The best prediction for the bacteria population after 8 days is approximately 14,301.67 bacteria.
At start experiment are 50 bacteria in dish. The bacteria expected to grow a rate 220% each day. What is the prediction for the bacteria population after 8 days?
To find the predicted population of bacteria after 8 days, we need to apply the given growth rate of 220% per day to the initial population of 50 bacteria for each day, starting from day 1 and continuing to day 8.
For each day, the population of bacteria is expected to be 220% or 2.2 times the population of the previous day. So, we can use the formula:
P = P0 \(x (1 + r)^n\)
where P is the predicted population after n days, P0 is the initial population, r is the growth rate per day (as a decimal), and n is the number of days.
Substituting the given values, we get:
P = 50\(x (1 + 2.2)^8\)
P ≈ 14,301.67
Learn more about prediction
brainly.com/question/31561722
#SPJ11
Please help i give 36 points please help and i only have three questions
name the 10 native american cultural groups found in north america.
why did each native american cultural group develop a distinct culture?
choose any two of these groups and provide a brief description of their cultures.
be certain to include an example or explanation telling how and why the cultures developed as they did.
Navajo, Lakota Sioux, Iroquois, Cherokee, Apache, Hopi, Ojibwe, Mohawk, Inuit and Nez Perce.
Native American cultural groups found in North America1. Navajo: The Navajo people are the largest Native American group in the United States, primarily residing in the Southwest. They have a rich culture centered around their language, art, weaving, and traditional ceremonies.
2. Lakota Sioux: The Lakota Sioux are a Plains Native American group known for their nomadic lifestyle and deep connection to the land. They were skilled hunters, relied on buffalo for sustenance and materials, and developed a warrior-based society.
3. Iroquois (Haudenosaunee): The Iroquois Confederacy, or Haudenosaunee, is a group of Native American tribes located in the northeastern United States and southeastern Canada. They are known for their longhouses, matrilineal kinship system, political governance, and the creation of the Great Law of Peace.
4. Cherokee: The Cherokee Nation is located primarily in the southeastern United States. They developed an agricultural society with advanced farming techniques and were known for their sophisticated government structure, written language (Cherokee syllabary), and cultural resilience.
5. Apache: The Apache tribes, including the Chiricahua, Jicarilla, and Western Apache, inhabited the southwestern United States. They were skilled warriors and hunters, adapting to their environment by utilizing guerrilla warfare tactics and developing deep spiritual beliefs.
6. Hopi: The Hopi people are located in northeastern Arizona. They are known for their religious ceremonies, intricate pottery, and architectural structures, including their adobe dwellings called pueblos. The Hopi have a strong spiritual connection to the land and maintain a communal lifestyle.
7. Ojibwe (Chippewa): The Ojibwe tribes reside primarily in the northern Great Lakes region. They have a rich cultural heritage rooted in storytelling, traditional crafts such as birch bark canoe building and beadwork, and the Midewiwin society, which is a spiritual and healing tradition.
8. Mohawk: The Mohawk Nation is part of the Iroquois Confederacy and resides in the northeastern United States and eastern Canada. They were historically agriculturalists, known for their farming techniques such as the Three Sisters (corn, beans, and squash) and were also skilled warriors.
9. Inuit: The Inuit people inhabit the Arctic regions of North America, including Alaska, Canada, and Greenland. They have a unique culture adapted to the harsh Arctic environment, relying on hunting, fishing, and the use of igloos and other snow shelters for survival.
10. Nez Perce: The Nez Perce Tribe traditionally resided in the Pacific Northwest. They were skilled horse breeders, hunters, and gatherers. They had a complex social structure and were known for their artistic expressions, including intricate beadwork and basketry.
Learn more about tribes here:
https://brainly.com/question/3271247
#SPJ4
The North American continent is home to numerous Native American cultural groups, each with its distinct history, traditions, and cultural practices. While it is challenging to encompass all of them, here are ten Native American cultural groups found in North America:
1. Navajo (Diné)
2. Cherokee (Tsalagi)
3. Lakota (Sioux)
4. Apache (Ndee)
5. Iroquois (Haudenosaunee)
6. Hopi (Hopituh Shi-nu-mu)
7. Ojibwe (Anishinaabe)
8. Cheyenne (Tsitsistas)
9. Choctaw (Chahta)
10. Mohawk (Kanien'kehá:ka)
Each Native American cultural group developed a distinct culture due to a combination of geographical factors, historical experiences, available resources, and interactions with neighboring tribes. Factors such as climate, landforms, flora, fauna, and proximity to water sources played significant roles in shaping their lifestyles, economies, and social structures. Additionally, migration patterns, trade networks, and intertribal conflicts influenced cultural exchange and differentiation.
Let's explore the cultures of the Cherokee and the Hopi as examples:
1. Cherokee (Tsalagi):
The Cherokee people were historically concentrated in the southeastern region of the United States. They developed an agricultural society, cultivating crops such as corn, beans, and squash. The Cherokee had a matrilineal kinship system, where descent and inheritance were traced through the mother's line. They had a complex political structure with a chiefdom, council, and clan system. The Cherokee are renowned for their unique syllabary, invented by Sequoyah, which enabled the written expression of their language. Despite facing significant challenges during European colonization, including forced removal on the Trail of Tears, the Cherokee managed to preserve their language, cultural practices, and sense of community.
2. Hopi (Hopituh Shi-nu-mu):
The Hopi people reside primarily in northeastern Arizona. Their culture is deeply rooted in agriculture and is centered around the cultivation of corn, beans, and squash, known as the Three Sisters. The Hopi developed an intricate system of terraced farming to optimize water usage in their arid environment. They have a matrilineal social structure, where property and clan membership are passed down through the female line. The Hopi are known for their religious ceremonies and ceremonial katsina dances, which reflect their spiritual beliefs and the cycles of the agricultural calendar. Their culture places great emphasis on community cooperation, harmony, and maintaining a balanced relationship with nature.
The Cherokee and Hopi cultures developed as they did due to their unique geographical locations and historical experiences. The Cherokee's agrarian society emerged in the fertile lands of the southeastern United States, while the Hopi's agricultural practices evolved to adapt to the arid conditions of northeastern Arizona. Both groups incorporated cultural practices and values that were essential for their survival and provided a framework for their social cohesion and identity. The resilience and determination of these cultures allowed them to withstand external pressures and maintain their distinct traditions throughout history.
to more about groups visit:
brainly.com/question/12932780
#SPJ11
The UN High Commission on Refugees (UNHCR) and other humanitarian crisis agencies and organizations have conducted a series of studies to assess the magnitude of the humanitarian crisis resulting from Russia's invasion of Ukraine. (Never mind the details - for the context of the problem, you can assume the techniques are best sampling practices.) One particular sample of 1275 Ukrainians found that 144 had become either internally displaced or had become refugees. Russian government sources dispute this finding and claim that no more than 10% of the pre-war Ukrainian population of 44 million has become displaced, and further adds that this is because they were fleeing Ukraini-Nazis into the arms of their Russian liberators. (Never mind Russia's explanation - we are just going to work with Russia's claimed number, not their explanation.)
a. Using a 5% significance level test, test Russia's claim that no more than 10% of the population has become displaced. Does the sample result allow us to reject the Russian claim at the 5% level? Explain. Include a graph with the answer (Hint - read the full question, including part (b) before answering. If you read it carefully, you can save yourself some time.)
b. What is the probability of committing a type 2 error if we fail to reject the null based on our computation in part (a)? For this, we can assume that the true population proportion of displaced Ukrainians is 12%. Include a graph with answer.
c. How would our answer change with a larger sample size? Explain. (This is an intuitive question - do not expect a quantitative answer.)
1. The data suggests that the proportion of displaced Ukrainians is likely higher than 10% of the population.
2. A larger sample size would likely provide stronger evidence to either support or reject Russia's claim regarding the proportion of displaced Ukrainians.
a. Hypothesis Test:
The null hypothesis (H0) is that the proportion of displaced Ukrainians is equal to or less than 10% of the population.
The alternative hypothesis (H1) is that the proportion of displaced Ukrainians is greater than 10% of the population.
Using a significance level of 5% (α = 0.05), we will conduct a one-tailed z-test.
First, we calculate the test statistic (z-score):
z = (P - p) / √(p(1-p) / n)
where P is the sample proportion, p is the hypothesized proportion, and n is the sample size.
In this case, P = 144/1275 ≈ 0.113
p = 0.10
n = 1275
Calculating the z-score:
z = (0.113 - 0.10) / √(0.10(1-0.10) / 1275)
z ≈ 1.668
Next, we find the critical z-value for a one-tailed test at a 5% significance level.
So, the critical z-value for a 5% one-tailed test is 1.645.
Since the calculated z-score (1.668) is greater than the critical z-value (1.645), we have evidence to reject the null hypothesis.
Therefore, based on the sample result, we can reject Russia's claim at the 5% significance level. The data suggests that the proportion of displaced Ukrainians is likely higher than 10% of the population.
c. Larger Sample Size:
With a larger sample size, our estimate of the proportion of displaced Ukrainians would become more precise. The margin of error would decrease, providing more accurate information about the true population proportion.
Learn more about Hypothesis Test here:
https://brainly.com/question/24224582
#SPJ4
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation. After how many months will the total cost be $58?
Answer:
y=4x+30
In 7 months, the total cost will be $58.
Step-by-step explanation:
Since the monthly fee is 4, it's going to be the constant, or the slope. And 30 is a one time fee, so it's the y-intercept.
How many Months?
58-30=28
28/4=7
So in 7 months.
Answer:
7 months
Step-by-step explanation:
y =4x + 30
58 = 4x + 30
28 = 4x
x = 7
it will take 7 months.
Which of the following is a point on the line defined by the parametric equations below?
[x(t)=t+7
y(t) = 5-2t
○ (3,10)
○ (7,0)
O (8,3)
O (2,1)
The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.
What is an example of a parametric equation?Well, a parametric equation is an equation where the variables (usually x and y) are expressed in terms of a third parameter, usually expressed as t. For example: Consider the equation of a circle with radius r and center at (0,0) : x2+y2=r2 x 2 + y 2 = r 2 .parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. More than one parameter can be employed when necessary.If there are m free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors: x = s1v1 + s2v2 + ··· + smvm. This is called a parametric equation or a parametric vector form of the solution.Types of Parametric test–
Two-sample t-test.Paired t-test.Analysis of variance (ANOVA)Pearson coefficient of correlation.To learn more about parametric refer to:
https://brainly.com/question/12297627
#SPJ1
Simplify the radical expression
please help omg what is this
Answer: -145x^5sqrt7x
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Suppose the company wants to improve its capability to a 5-sigma level by reducing the variability of its process. Which of the following standard deviations would meet a 5-sigma capablity for Cpk? Check all that apply, and assume the process mean remains unchanged from the original problem. a. 0.005 b. 0.015 c. 0. 025 d. 0.035 e. 0.045 f. 0.055
The standard deviations that would meet a 5-sigma capability for Cpk are 0.005, 0.015, and 0.025. (Options A, B and C).
How to Determine the Standard Deviation?To determine which standard deviations would meet a 5-sigma capability for Cpk, we need to use the following formula:
Cpk = minimum((USL - mean) / 3sigma, (mean - LSL) / 3sigma)
where USL is the upper specification limit, LSL is the lower specification limit, mean is the process mean, and sigma is the process standard deviation.
For a 5-sigma capability, we want Cpk to be at least 2.0, so we can set up the following inequality:
2.0 <= minimum((USL - mean) / 3sigma, (mean - LSL) / 3sigma)
Assuming the process mean remains unchanged, and the specification limits are at ±3 sigma from the mean (which is a common assumption), we can simplify the inequality to:
2.0 <= 1/3sigma
which can be rearranged as:
sigma <= 1/6
Therefore, the standard deviation should be less than or equal to 0.1667 to achieve a 5-sigma capability.
Now we can check which of the given standard deviations meet this criterion:
a. 0.005: Yes, this is less than 0.1667.
b. 0.015: Yes, this is less than 0.1667.
c. 0.025: Yes, this is less than 0.1667.
d. 0.035: No, this is greater than 0.1667.
e. 0.045: No, this is greater than 0.1667.
f. 0.055: No, this is greater than 0.1667.
Learn more about standard deviation here: https://brainly.com/question/28225633
#SPJ1
A quadratic function is defined by g(x) = 2x² + 12x + 1. Write this in the completed-square (vertex) form
and show all the steps.
The completed-square (vertex) form 2x² + 12x + 1 is 2(x+3)^2−17. Completing the Square is a technique to find maximum or minimum values of quadratic functions.
How to find completed-square ?Completing the square is a highly helpful technique or way to change a quadratic equation from also known as the "standard form," to its "vertex form,".
For some combinations of h and k, completing the square is a method for transforming a quadratic polynomial. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Finding the maximum or lowest values of quadratic functions can be done using the square method, sometimes known as "completing the square."
Use the form ax^2 + bx + c, to find the values of a, b, and c.
Consider the vertex form of a parabola.
a(x+d)^2+e
Find the value of d using the formula
d = b/2a.
d = 3
Find the value of e using the formula
e = c− b^2 / 4a.
e = −17
Substitute the values of a, d, and e into the vertex form 2(x+3)^2−17.
2(x+3)^2−17
To learn more about completed-square refer :
https://brainly.com/question/2044593
#SPJ1
An angle measures 48° more than the measure of its complementary angle. What is the
measure of each angle?
Answer:
The angles measure 21 degrees and 69 degrees.
Step-by-step explanation:
Complementary angles have a sum of 90 degrees when added together.
Let's call the complementary angle x. We can write the angle that we're looking for as in terms of x as x + 48.
Since these angles must sum to 90 we can write the equation and solve:
x + x + 48 = 90
2x + 48 = 90
2x + 48 - 48 = 90 - 48
2x = 42
x = 21
x + 48 = 69
21 degrees and 69 degrees.
Answer:
69° and 21° is the answer.
The height of a building is proportional to the number of floors. The figure shows the height of a building with 9 floors. help me with a and b please
Answer:
Step-by-step explanation:
69n² × 69n² =0
Can someone please help me with this question.
Answer:
Since FAB and GED are congruent they also create the same angle. The angle is shown with the curved line. AE is a straight line, or 180 degree angle. This means that FAB and ABC must create a 180 degree angle... and if FAB is congruent to GED then GED and EDC are also congruent.
Step-by-step explanation:
I hope this made sense, it's kind of messy but I hope it helps.
I will mark you brainiest if you can answer this
Answer:
D
Step-by-step explanation:
what temperature is 2°C higher than normal body temperature
\(it s \: fever \: \)
We get fever when our body temperature reaches to 100° C and our normal body temperature is 98°C.
A probability experiment is conducted in which the sample space of the experiment is S ={6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. Let event E={6, 7, 8, 9. 10, 11, 12, 13}. Assume each outcome is equally likely. List the outcome in E°. Find P(E°).
The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.
E° is the complement of event E. It is the set of all outcomes that are not in event E and can be expressed as E° = {14, 15, 16, 17}.The probability of event E° is calculated by summing the probabilities of all outcomes in the event, P(E°) = P(14) + P(15) + P(16) + P(17). Since all outcomes in the sample space are equally likely, the probability of each outcome is 1/12. This means that the probability of event E° is calculated as follows:
P(E°) = 1/12 + 1/12 + 1/12 + 1/12 = 4/12 = 1/3.
Therefore, The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.
Learn more about complement here:
https://brainly.com/question/22048070
#SPJ4
prove that √p is an irrational number , if p is not a perfect square.
\( \huge \frak \green{question}\)
prove that √p is an irrational number , if p is not a perfect square.
\( \huge \frak \red{answer}\)
Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-
=> √p = a/b
=> √p b = a
=> pb² = a² ….(i) [Squaring both the sides]
=> a² is divisible by p
=> a is divisible by p So, we can write a = pc for some integer c.
Therefore,
a² = p²c² ….[Squaring both the sides]
=> pb² = p²c² ….[From (i)]
=> b² = pc²
=> b² is divisible by p
=> b is divisible by p
=> p divides both a and b.
=> a and b have at least p as a common factor.
But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.
_____________________________________
\( \bold \green{i \: hope \: it \: is \: helpful}\)
________________________________
What is the value of X?
Answer:
x=12°
Step-by-step explanation:
180 - 90 = 4x - 2° + 3x + 8 °
90°= 7x + 6
90° - 6 = 7x
7x = 84
x= 84/7
x = 12
part d: using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)
To determine the scale factor relationship between the pizzas based on their diameters, we need to compare the sizes of the pizzas. The scale factor represents the ratio between the corresponding measurements of two similar objects.
In this case, we would compare the diameters of the pizzas. The scale factor can be calculated by dividing the diameter of one pizza by the diameter of another pizza. For example, if Pizza A has a diameter of 12 inches and Pizza B has a diameter of 8 inches, the scale factor between them would be: Scale Factor = Diameter of Pizza A / Diameter of Pizza B = 12 inches / 8 inches = 1.5. Therefore, the scale factor relationship between the pizzas is 1.5. This means that the diameter of Pizza A is 1.5 times larger than the diameter of Pizza B.
To know more about scale factors here: brainly.com/question/29464385
#SPJ11
The probability that a randomly selected student is on honor roll is 0.24 The probability that a randomly selected student is on the honor roll and takes an art class is 0.18 what is the probability that a randomly selected student takes an art class, given the student is on honor roll
Answer: 0.06
Step-by-step explanation: subtract them and you'll get your answer
The probability that a randomly selected student takes an art class, given the student is on honor roll is P ( A|B ) = 0.75
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
The conditional probability is given by
P(A|B) = P(A and B) / P(B)
where A and B are events.
In this case, let A be the event that a randomly selected student takes an art class, and let B be the event that the student is on honor roll.
The probability that a selected student is on honor roll P ( B ) = 0.24
The probability that a selected student is on honor roll and takes an art class P (A and B) = 0.18
Now , the probability that a randomly selected student takes an art class, given the student is on honor roll P(A|B) = P(A and B) / P(B)
P(A|B) = P(A and B) / P(B) = 0.18 / 0.24 = 0.75
Hence , the probability is 0.75 or 75%
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ3
a sequence is given by the rule 4n - 5. what is the 20th term in the sequence?
Answer:
a₂₀ = 75
Step-by-step explanation:
Substitute n = 20 into the n th term rule , that is
a₂₀ = 4(20) - 5 = 80 - 5 = 75
BC=8.5cm.
Angle ABC = 90°.
Angle ACB = 38°.
Work out the length of AB.
Give your answer correct to 3 significant figures.
Answer:
AB = 154
Step-by-step explanation:
Triangle Rectangle ABC = 90
Sen 38°=0.616 = 154/250
Sen 52°=0.788 =197/250
AC =250
AB = 154
BC = 197
VOCABULARYInstructionsList the 6 sign neatly and show an example of each one
Math signs
#1. Plus sign or addition sign
\(54+9\)#2. Minus sign or substraction sign
\(54-9\)#3. Times sign or multiplication sign
\(54\times9\)#4. Division sign
\(54\div9\)#5. Equals sign
\(5=2+3\)5 is equal to 2+3
#6. not equal sign
\(5\ne4\)5 is not equal to 4
1.8,1.35,2.5, squat root of 5 in least to greatest
Answer: 1.35, 2.5, 1.8
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) 2.5^=97.6
2) 1.8^5= 18.8
3) 1.35^5=4.4
or
1) 2.50
2) 1.80
3) 1.35
the scores on a standardized test are normally distributed with a mean of 90 and standard deviation of 15. what test score is 0.1 standard deviations above the mean?
The test score is 91.5.
z-score:
A z-score is the number of standard deviations from the mean value of the reference population.
Here we have to find the test score.
Mean(μ) = 90
Standard deviation(б) = 15
z-score = 0.1
Formula for z-score:
z = X - μ / б
Now putting the values in the equation:
0.1 = X - 90 / 15
1.5 = X - 90
X = 91.5
Therefore the test score is 91.5.
To know more about the z-score refer to the link given below:
https://brainly.com/question/25638875
#SPJ4
What is the solution to the following system of equations
4x+2y=6
X-y=3
Answer:
The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)
Step-by-step explanation:
4x + 2y = 6 ....… (1)
x − y = 3 …..... (2)
Example, for equation 2 is:
x - y = 3
x = 3 + y
Put in equation 1:
4(y + 3) + 2y = 6
4y + 12 + 2y = 6
6y = -6
y = -6/6
y = -1
We have the value of y, then the value of x will be:
x = 3 + y
= 3 + (-1)
= 3 - 1
= 2
So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)
show that a chessboard with 7 rows and 12 columns can be covered by non-overlappingdominoes.
The chessboard has 7 rows x 12 columns = 84 squares. Since 84 is an even number, it can be covered by non-overlapping dominoes. To achieve this, simply place the dominoes horizontally along the rows, covering two adjacent squares in each column.
To show that a chessboard with 7 rows and 12 columns can be covered by non-overlapping dominoes, we need to use the fact that each domino covers exactly two adjacent squares on the chessboard. Since there are an even number of squares on the chessboard (84), we know that we can cover all the squares with dominoes.
To ensure that the dominoes do not overlap, we can arrange them in pairs so that they cover adjacent squares in the same row. We can start by placing a domino on the first two squares in the first row, and then continue placing dominoes in pairs along each subsequent row until we reach the last row.
Since each domino covers two squares in the same row, we know that we can cover all the squares in the 12 columns using this method. However, we may have leftover squares in the last row that are not covered by the dominoes. To address this, we can simply place additional dominoes in the remaining columns in the last row, covering the remaining squares.
In this way, we can cover the entire chessboard with non-overlapping dominoes, using a total of 42 dominoes in this case.
A chessboard with 7 rows and 12 columns can indeed be covered by non-overlapping dominoes. Since each domino covers exactly two adjacent squares, you need to ensure that the total number of squares on the chessboard is even.
Visit here to learn more about Chessboard:
brainly.com/question/29504883
#SPJ11
f(x)=x-3/x+2 determine for each x-value where it is in the domain of f or not
-2 yes/no
0 yes/no
3 yes/no
PLS
f(x) = (x - 3)/(x + 2)
As the equation is basically a fraction the only thing that can be out of domain is if the denominator is equal to 0, so let's see when the denominator can be 0
x + 2 = 0
x = -2
So -2 is out of domain and all the other numbers are inside the domain.
Answer:
\(-2 \implies \sf no\)
\(0 \implies \sf yes\)
\(3 \implies \sf yes\)
Step-by-step explanation:
Given rational function:
\(f(x)=\dfrac{x-3}{x+2}\)
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
A rational function is not defined when its denominator is zero.
Therefore, to find when the given function f(x) is not defined, set the denominator to zero and solve for x:
\(x+2=0 \implies x=-2\)
Therefore, the domain is restricted to all values of x except x = -2.
This means that the domain of f(x) is (-∞, 2) ∪ (2, ∞).
In conclusion:
x = -2 is not in the domain of f(x).x = 0 is in the domain of f(x).x = 3 is in the domain of f(x).A rectangular box with a square base, an open top, and a volume of 32,000 cm3 is to be made. What is the minimum surface area for the box
the minimum surface area for the box is 4800 cm².
Forming the Equation of SurfaceArea
It is given that the given rectangular box is square-based and top is open. hence, it consists of square and 4 rectangles.
Let the side of the square be a, and height of the box be h.
Then, the total surface area of the box will be given by,
S = a² + 4ah _________ (1)
Also, it is given that the volume of the box is, V = 32000 cm³
The volume of the rectangular box, V = a² h
Eliminating One of the Variables From the Equation
The volume of the rectangular box, V = a² h
⇒ a² h = 32000
⇒ h = 32000/a² _______ (2)
Substituting this value of h in equation (1), we get,
S = a² +4a(32000/a²)
S = a²+128000/a
Minimizing the Surface Area Equation
To find the minima, put, dS/da = 0
dS/da = 2a-128000/a²
⇒ 2a-128000/a² = 0
Multiplying the whole equation with a², we get,
2a³-128000 = 0
⇒ 2a³ = 128000
⇒ a³ = 128000/2
⇒ a³ = 64000
⇒ a = 40 cm
Calculating the Minimum Surface Area
From, equation (2), h = 32000/(40)²
h = 32000/1600
h = 20 cm
Now, substituting the computed values of a and h in equation (1), we get,
S = (40)² +4(40)(20)
S = 1600 +3200
S = 4800 cm²
∴ The minimum surface area of the box is 4800 cm².
Learn more about surface area here:
https://brainly.com/question/2835293
#SPJ4
independent variable was contact plates placed on the tile for less than 5 seconds. the standardized variables were the length of time plates were on the tiles. the control was the inoculating floor tiles for five days in chicken broth. the dependent variable was the plates placed on the tile for more than 5 seconds.
Their experimental design was Independent variable was contact plates placed on the tile for less than 5 seconds. Option D is the correct answer.
The independent variable is the factor that is being manipulated by the experimenter. In this case, the experimenter is manipulating the length of time the plates are on the tiles. The dependent variable is the factor that is being measured by the experimenter. In this case, the experimenter is measuring the amount of bacteria on the plates.
The control is a group of subjects that are not exposed to the independent variable. In this case, the control group is the floor tiles that have been inoculated with chicken broth. The control group is used to compare the results of the experimental group, which is the group of plates that have been dropped on the tiles.
The standardized variables are the factors that are kept the same for both the experimental group and the control group. In this case, the standardized variables are the type of food, the surface of the tiles, and the temperature of the room. These factors are kept the same so that the only difference between the two groups is the length of time the plates are on the tiles.
This experimental design is a well-controlled experiment because the experimenter has taken steps to ensure that the only difference between the two groups is the length of time the plates are on the tiles. This will allow the experimenter to make accurate conclusions about the effect of the independent variable on the dependent variable. Option D is the correct answer.
For such more question on variable:
https://brainly.com/question/28248724
#SPJ8
The following question may be like this:
The Myth busters conducted an experiment to test the five second rule. Which of the following represented their experimental design?
The standardized variables were the length of time plates were on the tiles. The control was the inoculating floor tiles for five days in chicken broth. The dependent variable was the plates placed on the tile for more than 5 seconds. Independent variable was contact plates placed on the tile for less than 5 seconds.The volumes of two similar solids have an 125 : 216 ratio. What is the ratio of their side lengths
Answer:
5:6
Step-by-step explanation:
To find the ratio of side lengths you need to cube root of the ratio of the volumes. The reason you use the cube root is because you are multiplying 3 things together when you find volume.
\(\sqrt[3]{\frac{125}{216} } =\frac{5}{6}\)
5 : 6
one more lol sprry for a lot of post
Answer:
A
Step-by-step explanation:
list the clusters, gaps, outliers, and shape of this dot plot please!
Answer:
Cluster : 60,61,62,63
Gaps: 64,65 , 69,70
Outlier: 71
This is what I learned so don't blame me please!
Step-by-step explanation:
Cluster is numbers all on one side. Outlier can be the largest number or lowest. Normally the alone one.