As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is $43,200. (option d).
To calculate this, we can use the formula for future value of an annuity:
FV = PMT x (((1 + r)⁻¹) / r)
where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).
Plugging in the numbers, we get:
FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60
Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.
Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:
$200 x 12 x 18 = $43,200
Hence the correct option is (d).
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there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3 rd row, and so on. if the price per ticket is $32, how much will be the total sales for a one-night concert if all seats are taken?
Answer:
Step-by-step explanation:
To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.
To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:
S = n/2 * (a + l)
where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, we have:
n = 20 (since there are 20 rows)
a = 25 (since there are 25 seats in the first row)
d = 2 (since the difference between each row is 2 seats, the common difference is 2)
We can use d to find the last term as well:
l = a + (n-1)*d
l = 25 + (20-1)*2
l = 25 + 38
l = 63
Now we can plug these values into the formula:
S = 20/2 * (25 + 63)
S = 10 * 88
S = 880
So there are 880 seats in total.
To find the total sales, we just need to multiply by the price per ticket:
total sales = 880 * $32
total sales = $28,160
Therefore, the total sales for a one-night concert with all seats taken would be $28,160.
In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset.
What is data analytics?Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.
The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.
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If G is a group with subgroups A, B of orders m, n, respectively, where m and n are relatively prime, prove that the subset of G, AB = {abla E Ab E B}, has mn distinct elements.
The number of distinct elements of AB = m n.
Given that G is a group with subgroups A and B of orders m and n, respectively, where m and n are prime, we need to prove that the subset of G, AB = {abla E Ab E B}, has m n distinct elements. Step-by-step. Let, G is a group with subgroups A and B of orders m and n, respectively. Since, m and n are relatively prime, then we have gcd(m, n) = 1.By Lagrange's Theorem, the order of any subgroup of G divides the order of G.
Hence, the order of G is equal to the product of the orders of A and B, i.e. |G| = |A| * |B| = m * n Let, a and a' be two distinct elements of A and b and b' be two distinct elements of B. Thus, a and a' generate distinct subgroups of G, i.e. ≠ and b and b' generate distinct subgroups of G, i.e. ≠ .Now, the number of distinct elements of AB = {abla E Ab E B} is equal to |A||B| since any two elements ab and a'b' of AB will be distinct if either a and a' are distinct or b and b' are distinct or both are distinct. Hence, the number of distinct elements of AB = m n.
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#1 Brainlist!
Answer and show steps and I will make you brainlist.
Answer:
Multiplying the second equation by 5, we get:
15x + 20y = 180
Now, we can add this equation to the first equation:
26x = 208
x = 8
Substituting x = 8 in the second equation:
3(8) + 4y = 36
4y = 12
y = 3
Therefore, the solution to the system is (8, 3).
Whats 21 square root of 98 divided by 7 square root of 21
The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407
A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.
Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.
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pls help Are the following lines parallel, perpendicular, or neither?
y = 2/3x − 4
y = −3/2x − 7
Responses
Parallel
Perpendicular
Neither
Answer:
Perpendicular.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form
y = 2/3x - 4 ==> slope = 2/3
y = -3/2x - 7 ==> slope = -3/2
Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1
(2/3) * (-3/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular.
Therefore, the answer is: perpendicular.
Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 12.84
Step-by-step explanation:
if x = 3.2 and y = 6.1 and Z = 0.2
then plug in the numbers
(3.2)(0.2) + (6.1)(2)
0.64 + 12.2 = 12.84
Any variable next to a number means multiplication.
if I was wrong lmk
The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount received by the island = $32,000
The daily receipt of donations = $4,500
Let the number of days = x
Let the funds raised for aid = y
Inequality:y ≤ 32,000 + 4,500x
Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.
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Find the first 4 terms of the sequence represented by the expression 3n + 5
The first 4 terms of the sequence represented by the expression 3n + 5
is 8, 11, 14 and 17.
Sequence:
In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.
According to the Question:
Given, aₙ = (3n+5).
First four terms can be obtained by putting n=1,2,3,4
a 1=(3×1+5) = 8
a 2 =(3×2+5) = 11
a 3 =(3×3+5) = 14
a 4 =(3×4+5) = 17
First 4 terms in the sequence are 8, 11, 14, 17.
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F(x)=-(x+3)(x+10) pls help
Answer:
Zeros: x = -10 and x = -3
Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
Step-by-step explanation:
Pre-SolvingWe are given the following function:
f(x) = -(x+3)(x+10)
We want to find the zeros and the vertex of the parabola.
SolvingZerosThe zeros are the values of the function where f(x) = 0.
So, in order to find the zeros, we can set f(x) = 0.
0 = -(x+3)(x+10)
We can divide both sides by -1, to get:
0 = (x+3)(x+10)
To solve this, we will use zero product property.
Split and solve:
x+3 = 0
x = -3
x+10=0
x = -10
Vertex
Now, to find the vertex, we first get the average of the zeros.
Add the values of the zeros together, then divide by two:
[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]
Now, we plug this in for x to get the y value (found through f(x)) of the vertex.
[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]
So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
Can anyone solve this problem please? Thanks!
The trapezoid has a surface area of 480 square units.
What is the measurement for a trapezoid's area?So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.
We must apply the formula for a trapezoid's area to this issue in order to find a solution:
[tex]A = (1/2) * (a + b) * h[/tex]
where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.
The values for a, b, and h are provided to us, allowing us to change them in the formula:
A = (1/2) * (20 + 60) * 12
A = (1/2) * 80 * 12
A = 480 square units
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I need help with answer this question
Answer:
y = 2x/15 + 6
Step-by-step explanation:
3y/2 = x/5 + 9
3y = (x/5 + 9) (2) The 2 that was dividing goes on to multiply on the other side.
3y= 2x/5 + 18
y = (2x/5 + 18) / 3 The 3 that was multiplying goes on to divide on the other side.
y = 2x/15 + 6
a) if lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, what is lisa's percentile rank? (round your answer to the nearest whole number.)
Lisa's percentile rank is approximately 88%.
Percentile rank is a statistical measure that indicates the percentage of scores that fall below a particular score in a given distribution of data. It is commonly used to describe the relative position of a particular score in a set of scores.
If Lisa's score was 83 and that score was the 29th score from the top in a class of 240 scores, then her percentile rank can be calculated using the following formula:
Percentile Rank = [(Number of scores below Lisa's score) ÷ (Total number of scores)] × 100
Percentile Rank = [(240 - 29) ÷ 240] × 100
Percentile Rank = (211 ÷ 240) × 100
Percentile Rank = 0.8792 × 100
Percentile Rank ≈ 88 (rounded to the nearest whole number)
Therefore, her percentile rank is approximately 88%.
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An electric dipole with its center located at the origin of a Cartesian coordinate system oscillates along the z axis, creating an electromagnetic wave. At a position on the y axis far from the origin, what is the polarization of the wave and which axis are the magnetic (a) The wave is polarized parallel to the a axis and the magnetic field lines are parallel to b The wave is polarized parallel to the z axis and the magnetic field lines are parallel to (c) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (d) The wave is polarized parallel to the y axis and the magnetic field lines are parallel to (e) The wave is polarized parallel to the z axis and the magnetic field lines are parallel to field lines parallel to? the y axis the axis the r axis the z axis the z axis
The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.
The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.
The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.
According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.
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If all other factors are held constant, which of the following results in an increase in the probability of a Type II error? a. The true parameter is farther from the value of the null hypothesis. b. The sample size is increased. c. The significance level is decreased d. The standard error is decreased. e. The probability of a Type II error cannot be increased, only decreased
If all other factors are held constant, then the true parameter is farther from the value of the null hypothesis which is an increase in the probability of a Type II error.The correct option is A.
The true parameter is farther from the value of the null hypothesis.
When the true parameter is farther away from the value of the null hypothesis, it increases the probability of a Type II error. This is because the null hypothesis will have a harder time rejecting the true parameter.
The other factors - increasing sample size, decreasing significance level, and decreasing standard error - all result in a decreased probability of a Type II error.
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Which equation is equivalent to pq=r?
Responses
A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r
The equation is equivalent to pq=r is option (C) q=logR p
To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get
log(pq) = log(r)
Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation
log(p) + log(q) = log(r)
Now, we can compare this expression to each of the answer choices
A) p = logR q
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This is not equivalent to our expression, so A is not the correct answer.
B) p = logQ r
Substituting this into the equation, we get
log(logQ r) + log(q) = log(r)
This is also not equivalent to our expression, so B is not the correct answer.
C) q = logR p
Substituting this into the equation, we get
log(p) + logR(q) = log(r)
This matches our expression, so C is the correct answer.
D) q = logP r
Substituting this into the equation, we get
log(p) + log(q) = log(logP r)
This is not equivalent to our expression, so D is not the correct answer.
Therefore, the correct option is (C) q=logR p
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
What is the difference between the simple and compound interest if you borrow $3,000 at a 6% interest rate for 2 years?
$180.00
$10.00
$6.00
$80.00
Answer:
Correct option is C)
Simple interest =
100
3000×6×2
=360
Compound interest =3000(1+
100
6
)
2
−3000=18×20.6=370.8
∴ Difference is Rs.10.8.
you can convert this value to $$
or simply the answer will be 2. $10
(hob-evzw-zjw) come
Answer:
B is your answer.
10.80$ which you just round to 10. 10 is your answer.
Step-by-step explanation:
For simple interest, the formula is:
Simple Interest = Principal × Rate × Time
For compound interest, the formula is:
Compound Interest = Principal × (1 + Rate)^Time - Principal
Let's calculate the values:
Principal = $3,000
Rate = 6% or 0.06
Time = 2 years
Simple Interest = $3,000 × 0.06 × 2 = $360
To calculate compound interest, we need to use the formula:
Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000
= $3,000 × (1.06)^2 - $3,000
= $3,000 × 1.1236 - $3,000
= $3,370.80 - $3,000
= $370.80
The difference between simple and compound interest is:
$370.80 - $360 = $10.80
Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?
The expected value of cases in which juries got the right decision is 150, and the variance is 375.
1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.
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use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.
To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.
Let's consider a cross section of the solid taken at a distance x from the center of the circle.
Since the cross section is an equilateral triangle, all its sides have the same length.
Let this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:
[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]
Therefore, the area of the cross section at a distance x from the center of the circle is:
[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]
Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):
[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]
To find the limits of integration for y, we need to consider the equation of the circle:
[tex]x^2 + y^2= 3^2[/tex]
Solving for y, we get:
[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]
Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:
[tex]y = 3*\sqrt{3}[/tex]
Substituting this into the integral, we get:
[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]
[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]
Integrating, we get:
[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]
[tex]= 81/2*\sqrt{3}[/tex]
Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units
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PLEASE HELP!!! WILL MARK BRANLIEST!!!
Answer:
The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.
Step-by-step explanation:
qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]
where r = |z| = magnitude of z and theta = arg(z) = argument of z.
Calculate the magnitude of z:
|r| = sqrt((3)^2 + (4)^2) = 5
And the argument of z:
theta = arctan(4/3) = 0.93 radians
Now, find the two square roots of z:
sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]
= +/- 1.58 * [cos(0.47) + i sin(0.47)]
= +/- 1.58 * [0.89 + i*0.46]
Using a calculator, simplify this expression to:
sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8
josh borrowed $250 from his mother to buy an electric scooter. josh will pay her back in 1 year with 3% simple annual interest. how much interest will josh pay?
The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.
What is interest rate?Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.
The interest rate formula is:
Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}
Here,
Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.
The amount of interest that Josh will pay is calculated as:
Interest = Principal Amount × Rate of Interest × Time
Interest = 250 × 3
Therefore, Josh will pay his mother $7.50 in interest for the loan.
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Find the tangential and normal components of the acceleration vector for the curve → r ( t ) = 〈 − 3 t , − 5 t ^ 2 , − 2 t ^ 4 〉 at the point t = 1
The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459
How do we calculate the tangential component?The acceleration vector can be found from the following formula:
[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]
To find the tangential component of the acceleration vector, we first need the velocity vector v(t).
[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]
Next, we need to normalize the velocity vector using the following formula:
[tex]T(t) = v(t) / ||v(t)||,[/tex]
Where ||v(t)|| is the magnitude of the velocity vector.
[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]
Then, the tangential component of a(1) is:
[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]
How do we calculate the normal component?To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.
[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)} = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]
Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:
[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]
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Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded
continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%
compounded monthly. After 14 years, how much more money would Damian have in
his account than Sophie, to the nearest dollar?
Answer:
Step-by-step explanation:
To solve this problem, we need to use the formula for compound interest:
A = P*e^(rt)
where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
For Sophie's account, we have:
P = $92,000
r = 6 1/8% = 0.06125 (as a decimal)
t = 14 years
A = 92000*e^(0.06125*14)
A = $219,499.70 (rounded to the nearest cent)
For Damian's account, we have:
P = $92,000
r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)
t = 14*12 = 168 months
A = 92000*(1+0.005521)^168
A = $288,947.46 (rounded to the nearest cent)
Now we can subtract Sophie's final amount from Damian's final amount to find the difference:
Difference = $288,947.46 - $219,499.70
Difference = $69,447.76
Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.
Using c use the best term to identify the following.
The correct definition for the lines drawn to circle with centre C are:
FA is an secant.CD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.Explain about the circle?A circle is a spherical shape without boundaries or edges.
A radius describes the distance radiating from the centre.The Diameter passes through the centre of the circle in a straight line.The distance travelled through a circle is its circumference.A line that precisely crosses a circle at one point is said to be tangent.The circular region is divided into two sections by a circle's chord. The term "circular segment" refers to each component.The major segment and minor segment are distinguished by the arcs they contain. The major segment contains the minor arc.Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:
FA is an secantCD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.know more about the circle,
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a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is
The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
The probability that there are no repeated digits in a 3-digit pin number is 0.72.
Formula used:
[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]
There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.
Therefore, the total number of possible 3-digit pin numbers with no repeated digits is
[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]
The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].
Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]
Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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The dwarf lantern shark is the smallest shark in the world. At birth, it is about 55 millimeters long. As an adult, it is only 3 times as long. How many centimeters long is an adult dwarf lantern shark? centimeters
Answer: 165
Step-by-step explanation:
55 x 3 = 165