A bacterial culture that starts with 8000 bacteria of population and doubles every 20 minutes will reach 33000 bacteria in 40.887 minutes.
Calculate t in 33,000
33,000 = 8000 (2)^t/20
33,000/8000 = 2^t/20
log(33,000/8000) = (t/20) log2
t = 20 log(33,000/8000) / log 2 = 40.887 minutes.
Hence the time taken to reach 33000 population is 40.877mins.
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Find the solution of 20 = 5(7 - x) if the replacement set is {0, 1, 2, 3, 4, 5, 6}.
PLS HELP!!!!!!!!!
The solution for the agebraic equation 20 = 5(7 -x) is x = 3, which is correct option from the solution set.
What is algebraAlgebra is the branch of mathematics that helps to represent problems or values in the form of mathematical equation or expression
Solving for the solution in the given algebraic equation;
20 = 5(7 -x)
20 = 35 - 5x (expand bracket)
also
5x + 20 = 35 - 5x + 5x {add 5x to both sides}
5x + 20 - 20= 35 - 20 + 20 {subtract 20 from both sides}
5x = 15
x= 15/5 {divide through by 5}
x = 3
Therefore, algebraic equation 20 = 5(7 - x) is true for the value of x = 3.
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At the beginning of the season, MacDonald had to remove 555 orange trees from his farm. Each of the remaining trees produced 210210210 oranges for a total harvest of 417904179041790 oranges.
Write an equation to determine the initial number of orange trees (t)(t)left parenthesis, t, right parenthesis on MacDonald's farm.
The equation that can be used to to determine the number of trees can be presented as follows;
t = 41790 ÷ 210 + 5
What is an equation?An equation is a mathematical statement that consists of mathematical expressions joined by an equals to sign.
The number of orange trees MacDonald removes from his farm = 5 teres
The number of oranges produced by each of the remaining trees = 210
The number of oranges in the harvest = 41790 oranges
The initial number of orange trees is therefore;
The number of orange trees that produce the 41790 oranges is therefore;
41790 ÷ 210 = 199
The number of orange trees remaining after the 5 trees have been removed = 199 trees
The initial number of trees is therefore;
t = 5 + 41790 ÷ 210 = 204
The initial number of trees, t = 204 trees
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Which of the following inequalities are equivalent to the inequality 5 < -y + 6, where b is a constant? Select all that apply. Justify your answer.
The following inequalities are equivalent to the inequality 5 < -y + b.
y< b - 5 and b - 5 > y
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
5 < -y + b
Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged
5 < -y + b
Add y on both the sides, we get
5+y < b
subtract 5 on both sides
y< b - 5
Interchange the expressions .So inequality symbol changes
b - 5 > y
So, the following inequalities are equivalent to the inequality 5 < -y + b.
y< b - 5 and b - 5 > y
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Grayson biked 45 miles in 3 hours. Maya biked 26 miles in 2 hours. If they both kept a constant speed, how much faster did grayson bike than maya? write your answer as a decimal or a whole number. Miles per hour.
The required difference in the speed of Grayson ans Maya is 2 miles per hour.
What is speed ?Speed is characterized as. The pace of progress of position of an article toward any path. Speed is estimated as the proportion of distance to the time in which the distance was covered. Speed is a scalar amount as it has just bearing and no extent.
According to question:Grayson biked 45 miles in 3 hours
His speed = 45/3 = 15 miles/hour
Similarly,
Maya biked 26 miles in 2 hours
So, his speed = 26/2 = 13 miles /hour
Difference in their speed = 15-13 = 2 miles per hour
Thus, Speed of Grayson is 2 miles/hour greater than Maya.
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What is a positive number in math?.
Any number that represents something other than zero is considered to be positive.
In the given question we have to explain a positive number in math.
Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.
The natural, or counting, numbers 1, 2, 3, 4 and 5 are examples of positive numbers, as are fractions like 8/5 or 32/45 and decimals like 49.4.
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A elf-tanning lotion advertie that a 2-oz bottle will provide three application. Jen found a great deal on a 15-oz bottle of the elf-tanning lotion he had been uing. Baed on the advertiing claim, how many application of the elf-tanner hould Jen expect?
The number of applications Jen can expect from the self-tanner is 22.5.
What is applications?
Mathematical Applications focuses on developing students' mathematical expertise in both established and novel contexts. Financial modelling, matrix, network analysis, route as well as project planning, decision-making, as well as discrete growth and decay are a few of these contexts.
What is an advertising claim?
An advertising claim is a statement made in advertising about the advantages, features, and performance of a good or service with the intention of convincing the consumer to buy it.
First, to determine how many applications 1 -oz of the bottle can provide.
Number of applications 1 -oz of the bottle can provide = 3/2 = 1.5
Second, to determine the number of applications 15 oz of the bottle can provide = 15 x 1.5 = 22.5 applications
Hence, the total number of applications expected is 22.5
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A population has a mean μ=72 and a standard deviation σ=18. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=36.
The mean and standard deviation of a sampling distribution of sample means with sample size n=36 are 72,3
What is meant by sample size?The act of deciding on the number of observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study that seeks to draw conclusions about a population from a sample. In practice, the sample size employed in a study is frequently dictated by the cost, time, or convenience of gathering the data, as well as the necessity for statistical power. In complex research, sample sizes may vary: for example, in a stratified survey, sample sizes may fluctuate for each strata. Because data for an entire population is sought in a census, the targeted sample size is the population. During the experimental design process.
Given,
Mean μ=72
Standard deviation σ=18
Sample size n=36
The mean of the sample distribution is defined as:
E([tex]\bar{x}[/tex])=μ
E([tex]\bar{x}[/tex])=72
Standard deviation of a sample mean is,
SE([tex]\bar{x}[/tex])=σ/√n
SE([tex]\bar{x}[/tex])=18/√36
SE([tex]\bar{x}[/tex])=3
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dyan enters into a contract with eli, who claims to have access to a stock-trading algorithm that will multiply an investment many times over. when the results do not match this claim, dyan learns that eli does not have access to the algorithm and files a suit, alleging fraud. dyan must show harm to
Dyan must show harm to recover damages as he claims to have access to a stock-trading algorithm that will multiply an investment many times over.
What is algorithm?
In arithmetic and computing, an algorithm could be a finite sequence of rigorous directions, generally wont to solve a category of specific issues or to perform a computation. Algorithms ar used as specifications for acting calculations and processing.
Main body:
As he has the access to to a stock-trading algorithm , it becomes his obliged duty to help the customer with his recovery damages.
Hence , Dyan must show harm to recover damages
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Elena has received grant money to open a local community center. she will do many of the improvements herself to the old building she rents. while touring the building to make her project list, she uses a tape measure to check whether floors, doorways, and walls are square, meaning that they meet at right angles. a elena measures the lobby of the building for new laminate flooring. the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet. is the room square?
Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .
Given:
Elena has received grant money to open a local community center. she will do many of the improvements herself to the old building she rents. while touring the building to make her project list, she uses a tape measure to check whether floors, doorways, and walls are square, meaning that they meet at right angles. a elena measures the lobby of the building for new laminate flooring. the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet.
with sides 30, 16 and hypotenuse 34 the figure forms a right angled triangle.
According to pythagoream theorem:
30^2+16^2 = 34^2
900+16^2 = 34^2
900 + 256 = 1156
1156 = 1156
Therefore Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .
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What is the distance between the points (22, 11) and (6, 11) in the coordinate plane?.
The distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.
According to the question,
We have the following information:
The two points in the coordinate plane = (22,11) and (6,11)
Now, we know that the following formula is used to find the distance between two points in the coordinate plane:
Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]
We have the following values:
x1 = 22 and y1 = 11
x2 = 6 and y2 = 11
Distance between two points = [tex]\sqrt{(11-11)^{2} +(6-22)^{2} }[/tex]
Distance between two points = [tex]\sqrt{(-16)^{2} }[/tex]
Distance between two points = 16 units
Hence, the distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.
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Nakeisha's family took a road trip to Mount Rushmore. Nakeisha fell asleep 18% of the way through the trip. If the total length of the trip was 400 miles, how many miles had they travelled when Nakeisha fell asleep?
72 miles, distance travelled by Nakeisha's family when Nakeisha fell asleep.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Total distance of the trip = 400 miles,
The percentage of distance when Nakeisha fell asleep = 18%.
The distance when Nakeisha fell asleep,
= 400×18/100
= 72 miles
The distance travelled by Nakeisha's family when Nakeisha fell asleep is 72 miles.
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What is 5.37divied by 3 put 5.37 at the top and 3 at the bottom PLEASE I ONLY HAVE 19 MINS TO SUMMIT THIS!!
The value of 5.37/3 is 1.79.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given term is 5.37 divided by 3,
The mathematical expression for 5.37 divided by 3,
= 5.37/3
= 1.79
The value of 5.37 divided by 3 is 1.79.
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A sinusoidal function of the form y = a sin(x - c) + d is
changed by increasing d by 2. The new graph will have
moved:
A.2 units left
B.2 units up
C.expanded vertically by a factor of 2
D.2 units down
Answer:
A.2
Step-by-step explanation:
What is the scale factor of the dilation of triangle?.
The scale factor of the dilation of triangle DEF is 3/10
Given,
Triangle DEF's scale factor of dilation is equal to the ratio of its corresponding sides to those of triangle D'E'F':
f = D'F'/DF = D'E'/DE = E'F'/EF scale factor (1)
The comparable triangles OD'F' and ODF can be used to calculate the ratio D'F'/DF because their sides must be proportional:
D'F'/DF = OF'/OF = OD'/OD (2) (2)
According to the figure, we understand:
If F'F = 7 and OF' = 3, then
OF = OF' + F'F → OF = 3 + 7 → OF = 10
Then substituting in (2):
(2) DF/DF = 3/10 = OD/OD
Also substituting in (1):
(1) f = 3/10 = E'F'/EF = D'E'/DE
That is,
The scale factor of the dilation of triangle DEF is 3/10
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The question is incomplete. Completed question is given below;
What is the scale factor of the dilation of triangle DEF?
Figure is attached;
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) = (3/4)ˣ has its graph to be graph (a) and the table to be:
x -2 -1 0 1 2
y 16/9 4/3 1 3/4 9/16
How to find the table and graph for function f(x)From the question, we have the following equation that can be used in our computation:
f(x) = (3/4)ˣ
This function is an exponential function
The x values present on the tables of values are
x = -2, -1, 0, 1 and 2
These values are to be used to calculate the f(x) values of the function
To do this, we simply substitute x = -2, -1, 0, 1 and 2 f(x) = (3/4)ˣ
The above highlights give:
f(-2) = (3/4)⁻² = 16/9
f(-1) = (3/4)⁻¹ = 4/3
f(0) = (3/4)⁰ = 1
f(1) = (3/4)¹ = 3/4
f(2) = (3/4)² = 9/16
This means that the table of values is
x: -2 -1 0 1 2
y: 16/9 4/3 1 3/4 9/16
Next, we plot the graph of the function using the values in the above table
The graph that passes through the points in the above table (i.e. (-2, 16/9), (-1, 4/3).....) is graph (a)
Hence, the graph of the function is graph (a)
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How to solve question 1 and 2?
Answer:
question 1 isn't formatted properly, for question 2, k=-2
Step-by-step explanation:
5k-8+2=-16
5k-6=-16
5k=-10
k=-2
a sports guard thickness of about mm is desirable for heavy contact sports in which injuries are more likely. group of answer choices 1 2 4 8
Answer:
What is the question?! I don't understand, sry?!
Step-by-step explanation:
when using bayes theorem, why do you gather more information ? a. to help you make a better decision b. because you are missing a value c. you can't make a choice unless you do.
The Bayes's theorem help us to take an better prediction of even with the help of another occuring event.
About Bayes's theorem.Bayes' theorem, in probability hypothesis, a method for reexamining expectations considering important proof, otherwise called restrictive likelihood or opposite likelihood. The hypothesis was found among the papers of the English Presbyterian clergyman and mathematician Thomas Bayes and distributed after death in 1763.
According to question:Bayes' theorem expresses that the contingent likelihood of an occasion, in view of the event of another occasion, is equivalent to the probability of the subsequent occasion given the principal occasion duplicated by the likelihood of the main occasion.
This theorem gives us an idea to take better prediction of the event.
Option(a) to help you make a better decision is correct answer.
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by the age of ________, the ratio of women to men is about 2 to 1.
Answer: 85
Step-by-step explanation:
You have to specify the power output of a motor for a ski tow rope that will carry 25 skiers at a time. The grade of the ski slope is 32 above horizontal and the average coefficient of kinetic friction between skis and snow is 0.12. The tow speed is to be 2.0 m/s and each skier has an inertia of 60 kg (a reasonable average value)
The power output of a motor for a ski tow rope is 6925.333 Watt.
We are know that,
Speed = v = 2.0m/s
Mass = m = 60kg
Number of skier = N = 25
The slope formed angle = Ф = 32°
The acceleration due to gravity = 9.8m/s²
Thus, to calculate the power of motor for a ski tow rope then we use formula, and (we know that F = mg)
P = (Nmg)(vcosФ)
Where , P is the power and putting the all given values in above equation,
P =[(25× 60kg ×9.8m/s²)×(2.0km/hr)×{(1m/s})/(3.6km/h)} cos32°
P = 8166.66×0.848 Watt
P = 6925.333 Watt
Therefore, the power output of a motor for a ski tow rope would be 6925.333 Watt.
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The ditance to your uncle' houe i 728 mile, and the ditance to Atlanta i 624 mile. If it took 14 hour to drive to your uncle' houe, how long would you etimate the drive to Atlanta to be?
It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.
What is the distance?
Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Given that,
The distance to uncle's house = 728 miles
The time taken to drive to uncle's house = 14 hours
So,
speed = (728)/14 = 52 miles/hour
Then the time to drive 624 miles(to Atlanta) is calculated by,
time t = (624)/52 = 12 hours.
Hence, It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.
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i need help with number 14
Answer:
Step-by-step explanation:
again , you know that the two angles add up to 180°
you know that by the complementary angle rule.
set the two equations equal to 180 and solve for x
180= eq1 + eq2
What is the value of slope in Y =- 3x 2?.
The slope of the line is m = - 3
What is the line's slope, please?
The slope is calculated by dividing the rise by the run. By examining the rise and run of a line's graph, you can calculate the slope of that line. The fact that a line's slope is constant throughout is one of its characteristics.the equation of a line of slope-intercept form is given by
y = mx + c
an equation of the form y = -3x + 2
now compare with equation
m = -3
c = 2
Thus, the slope of the line is m = - 3
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The complete question is -
What is the slope of the line y = -3x+2
A is an n×n matrix. Check the true statements below: A. If Ax=λx for some vector x, then x is an eigenvector of A. B. A steady-state vector for a stochastic matrix is actually an eigenvector. C. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. D. The eigenvalues of a matrix are on its main diagonal. E. An eigenspace of A is just a null space of a certain matrix.
Options A,B are true and the other 3 C,D,E are false.
What is matrix?
The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.
A) If Ax=λx for some vector x, then x is an eigenvector of A
if x not equal to 0 then the statement is true.
B) A steady-state vector for a stochastic matrix is actually an eigenvector:
As it is an egien vector the statement is true.
C) If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.:
the statement is false.
D) The eigenvalues of a matrix are on its main diagonal:
It's only true for the trigonal matrix.
E) An eigenspace of A is just a null space of a certain matrix:
the statement is false.
Hence we have determined the true and false statement from the given option.
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The glee club has $90 to spend on pens and pencils. Each pen costs $0. 75 and each pencil costs $0. 15. Let x represent the number of pens, and let y represent the number of pencils.
The correct answer is 0.75x + 0.15y = 90 is the equation that describes the quantity of pens and pencils the glee club can purchase.
The maximum number of pens the club can purchase is 120.
The maximum number of pencils the club can purchase is 600.
Each pen costs $0.75.
Total number of pens = x
Each pencil costs $0.15
y = number of pencils
(Cost of each pen) x (Number of pens) + (Cost of each pencil) x (Number of pencils) = $90 which equals the total cost for pens and pencils.
The formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.
When 0.75x = 90
x = 90/0.75
x = 120, the club purchases the most pens.
The maximum number of pens the club can purchase is 120.
When the club purchases the most pens, 0.15x = 90
x = 90/0.15
x = 600
Hence, the maximum number of pencils the club can purchase is 600 and the formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.
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directions: use the simple interest formula to calculate the interest and the total amount to be repaid in one lump sum for the purchases below. simple interest rate formula i
To calculate the interest and the total amount , we use Simple interest formula S.I = ( P× r × t ) / 100.
Simple interest is a method of calculating the interest that is charged on fixed deposits , savings accounts and the loans .
The money you put in the bank is called the principal, the bank pays you interest.
The interest is computed as a certain percent of the principal; called the rate of interest. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent.
The variable for time, t, represents the number of years the money is left in the account.
The formula to calculate simple interest is :
S.I = ( P× r × t ) / 100
where P is principle , r = rate of interest and t is term of loan in year.
To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable.
To find the total amount ,
Amount = Principle + Interest
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1) there isn't a clear and straightforward way to find the optimal value of k in k-means clustering 2) it is sensitive to the starting positions of the initial centroids
The statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.
K-means Clustering is a vector quantization technique that seeks to split "n" observations into "k" clusters, with each observation referring to the cluster with the closest mean, which reflects a model of the cluster.
This means that the K-means algorithm recognizes the "k" number of centroids and then allocates every data point to the cluster with the fewest centroids.
Thus, the statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.
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What is the following quotient? startfraction 2 over startroot 13 endroot + startroot 11 endroot endfraction.
The quotient of division 2/( √13+√11) is (√13-√11).
A quotient is a quantity that is obtained by dividing two integers. The answer is D.
What is a quotient?
A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.
In order to find the quotient of the fraction, we need to take the rationalize of the fraction.
= 2/(√13 + √11)
= 2/(√13 + √11) x (√13 - √11)/(√13 - √11)
= 2(√13 + √11)/(√13)^2 - (√11)^2
= 2(√13 - √11)/13-11
= 2(√13-√11)/2
= (√13-√11)
Hence the answer is, the quotient of division 2/( √13+√11) is (√13-√11).
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left. How many friends were at Jack's party?
As per the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.
As given in the question,
Total number of chocolates given by Jack's mother is equal to 50
Number of chocolates given by Jack to his friends = 3
Number of chocolates left with Jack = 2
Let 'x' represents the number of friends
Requires equation to show the relation we have,
3x + 2 = 50
⇒ 3x = 50 - 2
⇒ 3x = 48
⇒ x = 48/ 3
⇒ x= 16 friends
Therefore, for the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.
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ectangular prism is made up of multiple layers with 9 cubes in each layer. Each cube measures 2/3 of an inch on each side. The volume of the rectangular prism is 10 2 /3 cubic inches. How many layers of cubes are in this prism? '
The number of layers of cubes present in the rectangular prism of volume 102/3 in³ is 7.
What is volume?Volume is defined as the space occupied within the boundaries of any three-dimensional solid.
To calculate the number of layers of cubes in the prism, we use the formula below.
n = V/9l³............Equation 1
Where:
n = Number of layers in the prismV = Volume of the rectangular prisml = Length of each cube.From the question,
Given:
V = 102/3 in³l = 2/3 in³Substitute these values into equation 1
n = 102/3/(9×2/3)n = 102/3/(18/3)n = 5.66n ≈ 7Hence, there are 7 layers in the rectangular prism.
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