€45,000 is loaned and after a year, 4 months and 15 days €52,500 is received.
Calculate interest as a percentage.
Answers
We calculate the time in days
\(\bf{365 + 120 + 15 = 500 \text{ days}}\)
We calculate the interest
52 500 € - 45 000 € = 7 500 €
We calculate the interest rate:
\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle t = \frac{7\:500}{45\:000 \cdot 500} = \frac{1}{3000}} \end{gathered}$}\)
However, this is the daily rate of interest. To have the annual rate we must multiply by 365. Also, to have the rate as a percentage, we must multiply by 100:
\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle t = \frac{1}{3000} \cdot 365 \cdot 100 = 12.16\% } \end{gathered}$}\)
Thus, the interest rate is 12.16% per year.
Related Questions
An airplane begins a descent to a sea-level airport at an angle of -4° to the horizon. What is the change in elevation after it flies 10,000 feet horizontally toward the runway if the original horizontal distance was 15000 feet ?
Answers
Using the slope concept, it is found that the change in elevation was of -699 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
The vertical change is of h.The horizontal change is of 10,000 feet.The angle is of -4º.Hence:
tan(-4º) = h/10000
h = 10000 x tan(-4º)
h = -699.
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Question:
This is the same dilation that you used in Question 3.
What scale factor was used to create the dilated Triangle M'S'V'?
In your answer, give the scale factor that was used and explain how you calculated it.
Question 3:
Is Triangle M'S'V' a reduction or an enlargement of the original Triangle MSV?
In your answer, specify whether this dilation is a reduction or an enlargement and explain how you know.
Answers
Answer:
22 -3 to y axis of 5
Step-by-step explanation:
got it right during math class
PLEASE ANSWERRRRRRRRRRRRR
How many total complex roots does the function have?
Answers
Total complex roots the function have is 4
To find the complex roots , we need the check the no.of alternative signs in f(x) and also in f(-x)
Given :
f(x) = x^8 + 2x^5 - 3x + 4
The alternative signs in f(x) is from 2nd term to 4th term
i.e. , 2nd term has '+' , 3rd term has '-' and again 4th term has '+'
So, there are 2 alternative sign changing in f(x) ,
that means it has two positive real roots.
f(-x) = (-x)^8 + 2(-x)^5 - 3(-x) + 4
= x^8 -2x^5 + 3x + 4
The alternative signs in f(-x) is from 1st term to 3rd term
i.e. , 1st term has '+' , 2nd term has '-' and again 3rd term has '+'.
So, there are 2 alternative sign changing in f(-x) ,
that means it has two negative real roots.
The degree of f(x) is 8 , that means it has 8 roots
In that 8 roots , 2 are positive real roots and 2 are negative real roots. Thus remaining 4 roots are complex.
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F(x)=x²-1/x+1
F'(x)= Lim h=0 (x+h) -f(x)/h
Answers
Answer:
So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.
Step-by-step explanation:
The derivative of the function F(x) = x^2 - 1/x + 1 can be found by using the limit definition of the derivative. The derivative is the rate of change of the function at a given point and it is calculated as:
F'(x) = Lim h=0 (x + h)^2 - 1/(x + h) + 1 - (x^2 - 1/x + 1)/h
Expanding the expression inside the limit and simplifying, we get:
F'(x) = Lim h=0 2xh + h^2 - (1 - hx)/(x + h)^2
Using L'Hopital's Rule, we get:
F'(x) = Lim h=0 2x + 2h - (x - 1)/(x + h)^2
As h approaches 0, the limit becomes:
F'(x) = 2x + 2(0) - (x - 1)/x^2 = 2x - (x - 1)/x^2
So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.
F(x)= 1/2sin(0/3-90)+1
Answers
The value of f(0) for the given function is 1÷2.
What is Function?In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.
To find the value of f(0) for the given function f(x) = 1/2sin(x÷3-90)+1, we need to substitute 0 for x in the expression for f(x) and simplify:
f(0) = 1÷2sin(x÷3-90)+1
f(0) = 1÷2sin(-90)+1
f(0) = 1÷2(-1)+1 [since sin(-90) = -1]
f(0) = -1÷2 + 1
f(0) = 1÷2
Therefore, the value of f(0) for the given function is 1÷2.
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Complete question:
Find the value of F(0) when F(x)= 1/2sin(0/3-90)+1.
WILL GIVE BRAINLIEST!!
TO CORRECT ANSWER.
You have four credit cards. Each has a balance of $950. 00, but their credit limits are $1,200. 00, $2,200. 00, $2,400. 00, and $3,000. 0. Paying off and closing which card would decrease your debt ratio?
A) $3,000. 00 limit
B) $2,400. 00 limit
C) $2,200. 00 limit
D) $1,200. 00 limit
Answers
Answer:
Im not too sure but it might be d?
Circle P is graphed in the coordinate plane with center (- 4, 7) Circle P contains the point (-1,9 9). What is an equation of circle P?
Answers
Given:
Center of the circle P = (-4,7)
Point on the circle = (-1,9).
To find:
The equation of the circle P.
Solution:
The standard form of a circle is:
\((x-h)^2+(y-k)^2=r^2\) ...(i)
Where, (h,k) is the center and r is the radius of the circle.
Center of the circle is at point (-4,7). So, \(h=-4,k=7\).
The center passes through the point (-1,9). So, the distance between the point (-1,9) and the center (-4,7) is the radius.
Distance formula:
\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Using the distance formula, we get
\(r=\sqrt{(-4-(-1))^2+(7-9)^2}\)
\(r=\sqrt{(-3)^2+(-2)^2}\)
\(r=\sqrt{9+4}\)
\(r=\sqrt{13}\)
Substituting \(h=-4,k=7\) and \(r=\sqrt{13}\) in (i), we get
\((x-(-4))^2+(y-7)^2=(\sqrt{13})^2\)
\((x+4)^2+(y-7)^2=13\)
Therefore, the equation of the circle P is \((x+4)^2+(y-7)^2=13\).
The equation of the circle P is (x +4)² + (y-7)² = 13
What is the standard equation for a circle ?The standard equation for a circle is
(x - h)² +(y-k)² = r²
here the centre of the circle is (h,k) and r is the radius
It is given that
Circle P is graphed in the coordinate plane with centre (- 4, 7)
The equation can be written as
(x +4)² + (y-7)² = r²
It is also given that
Circle P contains the point (-1,9)
Therefore
( -1 +4)² + (9-7)² = r²
3² + 2² = r²
r² = 9+4 = 13
r = √13
Therefore the equation of the circle P is
(x +4)² + (y-7)² = 13
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A pool has drained 1087.5 gallons of water after 1.5 hours at this rate how many gallons of water would have drained from the pool after 10.5 hours?
Will mark brainliest if use step by step
Answers
Answer:
761.25 gallons of water
Step-by-step explanation:
1087.5 gallons = 1.5 hours
362.5 gallons for 0.5 hours
10.5 hours is = 36.25 x 21
10.5 =761.25
Natsumi paints walls for a living. She paints at a constant speed, and then she takes a constant amount of time to clean up. The table compares the total area natsumi paints (in square meters) and the time it takes natsumi to finish painting and cleaning up (in hours). Area (square meters) time (hours) 303030 222 454545 2. 752. 752, point, 75 606060 3. 53. 53, point, 5 how long does it take natsumi to paint 111 square meter?.
Answers
To paint 111 square meters of walls, it takes 6.05 hours. The result is obtained by using the speed of Natsumi to paint per hour.
How to calculate the time to paint the wall?With a constant speed to paint the wall, Natsumi has done painting as the shown data in the table.
Area (square meters) - Time (hours)
30 square meters - 2 hours45 square meters - 2.75 hours60 square meters - 3.5 hoursThis is a problem with comparison. Let's take two samples of the data!
45 - 30 = 15 square meters3.5 - 2.75 = 0.75 hoursFrom the data, we know that for every additional 15 square meters, the time needed increases by 0.75 hours.
Then, we can continue the table.
75 square meters - 4.25 hours90 square meters - 5 hours105 square meters - 5.75 hours111 square meters - x hoursThe speed of Natsumi to paint per hour is
15/0.75 = 20 square meters/hour
The remain area
111 - 105 = 6 square meters
Time needed for the remain area is
6/20 = 0.3 hours
To paint 111 square meters of walls, it takes
x = 5.75 hours + 0.3 hours
x = 6.05 hours
Hence, time needed to finish painting and cleaning up 111 square meters of walls is 6.05 hours.
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Asap I really need help. Is the answer 1.54??!! Please help.
Answers
What is the vertex form of the parabola from daredevil dannys practice jump ?
Answers
Answer:
the vertex form of the parabola from daredevil dannys practice jump is: 47538Step-by-step explanation:
2+2+3+4+45+65+3=47538 jump in the vertex of the jump but then there's a other always 564*56*75+4=47538
The vertex form of Daredevil Danny’s practice jump is y=-32/100(x-25)2+32
But daredevil danny sucked I got a 100 here is the link to my whole worksheet (cant have a link so its tinyurl . com / Danny - Daredevil)
fyi the link is without spaces
Bivariate Probability Distribution
Answers
A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.
A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.
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Complete question:
Describe Bivariate Probability Distribution.
Although U.S. middle school students may lag behind their Japanese counterparts in international algebra tests, the differences disappear on later tests due to the:
Answers
The differences disappear on later tests due to the improved mathematics education and curriculum in the United States.
The initial lag in performance of U.S. middle school students compared to their Japanese counterparts in international algebra tests can be attributed to various factors, including differences in teaching methods, curriculum, and cultural emphasis on mathematics. However, over time, the differences tend to disappear as U.S. students progress through their education and benefit from improved mathematics education and curriculum.
In recent years, the United States has made efforts to enhance its mathematics education system, implementing reforms and adopting new teaching strategies to improve student outcomes. These changes aim to provide students with a deeper understanding of mathematical concepts and problem-solving skills. As a result, U.S. students have shown improvements in their performance on later tests, narrowing the gap with their Japanese peers.
While U.S. middle school students may initially lag behind their Japanese counterparts in international algebra tests, the differences tend to disappear on later tests due to the ongoing efforts to enhance mathematics education in the United States. Continuous improvements in curriculum, teaching methods, and student support contribute to closing the gap and ensuring that U.S. students can compete globally in mathematics proficiency.
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if sin x = 2 9 sinx=29 , x in quadrant i, then find (without finding x). sin(2x)
cos(2x)
tan(2x)
Answers
The value of Sin(2x) ,cos(2x) and tan(2x) are sin(2x) = \(29 \sqrt{\frac{643}{4} }\), cos(2x) = -\(\frac{-99}{2}\), and tan(2x) =-\(\frac{-29}{12}\).. We can use the identity sin(2x) = 2sin(x)cos(x) to find sin(2x).
How to find the value of Sin(2x) ,cos(2x) and tan(2x) ?First, we need to find cos(x) using the Pythagorean identity.
cos(x) = √(1 - sin²(x))
cos(x) = √(1 - (29/2)²)
cos(x) = √(1 - 841/4)
cos(x) = √(643/4)
Now we can find sin(2x):
sin(2x) = 2sin(x)cos(x)
sin(2x) = 2(\(\frac{29}{2}\))(\(\frac{643}{4}\))
sin(2x) = 29\(\frac{643}{4}\)
To find cos(2x), we can use the identity cos(2x) = cos²(x) - sin²(x):
cos(2x) = cos²(x) - sin²(x)
cos(2x) = \(\frac{643}{4}\) - (\(\frac{841}{4}\))
cos(2x) = -\(\frac{198}{4}\)
cos(2x) = -\(\frac{-99}{2}\)
Finally, to find tan(2x), we can use the identity tan(2x) =\(\frac{2tan(x)}{1-tan^{2}(x) }\) :
tan(x) = sin(x)/cos(x) \(\frac{sin(x)}{cos(x)}\)
tan(x) = \(\frac{29}{2} : \frac{\sqrt{643} } }{2}\)
tan(x) = \(\frac{29}{\sqrt{643} }\)
tan²(x) = \((\frac{29}{√643})}{2}\)
tan²(x) = \(\frac{841}{643}\)
tan(2x) = \(\frac{2tan(x)}{1-tan^{2}(x) }\)
tan(2x) = (2(29/√643))/(1 - 841/643) \(\frac{\frac{2(29)}{643} }{1-\frac{841}{643} }\)
tan(2x) = -\(\frac{-29}{12}\)
Therefore, sin(2x) = \(29 \sqrt{\frac{643}{4} }\), cos(2x) = -\(\frac{-99}{2}\), and tan(2x) =-\(\frac{-29}{12}\).
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find the distance,(-1,2)(4,1)
Answers
Answer:
√26
Decimal Form:
5.09901951
Answer:
2√2 I think
Step-by-step explanation:
Plz help will give brainliest
Simplify square root of five times the quantity six minus four square root of three.
Group of answer choices
9
thirty square root of three
six square root of five minus four square root of fifteen
square root of thirty minus twenty square root of three
Answers
Answer:
C
Step-by-step explanation:
Answer:
6√5-4√15
Step-by-step explanation:
√5(6-4√3)
6√5-4√3*√5 division property
6√5-4√3*5 combining like terms
6√5-4√15
if the probability of winning a carnival game was 2/5 and max played it five times, write an expression that would calculate the probability he won the first three games and lost the last two. use exponents to express your final answer, but do not evaluate.
Answers
x′(t)=[−18−2−1]x(t) x′(t)=⎣⎡102211302⎦⎤x(t)
Answers
Given the following differential equation below;x′(t)=[−18−2−1]x(t) x′(t)=⎣⎡102211302⎦⎤x(t)
Find the matrix exponential of the coefficient matrix
Here is the solution to the problemx′(t)=Ax(t) where A = [−18−2−1]. We have to find the matrix exponential of A.eAt=∑k=0∞(At)kk!`where e` is the exponential function.
We know that `A` is a 2x2 matrix so we have to compute `eA` using the Taylor series expansion. We can represent `eA` as a sum of matrices as follows:`eA`= `I` + `A` + `A2`/2! + `A3`/3! + · · · + `Ak`/k! + · · ·where `I` is the identity matrix of the same dimension as `A`.
Therefore we have to compute `A2`, `A3`, and so on to construct `eA`.
First, compute `A2` which is equal to `A` multiplied by `A` or `A2` = `AA`=`[−18−2−1][−18−2−1]=⎡⎣⎢−106−322−523⎤⎦⎥`.
Next, compute `A3` which is equal to `A2` multiplied by `A` or `A3` = `A2A`=`[−106−322−523][−18−2−1]=⎡⎣⎢212452661⎤⎦⎥`.
Thus, `eA` is given by;`eA`= `I` + `A` + `A2`/2! + `A3`/3! + · · ·`=`[1010020001]+[−18−2−1]+[−106−322−523]/2!+[212452661]/3! + · · ·`=`[3020403201]`
Therefore, the answer to the problem is that the matrix exponential of the given coefficient matrix `A` is given by `eA`= `I` + `A` + `A2`/2! + `A3`/3! + · · · which is equal to `[3020403201]`.
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pls help..
FAST!!!!!!!
Answers
Step-by-step explanation:
1/4+5/4 = 6/4
6/4^2 = 6/4*6/4 = 36/16 = 18/8 = 9/4
9/4 + 3/4 = 12/4 = 3
Answer:
= 3
Step-by-step explanation:
(1/4 + 5/4) ^2 + 3/4 = ? --> add 1/4 and 5/4
(6/4) ^2 + 3/4 = ? --> do (6/4) ^2
2.25 + 3/4 = ?
? = 3
What is the equation for a circle centered at the origin (0,0)?
a) r sqt = x sqt + y sqt
b) r sqt =(/x+y) sqt
c) r= /x+y
d) r=x+y
Answers
Answer:
\({ \sf{ \sqrt{r} = \sqrt{(x {}^{2} + {y}^{2} ) } }}\)
Step-by-step explanation:
General equation:
\({ \bf{ {x}^{2} + {y}^{2} + 2ax + 2by + c = 0}} \\ \)
but a and b are 0:
\({ \bf{ {x}^{2} + {y}^{2} = {r}^{2} }} \\ { \bf{ \sqrt{ {x}^{2} + {y}^{2} } = \sqrt{r} }}\)
The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.)
Answers
Answer:
90.91 years
Step-by-step explanation:
If the rate of population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year, increase in yearly population = 1.1/100 × 7,100,000,000
= 1.1 × 71,000,000
= 78,100,000
The amount increases by 78.1million every year.
To know how long it will take the population to double.
double of the initial population = 2×7,100,000,000 = 14,200,000,000
Increment per year = 78,100,000
Time it will take for the population to double = 7,100,000,000/78,100,000
= 90.91
≈ 91
This means it will take about 90.91years for the population to double
an ostrich is 255 cm.Suppose that you want to make a scale drawing of an ostrich. The scale is 30:1. What height will you make the ostrich in your drawing
Answers
Answer:
The height of the drawing should be: 8.5 cm
Step-by-step explanation:
Use the proportion given by the scale in order to find the height "h" that you need to draw:
\(\frac{30}{1} =\frac{255}{h} \\30=\frac{255}{h}\\30\,h=255\\h=\frac{255}{30}\\ h=8.5\,\,cm\)
a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?
Answers
The ladder would reach a distance of 6 feet up the wall.
The Pythagorean theorem.This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:
/hyp/^2 = /opp/^2 + /adj/^2
In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.
So that, let the height of the ladder on the wall be represented by t. Then;
10^2 = t^2 + 8^2
100 = t^2 + 64
t^2 = 100 -64
= 36
t = (36)^1/2
t = 6 feet
Thus the ladder is placed 6 feet up the vertical wall.
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Convert this number expressed in standard form to scientific notation. 28,500,000 1. Move the decimal to create the coefficient: 2.8500000 2. Write in scientific notation: 2.85 × 10x What is the value of x in the scientific notation?
Answers
Answer:
2.85 x 10⁷
Step-by-step explanation:
Answer:
The value of x is 7.
Step-by-step explanation:
Someone please help me!! I will mark as brainliest
Answers
Answer:
if it's not on a test, just guess
Step-by-step explanation:
John’s current salary is $40,000 per year. His annual pay raise is always a percent of his salary. For the foreseeable future, his pay increases will be 4%. Write an explicit formula for the sequence of amounts. Let s represent John's salary and y represent the number of years.
Answers
Answer:johns my fraind
Step-by-step explanation:
Show that for a decaying population dN/dt = -KN (K > 0) the time at which only half of the original population remains (the half-life) is T1/2 = ln 2/K.
Answers
The decay of a population can be modeled using exponential decay, where the rate of decrease is proportional to the current population. The differential equation that describes this process is:
dN/dt = -KN
where N is the population, K is a constant that determines the rate of decay, and the negative sign indicates that the population is decreasing.
To find the half-life of the population, we need to determine the time at which the population is half its original size. Let N0 be the initial population size, and let N(t) be the population size at time t. Then, we have:
N(t) = N0 e^(-Kt)
We want to find the time t1/2 at which N(t1/2) = N0/2. Substituting this into the equation above, we get:
N0/2 = N0 e^(-Kt1/2)
Dividing both sides by N0 and taking the natural logarithm of both sides, we get:
ln(1/2) = -Kt1/2
Solving for t1/2, we get:
t1/2 = ln(2)/K
This is the half-life of the population, which is independent of the initial population size N0. The half-life is inversely proportional to the decay constant K, which makes sense since a larger decay constant means a faster rate of decay and a shorter half-life.
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PLEASE ANSWER BRSINLEST BRAINLEST ANSWER NOW PLEASE DUE!
Stacy likes to do aerobics 10 hours a week to stay in shape. She tracks the amount of time she does aerobics each week relative to her goal.
The table shows the data for the last five weeks.
Week 1 2 3 4 5
Aerobics time (hours) 2.8 −2 1 3/4 0 −3
What is the average aerobics time per week for Stacy relative to her goal number of hours?
Drag a value to the box to complete the statement.
PLease explain it too if you can
Answers
Answer:
-0.09
Step-by-step explanation:
Francis is 9 years older than Vincent. Francis is 17 years old. Let v represent how old Vincent is.
Which equation shows an equality between two different ways of expressing how old Francis is?
A. v + 9 = 17
B. v – 9 = 17
C. v x 9 = 17
D.
Answers
Answer: A
Step-by-step explanation:
Francis = v+9
17 = v +9 so A
Answer:
it would be a
a company that develops over-the-counter medicines is working on a new product that is meant to shorten the length of sore throats. to test their product for effectiveness, they take a random sample of 110 people and record how long it took for their symptoms to completely disappear. the results are in the table below. the company knows that on average (without medication) it takes a sore throat 6 days or less to heal 42% of the time, 7-9 days 31% of the time, 10-12 days 16% of the time, and 13 days or more 11% of the time. can it be concluded at the 0.01 level of significance that the patients who took the medicine healed at a different rate than these percentages? after running a goodness of fit test, can it be concluded that there is a statistically significant difference in duration of a sore throat for those that took the medicine and what is the p-value? 6 days or less 7-9 days 10-12 days 13 or more days duration of sore throat 49 40 12 9 expected counts 46.2 34.1 17.6 12.1
Answers
Yes, it can be concluded at the 0.01 level of significance that the patients who took the medicine healed at a different rate than the percentages given.
After running a goodness of fit test, it can be concluded that there is a statistically significant difference in duration of a sore throat for those that took the medicine.
The p-value for this test is 0.003, which is below the 0.01 threshold for significance.
This means that we can reject the null hypothesis that there is no difference between the expected counts and the actual counts of the medicine. Thus, it can be concluded that the medicine has an effect on the duration of a sore throat.
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