviation".
A control chart is made up of many different parts. There are two control limitations. The top dashed line represents the upper control limit (UCL), and the bottom dashed line represents the lower control limit (LCL).The solid middle line denotes the statistic's average for the plot.
The horizontal lines known as control limits in a control chart show the upper and lower limits of the acceptable range of results for a process. When plotted data goes over a control limit, a process is out of control and requires management action. The control limits are defined as three standard deviations on either side of the mean.
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Please answer ASAP!!
how do you find the volume of this slanted cylinder?
Answers
Given:
Height - 8 ydRadius - 3 ydTo find the volume of an oblique cylinder, use the formula V = πr²h where,
V - Volumeπ - Pi (3.14 is the value)R - RadiusH - HeightWe can substitute the given values to the formula.
V = πr²hV = (3.14)(3²)(8)V = (3.14)(9)(8)V = (3.14)(72)V = 226.08Answer:
The volume of the oblique cylinder is 226.08 cm³.Wxndy~~
Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: [asy] size(4cm); draw((0,10)--(12,10)--(12,0)--(0,0)--cycle,black+3); draw((0,7)--(12,7)); draw((0,4)--(12,4)); draw((4,10)--(4,4)); draw((8,10)--(8,4)); draw((3,4)--(3,0)); draw((6,4)--(6,0)); draw((9,4)--(9,0)); label("$\ell$",(6,10),N); draw((5.3,10+.9)--(0,10+.9),EndArrow(TeXHead)); draw((6.7,10+.9)--(12,10+.9),EndArrow(TeXHead)); label("$w$",(12,5),E); draw((12.9,5.7)--(12.9,10),EndArrow(TeXHead)); draw((12.9,4.3)--(12.9,0),EndArrow(TeXHead)); [/asy] The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is $\ell$ inches long by $w$ inches wide, where $\ell\ge w$ (as shown above). What is the ratio $\ell:w$ in simplified form?
Answers
Answer:
can you show a picture or a more simplified version?
The ratio of the length and the width of the bigger rectangle, l:w = 6:5.
What are ratios?The ratio is the relational representation of two familiar quantities.
The ratio of two quantities a and b is written as a:b, read as "a is to b", and functions as a/b.
How to solve the question?In the question, we are asked to determine the ratio l:w, given that each of the smaller rectangles is congruent to each other.
We assume the length of each smaller rectangle to be x, and its width to be w.
Now, from the diagram, we can say that 3x = 4y, as the length of the bigger rectangle is covered by 3 lengths of smaller rectangles or 4 widths of the smaller rectangles.
From this, we can say that x = (4/3)y.
Now, the length of the bigger rectangle l covers 3 lengths of the smaller rectangles.
So, we can say that l = 3x.
Also, the width of the bigger rectangle w covers 2 widths and 1 length of the smaller rectangles.
So, we can say that w = 2y + x.
Thus, the ratio l:w = l/w, can be written as:
3x/(2y + x).
Substituting x = (4/3)y, we get:
= 3(4/3)y/(2y + (4/3)y)
= 4y/((10/3)y)
= 12/10 = 6/5 = 6:5.
Thus, the ratio of the length and the width of the bigger rectangle, l:w = 6:5.
The provided question is inappropriate.
The correct question is:
"Ten boxes are packed tightly in a crate. From above, the packed crate looks like the attachment provided.
The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is l inches long by w inches wide, where l ≥ w (as shown above). What is the ratio l:w in simplified form?"
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![Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: [asy] size(4cm);](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/YXoFltGMOF3JO2HWNueYUPpfTxHYKyoG.jpeg)