A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Since both old bills and new bills will come into the banks while the new currency is gradually introduced, we will need to solve a differential equation to track the amount of new currency in circulation at a given time. Let x (t) denote the amount of new currency, in billions of $, in circulation after t days. We've shown that new currency is introduced at the rate 10 - x (t) / 10 0.05, which simplifies to 0.005 (10 - x (t)). This justifies that x (t) satisfies the differential equation dx / dt = 0.005 (10 - x). (a) Solve the differential equation to find x (t). (b) At what time t will new bills make up 90% of the currency in circulation?
(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))
To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:
dx / (10 - x) = 0.005 dt
Integrating both sides:
-ln|10 - x| = 0.005t + C
where C is the constant of integration. Solving for x:
|10 - x| = e^(-0.005t - C)
Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:
C = -ln(10)
Therefore, the solution to the differential equation is:
x(t) = 10 - e^(-0.005t - ln(10))
Simplifying:
x(t) = 10(1 - e^(-0.005t))
(b) New bills will make up 90% of the currency in circulation after approximately 461 days.
We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):
9 = 10(1 - e^(-0.005t))
Dividing both sides by 10 and taking the natural logarithm:
ln(0.1) = -0.005t
Solving for t:
t = 200 ln(10) = 460.51
Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.
For more questions like Equation click the link below:
https://brainly.com/question/16663279
#SPJ11
Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
Benito made a wooden box to grow herbs on his patio. The box is 16 inches wide, 12 inches tall, and 28 inches long. He plans to fill the box exactly two-thirds full with potting soil. What volume of soil does Benito need? I know how to do this I just need to know if the two-thirds part is trying to throw me off
To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.
The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.
The volume of the box can be calculated by multiplying the width, height, and length:
16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.
Two-thirds of this volume can be found by multiplying the total volume by 2/3:
5,376 cubic inches x 2/3 = 3,584 cubic inches.
Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.
Learn more about volume here: brainly.com/question/1578538
#SPJ4
Expand and simplify (3x - 1)(9x² + 3x + 1)
Identify and name congruent triangles
The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.
What is Congruence ?Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.
According to question:a) ∠GIH is corresponding to ∠LJK
GH = KL
∠IHG = ∠KLJ
By ASA congruence rule
ΔGIH ≅ ΔJKL
b) AB = DF
AC = DE
BC = EF
By SSS congruence rule
ΔABC ≅ ΔDEF
c) Two Corresponding sides are congruent, which is not enough to make them congruent.
So, it is not necessary congruent.
To know more about Congruent visit:
brainly.com/question/12413243
#SPJ1
Write the percent as a decimal.
95%
Answer:
9.5 decimal
espero y te ayude
please help ill give brainliest to the first correct answer.
i really dont understand this question
The required time is mathematically given as
t-150 minutes.
This is further explained below.
What is the time?We know that the volume of the prism is given by.
[tex]\text{Volume}=\text{(Base Area)}\times\text{height}[/tex]
[tex]\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2[/tex]
[tex]\text{Base Area}=2\ \text{m}^2[/tex]
Now,
[tex]\text{Volume}=2\times1=2\ \text{m}^3[/tex]
Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.
Because of this, the volume increases.
[tex]\text{Volume}=2\times0.8=1.6\ \text{m}^3[/tex]
Now, the rate of emptying the tank is,
[tex]=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}[/tex]
In conclusion, We also know that,
$$
[tex]\text{time}=\dfrac{\text{volume}}{\text{rate}}[/tex]
[tex]\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}[/tex]
Therefore, Colin must wait for the pond to drain for a total of 150 minutes.
Read more about the time
https://brainly.com/question/28050940
hihihihihihihihihihihihihihihihihi
Write the linear equation of a line going through (-2,7) with a y-intercept of -3.
Answer:
y = -5x - 3
Step-by-step explanation:
A linear equation is y = mx + b
m = the slope
b = y-intercept
We know
Points (-2,7) (0,-3)
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 10 and the x increase by 2, so the slope is
m = -10/2 = -5
Y-intercept is located at (0, -3)
So, the equation is y = -5x - 3
How much greater is 0.05723 then 0.005?
0.05723 is 0.05223 greater than 0.005.
What is greater than?"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".
What is lesser than?"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".
In the given question,
To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223
Therefore, 0.05723 is 0.05223 greater than 0.005.
To know more about comparison, visit:
https://brainly.com/question/29163855
#SPJ1
A line passes through the point (-4,4) and has a slope of -3
there are black, blue, and white marbles in a bag. the probability of choosing a black marble is 0.36 . the probability of choosing a black and then a white marble is 0.27 . to the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?
There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.
Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.
Using the same method, we can say that the probability of choosing a white marble after drawing a black one is [tex]\frac{0.27}{0.36}= 0.75[/tex] (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.
Therefore, the probability of the second marble being white if the first marble chosen is black is
Learn more about Probability here:
brainly.com/question/13604758
#SPJ11
Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
2x+2y= 24
x=3y
What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS
Answer:
x + y = 12
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
2x + 2y =24
x = 3y
We want to find the value of x + y.
SolvingWe first need to find the values of x and y, which we will do by solving the system.
We can solve this system by substitution.
We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.
This gives us:
2(3y) + 2y = 24
Multiply.
6y + 2y = 24
Add the terms together.
8y = 24
Divide both sides by 8.
y = 3
We found the y value, now let's find the value of x.
The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.
Substitute 3 as y.
x = 3(3) = 9
The value of x is 9.
So, to find x+y, we substitute the values we found.
x + y = 3 + 9 = 12
Suppose you have a certain amount of money in a savings account that earns compound monthly interest, and you want to calculate the amount that you will have after a specific number of months. The formula is as follows: f=p*(1 + i)^t f is the future value of the account after the specified time period. p is the present value of the account. i is the monthly interest rate. t is the number of months. Write a program that takes the account's present value, monthly interest rate, and the number of months that the money will be left in the account as three inputs from the user. The program should pass these values to a function that returns the future value of the account, after the specified number of months. the program should print the account's future value. SAMPLE RUN #2: python3 FutureValue.py None Show Highlighted Only Interactive Session Hide Invisibles Highlight: Enter current bank. balance: 35.72 Enter.interest rate:0 Enter the amount of time that passes: 100 35.7
Answer:
Step-by-step explanation:
Hi there! Just multiply by x and find the value of f=p. Good luck!
Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. After how many seconds will Jada pass Elena?
Jada overtakes Elena after 7.5 seconds.
The set of equations that best captures the scenario is =y=15+20x.
Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x
y1 = 15 + 20x
Jada's distance from the origin at time x is determined similarly by:
y2 = 22x
Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.
y1 = y2
With the formulas for y1 and y2 substituted, we obtain:
15 + 20x = 22x
When we simplify this equation, we obtain:
2x = 15
x = 7.5
Jada therefore overtakes Elena after 7.5 seconds.
To know more about set of equations, click the below link
https://brainly.com/question/90105
#SPJ4
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
to know more about statistics, visit;
https://brainly.com/question/29093686
#SPJ1
The Book Nook makes four times as much revenue on paperback books as on hardcover books. If last month's sales totaled $124,300, how much was sold of each type book?
The revenue from hardcover books was $24,860 and the revenue from paperback books was $99,440.
How much was sold of each type book?Let's assume the revenue from hardcover books as "x" dollars.
Then, the revenue from paperback books will be 4 times the revenue from hardcover books, i.e., 4x dollars.
The total revenue is given as $124,300, so we can set up the following equation:
x + 4x = 124300
Simplifying the above equation, we get:
5x = 124300
x = 24860
Therefore, the revenue from hardcover books was $24,860 and the revenue from paperback books was 4 times that amount, i.e., $99,440.
Read more about sales at
https://brainly.com/question/9437038
#SPJ1
from a survey involving 1,000 university students, a market research company found that 750 students owned laptops, 450 owned cars, and 350 owned cars and laptops. if a university student is selected at random, what is the (empirical) probability that
The probability that a student selected randomly owns either a laptop or a car is 85%.
Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?
For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:
P(A) = probability of owning a laptop = 750/1000 = 0.75
P(B) = probability of owning a car = 450/1000 = 0.45
P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35
Now, substituting values into the formula:
P(A∪B) = 0.75 + 0.45 - 0.35= 0.85
Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.
To learn more about probability refer :
https://brainly.com/question/22544647
#SPJ11
*CORRECT AND FASTEST ANSWER GETS BRAINLIEST!!!*
A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
List all prime numbers in the 2023 February calendar
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)
Answer:
3x -y = -6
Step-by-step explanation:
You want the equation of the line with intercepts (0, 6) and (-2, 0).
Intercept formThe equation of the line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
For the given intercepts, the equation is ...
x/(-2) +y/6 = 1
Standard formIn standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:
3x -y = -6
__
Additional comment
You can get slope-intercept form by solving for y, or you can recognize that ...
slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3
Since you already know the y-intercept, you can write the slope-intercept equation as ...
y = 3x +6
There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.
Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
Learn more about Regression
brainly.com/question/30011167
#SPJ11
Q3 NEED HELP PLEASE HELP
Answer:
C. Rachel is saving $5 per week.
Step-by-step explanation:
The initial savings are $10, as it is the y-intercept.
And to obtain the slope we can take 2 points from the graph.
A(0,10)
B(1,15)
m=(y2-y1)/ (x2-x1)
m=(15-10)/ (1-0)
m= 5/1
m= 5 savings in dollars per (1) week
mr warren the physical education teacher has 7 boxes of helmets each box has h helmets write an expression to represent the total number of helmets
Answer:
t = 7h
Step-by-step explanation:
lets have the total amount of helmets as t and helmets per box as h. Then it is t = 7h
Megan's standard pay is £17.70 per hour. She gets paid 1.5 times this rate for working overtime. How much will Megan get paid for working 11 hours of overtime? Give your answer to the nearest pound.
Answer:
Step-by-step explanation:
Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]
[tex]= 17.70 \times \frac{3}{2}[/tex]
[tex]=\frac{53.10}{2}[/tex]
[tex]=\pounds26.55[/tex]
Pay [tex]=11*26.55=\pounds 292.05[/tex] (I assume you can use a calculator for this)
Solution: [tex]\pounds 292[/tex]
The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
Graph the line with slope -1/5 and y-intercept of -5
A graph of the line with slope -1/5 and y-intercept of -5 is shown in the image attached below.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial value.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = -x/5 - 5
In this exercise, we would use an online graphing calculator to plot the above equation as shown in the graph attached below.
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ1
BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
Read more about breakeven
brainly.com/question/15281855
#SPJ1
