The equivalent expression of i⁴¹ is i.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression i⁴¹.
Simplifying,
i⁴¹ = {(i⁴)¹⁰} i
i⁴¹ = {(1)¹⁰} i {i⁴ = 1}
i⁴¹ = i
Therefore, the equivalent expression is i.
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Peyton had a balance of -$21.46 in his bank account according to his
last statement. He immediately deposited $35.50 into his account.
What was Peyton's account balance AFTER he made the deposit?
Answer: $14.04
Step-by-step explanation: -21.46+35.50 = 14.04
let abcd be a regular tetrahedron and m,n distinct points in the planes abc and adc respectively. show that the segments mn,bn,md are the sides of a triangle.
The segments MN, BN, and MD are the sides of a triangle.
Let AM intersect BC at point P and let AN intersect CD at point Q. Spin A about PQ to obtain E where AE = AB. We want to prove that EMN is the required triangle. For that, it is adequate to show that EM = MD and EN = BN.
Let h be the distance of A from the BCD. Then the distance of A from the line PQ is minimum h, so point E exists provided that the side length maximum is 2h. It is √(3/2) h.
We have by construction AD = AE and EP = AP. Also, since P lies on the line BC, then PA = PD. Hence PA = PA, PD = PE, AD = AE, so PAD and PAE are congruent triangles. Hence E can also be acquired by spinning D about AP. Since M lies on AP, it gives EM = DM.
Similarly, with B and D interchanged and M and N interchanged, we get EN = BN.
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Average monthly expenditure (£)
600
500
400
300
200
100
Clip 15
Key:
2010
2020
I
Transport Utility Food Housing Leisure
bills Category
a) Which category shows a decrease
in the average monthly expenditure
between 2010 and 2020?
leisure
b) How much more was the average
monthly expenditure on Food in
2020 than in 2010?
c) The total average monthly
expenditure in 2010 was £1200.
What was it in 2020?
Help on question c
Answer:
the total average monthly expenditure in 2020 was £2400.
Step-by-step explanation:
c) To find the total average monthly expenditure in 2020, we need to add up all the individual expenditures in each category. From the given data, we have:
Average monthly expenditure in 2020 = 600 + 500 + 400 + 300 + 200 + 100 = £2400
So, the total average monthly expenditure in 2020 was £2400.
Joe’s garden hose fills the pool in hours. His neighbor has a thinner hose that fills the pool in hours. How long will it
take to fill the pool using both hoses?
The length of time it would have taken for both garden hoses to fill the pool would be 6.67 hours.
How to find the time taken ?To solve this problem, we can use the formula:
1/rate = time
In the case of Joe's hose, the rate is 1/12 of the pool per hour. For his neighbor's hose, the rate is 1/15 of the pool per hour.
So, the combined rate is:
= (1/12) + (1/15)
= (5/60) + (4/60)
= 9/60 of the pool per hour
So, the time it will take to fill the pool using both hoses is:
= 1 / (9/60)
= 60/9 hours
= 6.7 hours
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The full question is:
Joe's garden hose fills the pool in 12 hours. His neighbor has thinner hose that fills the pool in 15 hours. How long will it take to fill the pool using both hoses?
the quotient of ten less than negative four and negative one half
Answer:
Step-by-step explanation:
28
the base of a certain solid is the region r. cross sections through the solid taken perpendicular to the x-axis are squares. an integral that expresses the volume of the solid is:
The integral[tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid, where f(x) is the side length of the square cross sections taken perpendicular to the x-axis in the region r.
The given integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid whose base is the region r. The integral is calculated by taking the cross sections of the solid perpendicular to the x-axis and consider them as squares. The side length of each square is denoted by f(x). The integral is calculated over the region r, which is the base of the solid. This integral is the sum of the areas of all the squares, which is equivalent to the volume of the solid. The integral is calculated by taking the lower limit of integration as[tex]$-\infty$[/tex] and the upper limit of integration as[tex]$\infty$[/tex]. Hence, the integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid with the base region r and square cross sections.
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Captain Ben has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Luis and his merciless band of thieves.
If his ship hasn't already been hit, Captain Ben has probability
2
3
3
2
start fraction, 2, divided by, 3, end fraction of hitting the pirate ship. If his ship has been hit, Captain Ben will always miss.
If his ship hasn't already been hit, dread pirate Luis has probability
1
3
3
1
start fraction, 1, divided by, 3, end fraction of hitting the Captain's ship. If his ship has been hit, dread pirate Luis will always miss.
If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that the pirate hits the Captain's ship, but the Captain misses?
The probability that the pirate hits the Captain's ship, but the Captain misses is 1/6.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
P(Captain Ben hit the ship) = 2/3
P(Captain Ben misses to hit the ship) = (1 - 2/3) = 1/3
P(Pirate hit the ship) = 1/3
P(Pirate misses to hit the ship) = (1 - 1/3) = 2/3
Now,
The probability that the pirate hits the Captain's ship, but the Captain misses.
= P(Pirate hit the ship) x P(Captain Ben misses to hit the ship)
= 1/3 x 1/3
= 1/6
Thus,
The probability is 1/6.
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(x+5)(x-7) expand and simplify
The expansion gives x² - 7x + 5x - 35
It is simplified to x = -5 and x = 7
What is an algebraic expression?An algebraic expression can be described as an expression that is comprised of terms, factors, constants, coefficients and variables.
They are also known to be made up of mathematical operations, such as;
DivisionBracketParenthesesFloor divisionAdditionSubtractionMultiplicationFrom the information given, we have that;
(x+5)(x-7)
Now, expand the bracket
x² - 7x + 5x - 35
factorize in pairs
(x² - 7x) + (5x - 35)
factor the common terms
x(x - 7) + 5(x - 7)
then,
x = -5 and x = 7
Thus, the expansion is x² - 7x + 5x - 35
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The number of tricycles in the preschool play yard was?
2
4
No answer text provided
3
The number of tricycles in the preschool play yard is given as follows:
10.
How to obtain the number of tricycles?The variables for the system of equations are given as follows:
Variable x: number of bicycles.Variable y: number of tricycles.There are 30 seats, hence:
x + y = 30
x = 30 - y.
There are 70 wheels, hence:
2x + 3y = 70.
Replacing x = 30 - y on the second equation, the number of tricycles is obtained as follows:
2(30 - y) + 3y = 70.
y = 10.
Missing InformationA preschool playground has both bicycles and tricycles. There is a total of 30 seats and 70 wheels. What is the number of tricycles?
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Kathleen has 21 marbles some of the marbles are green the other 12 marbles are blue How many green marbles does she have?
Answer: 9
Step-by-step explanation:
21 - 12 = 9
20 people fit comfortably in a 10 feet by 10 feet area. Use this value to estimate the size of a
crowd that is 7 feet deep on ONE side of the street along a 1 mile section of a parade route.
The size of the crowd is 7392 people.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
20 people fit comfortably in a 10 feet by 10 feet area.
So,
the ratio of the number of people per unit area = 20/(10 × 10) = 20/100 = 1/5
The area, A, occupied by the crowd = 7 feet × 1 mile × 1
1 mile = 5280 feet
A = 7 feet × 5280 feet × 1 = 36960 feet².
Now, number of people = 36960 x 1/5
= 7392 people.
Therefore, the required value is 7392 people.
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A cross between a plant with flowers and a plant with white flowers yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plant? Explain
The genotype must be Rr and rr because the outcome is close to the 1:1 ratio of red to white flowering plants.
What is meant by Law of Dominance?According to Mendel's law of dominance, one feature in a heterozygote will mask the existence of another trait for the same attribute. The dominant allele will be exclusively expressed, as opposed to both alleles contributing to a trait.
When parents with distinct, opposing qualities are crossed, only one form of the trait manifests itself in the offspring, according to Mendel's law of dominance. Only the dominant phenotypic characteristic will be present in the hybrid offspring. The first law of inheritance is the dominance principle.
This regulation states that the first generation of offspring from purebred parents shall exhibit solely dominant features.
There will be a 1:1 ratio between the dominant and recessive traits when a heterozygous dominant parent mates with a pure recessive parent.
The cross:
r r
R Rr Rr
r rr rr
The genotype must be Rr and rr since the outcome is close to the ratio of red to white flowering plants.
Therefore, the correct answer is option A. The result is close to the 1:1 ratio of red to white flowering plants, so the genotype must be Rr and rr.
The complete question is:
A cross between a plant with red flowers (R = dominant) and a plant with white flowers (r = recessive) yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plants? Explain
A. The results are close to a 1:1 ratio of plants with red flowers to plants with white flowers. Therefore, the genotypes of the Rr and ir
B. The results should yield plants with red flowers and plants with white flowers in a 3:1 ratio due, so the genotype of each parent is Rr. The number of offspring was not large enough to produce the expected results
C. The results differ from the predicted values. Therefore, the genotypes of the parents cannot be determined.
D. The results should show a ratio of 3 plants with white flowers to 1 plant with red flowers, so the genotypes of the parent plants are RR and rr.
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Sample Questions Chapters 3, 12, 13, 14. All of the following contribute to the success of incumbent members of Congress n election campaigns EXCEPT Incumbents.
All of the following contribute to the success of incumbent members of Congress n election campaigns EXCEPT Incumbents tend to understand national issues better than do their challengers.
What does the term incumbent mean?The term "incumbent" has several meanings depending on the context, but it generally refers to someone who holds a particular position or office. The most common usage of this term is in the context of politics, where an incumbent is the current holder of a political office, such as a president, governor, or member of Congress. An incumbent candidate is the candidate who is currently holding a political office and is running for re-election.
In other fields, the term incumbent is used to describe someone who holds a particular job, position or role and is responsible for certain tasks or duties, for example an incumbent employee, an incumbent contractor, an incumbent provider, etc.
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Complete question not found
6. How can you be certain that the angles you have created form a square inside the circle? (4
points for a thorough explanation)
To be certain that the angles created form a square inside a circle, it is important to first understand the properties of a square and a circle.
How to sure that Angles created form a Square inside a Circle?A square is a four-sided polygon with all sides of equal length and all angles of 90 degrees. This means that if we draw a square inside a circle, the four corners of the square should be tangent to the circle.
A circle is a shape with all points on the circumference equidistant from the center. This means that if we draw a square inside a circle, the distance from the center of the circle to the midpoint of each side of the square should be equal to the radius of the circle.
By verifying that the above two conditions are met, we can be certain that the angles created form a square inside the circle. Additionally, we can also check that all the four angle of the square is 90 degrees and the opposite sides are parallel.
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The World Future Society predicts that by the year 2020, airplanes will be able to carry 1400 passengers. Today’s biggest jets can carry 600 passengers. What will be the percent of increase of airplane passengers? nearest percent
To calculate the percent increase in airplane passenger capacity, we first need to find the difference between the current capacity (600 passengers) and the predicted future capacity (1400 passengers).
1400 - 600 = 800
Then divide this difference by the current capacity, and multiply by 100 to express the answer as a percentage.
(800/600) * 100 = 133.33
So the predicted percent increase in airplane passenger capacity is approximately 133%.
The nearest percent is 133%.
the question is in the picture
The positive interval and the negative interval for the function given is (-∞, 3) and (3, ∞).
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is f(x) = [tex]-2\sqrt{x+1} +4[/tex]
Positive interval of the function is the values of x when function > 0.
To get the function > 0, the value [tex]2\sqrt{x+1}[/tex] < 4.
[tex]\sqrt{x+1}[/tex] < 2
x + 1 < 2²
x + 1 < 4
x < 3
Positive interval is (-∞, 3).
Negative interval of the function is the values of x when function < 0.
To get the function value < 0
[tex]-2\sqrt{x+1} +4[/tex] < 0
[tex]2\sqrt{x+1}[/tex] > 4
[tex]\sqrt{x+1}[/tex] > 2
x + 1 > 2²
x + 1 > 4
x > 3
Negative interval is (3, ∞).
Hence the positive interval of the function is (-∞, 3) and the negative interval is (3, ∞).
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The second bus company that Ms. Baudy contacted wanted to charge each student $5.00 for
roundtrip service. If the total price of the trip per student was $7.00, approximately what
percentage of the trip would go towards the price of the bus?
If the total price of the trip per student was $7.00, approximately the percentage of the trip that would go towards the price of the bus is 71.43%.
What is the percentage?The percentage is the ratio of a variable or value to another.
Percentages are fractional values, computed as the quotient of a numerator over a denominator multiplied by 100.
The bus roundtrip charge per student = $5.00
The trip price per student = $7.00
Percentage of the trip going towards the price of the bus = 71.43% ($5/$7 x 100).
Thus, we expect that 71.43% of the trip amount will be consumed for the bus charter.
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Which expression is a factor of -2x2 - 11x - 20
No real Factors
(2x + 10)
(x - 10)
(2x - 5)
The given expression will not have real factors. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the quadratic expression is -2x² - 11x - 20. The expression will be solved as below:-
E = -2x² - 11x - 20
Apply the quadratic factorization formula,
x = [ -b ± √( b² - 4ac ) ] / 2a
x = [ 11 ± √ ( 121 - ( 4 x - 2 x - 20 ) ] / ( 2 x - 2 )
x = [ 11 ± 39i } / -4
The roots of the quadratic equation are not real.
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Answer:
no real factors
Step-by-step explanation:
i took the test
please help will mark BRAINLIEST
Answer:
90
Step-by-step explanation:
the bottom of the picture is cut off but it's 90°
becuase the picture shows you the 2 sides of the triangle r equal
the angles on the top are also equal
so that means the middle line has to be perpendicular to the base.
so Y is 90
3) Six of the students in Ms. Collier's class play an
instrument. These six students make up 20% of
the class. How many students are in the class?
Construct a 3x3 matrix A, with nonzero entries, and a vector b in R3 such that b is not in the set spanned by the columns of A. Choose the correct answer below : A. A= | 1 1 1 | | 3 | B. | 1 1 1 | |4| . |2 2 2 | b = | 6 | A= | 2 2 2 | b = |5| . |3 3 3 | | 9 | | 3 3 3 | |6| . . C. A= | 1 1 1 | | 1 | D. | 1 2 3 | |3| . |2 2 2 | b = | 2 | A= | 2 1 1 | b = |2| . |3 4 5 | | 5 | | 3 3 2 | |1|
A 3x3 matrix A, with nonzero entries, and a vector b in R3 such that b is not in the set spanned by the of A= | 1 1 1 | | 1 | . |2 2 2 | b = | 2 |
In order for b to not be in the set spanned by the columns of A, we need to ensure that the system of equations Ax=b has no solution. This means that the system of equations needs to be inconsistent. We can achieve this by making sure that the determinant of A is not equal to zero, i.e. the matrix must be invertible.
The matrix given in option C satisfies this requirement. A = | 1 1 1 | | 2 2 2 | | 3 3 3 |
The corresponding vector b is | 1 | | 2 | | 3 |
Thus, the correct answer is C.
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to find the average amount of money that american college students spend on food per week, a researcher surveys 300 college students across the u.s.
The result of the calculation was $93.41 per week.
To find the average amount of money spent on food by American college students per week, a researcher conducted a survey of 300 college students across the U.S. The researcher collected data on the amount of money spent by each student on food per week and then calculated the average using the formula: Average = (sum of all the scores)/(number of scores). The researcher then added up the money spent by all 300 students and divided it by 300 to get the average amount of money spent on food per week by American college students. The result of the calculation was $93.41 per week.
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At a family reunion, each of Shamar's aunts and uncles is getting photographed once. The aunts are taking
pictures in groups of 5 and the uncles are taking pictures in groups of 10. If Shamar has the same total number
of aunts and uncles, what is the minimum number of aunts that Shamar must have?
The minimum number of aunts that Shamar must have based on the information provided is 10.
What are the possible number of uncles and aunts?It is known that uncles will take a photograph in groups of 10, while aunts will take a photograph in groups of 5. Based on this, the possible number for each are:
Uncles: 10, 20, 30, 40, 50
Aunts: 5, 10, 15, 20, 25
How to find the minimum number of relatives?In this case, the minimum number is the LCM or Least Common Multiple and based on the previous list, this number is 10.
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Show me 2/4 comparing 5/8 on a number line
Using a number line, the number 5/8 is greater than 2/4
How to compare the numbers on a number lineFrom the question, we have the following parameters that can be used in our computation:
Comparing 2/4 and 5/8 on a number line
Here is a number line that shows the comparison of 2/4 and 5/8:
1/2 2/4 3/4 5/8 3/4 2/4 1/2
--|---------|---------|---------|---------|---------|--
As you can see, 2/4 is located halfway between 1/2 and 3/4, while 5/8 is located halfway between 3/4 and 3/4.
Therefore, 5/8 is larger than 2/4.
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estimate the distance (in mi) the race car traveled during this time period using the velocities at the beginning of the time intervals
The distance the race car traveled during this time period using the velocities at the beginning of the time intervals is 23.886 mi
Use areas of rectangles to approximate the area under the curve. The width of each rectangle is 10 sec = 1/36 hrs and the lengths are the velocities.
LH = 1/36 ( 183.9 + 167 + 107.6 + 98.8 + 125.5 + 177.1)
LH=1/36(862.9)
LH≈ 23.886 mi
To find the right-hand approximation:
RH = 1/36 (167 + 107.6 + 98.8 +125.5 +177.1 + 176.6)
RH=1/36(852)
RH≈ 23.683 mi
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Julia sorted candies and found there were
10 each of these colors: green, red, and
pink and 20 blue in the package. Which
answer matches the percentage, decimal
and fraction of the blue candies in the
package?
F 20%, .2, 1/5
G 30%, .3, 3/10
H 40%, .4, 2/5
J 50%, .5, 1/2
The percentage is 40%, decimal point of blue candies is 0.4, and the fraction of blue candies is 2/5. The correct option is H. 40%, 0.4, 2/5.
How to calculate the percentage and decimal? Percentage is a unit of measurement used to express a proportion of a whole number in terms of hundredths. To calculate a percentage, divide the number of items in question by the total number of items and then multiply the result by 100. For instance, if you were to calculate the percentage of apples in a basket that contained 12 apples and 8 oranges, you would divide 12 by 20 (12 + 8) and then multiply the result by 100. The answer would be 60 percent.Decimals are numbers that are expressed in tenths, hundredths, or thousandths of a unit. To calculate a decimal, divide the number of items in question by the total number of items. For instance, if you were to calculate the decimal amount of apples in a basket that contained 12 apples and 8 oranges, you would divide 12 by 20 (12 + 8). The answer would be 0.6.Given,
Julia has 10 candies in green, 10 candies in red, 10 candies in pink and 20 candies in blue. There are 50 candies in Julia's hand.
We have to find percentage, decimal and fraction of blue candies = ?
Percentage = 20/50 x 100 = 40%
Decimal = 20/50 = 2/5 = 0.4
Fraction = 20/50 = 2/5.
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The length of a new rectangular playing field is 4 yards longer than triple the width. If the perimeter of the rectangular playing field is 416 yards, what are its dimensions?
Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:
l = 3w + 4 (the length is 4 yards longer than triple the width)
We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:
P = 2l + 2w
We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:
416 = 2(3w + 4) + 2w
Simplifying and solving for w:
16 = 6w + 8
8 = 6w
w = 8/6 = 4/3
We can now substitute that back into the equation for the length:
l = 3w + 4
l = 3(4/3) + 4
l = 4 + 4
l = 8
So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.
Step-by-step explanation:
What basic trigonometric identity would you use to verify that ?
Question 20 options:
The identities in verifying the trigonometric expression sinx cosx tanx=1-cos^2x include:
tanx = sinx/cosx
sin^2x+cos^2x = 1
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.
Anytime trigonometric functions are used in an expression or equation, trigonometric ifentities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity holds true. These trigonometric functions (such as sine, cosine, and tangent) of one or more angles are involved geometrically in these identities.
Based on the question, tanx = sinx/cosx and sin²x+cos^²x = 1 are applicable.
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What basic trigonometric identity would you use to verify that sinx cosx tanx=1-cos^2x
Find the exact circumference of each circle
The exact circumference for the circles are;
5. C = 94.26mi
6. C = 879.76in
7. C = 91.118in
8. C = 62.84m
9. C = 12.568m
10. C = 29.535cm
What is Circumference of a Circle?The circumference of a circle is its boundary or the length of the complete arc of a circle. The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.
Circumference = πd
or
Circumference = 2πr
where π = 3.142 or 22/7
r = radius
d = diameter
5. C = 2πr
C = 2 x 3.142 x 15
C = 94.26mi
6. C = 2πr
C = 2 x 3.142 x 140
C = 879.76in
7. C = πd
C = 3.142 x 29
C = 91.118in
8. C = 2πr
C = 2 x 3.142 x 10
C = 62.84m
9. C = 2πr
C = 2 x 3.142 x 2.1
C = 12.568m
10. C = πd
C = 3.142 x 9.4
C = 29.535cm
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Macmillan Learning
Assume the Pacific Ocean has a surface area of 1.5 x 108 km² and an average depth of 3700 m.
Calculate the volume of water in the ocean in liters:
5.6 x 10¹2 L
5.6 x 10¹7 L
O 5.6 x 10¹¹ L
5.6 x 10^20 L
The volume of water in the ocean in litters, 5.6 x 10¹¹ L.
How do you calculate the size of the Pacific Ocean?In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms. The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.
The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.
In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms.
Volume is calculated as Area x Depth.
1.5 × 108/3700 = 5.6 x 10¹¹ L.
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