The greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h.
The given data is the height and radius of a right circular cylinder are equal.
[tex]$$\begin{aligned}V & =\pi h^3 \\\frac{d V}{d h} & =3 \pi h^2 \\d V & =3 \pi h^2 d h\end{aligned}$$[/tex]
A differentiable function is a function in one variable in calculus such that its derivative exists at each point in its entire domain. The tangent line to the graph of a differentiable function is always non-vertical at each interior point in its domain.
A differentiable function does not have any break, cusp, or angle.
Find the derivative of V in terms of h. Then multiply both sides by dh.
The maximum percentage error of the volume is 1%.
[tex]$$\begin{aligned}0.01 \pi h^3 & =3 \pi h^2 d h \\\frac{0.01}{3} h & =d h \\\frac{1}{300} h & =d h\end{aligned}$$[/tex]
The maximum percentage error of the volume is 1% which means
dV=0.01=0.01[tex]\pi[/tex][tex]h^{3}[/tex]. Substitute this into the equation and then solve for
dh.
The maximum error in the height is then [tex]\frac{1}{300}h=\frac{1}{3}[/tex]%h.
Therefore, the greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h
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Can someone help me? Write a rule for nth term of the arithmetic sequence with a1=7 and the common difference is 3
Answer:
[tex]a_n=3n+4[/tex]
Step-by-step explanation:
If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:
[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]
2. Evaluate (5+5√3i)^7 using DeMoivre’s theorem.
Write your answer in rectangular form.
Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i
How do we Evaluate (5+5√3i)⁷ using DeMoivre’s theorem?The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.
Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),
r = |z| magnitude of z
it becomes
r = √((5)² + (5√3)²) = 10
θ = arg(z) is the argument of z.
θ = atan2(b, a) = atan2(5√3, 5) = π/3
(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)
De Moivre's theorem to raise the complex number to the 7th power
(5 + 5√3i)⁷
= 10⁷× (cos 7π/3 + i sin 7π/3)
= 10⁷ × (cos 2π/3 + i sin 2π/3)
Convert this back to rectangular form:
Real part = r cos θ = 10⁷× cos (2π/3) = -5000000
Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i
∴ (5 + 5√3i)⁷ = -5000000 + 8660254.03i
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Answer:10^7 (1/2 - √3/2 i)
Step-by-step explanation:
To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:
Magnitude:
|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10
Argument:
arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3
So the number can be written in polar form as:
5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))
Now we can use DeMoivre's theorem:
(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))
To simplify, we need to find the cosine and sine of 7π/3:
cos(7π/3) = cos(π/3) = 1/2
sin(7π/3) = -sin(π/3) = -√3/2
Explanation:
So the final answer in rectangular form is:
10^7 (1/2 - √3/2 i)
What is the length of this circle?
The length of arc length s is 1152π² or 11358.26.
We have,
The arc length of a circle can be calculated using the formula:
Arc Length = 2πrθ/360
Where:
π is a mathematical constant approximately equal to 3.14159.
r is the radius of the circle.
θ is the central angle subtended by the arc, measured in degrees.
The arc length of a circle can be written as:
s = angles/360 x 2πr _______(1)
Now,
r = 4 cm
Angle = (2/5)π
Now,
Substitute in (1).
s = angles/360 x 2πr
s = (2/5)π/360 x 2π x 4
s = 2π x 72 x 2π x 4
s = 4π² x 288
s = 1152π²
or
s = 11358.26
Thus,
The length of arc length s is 1152π² or 11358.26.
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Use the conversion factor 1 gallon=3.785 to convert 4 liters into gallons
Using the conversion factor, we can convert the liters into the number of gallons of 1. 057 gallons.
How to convert the liters ?A conversion factor is a mathematical ratio that is used to convert one unit of measurement to another. It is a multiplier or divisor that relates two different units of measurement for the same quantity.
To convert 4 liters into gallons using the conversion factor 1 gallon = 3.785 liters, you divide the given value (in liters) by the conversion factor.
This means that the number of gallons in 4 liters would be:
= 4 liters ÷ 3. 785 liters/gallon
= 1. 057 gallons
Therefore, 4 liters is approximately equal to 1. 057 gallons.
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8 +[13-(2+1] =
20
18
-3
Answer: false
Step-by-step explanation:
A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
Answer:
width = 6
length = 9
Step-by-step explanation:
Perimeter = 2(length + width) or P = 2(l + w)
2(l + w) = 50
l + w = 25
l = 25 - w
Area = length x width or A = lw
lw = 114
Substitute l = 25 - w into the lw = 114
(25 - w)w = 114
25w - w^2 = 114
-w^2 + 25w - 114 = 0
=> w^2 - 25w + 114 = 0
we have x = [-b ± √(b^2 - 4ac)] / 2a
w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)
w = [25 ± √(625 - 456)] / 2
w = [25 ± √(169)]/2
w = [25 ± 13]/2
w = [25 + 13]/2 = 38/2 = 14
or
w = [25 - 13]/2 = 12/2 = 6
if width = 14, length = 25 - 14 = 11
then area = 14 x 11 = 154, this is incorrect answer
if width = 6, length = 25 - 6 = 19
then area = 6 x 19 = 114, this is correct answer
The first shelf of one bookcase is 2 inches off the ground. The second shelf is 1’5” above the first the third shelf is 1’3” above the second and the fourth shelf is 1’2” above the third. The top shelf is 1’4” above the fourth how high off the ground is the top shelf.
answer: 5'6"
step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"
D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
Answer:
zero product property
Step-by-step explanation:
To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.
The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.
Can someone please answer and provide an explanation for these problems?
The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
What are the segments tangent to the circleA theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.
(25). 2x - 1 = x + 1 {equal tangent segments}
2x - x = 1 + 1 {collect like terms}
x = 2
(26). 2x - 4 = x {equal tangent segments}
2x - x = 4 {collect like terms}
x = 4
Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
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Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a
1
52
probability.
(a)
List the sample points in the event an ace is selected.
S = {x | x is a card from the deck that is not a club a spade or a diamond}
S = {x | x is a card from the deck but not king, jack, or queen}
S = {1 of clubs, 1 of diamonds, 1 of hearts, 1 of spades}
S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}
S = {king of clubs, king of diamonds, king of hearts, king of spades}
If Each card corresponds to a sample point with a 1/52 probability then the sample points in the event an ace is selected is S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}
In a standard deck of 52 playing cards, there are four aces.
Each ace corresponds to a different suit: clubs, diamonds, hearts, and spades.
So, when we talk about the event of selecting an ace, we are referring to the act of choosing one of these four specific cards from the deck.
The sample points in the event "an ace is selected" are the individual cards that match this criteria.
Therefore, the sample points in this event are:
S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}
These four cards are the possible outcomes when we randomly select a single card from the deck, focusing only on the event of selecting an ace.
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lin's family needs to travel 325 miles to reach her grandmother's house at 377 miles what percentage have they completed
Lin's family has completed approximately 86.15% of the total Distance to her grandmother's house.
The percentage of the distance Lin's family has completed, the ratio of the distance they have traveled to the total distance.
The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.
To calculate the percentage, we can use the following formula:
Percentage = (Distance Traveled / Total Distance) * 100
Plugging in the values, we have:
Percentage = (325 / 377) * 100
= 0.8615 * 100
= 86.15
Therefore, Lin's family has completed approximately 86.15% of the total distance to her grandmother's house.
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What is the value of i 20+1
1
-1
i
-i
Sarah is setting up a garden plot in the shape of a right triangle. One leg of the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show your work algebraically and be sure to use proper units in your answer.
value of the sides of the triangle are given as follows;
shorter leg = 5
longer leg = 12
hypotenuse = 13
What is Pythagoras theorem?Pythagoras Theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If the short leg = x
the longer length = x+7
the hypotenuse = x+7+1 = x+8
Using Pythagorean theorem
(x+8)² = x² + (x+7)²
x² +16x +64 = x²+ x² + 14x +49
collecting like terms
x²-2x²+16x -14x+64 -49= 0
-x² + 22x +15 = 0
x² -2x -15 = 0
x² -5x +3x -15 = 0
(x² -5x) (3x -15) = 0
x(x-5) +3(x-5)
(x+3)(x-5) = 0
x= -3 or +5
Since length is discreet we choose the positive answer
therefore x = 5
shorter leg = 5
longer leg = 5+7 = 12
hypotenuse = 5+7+1 = 13
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Haru recorded how long his bus ride to school took for `16` days.
Here are the values of the quartiles.
About how many rides would you expect to be less than `6.5` minutes long?
The number of rides that one would expect to be less than `6.5` minutes long is 4 rides.
How to determine the number of ridesTo determine the number of rides, we will first begin by classifying the quartiles. There are 4 quartiles that each constitute 25% of the ride timing.
The number of rides that one would expect to be less than 6.5 minutes can be gotten by finding 25% of 16, the total days recorded. This is 1/4 * 16 = 4. So, the number of rides that will be less than 6.5 minutes will be 4 rides.
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Gillian's Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons total of both products.
A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs SO.93, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15. and profit per gallon of yogurt is $3.60.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis
The constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire Feasible region in three dimensions.
The linear programming model for decision variables, objective function, and constraints.
Decision Variables:the number of gallons of frozen yogurt purchased each week as Y and the number of gallons of ice cream purchased each week as I.
Objective Function:
The objective is to maximize the total profit. The profit from frozen yogurt can be calculated as 3.60Y, and the profit from ice cream can be calculated as 4.15I. Thus, the objective function is:
Maximize Profit: Z = 3.60Y + 4.15I
Constraints:
1. Budget constraint: The total cost of frozen yogurt and ice cream should not exceed the weekly budget of $90.
Cost Constraint: 0.75Y + 0.93I ≤ 90
2. Freezer space constraint: The total gallons of frozen yogurt and ice cream should not exceed the available freezer space of 115 gallons.
Space Constraint: Y + I ≤ 115
3. Ice cream sales constraint: The weekly ice cream sales should be at least twice the frozen yogurt sales.
Ice Cream Sales Constraint: I ≥ 2Y
4. Non-negativity constraint: The number of gallons for both products cannot be negative.
Non-negativity Constraint: Y ≥ 0, I ≥ 0
The model using graphical analysis, we can plot the constraints on a graph and find the feasible region. Then, we can evaluate the objective function at each corner point of the feasible region to determine the optimal solution.
Since the constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire feasible region in three dimensions.
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Which expressionis equivalent to 60m-2n6/5m-4n-2 for all values of m and n where the expression is defined?
The expression that is equivalent to [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex] for all values of m and n where the 5m-4n-2 expression is defined is [tex]12m^{2} n^{8}[/tex]
How can the expression be known?In mathematics, an expression or mathematical expression can be described as the finite combination of symbols which is been analyzed and well-formed according by following some set of rules which could be varies base on the kind of the symbol as ll as the operation that are involved in the expression and it s been done depending on the context so that another expression can be gotten.
This is given as [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex]
Then we have it defined by; [tex]12m^{2} n^{8}[/tex]
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find the center and radius by completing the square x2+6x+y2-16y-8=0
Cual es la sucesión aritmética de 3,8,13,18,23
Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.
We have,
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a student who used the explicit formula a[n] = 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term.
The given sequence is -
3 , 8 , 13 , 18 , 23, ..
Here -
d = 8 - 3 = 13 - 8 = 5
a = 3
a(n) = a + (n - 1)d {for arithmetic sequence}
a(n) = 3 + (n - 1)5 ...Eq[1]
a(n) = 3 + 5n - 5
a(n) = 5n - 2
Therefore, Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.
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complete question:
A student uses the explicit formula an= 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term. Explain the error the student made.
Which data set has a variation, or mean absolute deviation, similar to the data
set in the given dot plot?
50 51 52 53 54 55 56 57 58 59 60 61
Ο Α.
OB.
O C.
D.
4612
15 17 19
0123
8 9 1011
55 57 59 61 63 65
Option C (15 17 19) has a similar mean absolute deviation to the data set in the given dot plot.
The informational collection in the given speck plot has a mean of roughly 55 and a moderately little scope of values, with most of the information bunched around the mean. An informational index with a comparable mean outright deviation would have a comparative degree of variety in the information values.
Out of the given choices, the informational index that has a variety like the given informational collection is choice C: 15 17 19. This informational collection has a mean of roughly 17 and a little scope of values, with most of the information bunched around the mean.
The mean outright deviation of this informational collection is around 1.63, which is like the mean outright deviation of the given informational collection. Choice A (50 51 52 53 54 55 56 57 58 59 60 61) has a bigger scope of values and a bigger mean outright deviation contrasted with the given informational collection.
Choice B (4612) and Choice D (8 9 1011 and 55 57 59 61 63 65) have altogether unique mean qualities and scopes of values, and consequently their mean outright deviations are not quite the same as the given informational collection.
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evaluate 6a +4b -3c when a=4 , b=7 , and c=-2 (a) 26 (b) 16 (c) 46) (d) 58
Answer:
(d) 58
Step-by-step explanation:
Let's start with the equation:
6a+4b-3c
Now, since we got the values of a, b, and c, we can just plug them into the equation:
6(4)+4(7)-3(-2)
24+28+6=58
So the answer is d) 58
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The total cost of the meal if the meal costs $50 is $60
How to calculate the total cost of the mealFrom the question, we have the following parameters that can be used in our computation:
Tip percent = 20%
From the question, we can use any value as the cost of the meal
So, we can use the following
Meal cost = $50
So, we have
Tip amount = Tip percent * Meal cost
This gives
Tip amount = 20% * 50
Tip amount = 10
Next, we have
Total meal cost = Tip amount + Meal cost
This gives
Total meal cost = 10 + 50
Evaluate
Total meal cost = 60
Hence, the total cost of the meal is $60
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In Algebra, a minus symbol [-] will represent two things, an operation of subtraction and a negative number, depending on where it's placed.
(a) True
(b) False
Answer:
It is true that in algebra minus symbol represent two things
Step-by-step explanation:
And it is true that it depend on where it placed such as
8-2 this minus indicate the substraction of two terms
-3 this show that the number has negative quantity
when y is directly proportional to x. When x= 2.5, y=20. what is the value of y when x= 22?
What is x? Because I don’t know g how to work it out
Answer:
45 degrees
Step-by-step explanation:
The 4 angles of a quadrilateral will add to 360.
We know 1 of them (angle B) is 90 degrees.
We can set up an equation to solve the others.
2x+3x+x+90 = 360
Now solve for x.
Start by combining the x terms together.
6x+90 = 360
6x = 360-90
6x = 270
(6x/6) = 270/6
x = 45 degrees
Check back to see if that makes sense and if the equation equals 360 when x is 45:
2x+3x+x+90 = 360
2(45)+3(45)+45+90=360.
Graph by completing the square x2+8x+y2-10y-32=0
The circle equation x² + 8x + y² -10y - 32 = 0 can be graphed using (x + 4)² + (y - 5)² = 73
Graphing the circle equation by completing the squareFrom the question, we have the following parameters that can be used in our computation:
x² + 8x + y² -10y - 32 = 0
Add 32 to both sides of the equation
This gives
x² + 8x + y² -10y = 32
Group the terms in two's
So, we have
(x² + 8x) + (y² -10y) = 32
When we complete the square on each group, we have
(x + 4)² + (y - 5)² = 16 + 25 + 32
Evaluate the like terms
(x + 4)² + (y - 5)² = 73
Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73
See attachment for the graph
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A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?
The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ
The student can use the following information to establish the AA criterion:
Angle MLN congruent angle QLR (already given)Angle LMN congruent angle LQR or angle LMN congruent angle LRQ (either one will work)These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).
Therefore, the AA congruent for similarity can be congruent .
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The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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2. Six months after John William becomes a shareholder, Peixotto Media announces
its first shareholder meeting. Because the co-presidents will be making some very
important announcements about decisions that will be voted upon by the
shareholders, John William attends. He finds that of the 20,000 shares that have
been offered so far, the shareholders who attend the meeting own 6,000 of them.
a. The co-presidents propose adding a new member to the company's board of
directors. The shareholders are allowed to vote on this matter. What percentage of
the total vote will John William control? (2 points)
b. The company's co-presidents announce that Peixotto Media will be issuing
another offering of stock, this time in the amount of 50,000 shares. Given his
preemptive rights as an existing shareholder, how many shares of this stock is John
William entitled to purchase before the offering is made to the public? (3 points)
John William is entitled to purchase 15,000 shares before the offering is made to the public.
a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.
John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.
To convert this proportion to a percentage, we multiply by 100:
Percentage of the total vote = 0.3 * 100 = 30%
Thus, John William will control 30% of the total vote at the. shareholder meeting.
b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.
John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.
If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:
Entitlement = (3/10) * 50,000 = 15,000 shares.
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What is the value of x *
7+5x
47°
Answer: X = 8
Step-by-step explanation:
47 - 7 = 40
40 / 5 = 8
x = 8
Which type of retirement account is an investment option for ANY young person?
a. traditional IRA
b. pension
c. 401(k)
d. social security
The type of retirement account is an investment option for ANY young person is 401(k). option C
What is a 401(k) retirement account?A 401(k) retirement account is described as an option for investing money, created and arrangement for youths with access to any lucrative job that pays a reasonable amount of money.
This retirement account creates room for individuals to contribute a portion of their tax income towards retirement savings, and also contributes to grow tax-deferred until withdrawal.
However, pensions are employer-funded retirement plans and may be unavailable to all young individuals
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