Answer:A complex number will, in general, have five(5) fifth complex roots./
Step-by-step explanation:
K
At a computer store, a customer is considering 8 different computers, 7 different monitors,
9 different printers and 2 different scanners. Assuming that each of the components is
compatible with one another and that one of each is to be selected, determine the number
of different computer systems possible.
there are 1,008 different computer systems possible, given the constraints provided.
what is constraints?
Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.
In the given question,
To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.
So, for this problem, we have:
8 different choices for computers
7 different choices for monitors
9 different choices for printers
2 different choices for scanners
Using the multiplication principle, the total number of different computer systems possible is:
8 x 7 x 9 x 2 = 1,008
Therefore, there are 1,008 different computer systems possible, given the constraints provided.
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Lamont works at an electronics store where he receives a commission on his sales. He must choose between two plans for his pay structure for the next year.
For Plan A Lamont's monthly salary is $1,775 and he gets a 19% commission on his monthly sales. For Plan B his monthly salary is $2,100 and he gets a 7% commision on his monthly sales.
Use a system of equations to model Lamont's situation and choose the best response below.
If Lamont's sales are more than $2708.33, Plan A is a better plan because he earns more money in one month.
1. If Lamont's sales are $2708.33, he earns $2292.43 with Plan A.
2. If Lamont's sales are $2708.33, he earns $2290.63 with Plan B.
3. If Lamont's sales are more than $2708.33, Plan B is a better plan because he earns more money in one month.
4. If Lamont's sales are exactly $2,709.28, he earns the same amount of money with either plan.
The correct answer is option 2: if Lamont's sales are $2708.33, he earns $2290.63 with Plan B.
To determine which pay structure is better for Lamont, we need to compare the total amount of money he earns under each plan for different levels of sales. We can set up a system of equations to represent the two plans:
Plan A:
Total Pay = 1775 + 0.19S
where S is Lamont's total monthly sales
Plan B:
Total Pay = 2100 + 0.07S
To find the point at which the two plans yield the same result, we can set the two equations equal to each other and solve for S:
1775 + 0.19S = 2100 + 0.07S
0.12S = 325
S = 2708.33
If Lamont's monthly sales are exactly $2,708.33, then he earns the same amount of money under both plans - this is the break-even point.
However, for sales above this amount, Plan A becomes the better option as the commission rate is higher. Option 1 is incorrect because it assumes that Plan A is always better, whereas we know from the calculations that this is not the case. Option 3 is correct for sales above $2,708.33, but not for sales below this amount. Option 4 is also incorrect as we know that Plan B yields a slightly higher payout for sales exactly equal to the break-even point.
Therefore, option 2 is the correct answer as it accounts for the break-even point and accurately reflects the difference in total pay between Plan A and Plan B for Lamont's sales of $2,708.33.
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Identify the solid formed by rotating the two-dimensional shape about the line.
Select Choice
pls help ill mark brainliest + 60 points!!!!!
Answer:
The solid formed by rotating the two-dimensional shape (which appears to be a right-angled triangle) about the line is a cone.
Answer:
identy the solid formed by
A contestant draws a sequence of three cards, one question per card, and tries to answer the three questions. There are five cards with history questions, six cards with literature questions, and seven cards with science questions. Find the probability of each of the following. (Round your answers to four decimal places.) (a) the questions are history, literature, and science, in that order (b) all three are literature questions (c) the first is science, the second is history, and the third is science
(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.
(b) The probability of all three cards being literature questions is 2.4%.
(c) 5%.
What is probability in cards?Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.
(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.
To calculate this probability, we use the formula
P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.
The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.
The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.
(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.
To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.
The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.
The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.
(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.
To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).
The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.
The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.
The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.
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Please help!!
I don’t understand how to solve this since it’s format confuses me
Can someone explain how to answer it has to be a whole number or fraction.
Write as a single logarithm:
log 5 + 2
There is no logarithm base provided in the expression "log 5 + 2". Therefore, we assume that the base is 10, which is the default base for logarithms when no base is specified.
Using the logarithmic identity that states
"log a + log b = log(ab)",
we can combine the terms as follows:
log 5 + 2 = log(5) + log(10^2) [Note that 10^2 = 100]
Now, using the same identity, we can simplify this further:
log(5) + log(100) = log(5 * 100) = log(500)
Therefore, the expression "log 5 + 2" can be simplified as a single logarithm of "log 500" with base 10.
Consider a triangle A BC like the one below. Suppose that a = 21, b = 26, and A = 349. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or"
The angles of the triangle are A=146.8°,B=22.3° and C=10.9°
define cosine ruleThe cosine rule states that for any triangle with sides of length a, b, and c and angles A, B, and C (with the side opposite each angle labeled with the corresponding lowercase letter), the following equation holds:
a² = b² + c²- 2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Using the cosine rule,
a²=b²+c²-2bcCosA
2bcCosA=b²+c²-a²
A=cos⁻¹(b²+c²-a²/2bc)
A=cos⁻¹(18²+9²-26²/2×18×9)
A=cos⁻¹(-0.83642)=146.8°
Also from b²=a²+c²-2acCosB
B=cos⁻¹(a²+c²-b²/2ac)
B=cos⁻¹(26²+9²-18²/2×26×9)
B=cos⁻¹(0.925)=22.3°
The total angle of the triangle is 180°
A+B+C=180°
C=180°-146.8°+22.3°=10.9°
Thus, the angles of the triangle are A=146.8°,B=22.3° and C=10.9°
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The compelte question is;
Image is attached below
Please help ASAP! Thank you
Answer:
a. lines intersecting at a single point
b. one solution
Step-by-step explanation:
a. The equations can be rewritten as:
y = -5x+23 and y = -1/6x+1
Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.
Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.
b. The equation will have one solution as below.
The equations can be rewritten as:
5x+y=23
5x+30y=30
Subtracting both equation will result in,
29y=7
=> y=7/29
Hence x= 660/29
Amy is single with a salary of $50,000. She has been offered a new position that will raise her salary to $53,000.
The cut-off between the 18% and 25% tax brackets is $51,250. How much will her tax liability increase if she accepts the new position?
Given in Quadrilateral WXYZ, WY and XZ bisect each other at point a
Prove Quadrilateral WXYZ is a parallelogram
What is the missing statement in this proof?
Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.
What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?
Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.
Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:
AW = AY (given)
AZ = AX (given)
WY = XZ (as WY and XZ bisect each other)
Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.
By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.
Since opposite sides are congruent, we have WX || YZ.
Similarly, we can show that WZ || XY.
Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.
Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."
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How to solve for x?????
The value of x using Pythagoras theorem to solve the diagram is 1.25 m.
What is pythagoras theorem?Pythagoras theorem states that the square of the hypotenus in a right angled triangle is equal to the sum of the of the two other sides.
To solve for x we use pythagoras theorem in the diagram below.
Formula:
a² = b²+c².......................... Equation 1From the diagram,
c = 3 mb = x ma = (x+2) mSubstitute these values into equation 1 and solve for x
(x+2)² = x²+3²x²+4x+4 = x²+94x = 9-44x = 5x = 5/4x = 1.25 mHence, x is 1.25 m.
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please help quick its due by 11 am
Each of the value of x in the diagram above are as follows
x = 141 degreesx = 39 degreesx = 21 degreesx = 88 degreesx = 98 degreesx = 139 degreesx = 63 degreesx = 102 degreesx = 50 degreesx = 166 degreesx = 36 degreesx = 74 degreesx = 83 degreesx = 95 degreesx = 162 degreesWhat are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.
Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;
x = 141° (alternate interior angles theorem).
x = 39° (corresponding angles).
x + 169 = 180
x = 180 - 169 = 21°.
x = 88° (vertically opposite angles).
x = 180°- 82°
x = 98°
x + 41 = 180
x = 180 - 41 = 139°.
x + 117 = 180
x = 180 - 117 = 139°.
x = 102° (vertically opposite angles)
x + 130 = 180
x = 180 - 130 = 50°.
x + 14 = 180
x = 180 - 14 = 166°.
x + 18 = 180
x = 180 - 18 = 162°.
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Can someone help me on this pls
The two-column proofs of the line segments are shown below
Proving that HI ≅ JHGiven that
HI = 13
IJ = 13
IJ ≅ JH
The proof is as follows
Statement Reason
HI = 13, IJ = 13, IJ ≅ JH Given
HI ≅ IJ Substitution property
HI ≅ JH Substitution property (proved)
Proving that AS = LKGiven that
AL = SK
The proof is as follows
Statement Reason
AL = SK Given
AL + LS = AS Point–line–plane postulate
LS + SK = LK Point–line–plane postulate
LS + AL = LK Substitution property
AS = LK Point–line–plane postulate
(proved)
Proving that DG ≅ EFGiven that
DG = 11
GF = 11
GF ≅ EF
The proof is as follows
Statement Reason
DG = 11, GF = 11, GF ≅ EF Given
DG ≅ GF Substitution property
DG ≅ EF Substitution property (proved)
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Need some help
100 points!!
Answer:
145°
Step-by-step explanation:
∠1 + ∠2 = ∠3
5x + (4x + 10) = 10x - 5
9x + 10 = 10x - 5
10x - 9x = 10 + 5
x = 15
∠3 = 10x - 5 = 10(15) - 5 = 150 - 5 = 145
What does it mean to the rise over run when the slope is an integer? a. the rise number is one c. the run part of the slope is going to be one b. the run number is always negative d. there will be no slope Please select the best answer from the choices provided
When the slope is an integer the best answer would be a. the rise number is one.
What is integer?Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.
When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:
Therefore, the correct answer is a. the rise number is one.
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Draw a model to find a fraction equivalent to 1/4 show your work
A model to find a fraction equivalent to 1/4 is found to be 0.25.
Explain about the fraction:The intervals among two integers are illustrated by the display of fractions on a number line, which also reveals the basic idea behind the generation of fractional numbers.
The fractions on even a number line can be shown by splitting a whole into equal pieces, ranging from 0 to 1. The fraction's denominator would correspond to the number of equally spaced divisions that will be marked on the number line. To depict 1/8 on a number line, for instance, we would mark 0 and 1 on the two ends then divide that number line into 8 equal segments. The first interval can thus be designated as 1/8.Now, for the given fraction 1/4.
To get the model of 1/4, draw number line and mark number starting from
0 to 4.
Divide in 4 equal part.
The first part shows the fraction 1/4 = 0.25.
Thus, a model to find a fraction equivalent to 1/4 is found to be 0.25.
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How can you eliminate the x-terms in this system?
Answer:
3 times the second equation, plus the first
Step-by-step explanation:
You want a strategy for eliminating x-terms in the system of equations ...
9x -7y = -3-3x +5y = 9EliminationYou can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.
Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...
9x -7y = -3-9x +15y = 27Adding these two equations together will eliminate the x-terms:
(9x -7y) +(-9x +15y) = (-3) +(27)
8y = 24 . . . . . . . simplify; x-terms are gone
You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.
I need this answer please
Answer:
the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points
Use properties of logarithms with the given approximations to evaluate the expression.
log 3≈ 0.477 and log 5≈ 0.699. Use one or both of these values to evaluate log 27.
log27=
The value of log(27) is 1.431.
What is logarithm?
The power to which a number must be raised in order to obtain other numbers is referred to as a logarithm. The easiest method to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms.
We can use the property of logarithms that states that log a (b^c) = c log a (b) to evaluate log 27 using the given approximations:
log 27 = log (3³) = 3 log 3 ≈ 3(0.477) ≈ 1.431
Therefore, log 27 ≈ 1.431.
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The bearing of F from A is 232°.
What is the bearing of A from F?
Hint: remember that co-interior angles sum to 180°.
The bearing from A to F is 38
1. The product of th roots of the quadratic 6x + cx + 4 is 2 greater than the sum of the roots, and c is a constant. What is the c?
The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4
What is quadratic equatiοn in math?ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.
By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:
α + β = -c/6
And the prοduct οf the rοοts is given by:
αβ = 4/6 = 2/3
We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:
αβ = α + β + 2
Substituting the values we knοw, we get:
2/3 = -c/6 + 2 + α + β
Simplifying this expressiοn, we get:
2/3 = -c/6 + 2 - c/6
Multiplying bοth sides by 6, we get:
4 = -c + 12 - c
Simplifying, we get:
2c = 8
c = 4
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solve 3k-81ksquare=0
Answer:
k=0 or k=1/27
Step-by-step explanation:
3k-81k^2=0
3k(1-27k) =0
3k=0 or 1-27k=0
k=0 or -27k= -1
k= 1/27
What is the width of a calculator?!!
pleaseeeeeeeeee and ty
The graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).
What is graph?
A graph is a data structure consisting of a set of vertices (also called nodes or points) connected by edges (also called arcs or lines). It is used to represent relationships between objects or entities in a system or network. Graphs are commonly used in computer science, mathematics, and other fields where complex data structures need to be analyzed and visualized.
In a graph, each vertex may be connected to one or more other vertices by edges. The edges may be directed (pointing from one vertex to another) or undirected (connecting vertices without a specific direction). A graph can be represented mathematically as a set of vertices and a set of edges that connect them.
To find where the graph of the equation x²-x-2=y crosses the x-axis, we need to find the values of x when y=0.
So, let's set y=0 and solve for x, x²-x-2=0
We can factor this quadratic equation as (x-2)(x+1) = 0
So, the solutions are
x-2=0 or x+1=0
which give:
x=2 or x=-1
Therefore, the graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).
So the answer is option D: (-1,0) and (2,0).
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pls help me i need an answer
The first statement given is not a random sample because athletes leaving practice are not representative of all athletes.
"Athletes leaving practice are asked what their favorite sport is". Is this sampling a random sample or not?A random sample is a sample in which every member of the population being studied has an equal chance of being selected. In the given statement, the sample is not random because the athletes leaving practice are not representative of all athletes, as they may have different preferences or levels of skill in their favorite sport.
Additionally, the sample is not chosen through a random selection process, but rather through a convenience sampling method, in which participants are chosen based on their availability and willingness to participate.
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The graph shows two linear equations y = 2x + 1 and y = -3x - 4. Write the coordinates of the solution. (___ , ___)
y= 2x+1 y = -3x-4
2x-y+1 = 0. 3x+y+4 = 0
a1 + b1 + c1 = 0 a2+ b2 + c2 = 0
x,y = b1c2- b2c1/ a1b2-a2b1 , a2c1-a1c2/a1b2-a2b1
x,y = -1×4 - 1×1 /2×1 - 3×-1 , 3×1-2×4 / 2×1 -3×-1
x,y = -5/-1 , -5/2
x,y= 5, 5/2
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Which equation can Sharon use to find c, the average amount the cable company charges per channel?
The equation that Sharon can use to find c is
300(c-0.20)= 180
The average amount the cable company charges per channel was $0.8.
What is equation?An equation is a mathematical statement which can be constructed by two expressions connected by an sign which is called equal '=' sign to find out the value of unknown variable.
For example, 3x – 11 = 16 is an equation. Solving this equation, we get the value of x as x = 9.
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Let us take in previous case the bill was $c for one channel.
so for 300 channels it will be $300c.
If Sharon has for $0.20 less per channel
Then price per channel will be $(c-0.20)
For 300 channels it will be $300(c-0.20)
It equals to $180
so equating both values we get the equation and the equation will be,
300(c-0.20)= 180
The equation that Sharon can use to find c is
300(c-0.20)= 180
To find the average amount we will solve c from the equation.
300(c-0.20)= 180
⇒ c-0.20 = 180/300 [ dividing both sides by 300 we get]
⇒ c- 0.20 =0.6
⇒ c= 0.8 [ Adding both sides 0.20 we get]
Hence, The average amount the cable company charges per channel was $0.8.
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A LITTER OF STAIN COVERS 100 SQUARES HOW MANY FEET LITTER SHOULD YOU BUY TO STAIN THE WHEEL CHAIR RAMP?
You would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.
Dimensional analysisThe answer to this question depends on the dimensions of the wheelchair ramp and how much area needs to be covered with stain.
Assuming that the wheelchair ramp has an area of 100 square feet, and that the stain coverage is similar to the area covered by paint, then the amount of stain required can be estimated by using the following formula:
Amount of stain (in liters) = Area to be covered (in square feet) ÷ Coverage per liter (in square feet per liter)
If the stain coverage is 25 square feet per liter, then the amount of stain required to cover 100 square feet would be:
Amount of stain = 100 ÷ 25 = 4 liters
Therefore, you would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.
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Becky recorded data for shoe size from 5 students: 3, 4.5, 4, 5, 4. Are the data an example of numerical data? Explain.
Answer:
Yes, the data is an example of numerical data.
1. This is about data, which means information that we can measure and count.
2. There are two types of numerical data: continuous and discrete.
3. Continuous numbers CAN have fractions, like 3.5, 4.2, or 5.0. 4. like show sizes
4. Discrete data CANNOT have fraction. only whole numbers, like 0, 1, 2, 3, and so on. like number of students in a class
7. "range" formula used to find the difference between discrete & continuous numerical data
8. "range" formula is largest value minus smallest value
Step-by-step explanation:
chatgpt
Answer: yes because it records the shoe sizes and you can calculate average, median, mode and range from this
Step-by-step explanation:
In which quadrant is the point (7, -2) located on the coordinate plane?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
SHOW YOUR WORK PLEASE.
You are a new parent and would like to have $100,000 saved for your child’s college
education 18 years from now.
a. How much would you need to invest each year, starting now, to reach your goal
assuming 5% continuous annual interest?
b. What is the present value of that $100,000 when your child is born?
a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000
b. The present value of $100,000 when your child is born is $100,000.
What is Compound Interest?Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.
a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:
[tex]FV = PMT*((1 + r)^n - 1)/r[/tex]
where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).
Plugging in the values, we get:
$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05
Solving for PMT, we get:
PMT = $3,436.76
Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.
b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:[tex]PV = FV/(1 + r)^n[/tex]
where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).
Plugging in the values, we get:
PV = $100,000/(1 + 0.05)^0
Solving for PV, we get:
PV = $100,000
Therefore, the present value of $100,000 when your child is born is $100,000.
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