1 point) Consider the linear system -3-21→ a. Find the eigenvalues and eigenvectors for the coefficient matrix. 0 and 42 b. Find the real-valued solution to the initial value problem yj 5y1 +3y2, y2(0) = 15. = Use t as the independent variable in your answers. y (t) = y(t) =
(a) The eigenvalues of the coefficient matrix is [-1,3] and for λ=42, we get the eigenvector [1,5].
Itcan be found by solving the characteristic equation |A-λI|=0, where A is the coefficient matrix and λ is the eigenvalue. Solving for λ, we get λ=0 and λ=42.
o find the eigenvectors, we substitute each eigenvalue into the equation (A-λI)x=0 and solve for x. For λ=0, we get the eigenvector [-1,3]. For λ=42, we get the eigenvector [1,5].
(b) The solution is y(t) = c1e^(0t)[-1,3] + c2e^(42t)[1,5].
To find the real-valued solution to the initial value problem, we can use the eigenvectors and eigenvalues to diagonalize the coefficient matrix. We have A = PDP^-1, where P is the matrix whose columns are the eigenvectors and D is the diagonal matrix with the eigenvalues on the diagonal.
Using the initial condition y2(0) = 15, we can solve for the constants c1 and c2.
The solution is y(t) = c1e^(0t)[-1,3] + c2e^(42t)[1,5]. Solving for c1 and c2 using the initial condition, we get
y(t) = [-15e^(42t) + 3e^(0t), 15e^(42t) + 5e^(0t)].
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Dos veces un número es a lo sumo 24? Ayuda porfavor
After solving the linear inequality, the number can have any value less than or equal to 12 (x ≤ 12). So the maximum possible value of the number is 12.
Let's suppose the number be "x".
From the given statement, we can write the following inequality:
2x ≤ 24
To solve for x, we can divide both sides by 2:
x ≤ 12
Therefore, the number "x" is at most 12. The exact value of "x" could not be found out. As it could be any number less than or equal to 12 that satisfies the inequality.
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The complete question is :
If twice a number is at most 24, find the number.
A company charges $7 for a t-shirt and ships any order for $22. a school principal ordered a number of t-shirts for the school store. the total cost of the order was $1,520. how many t-shirts did the principal order?
Answer:
1,520
Step-by-step explanation:
suppose sat writing scores are normally distributed with a mean of 497 and a standard deviation of 114 . a university plans to admit students whose scores are in the top 30% . what is the minimum score required for admission? round your answer to the nearest whole number, if necessary.
Suppose sat writing scores are normally distributed with a mean of 497 and a standard deviation of 114. A university plans to admit students whose scores are in the top 30%, the minimum score required for admission is 434
How we calculate the minimum score required for admission?Given information:
Mean (μ) = 497Standard Deviation (σ) = 114Probability (p) = 0.30 (for the top 30% of the scores)Let X be the random variable which represents the SAT writing scores. Then X ~ N(497, 114)Now we have to find the minimum score required for admission. We can solve the problem using the standard normal distribution table. Here we need to find the z-score.
The formula for z-score is given below:z = (X - μ) / σ z-score corresponding to the probability (p) can be calculated as:z = ZpWhere Zp is the standard normal variable, which gives the area to the left of the z-score. So, Zp = InvNorm(0.30) = - 0.524For the top 30% of the scores, we have Zp = -0.524. Now the z-score is known. So we can calculate the minimum score required for admission as :X = μ + z * σ = 497 + (-0.524) * 114 = 433.584 ≈ 434The minimum score required for admission is 434.
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for each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. explain your choice. (a) weight of a car and gas mileage there is a positive correlation, because heavier cars tend to get lower gas mileage. there is a positive correlation, because heavier cars tend to get higher gas mileage. there is a negative correlation, because heavier cars tend to get lower gas mileage. there is a negative correlation, because heavier cars tend to get higher gas mileage. there is a correlation close to 0, because there is no reason to believe that weight of a car and gas mileage are related to each other. (b) size and selling price of a house there is a positive correlation, because larger houses tend to be more expensive. there is a positive correlation, because larger houses tend to be less expensive. there is a negative correlation, because larger houses tend to be more expensive. there is a negative correlation, because larger houses tend to be less expensive. there is a correlation close to 0, because there is no reason to believe that size and selling price of a house are related to each other. (c) height and weight there is a positive correlation, because taller people tend to be heavier. there is a positive correlation, because taller people tend to be lighter. there is a negative correlation, because taller people tend to be heavier. there is a negative correlation, because taller people tend to be lighter. there is a correlation close to 0, because there is no reason to believe that height and weight are related to each other. (d) height and number of siblings there is a positive correlation, because taller people tend to have more siblings. there is a positive correlation, because taller people tend to have fewer siblings. there is a negative correlation, because taller people tend to have more siblings. there is a negative correlation, because taller people tend to have fewer siblings. there is a correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
The correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. Explain your choice. (a) Weight of a car and gas mileage: There is a negative correlation, because heavier cars tend to get lower gas mileage. (b) Size and selling price of a house: There is a positive correlation, because larger houses tend to be more expensive. (c) Height and weight: There is a positive correlation, because taller people tend to be heavier. (d) Height and number of siblings: There is a correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
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what are the dimensions of the soup can of greatest volume that can be made with a 150 square inches of tin
The dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
What are the dimensions?The dimensions of the soup can of greatest volume that can be made with 150 square inches of tin are given by the formula [tex]V = \pi r^2h[/tex], where V is the volume of the can, r is the radius of the base, and h is the height of the can. We can solve for the radius and height of the can using the given information.
Let the radius of the base be r and the height of the can be h. Then, the surface area of the can is given by the formula [tex]A = 2\pi rh + 2 \pi r^2[/tex]. We are given that the surface area of the can is 150 square inches, so we can write the equation [tex]2 \pi rh + 2 \pi r^2 = 150[/tex]. We need to find the dimensions of the can that maximize its volume, V. To do this, we can use the formula for the derivative of V with respect to r, which is [tex]dV/dr = 2 \pi rh + \pi r^2 dh/dr[/tex].
Setting this equal to zero and solving for h, we get [tex]h = -2r/3[/tex]. Substituting this into the equation for A, we get the equation [tex]2 \pi r(-2r/3) + 2 \pi r^2 = 150[/tex], which simplifies to [tex]-4 \pi r^2/3 + 2 \pi r^2 = 150[/tex]. Solving for r, we get [tex]r = 5.78[/tex] inches. Substituting this into the equation for h, we get [tex]h = -3.85[/tex] inches.
Since we cannot have a negative height, we must discard this value and take the positive value of h, which is approximately 3.85 inches. Therefore, the dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
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Solve for x, using the tangent lines.
X
46°
× = [ ? ]°
Please answer ASAP, if you could include an explanation that would also help!
Considering the tangent-secant theorem, the value of x is given as follows:
x = 55º.
What is the secant-tangent theorem?The secant-tangent theorem states that when a tangent and a secant line intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.
Hence the equation is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
far arc = 145º.near arc = 35º.Angle = x.Then, applying the theorem, the value of x is given as follows:
x = (145 - 35)/2
x = 55º.
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Find the derivative of the function h(w), below. It may be to your advantage to simplify before differentiating: h(w) = 7w arcsin w h' (w)=
Therefore, the derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7.[/tex]
The derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7[/tex]. To find this, first simplify the original function using the identity arcsin(w) = sin-1(w), then use the chain rule. We get:
h'(w) = 7*sin-1(w) + w*cos(sin-1(w))*7
Since sin-1(w) is the inverse of sin(w), we can substitute w for sin(w). This gives us:
h'(w) = 7*sin-1(w) + w*cos(w)*7[tex]7*sin-1(w) + w*cos(w)*7[/tex]
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Determine all solutions to the equation 2sin2x = 1 − cos x on the interval [0, 2π).
a: x equals pi over 2 comma 2 times pi over 3 comma 4 times pi over 3
b: x equals 0 comma pi over 3 comma 5 times pi over 3
c: x equals pi over 2 comma pi over 3 comma 5 times pi over 3
d: x equals 0 comma 2 times pi over 3 comma 4 times pi over 3
The solution to the given equation 2sin2x = 1 − cos x on the interval [0, 2π) as required is; Choice D; x equals 0 comma 2 times pi over 3 comma 4 times pi over 3.
What are the solutions to the given equations?It follows from the task content that the solutions to the given equation be determined.
On this note, since the give equation is;
2sin²x = 1 − cos x on the interval [0, 2π).
Recall sin²x = 1 − cos²x; therefore we have that;
2 - 2cos²x = 1 - cos x
2cos²x - cos x - 1 = 0.
let y = cos x so that we have;
2y² - y - 1 = 0
x = 1 or x = -1/2.
Therefore; cos x = 1 or cos x = -1/2.
Ultimately, the values of x in the given interval are; 0, 2π/3, 4π/3.
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42 Développer chaque produit, puis réduire les expres-
sions obtenues.
A= 5x-3(x+12)
C = 2x² + x(4x - 5)
B=3x-6+7(2x+4)
D=4x²-x+x(5x-9)
Miguel bought 22 pounds of flour for $12. How many dollars did he pay per pound of flour?
Keilantra and Samantha work at a dry cleaners ironing shirts. Keilantra can iron 30 shirts per hour, and Samantha can iron 15 shirts per hour. Keilantra and Samantha worked a combined 11 hours and ironed 240 shirts. Graphically solve a system of equations in order to determine the number of hours Keilantra worked, x, and the number hours Samantha worked, y.
Answer: Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours
Step-by-step explanation:
We will use the variables x and y the question provides. We know the time worked by each person added together will equal the combined total time. We can write an equation to show this using addition.
x + y = 11 hours
Next, we know that Keilantra ironed 30 per hour, Samantha ironed 15 per hour and that they ironed 240 shirts. We can write another equation to represent this using addition and multiplication.
30x + 15y = 240
Next, we will graph these two equations. See attached. The solution is the point of intersection written as (x, y). This is (5, 6) meaning that Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours.
The sides of a triangle are 5p^2 − q^2 ; 6p^2 − 8 + 5q^2
− 5p^2+ 8 + 9q^2 . Find its perimeter.
Answer:
Step-by-step explanation:
To find the perimeter of the triangle, we need to add the lengths of all three sides. So,
Perimeter = (5p^2 − q^2) + (6p^2 − 8 + 5q^2) + (−5p^2+ 8 + 9q^2)
Simplifying the above expression, we get:
Perimeter = 6p^2 + 14q^2 - 8
Therefore, the perimeter of the triangle is 6p^2 + 14q^2 - 8.
The product of two numbers is 19,200 and HCF is 40 find the LCM
If product of two numbers is 19,200 and HCF is 40, then the LCM is 480
Given that the product of two numbers is 19,200 and the highest common factor (HCF) is 40.
Let us assume the two numbers to be x and y.
Therefore, x × y = 19,200
Also, HCF of x and y is 40.
We can write x = 40a and y = 40b, where a and b are co-prime.
Then, x × y = 40a × 40b = 1600ab = 19,200
Therefore, ab = 12
Now, we need to find the LCM of x and y.
LCM(x, y) = (x × y)/HCF(x, y) --- (1)
Substituting the values of x, y and HCF in the above equation, we get,
LCM(x, y) = (40a × 40b)/40 = 40ab
= 40 × 12 (as ab = 12)
= 480
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Shouldn't be correct answer be option 2?
2+1=3 is the solution to the differentiation equation.
What does a calculus differential equation mean?A differential equation is an equation that explains a function's unknown derivative or derivatives. Take the equation, for example. The expression d y d x = x sin expresses the derivative of an unknown function.
Chain rule evaluation of the derivative on the left hand side yields the following results:
[tex]dxd {( dxdy ) 3 } =0. ⇒3( dxdy ) 2 dx 2 d 2 y =0[/tex]
Because the highest order derivative that appears in the equation is second order, the order of this differential equation is 2.
Its highest order derivative's power is the degree. Degree in this instance is 1.
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If you have the following data about
a box of bouncy balls, about how
many bouncy balls are estimated to
be in the box?
Mass of Bouncy Balls + Box = 17,342
grams
Mass of 45 Balls = 505 grams
Mass of Box ONLY = 429 grams
Approximately, how many bouncy
balls are in the box?
Bouncy Balls in Box
Enter
there are approximately 1506 bouncy balls in the box.
What is mass ?
Mass is a physical property of matter, which refers to the amount of substance present in an object. It is typically measured in units of grams or kilograms, and can be thought of as a measure of the object's inertia or resistance to acceleration. Mass is often used interchangeably with weight in everyday language, but they are technically different concepts. Weight is a measure of the force of gravity acting on an object, and varies depending on the object's location in the gravitational field.
According to the question:
First, we need to find the mass of the bouncy balls in the box by subtracting the mass of the box only from the mass of the box and bouncy balls.
Mass of bouncy balls in box = Mass of box and bouncy balls - Mass of box only
Mass of bouncy balls in box = 17,342 - 429
Mass of bouncy balls in box = 16,913 grams
Next, we need to find the mass of one bouncy ball by dividing the mass of 45 balls by 45.
Mass of one bouncy ball = Mass of 45 balls / 45
Mass of one bouncy ball = 505 / 45
Mass of one bouncy ball = 11.222 grams
Finally, we can estimate the number of bouncy balls in the box by dividing the mass of the bouncy balls in the box by the mass of one bouncy ball.
Number of bouncy balls in box = Mass of bouncy balls in box / Mass of one bouncy ball
Number of bouncy balls in box = 16,913 / 11.222
Number of bouncy balls in box ≈ 1506
Therefore, there are approximately 1506 bouncy balls in the box.
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during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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A car is purchased for £8500
In its first year, the value of the car will depreciate
by 10%.
Each year after that, the value of the car will
depreciate by 5%.
What is the value of the car at the end of 3 years?
Answer:
£ 6904.13
Step-by-step explanation:
the final value is given by
[tex]8500 (0.90)[/tex] at the final of the first year
then you need to add (0.95) twice (one from second and one from third year)
Notice if the depreciation is 5% the final value is 0.95 of the initial value at the beginning of the year
finally:
[tex]8500 (0.90) (0.95)^2 = 6904.13[/tex] (rounded to nearest cent!)
Rewrite the following in the form log(c).
log(15) -log(3)
The logarithmic expression given as log(15) -log(3) when simplified is log(5).
How to rewrite the logarithmic expressionGiven that
log(15) -log(3)
The form is
log(c)
Using the logarithmic identity that states log(a) - log(b) = log(a/b), we can rewrite the given expression as:
log(15) - log(3) = log(15/3)
And simplifying the expression inside the logarithm, we get:
log(15) - log(3) = log(5)
So the given expression, log(15) - log(3), can be written in the form log(c) as log(5).
This means that the logarithm of 5 is equivalent to the difference between the logarithms of 15 and 3.
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A team of 3 identical robotic lawn mowers can cut 15.6 acres of grass in a garden for
a single battery charge. How many acres can cut a team of 5 identical robotic lawn
mowers for a single battery charge?
Answer:
HOPE THIS HELPS
Step-by-step explanation:
Midsize robot lawnmowers cut up to half an acre or about 22,000 square feet. Large robot lawnmowers can cut up to 1 acre, or 43,560 square feet, or more
Answer: 26 acres
Step-by-step explanation:
26 acres
Divided 15.6/3 to get unit rate, then multiply by 5 to get answer.
If the block suppported by the pulley system has a weight of 20N what is the input force(effort) on the rope?(Assume the pulley system is frictionless ).
Answer: The input force (effort) on the rope is 20 N.
Step-by-step explanation:
In a frictionless pulley system, the tension in the rope is constant throughout. Therefore, the force applied to the rope on one side of the pulley system is equal to the force exerted on the other side of the system.
In this problem, we know that the weight of the block is 20 N. This means that there is a force of 20 N acting downwards on one side of the pulley system.
Since the pulley system is frictionless, the tension in the rope is also 20 N. Therefore, the force applied to the rope on the other side of the pulley system (i.e., the input force or effort) must also be 20 N in order to balance the weight of the block.
So the input force (effort) on the rope is also 20 N.
when the expression -3x^5+6x^2-9x^3-x is written with terms in descending order (from highest to lowest), which list represents the coefficients of the term?
a. 6, -9, -3, -1
b. -3, 6, -9, -1
c. 1, 6, -9, -3
d. -3, -9, 6, -1
Due tomorrow!!! Pls help
Answer:
Step-by-step explanation:
[tex]P=\frac{\theta}{360} \pi d[/tex]
[tex]= \frac{120}{360} \pi \times 10[/tex] (diameter = 2 x radius)
[tex]=\frac{10\pi}{3}[/tex]
[tex]=10.5cm[/tex]
The new town jewelry company purchased 501 carat diamond rings for $125,000 based on the following information find the selling price purring to the nearest cent
The selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
To find the selling price of the 501-carat diamond rings, we need to use the information given about the cost of the purchase and the markup percentage.
Let's assume the markup percentage is m. Then, the selling price S can be calculated as:
S = C * (1 + m/100)
where C is the cost of the purchase ($125,000 in this case).
If the markup percentage is not given, we can use another piece of information to calculate it. For example, if we know that the company wants to earn a profit of P dollars on the sale, we can set the equation:
S - C = P
and solve for the markup percentage:
m = (P/C) * 100
Assuming a markup percentage of 35%, we can calculate the selling price as:
S = 125,000 * (1 + 35/100)
S ≈ $168,750.00
Therefore, the selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
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Two percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 95% detection rate for carriers and a 3% detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual. A. What is the probability that both tests yield the same result?
The probability that both tests yield the same result is 7.7%.
Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-
0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-
[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]
hence, the probability of the two tests yield the same result is 7.7%.
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the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
The probability that a person in a certain town has brown eyes is 2 out of 5. A survey of 450 people from that same town was taken. How many people would be expected to have
brown eyes?
A. 45
B. 90
C. 180
D. 225
From the given information provided, the number of people having brown eyes in town is 180.
If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.
To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:
(2/5) = (x/450)
where x is the number of people expected to have brown eyes.
Solving for x, we can cross-multiply:
5x = 2 × 450
5x = 900
x = 180
Therefore, the expected number of people in the survey who would have brown eyes is 180.
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Make a number line and mark the points that represent the following values of x. x²=16
please show with numberline for brainliest :) please help my class is tomorrow and im finishing homework
Answer:
See below.
Step-by-step explanation:
Here's a number line showing the points that represent the values of x that satisfy the equation x² = 16
|---------------------------|---------------------------|
-4 0 4
On this number line, I have marked the points -4, 4, which are the two solutions to the equation x² = 16. These values of x make the left-hand side of the equation equal to 16.
wright fraction as a decimal and as a percent. Divide decimals to the hundredths place and write any remainders as fractions
1/3
The value of 1/3 in decimals is 0.33 and the value in percent is 33 1/3%.
How to covert a fraction into decimal?We must divide a fraction to get it to a decimal form. To convert a fraction to decimal form, divide the fraction's numerator by its denominator. If the division is not accurate, we can round the decimal to the closest desired place value or divide again until the appropriate number of decimal places is obtained.
The given number is 1/3.
Using division the value of 1/3 = 0.33.
Now, to calculate the percentage we multiply the value by 100:
0.33 x 100 = 33.33% = 33 1/3%.
Hence, the value of 1/3 in decimals is 0.33 and the value in percent is 33 1/3%.
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Katherine is going to invest in an account paying an interest rate of 3.8%
compounded daily. How much would Katherine need to invest, to the nearest dollar,
for the value of the account to reach $1,180 in 17 years?
619 would Katherine need to invest, to the nearest dollar, for the value of the account.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount every year. The interest rate for the loan is denoted by this proportion.
x. (1 + 3.8%/365)¹⁷ˣ³⁶⁵ = 1180
= x * ( 1 + 38/365000)¹⁷ˣ³⁶⁵ = 1180
= x * ( 1 + 19/182500)¹⁷ˣ³⁶⁵ = 1180
= common denominator and write the numerators above common denominator x * ( 182500 + 19/182500)⁶²⁰⁵ = 1180
= x * (182519/182500)⁶²⁰⁵ = 1180
Divide both sides of the equation by the coefficient of variable
x = 1180/(182519/182500)⁶²⁰⁵
x = 1180 * 182500⁶²⁰⁵/182519⁶²⁰⁵
x = 619
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