The voltage is therefore between 20 and 29 volts as the formula for Ohm's law can be used to get the voltage V.
what is voltage ?The measurement of the potential energy per unit charged in an electric circuit is voltage, sometimes referred to as the difference in electric potential. It is the force behind how an electric charge travels through a conductor. The sign V stands for voltage, which is denoted by the unit volts (V).
given
The formula for Ohm's law can be used to get the voltage V:
V = I * Z
where Z is the impedance and I is the current.
Here are the facts:
Z = 1 - 4i ohms, I = 8 + 3i amps.
When we multiply these values, we obtain:
V = (8 + 3i) * (1 - 4i) (1 - 4i)
[tex]V = 8 - 32i + 3i - 12i^2[/tex]
V = 20 - 29i
The voltage is therefore between 20 and 29 volts as the formula for Ohm's law can be used to get the voltage V.
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Which expression is an expanded form of ln10m‾‾√?
The expression 10m‾‾√ is an expanded form of the mathematical term ln10.
A random sample of 20 students obtained scores with a mean of 72 and a variance
of 16 on a quiz in statistics. Using a normality assumption, first construct a random
interval for (not 2) with 0.92 confidence level, and then use the result with the
given data information to get a 92% C.I. for
The answer of the given question based on the variance is , 92% confidence that the true population mean lies between 69.11 and 74.89.
What is Mean?In statistics, the mean is a measure of central tendency that represents the average of a set of numerical data. It is also known as the arithmetic mean or simply the average. The mean is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.
To construct a random interval with a 0.92 confidence level, we need to find the corresponding z-score for the level of confidence. Since the interval is not two-sided, we will use a one-tailed z-score.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to a 0.92 confidence level is approximately 1.41.
To find the 92% confidence interval for the population mean, we can use the following formula:
CI = ₓ⁻ ± zα/2 * σ/√n
where ₓ⁻ is the sample mean, σ is the population standard deviation (unknown in this case), n is the sample size, and zα/2 is critical value of standard normal distribution corresponding to desired level of confidence.
Substituting the given values, we get:
CI = 72 ± 1.41 * (4 / √20)
CI = (69.11, 74.89)
Therefore, we can say with 92% confidence that the true population mean lies between 69.11 and 74.89.
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Find the area of a shaded region
Answer:
40 cm²
Step-by-step explanation:
you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm
coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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If you are performing a left-tailed z-statistic test with a sample size n = 85 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = −1.95, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
This null hypothesis prompt is actually straight forward. Note that where the above conditions exist, we must NOT reject the null hypothesis due to the values of the z-statistics and the significance level.
What is a nyll hypothesis?The idea that there is no influence on the population is known as the null hypothesis. We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no impact in the population (p≤α ).
So to determine whether or not to accept or reject the null hypothesis, we must determine dthe z-score.
To find the the critial value for a left-tailoed test, where the signifiance level is 0.01, note that we must find the z-score that leaves 1% of the area in the left tail.
Using the standard distribution table, the z-score for 0.01 left tail is about -2.33.
Since
z-satistics which is equal to -1.95 (as given) is greater than the z-score, we must NOT reject the null hypothesis.
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If 1 US dollar in 1860 had the same purchasing power as $28.95 in 2018, what is the yearly average inflation rate during that time?
A. 2.15%
B. 2.75%
C. 3.15%
D. 3.75%
Step-by-step explanation:
From 1860 to 2018 is 158 years
Use compounding formula
$ 28.95 = $ 1 ( 1 +i) ^158 where i is decimal inflation rate %
[tex]\sqrt[158]{28.95}[/tex] = 1 + i
i = .0215 = 2.15 %
A boat traveled 350 miles each way downstream and back. The trip downstream took 14 hours.
The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of
the current?
Answer:
The speed of the boat in still water is 15 mi/hr while the speed of the current is 10 mi/hr.
Step-by-step explanation:
Given: d = 350 miles
[tex]t_{ds}[/tex] = 14 hours
[tex]t_{us}[/tex] = 70 hours
Asked: Speed of the boat [tex]V_b[/tex] in still water and speed of the current [tex]V_c[/tex]
Solve:
Note that when the boat is going downstream, the current is helping the boat to speed up and when the boat is going upstream, the current is slowing it down.
Get the speed downstream
[tex]V_{ds} = V_b + V_c[/tex]
350mi/14hrs = [tex]V_b + V_c[/tex]
25 mi/hr = [tex]V_b + V_c[/tex]
Transpose to get the value of Vb
25 mi/hr - Vc = Vb ---equation 1
Get the speed upstream
[tex]V_{us} = V_b - V_c[/tex]
350mi/70hrs = Vb - Vc
5 mi/hr = Vb - Vc
Transpose to get the value of Vb
5 mi/hr + Vc = Vb ----equation 2
Equate equations 1 and 2
25 mi/hr - Vc = 5 mi/hr + Vc
Transpose
25 mi/hr - 5 mi/hr = Vc + Vc
20 mi/hr = 2 Vc
Divide both sides of the equation by 2
10 mi/hr = Vc
Vc = 10 mi/hr
From 25 mi/hr = [tex]V_b + V_c[/tex] we then solve the speed of the boat
25 mi/hr = Vb + 10 mi/hr
25 mi/hr - 10 mi/hr = Vb
15 mi/hr = Vb
Vb = 15 mi/hr
A wall is 2000 sq ft. A gallon of paint covers 400 sq ft. Complete the conversion factor: 1 gallon / ? sq ft
To cover a 2000 sq ft wall, we will need 5 gallons of paint.
what is area?
Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.
To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:
Conversion factor = 1 gallon / (400 sq ft/gallon)
So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:
Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons
Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.
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3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.
The statements are classified as Exponential decay and Linear growth.
What are the classification of the statements?
a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.
c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.
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F(x)=2/3x-1 show creat points to graph
Label values on thex&y axis
To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). See explanation below and attached graph.
What is the explanation for the above response?To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). For example:
When x = -3, f(x) = (2/3)(-3) - 1 = -3 - 1 = -4When x = -2, f(x) = (2/3)(-2) - 1 = -2 1/3When x = -1, f(x) = (2/3)(-1) - 1 = -1 2/3When x = 0, f(x) = (2/3)(0) - 1 = -1When x = 1, f(x) = (2/3)(1) - 1 = -1/3When x = 2, f(x) = (2/3)(2) - 1 = 1/3When x = 3, f(x) = (2/3)(3) - 1 = 1So, we have the following points for the graph: (-3, -4), (-2, -2 1/3), (-1, -1 2/3), (0, -1), (1, -1/3), (2, 1/3), (3, 1).
We can now plot these points on a graph, with x-values on the horizontal axis and f(x) values on the vertical axis. We can label the horizontal axis as "x" and the vertical axis as "f(x)" or "y".
Note that the graph of f(x) = (2/3)x - 1 is a straight line with slope 2/3 and y-intercept -1.
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Can someone help me with this problem, and explain how to solve it?
Thus, the height of flagpole from the ground is found as 23.34 feet.
Explain about the angle of elevation:The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.
The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.
Given data:
height of boy = 5 ftDistance of boy from flagpole = 30 ft angle of elevation = 35 degreesLet the height of pole above the boy be 'h'feet.Using the trigonometric ratios in the right triangle ABE.
tan 35 = h / 30
h = 30* tan(35)
h = 18.34
Height of flagpole = 18.34 + 5 = 23.34 feet
Thus, the height of the flagpole from the ground is found as 23.34 feet.
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Please help will mark Brainliest
Step-by-step explanation:
5 cos (307) = 3
5 sin (307) = -4
just plot the point ( 3, -4 ) Done.
Answer:
The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4
If 4 apples have a mass of 1 kg about how many grams is each apple
PLEASE I NEED HELP
1 kg = 1000 G
so 1000/4g = 250g
I hope it’s helpful
Convert the following General Form Equations into Standard Form and then find the center and radius
Answer:
good luck
Step-by-step explanation:
HELP GIVING 20 POINTS AND BRAINLIST
Answer: 61.03
Step-by-step explanation:
c = a2 + b2 = 502 + 352 ≈ 61.03278
Bill Spends time each evening watching television. This amount of time, in minutes, can be represented by the variable t. Write and algebraic expression to represent the time Bill's friend Jill spends watching television if she watched 30 in more an evening that Bill.
Required algebraic expression is (t+30).
What is algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It may also contain brackets or parentheses to indicate the order of operations.
Algebraic expressions can be written using letters or symbols to represent variables, and they are used to represent mathematical relationships or formulas. For example, the expression "3x + 4" represents the sum of three times a variable x and the constant 4.
Let's represent the amount of time that Jill spends watching television as the variable j. We know that she watches 30 minutes more than Bill, so we can write:
j = t + 30
This algebraic expression says that Jill's time j is equal to Bill's time t, plus 30 additional minutes.
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i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available
The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%
What is a percentage?A percentage is a proportion of a number expressed as fraction of a 100
The dimensions in mixed fractions can be expressed as follows;
Height of the box = 1 2/3 feet = 5/3 feet
Width of the box = 4 feet
Length of the box = 5 1/2 feet = 11/2 feet
Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches
The percent of the box that will remain unwrapped is therefore;
Percentage = 60/(227/3) × 100 ≈ 79.3%
The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%
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1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.
When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.
When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.
How to get the Angle?(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.
(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.
(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.
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Pls help with this question
The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.
How to find the degrees off course ?To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.
W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr
Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr
Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr
Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees
So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.
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A cone with a radius of 4 inches and a slant height of 10 inches is shown.
What is the surface area of the cone, in square inches?
62.8
125.7
150.8
O 175.9
4 in.
10 in.
Answer:
167.6190 approximately 167.62 inches
Step-by-step explanation:
formula for surface area of a cone is 1/3πr×r×slant height. How this helps.
2298/24 what is the quotient step by step
2298 divided by 24 using long division shows what is the quotient and remainder while 2298 divided by 24 and the complete steps for how to find it.
Question:
2298/24 = (?)
what is 2298 divided by 24?
Answer:the quotient is 95 and the remainder is 18 when 2298 is divided by 24.
4x+3y=-23and-x+y=-8 algebra elimination
I hope this helps you.
you can check your ans. by sub. in the value of x and y into both the equation which must give you the same answer.
^4√p7
in exponential form.
Answer:1111
Step-by-step explanation:
What’s 9 more then the quotient of 2 and x
Answer:
9+2/x or 2/x+9
Step-by-step explanation:
Answer:
I think it will be 2/x+9
Step-by-step explanation:
Hello, I am confused on how to answer this question.
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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All the students in a class are more than 10 years old. What inequality represents the ages of the students?
Since all the students in the class are more than 10 years old, we can write the inequality: greater than
x > 10
what is greater than ?
The symbol ">" is commonly used in mathematics to represent "greater than." It is used to indicate that one quantity or value is larger than another. For example, if we say that 5 > 3, we mean that 5 is greater than 3. Similarly, if we say that x > y, we mean that x is greater than y.
In the given question,
The symbol ">" is commonly used in mathematics to represent "greater than." It is used to indicate that one quantity or value is larger than another.
Let "x" be the age of a student in the class.
Since all the students in the class are more than 10 years old, we can write the inequality:
x > 10
This inequality means that the age "x" of any student in the class must be greater than 10 years.
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(6x^2+10x-7) + (-x^2-8x)
For the given expression, the addition of coefficients is [tex]5x^2 + 2x - 7[/tex].
What are coefficients?In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.
What is addition?Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.
According to given information:First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.
[tex](6x^2 + 10x - 7) + (-x^2 - 8x)[/tex]
[tex]= 6x^2 + (-x^2) + 10x + (-8x) - 7[/tex] (grouping like terms together)
[tex]= (6x^2 - x^2) + (10x - 8x) - 7[/tex] (rearranging terms)
[tex]= 5x^2 + 2x - 7[/tex] (combining the coefficients)
Therefore, the final answer for the addition of coefficients is [tex]5x^2 + 2x - 7.[/tex]
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Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
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2. The designers need to know the total surface area of the
entire robot in order to determine painting costs. If it costs
$0.02 per square centimeter, determine the cost to paint
each action figure.
12 cm
3. The designers also need to determine the total amount
of plastic to be used in the molds for each robot. If each cubic centimeter of
plastic costs $0.03, determine the total cost to mold each action figure.
4. The designers are discussing the best figure to use for the neck of the robot.
They have narrowed their decision to three options: a right circular cone with
a radius of 1 cm and a height of 2 cm, a square pyramid with base edge 2 cm
and a height of 2 cm, and a right hexagonal pyramid with base edges of 1 cm
and a height of 2 cm. Which figure will cost the least amount to produce?
Justify your answer.
Answer:
it's complex but i will justify wait me