C) The Central Limit Theorem states that the sample mean's sampling distribution is very similar to a normal distribution.
The central limit theorem is founded on what?The idea of a sampling distribution, which is the probability distribution of a statistic for a large number of samples taken from a population, is the foundation of the central limit theorem.
What are the central limit theorem's two main tenets?To summarize, the following two distributions are linked by the central limit theorem: The population's distribution of the variable. The testing dissemination of the mean.
What is As far as possible Hypothesis?The CLT is a statistical theory that holds that the mean of all samples taken from a population with a finite level of variance will roughly match the population mean if a sufficient number of samples are taken from that population.
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Full Question = The sampling distribution of the sample mean is close to the normal distribution
A. only if the parent population is unimodal, not badly skewed, and does not have outliers.
B. no matter what the distribution of the parent population of what the value of n.
C. if n is large, no matter what the distribution of the parent population.
D. if the standard deviation of the parent population is known.
E. only if both n is large and parent population has a normal distribution.
Suppose That A Vector Y Is Orthogonal To Vectors U And V. Show That Y Is Orthogonal To The Vector U + V.
A vector Y is orthogonal to vectors U and V, so Y is orthogonal to the vector (U+V).
In the given question,
Suppose that a vector Y is Orthogonal to vectors U And V.
We have to show that Y is orthogonal to the vector U + V.
As to vectors are orthogonal if and only if their dot product is zero.
So Y∙U = 0 and Y∙V = 0.
To prove that Y is orthogonal to the vector(U+V), we have to show that Y∙(U+V) = 0.
As dot product is distributive. Now
Y∙(U+V) = Y∙U + Y∙V
As Y∙U = 0 and Y∙V = 0. So
Y∙(U+V) = 0 + 0
Y∙(U+V) = 0
Hence, Y is orthogonal to the vector (U+V).
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a wooden cube, whose edges are one centimeter long, rests on a horizontal surface. illuminated by a point source of light that is x x centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. the area of the shadow, which does not include the area beneath the cube, is 48 48 square centimeters. find the greatest integer that does not exceed 1000 x . 1000x. (1996,
The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.
What is the area?
The area of a shadow is the amount of surface area that is covered by the shadow. It is the two-dimensional projection of an object onto a surface.
Let the distance between the point source of light and the horizontal surface be h. Since the shadow is a projection of the cube onto the horizontal surface, the shadow has the same proportions as the cube. Therefore, the height of the shadow is h/x times the length of the shadow, which is 48x. The area of the shadow is then:
48x * h/x = 48h
Since the area of the shadow is 48x^2, we have:
48h = 48x^2
h = x^2
We are asked to find the greatest integer that does not exceed 1000x. Substituting the expression for h into the equation, we get:
1000x = 1000x^2
x = 1/1000
Hence, The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.
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Let W Span {V1. every vector in W Vp Show that if x is orthogonal to each Vj, for ] < j < P,then xis orthogonal to'
Assume that the basis for a subspace V in Rn is v1,..., vp. Show that a vector in Rn is orthogonal to a vector in V if and only if it is orthogonal to every vector v1,..., vp.
What is a orthogonal vector?An orthogonal vector , In mathematics, orthogonality is an extension of perpendicularity, particularly in vector calculus and linear algebra. Basic geometry dictates that two lines or line segments are only perpendicular if they form a straight angle.
It makes sense to think of vectors as arrows, such as R 2 and R 3, when discussing orthogonal vectors in an inner product space (a real or complex vector space with a notion of vector multiplication).
There are inner product spaces where it makes no sense to conceive of vectors as arrows, yet one still needs to have some understanding of what it means when discussing orthogonal vs. perpendicular.
Hence, It is orthogonal to every vector in vector space, or o V. Every vector in V is a linear combination of these vectors since v1,..., vp serves as the basis for V.
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Consider the matrices
A= 4 7 , B= -2 3 . C= 3 4 -1, and D= 6
-3 8 0 5 2
-5 -2
What are the dimensions of the product matrix of two of these matrices?
Drag the matrix dimensions to each box to match the product.
BD 2 x 1
CA 3 x 3
DC 2 x 3
The dimensions of the product matrix of two of these matrices is BD = 2 * 1 , CA = 1 * 3 and DC = 2 * 3 .
Given :
The dimension of BD :
B dimensions = ( 2 * 2 )
D dimensions = ( 2 * 1 )
Product of BD dimensions = Numbers of rows of B * number of columns in D
= 2 * 1
The dimension of CA :
C dimensions = ( 1 * 3 )
A dimensions = ( 3 * 3 )
Product of CA dimensions = Numbers of rows of C * number of columns in A
= 1 * 3
The dimension of DC :
D dimensions = ( 2 * 1 )
C dimensions = ( 1 * 3 )
Product of CA dimensions = Numbers of rows of D * number of columns in A
= 2 * 3
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c.96 test to see if there is evidence that the lie detector says a person is lying more than 50% of the time, regardless of what the person reads.
It is not possible for a lie detector, or any other type of technology, to accurately determine whether a person is lying more than 50% of the time. Lie detectors, also known as polygraph machines, measure physiological responses such as changes in heart rate, blood pressure, and respiration to determine if a person is telling the truth or not. However, these responses can be affected by many factors, such as anxiety or stress, and are not always reliable indicators of deception. In addition, people can learn how to manipulate their physiological responses in order to deceive the polygraph machine. Therefore, it is not accurate to say that a lie detector can determine whether a person is lying more than 50% of the time
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Sorry I’m slow I need my mathematicians. If I make $11 and hour work 9 hours Sunday-Friday and get paid bi weekly how much would my check be?
Your's check would be $198 for two weeks with 9 hours of work from Sunday-Friday.
Word problems:In a word problem, the mathematical operations are written in text format. To solve such a problem, the text should be understood and simple basic arithmetic operations are applied.
Calculation:It is given that,
He/She makes $11 for 1 hour and works for 9 hours from Sunday to Friday.
For 9 hours of work, he/she gets, $11 × 9 = $99
Then, for two weeks, the payment = $99 + $99 = $198
So, he gets a biweekly check with $198.
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For a company picnic, Kylie ordered a box of fresh-baked gingerbread cookies and sugar
cookies. She got 60 cookies in all. 54 of the cookies were gingerbread. What percentage of
the cookies were gingerbread?
Write your answer using a percent sign (%).
Use the diagram to answer the questions.
What is the value of x?
x =
What is the measure of angle B?
B =
What is the measure of the exterior angle ACD?
ACD =
The value of x is 21
The measure of angle B is 28°
The measure of exterior angle ACD is 63°
Calculating the measure of anglesFrom the question, we are to determine the measure of the angles.
From the given diagram, we can write that
35° + (x + 7)° = 3x° (Exterior angle theorem)
Solve for x in the equation
35° + (x + 7)° = 3x°
35° + x° + 7° = 3x°
35° + 7° = 3x° - x°
42° = 2x°
Divide both sides by 2
42°/2 = 2x°/2
21° = x°
Therefore,
x = 21
The measure of angle B is
Measure of angle B = (x + 7)°
Measure of angle B = (21 + 7)°
Measure of angle B = 28°
The measure of exterior angle ACD
Measure of exterior angle ACD = 3x°
Measure of exterior angle ACD = 3(21)°
Measure of exterior angle ACD = 63°'
Hence, the measure of the exterior angle is 63°
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Please read both questions first, and guess whether the two answers would be the same, except one is positive and one is negative. Check whether you guessed correctly after you have done the calculations.
a) A company has increased its sales team from 40 people to 50 people. What is the percent change?
b) A company has reduced its management team from 50 people
to 40 people, what is the percent change?
PLEASE HELP
Answer:
Step-by-step explanation:
Write 2 different equations you could use to solve for side m?
2. The Equation for value x is, x= 13 sin 52.
3. The value of m, m = l cos <N
4. The length of Hypotenuse is 7.92 m.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Given:
2. P= x
H= 13 cm
Using Trigonometry
sin 52 = P/ H
sin 52 = x/ 13
x= 13 sin 52.
3. P = n, B= m and H= l
Using Trigonometry
cos <N= B/H
cos <N= m / l
m = l cos <N
and, using Pythagoras theorem
H² = P² + B²
l²= m² + n²
m= √( l² - n²)
4. P = 7m
angle= 62
Using Trigonometry
sin 62 = 7/ H
0.88295 = 7/ H
H = 7/ 0.88295
H = 7.92 m
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Graph: y > 6
Is (-2,7) a solution? yes or no
Is ( 2,6) a solution? yes or no
Answer:(-2,7) is a yes
(2,6) is no pls mark brainiest
Step-by-step explanation: did a question like this and i mastered this subject
-10 (x+3) - 6x + 5
O -41x
0 -16x - 25
O 3x + 5
O 4x + 35
A photograph is 8 centimeters wide. After Kari enlarges the photograph, it is 3 times as wide as the original. How wide is the photograph in millimeters?
answer: should be
8 *3 =24 centimeters
1cm = 10mm
24cm = 240mm
the photograph is 240 mm
The width of the photograph in millimeters is 240 mm.
How to illustrate the scale?It should be noted that a scale factor simply shows the relationship between a shape abd the original value given.
In this situation, the photograph is 8 centimeters wide and after Kari enlarges the photograph, it is 3 times as wide as the original.
The photograph in millimeters will be:
= 8 × 3 × 10
= 240 millimeters.
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cash received from long-term notes payable $ 67,000 purchase of investments 16,900 cash dividends paid 54,200 interest paid 27,100 compute cash flows from financing activities using the above company information. (amounts to be deducted should be indicated by a minus sign.)
cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300
With regards to the above, information, the amount of cash dividends paid that should be recorded is computed as;
= Cash dividends payable at the beginning of the year + Cash dividends declared for the year - Cash dividends payable at the end of the year
= $27,100 + $67,000 - $54,200
= $ 148 300
Therefore, cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300
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the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago. if the sample has a mass of today, find the initial mass of the sample. round your answer to two decimal places.
The initial mass of the sample is =2.39 kg
Radioactivity=Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.Radioactive describes something that exhibits or is caused by radioactivity. If something is radioactive, it emits radiation, which usually takes the form of electromagnetic waves or fast-moving elementary particles, such as protons or neutrons.
M(t)= Mo E =2.546 M(3)=2.54-02(3)
=2.54e -0.06
=2.39 kg (initial mass of the sample)
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In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at $220 before tax.
How much sales tax does Yuki pay for her handbag purchase?
Answer:
$18.15 of taxes
Step-by-step explanation:
based on the givens: 220 (4.6% + 3.65% )
calculate the sum or difference: 220 x 0.0825
calculate the product: 18.15
what should i write blank can someone help pls
The blanks are completed as follows:
s/(s² - 18s + 81) = s/(s - 9)².F(s) = s/(s - 9)².Then the inverse Laplace transform is given as follows:
f(t) = e^(9t) + 9te^(9t).
How to obtain the inverse Laplace transform?The function for this problem is given as follows:
F(s) = s/(s² - 18s + 81).
Completing the squares at the denominator, we have that:
F(s) = s/(s - 9)².
Applying partial fraction decomposition, the function can be defined as follows:
s/(s - 9)² = A/(s - 9) + B/(s - 9)²
Expanding the right side, we have that:
s/(s - 9)² = [A(s - 9) + B]/(s - 9)²
Hence:
As - 9A + B = s.
Then the system for the coefficients is given as follows:
A = 1.-9A + B = 10-> B = 9A -> B = 9.Thus the function in the transform domain is of:
F(s) = 1/(s - 9) + 9/(s - 9)².
Applying the inverse Laplace transform, the function in the time domain is given as follows:
f(t) = e^(9t) + 9te^(9t).
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Which statements are true regarding the sequence below? Check all that apply.
20.4, 24, 244.
It can be represented using the formula f(x + 1) = (f(x)) when f(1) = 10.
It can be represented using the formula x=4
It can be represented using the formula fox)=
The domain of the sequence is all real numbers.
The range of the sequence is all natural numbers.
The statements that are true regarding the sequence below are
It can be represented using the formula f(x) = 10/3 (6/5)ˣ⁻¹The domain of the sequence is all real numbers.How to find the true statementsThe given sequence include 10/3, 4, 24/5, 244/25
Applying the formula f(x) = 10/3 (6/5)ˣ⁻¹ to it
for x = 1, f(x) = 10/3 (6/5)¹⁻¹ = 10/3
for x = 2, f(x) = 10/3 (6/5)²⁻¹ = 4
for x = 3, f(x) = 10/3 (6/5)³⁻¹ = 24/5
This shows that the formula works for it hence a correct statement
Real numbers include all positive and negative numbers, fractions and decimals alike and the domain are natural numbers which are part of real numbers
The range are also all real numbers and this go beyond natural numbers
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Please help!! Solve x^2 = 36 for x. I think it may be A not so sure tho.
Answer: You are correct
Step-by-step explanation:
se green's theorem to evaluate the line integral along the given positively oriented curve. c 5y 7e x dx 10x 9 cos(y2) dy c is the boundary of the region enclosed by the parabolas y
By using Green's Theorem, it can be calculated that
[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] = [tex]\frac{5}{3}[/tex]
What is Green's Theorem?
Green's Theorem gives a relationship between a line integral along a closed curve C and surface integral around plane region D bounded by C
By Green's Theorem,
[tex]\int_c Pdx+ Qdy = \int\int_D (\frac{\partial P}{\partial y} - \frac{\partial Q}{\partial x})dxdy[/tex]
To evaluate [tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] using Green's Theorem,
Region is between the parabola [tex]y = x^2[/tex] and [tex]x = y^2[/tex]
To find point of intersection,
[tex]x = y^2\\x = (x^2)^2\\x = x^4\\x^4 - x = 0\\x(x^3 - 1) = 0\\x = 0 \ or \ x^3 - 1 = 0\\x = 0 \ or \ x^3 = 1\\x = 0 \ or \ x = 1[/tex]
Along y- axis the limit of integration is from y = [tex]x^2[/tex] to y = [tex]\sqrt{x}[/tex]
P = [tex]5y + 7e^x[/tex]
[tex]\frac{\partial P}{\partial y}[/tex] = 5
Q = [tex]10x + 9(cos(y^2))[/tex]
[tex]\frac{\partial Q}{\partial x}[/tex] = 10
By Green's Theorem,
[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex]
= [tex]\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}(10 -5)dxdy\\\\\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}5dxdy\\\\\int_{x = 0}^1 5(\sqrt{x} - x^2)\\\\5[(\frac{2}{3})x^{\frac{3}{2}} - \frac{x^3}{3}]_0^1\\\\5(\frac{2}{3} -\frac{1}{3})\\\\\frac{5}{3}[/tex]
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use implicit differentiation to find the derivative dy dx. b. find the slope of the curve at the given point. cos(y)
The slope of the curve at the given point is approximately -28
What is the derivative of a function?
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
To find the derivative of y with respect to x using implicit differentiation, we need to take the derivative of both sides of the equation cos(y) = 7x^4 - 7.
On the left side of the equation, we can use the chain rule to find the derivative of cos(y) with respect to x:
d/dx[cos(y)] = -sin(y) * dy/dx
On the right side of the equation, we can use the power rule to find the derivative of 7x^4 - 7 with respect to x:
[tex]d/dx[7x^4 - 7] = 28x^3[/tex]
Substituting these expressions into the original equation, we get:
[tex]-sin(y) * dy/dx = 28x^3[/tex]
To solve for dy/dx, we can divide both sides of the equation by -sin(y):
[tex]dy/dx = -(28x^3)/sin(y)[/tex]
To find the slope of the curve at the given point, we need to substitute the values of x and y into the expression for dy/dx.
The slope at (1, π/2). would be
slope = -(28((1)^3))/sin(π/2) = -28.
Hence, the slope of the curve at the given point is approximately -28.
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HELP THERS MORE OF THESE
Answer:
y=5x
Step-by-step explanation:
intercept is 0
Slope is 5
the post offices calculate shipping costs based on the weight of the item in addition to a fee. The cost to ship a 2 pound item is 6.09, while the cost to ship a 7 pound item is
8.84. Find the rate of change of the cost with respect to the weight of the item
The rate of change of the cost with respect to the weight of the item is equal to 0.55.
What is the rate of change?Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the shipping costs (y) with respect to the weight of the item (x), with the following data points (2, 7) and (6.09, 8.84):
Rate of change, m = (8.84 - 6.09)/(7 - 2)
Rate of change, m = 2.75/5
Rate of change, m = 0.55.
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A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1 If you make this wager very many times, what will be the mean amount you win? (a) About - $1, because you will lose most of the tim
(b) About $9 because you win $10 but lose only $1 . (c) About -$10.15 that is, on average you lose about 15 cents. (d) About $0.77 that is, on average you win about 77 cents. (e) About $0 because the random draw gives you a fair bet.
About -$10.15 that is, on average you lose about 15 cents.
Using the principle of discrete probability, the expected value, which is a measure of the mean amount after many plays is - 2/13
Calculating the required probabilities :
P(winning) = P(drawing an Ace) = 4/52 = 1/13
Hence, P(losing) = 1 - 1/13 = 12/13
X :____ 10 _____ - 1
P(X) : _ 1/13_____ 12/13
The expected value :
E(X) = 10 × (1/13) + - 1(12/13)
E(X) = 10/13 - 12/13
E(X) = - 2/13
Hence, the measure of the mean amount is -2/13.
The victory value is $10, and the loss value is $-1.
Out of a total of 52 cards, this deck has 4 aces.
The probability can then be defined as the ratio of the number of desirable outcomes to the number of possible outcomes.
P(win) = number of favorable outcome/number of the possible outcome
= 4/52
= 1/13
P(loss) = number of favorable outcome/number of the possible outcome
= 48/52
= 12/13
Then we have
$10x1/13 + (-1)x12/13
= 10/13-12/13
= -2/13 dollars
= -$0.15
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Please help:
89345+7899-5/2*8=?
Answer:
97224
Step-by-step explanation:
BODMAS
B ×
O ×
Division (5/2)
Multiplication (5/2*8)
Addition (89345+7899)
S ×
Do it in this order
Evaluate the line integral, where C is the given plane curve. 1649 (x®y + sin(x)) dy, C is the arc of the parabola y = x2 from (0, 0) to (1, x2)
Line integral will be ∫c(x²y + sinx )dy = 1/3π²×π³ + 2π
Given:
C is the arc of parabola y = x² from (0,0) to (π,π²)
Let x be the parameter ; since the parabola is given as function of x
the parametric equations are
x=x,y=x², for 0≤x≤π
By using concept
∫c(x²y + sinx)dy = [tex]\int\limits^0_x {(x^2(x^2) + sinx} \, ).2xdx[/tex]
by applying the limits of integration we get ,
= 2 [ π².π³/6 + [ -πcosπ + sinπ - (0 + sin0)] ]
by calculating,
= 2 ( π².π³/6 + π )
= 1/3 π².π³ + 2π
Thus,
∫c(x²y + sinx )dy = 1/3π²×π³ + 2π
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A population numbers 12,000 organisms initially and grows by 17.5% each year.
Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a â‹… b t where
P =
A population numbers 12,000 organisms initially and grows by 17.5% each year. The growth function of the population is P = 12,000 x 1.175^t
An exponential growth function can be written as:
P = A (1 + r)ⁿ
Where:
P = quantity after n periods
n = number of periods
r = growth rate per period
A = initial quantity
In the given problem, the period is the number of years t
A = 12,000
r = 17.5% = 0.175
Hence, the growth function:
P = 12,000 (1 + 0.175)^t
P = 12,000 x 1.175^t
Your question is incomplete, but most probably your question was:
A population numbers 12,000 organisms initially and grows by 17.5% each year. Suppose P represents population, and t the number of years of growth, write the function in terms of t.
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assume that x is uniformly distributed on [0,3]. using the central limit theorem, find the shortest interval (around hn) that has 95% probability of containing the true value of h. (such an interval is known as 95% confidence interval for h).
The probability density function (pdf) for the uniform distribution has the basic formula: f(x) = 1/ (B-A) for A x B.
A continuous probability distribution, the uniform distribution is concerned with equally likely outcomes. It is referred to as having a rectangular distribution on the interval [a,b] or having a uniform distribution for the continuous random variable X. Above is a representation of the probability density function of a continuous uniform distribution. The probability of drawing a heart, club, diamond, or spade is equally likely; hence, the area under the curve is 1, which makes sense given that the total of all probabilities in a probability distribution is 1.
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How do I solve this problem?
5 + 2/3 ( 2p - 6 ) = 9
Answer:
p = 6
Step-by-step explanation:
5 + 2/3 (2p - 6) = 9
5 + 4/3p - 4 = 9
1 + 4/3p = 9
4/3p = 8
p = 6
Answer:
p= 6
Step-by-step explanation:
Solve for p:
(2 (2 p - 6))/3 + 5 = 9
Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:
(15/3 + (2 (2 p - 6))/3) = 9
15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:
((2 (2 p - 6) + 15)/3) = 9
2 (2 p - 6) = 4 p - 12:
((4 p - 12) + 15)/3 = 9
Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):
(4 p + (15 - 12))/3 = 9
15 - 12 = 3:
(4 p + 3)/3 = 9
Multiply both sides of (4 p + 3)/3 = 9 by 3:
(3 (4 p + 3))/3 = 3×9
(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:
(4 p + 3) = 3×9
3×9 = 27:
4 p + 3 = 27
Subtract 3 from both sides:
4 p + (3 - 3) = 27 - 3
3 - 3 = 0:
4 p = 27 - 3
27 - 3 = 24:
4 p = 24
Divide both sides of 4 p = 24 by 4:
(4 p)/4 = 24/4
4/4 = 1:
p = 24/4
The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:
Answer: p = 6
Part A:
Describe two possible financial goals for which you may require $12,000. Classify each as a want or need. Do research to ensure that amount is enough for your goal.
Part B:
Create and describe three possible investments to reach your goal within five (5) years. Investment 1 is a simple interest investment with 3% annual interest. How much would you need to invest at the beginning? Investment 2 is a compound interest investment, with 3% annual interest compounded monthly. How much would you need to invest at the beginning?
Investment 3 is a regular deposit in an account that earns 3% compound interest, compounded once per year. How much do you need to deposit, and how often will you deposit it, to reach it Part C:
Calculate and describe the total interest earned on each of your three investments. Explain your thinking and show your work.
Part A: Two possible financial goals that may require $12,000 is to save for home ownership and education.
Part B: Three possible initial investments to reach the goal of having a future value of $12,000 in 5 years are:
Investment 1: initial investments of $10,435Investment 2: initial investments of $10,330.43Investment 3: Annual Deposit of $2,194.42.Part C: The total interest earned on each investment is as follows:
Investment 1: $1,565Investment 2: $1,669.57Investment 3: $1,027.90.How are the total interests computed?The total interest for investment 1 is a product of simple interest formula, which multiplies the principal, interest rate, and time.
The total interests for investments 2 and 3 are the results of the online finance calculator., which inputs the future value, compound interest rate, and compounding period.
Investment 1:Future value = $12,000
Investment Period = 5 years
Simple interest rate = 3% or 0.03
Initial investment, P = A/(1 + rt)
Where P = principal
A = Future Value
r = interest rate
t = time
P = $12,000/(1 + 0.03 x 5)
= 12,000/(1.15)
= $10,435
Total Interest = $1,565 ($12,000 - $10435) or ($10,435 x 3% x 5)
Investment 2:Future value = $12,000
Investment Period = 5 years
Compound interest rate = 3% or 0.03 monthly
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $0
FV (Future Value) = $12,000
Results:
Present Value (PV) = $10,330.43
Total Interest = $1,669.57
Investment 3:Future value = $12,000
Investment Period = 5 years
Compound interest rate = 3% or 0.03 annually
N (# of periods) = 5 years
I/Y (Interest per year) = 3%
PV (Present Value) = $0
FV (Future Value) = $12,000
Results:
Periodic Deposits = $2,194.42
Sum of all periodic payments = $10,972.10
Total Interest = $1,027.90
Learn more about simple and compound interests at https://brainly.com/question/3402162
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