for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, p value will be pchisq(8.4345,5)
To test a hypothesis' validity against actual data, a statistical calculation called a p-value is used. The probability of experiencing the results that were observed is calculated using a p-value, assuming that the null hypothesis is true. The p-value can be calculated by looking up the 8.4345 value in the Chi-Square distribution table with 5 degrees of freedom (6-1=5). The resulting p-value will depend on the significance level you choose.
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please help me!!!
Which number is greatest?
Answer:
It would be the third option, because the square root of 85 is 9.22, and 28/3 is 9.33 repeated.
Hope this helps, have a great day! :D
Step-by-step explanation:
is Pavers that cost a set amount per square foot proportional
(This is an imagine math quistion)
Answer:
Step-by-step explanation:
Yes it is because if the amount of Pavers change so does the cost.
when severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated?
The fundamental regression assumption that the error terms are independent of one another is broken when substantial autocorrelation is shown following the estimation of a regression model. Here option C is the correct answer.
The two error factors must be somewhat co-correlated in order for there to be autocorrelation. Having it indicates that the correlation between the two error factors is not equal to zero. It goes against the fundamental tenet of the traditional linear regression approach.
Autocorrelation measures the relationship between a variable's current value and its historical values. A perfect positive correlation is represented by an autocorrelation of 1, whereas a perfect negative correlation is represented by an autocorrelation of 1.
An explanation of how one or more independent variables relate to the target variable, response variable, or dependent variable that the regression model predicts.
Complete question:
When severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated? A - The dispersion of population data points around the population regression line remains constant everywhere along the line
B - The population of values is normally distributed about the population regression line.
C - Heteroscedasticity
D - The error terms are independent of each other.
E - A linear relationship exists between X and Y in the population
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Please Help!! Hurry!!!
Answer:
Step-by-step explanation:
(3, 12721) and (5,10835)
(10835 -12721) - (5-3)
-1886/2 = -943
Define a generic method called checkorder() that checks if four items are in ascending, neither, or descending order. The method should return -1 if the items are in ascending order, 0 if the items are unordered, and 1 if the items are in descending order. The program reads four items from input and outputs if the items are ordered. The items can be different types, including integers, strings, characters, or doubles.
The first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
What is JAVA?In order to have as few implementation dependencies as feasible, Java is a high-level, class-based, object-oriented programming language.
Java is an object-oriented, cross-platform programming language (OOP).
JavaScript, a scripting language used to build dynamic web pages, should not be confused with it.
Java is one of the most widely used programming languages in the world because of its dependability and simplicity.
So, the generic class needed to compare any kind of data structure is created by the Java code that follows.
Both integers and strings were employed in three different test situations.
The first is a list of integers in ascending order, the second is a list of integers in descending order, and the third is a list of texts that are not sorted.
The image below that is attached shows the results.
import java.util.Scanner;
class Brainly {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.println("Order: " + checkOrder(10, 22, 51, 53));
System.out.println("Order: " + checkOrder(55, 44, 33, 22));
System.out.println("Order: " + checkOrder("John", " Gabriel", "Daniela", "Zendaya"));
}
public static <E extends Comparable<E>> int checkOrder(E var1, E var2, E var3, E var4) {
E prevVar = var1;
if (var2.compareTo(prevVar) > 0) {
prevVar = var2;
} else {
if (var3.compareTo(prevVar) < 0) {
prevVar = var3;
} else {
return 0;
}
if (var4.compareTo(prevVar) < 0) {
return 1;
} else {
return 0;
}
}
if (var3.compareTo(prevVar) > 0) {
prevVar = var3;
}
if (var4.compareTo(prevVar) > 0) {
return -1;
}
return 0;
}
}
Therefore, the first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
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data set 1 has a mean of 84 and a mad of 6. data set 2 has a mean of 78 and a mad of 8. what can be concluded about the two distributions? select each correct answer. responses the means-to-mad ratio is 1. the means-to-mad ratio is 1. the distributions are somewhat similar. the distributions are somewhat similar. the means-to-mad ratio is 0.75. the means-to-mad ratio is 0.75. the distributions are similar.
The correct answer for the question that is being presented above is this one: "D.The distributions are somewhat similar; C.The distributions are similar." Data Set 1 has a mean of 84 and a MAD of 6. Data Set 2 has a mean of 78 and a MAD of 8. You conclude about the two distributions: .The distributions are somewhat similar; The distributions are similar.
6. 112 how big is the tip percentage at a restaurant? use technology and the restauranttips dataset to find a 95% confidence interval for the mean tip percentage (pcttip) at the restaurant. Interpret the answer in context
The 95% confidence interval for the mean tip percentage is (3.49, 4.22)
How to find confidence interval?Confidence interval is the two-sided limit consisting of the lower limit and the upper limit and the value between the two limits is the parameter value.
For this question, we have given a graph of the data, so we only need to see the data and interpret that to answer the question.
First, since confidence interval is 95% so we must see 2.5% limit for two side or equal to 0.025.
For the lower limit, see upper value of dot plot then see separate lowest 0.025 of data is 3.491 or 3.49.
For the upper limit, see lower value of dot plot then see separate highest 0.025 of data is 4.224 or 4.22.
Thus, the 95% confidence interval is (3.49, 4.22) for the mean tip percentage.
Your question is incomplete, but most probably your full question was (image attached)
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In recent years, 64% of students at ACME University were women. Administrators wondered if this proportion has diminished. In a recent survey of 300 ACME University students, 178 were women. a. Check all assumptions for performing the binomial test for a population proportion. Are they satisfied?SRS
b. Write the null and alternative hypotheses. Null- true proportion= 0.64Alternative- the true proportion= <0.64
c. Carry out the binomial test at the α = 7% significance level. Calculate the p-value, and state your conclusion in a complete sentence.
p-value= 0.05309if the null hypothesis is true, there is a 5.3% chance of getting a small sample proportion. We should reject the null if favor of the alternative if a=7
d. How would your conclusion in part c. change if the significance level α was changed to 5%? Explain. We would fail to reject the null hypothesis
As per the question, the following presumptions need to be true in order to run the binomial test for a population proportion:
a) A simple random sample (SRS) drawn from the population of interest must be used to gather the data. The sample's observations must be unrelated to one another. A binary answer variable is required (i.e., it can only take on two possible values, such as "success" and "failure").
The Central Limit Theorem must be applicable, hence the sample size must be sufficient (i.e., np and nq must both be greater than 5, where p is the proportion of successes in the population and q is the proportion of failures in the population).
From the facts given, it is unclear whether these presumptions are true. In example, it is unclear whether the observations are independent or whether the data was gathered from a straightforward random sample.
b) For this test, the following alternative and null hypotheses are presented:
The actual percentage of female students at ACME University is 0.64, which is null. Alternately, the actual percentage of female students at ACME University is less than 0.64.
c) The p-value must be determined before the binomial test can be run at the = 7% significance level. A statistical software program or a binomial test calculator can be used for this.
The p-value for this test is 0.05309 assuming the binomial test assumptions are met. This suggests that there is a 5.3% chance of generating a sample proportion as little as or smaller than the one seen in the survey if the null hypothesis is true (i.e., the true proportion of women among ACME University students is 0.64).
We can reject the null hypothesis in favor of the alternative hypothesis because the p-value is smaller than the significant level (0.05309 0.07). In other words, we can infer that the actual percentage of female students at ACME University is less than 0.64.
d) Our findings would remain unchanged if the significance criterion was raised to 5%. Because the p-value is still below the significance level (0.05309 0.05), the alternative hypothesis would still be accepted instead of the null hypothesis.
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Evaluate each expression for the given value of the variable. 4(x-4);x=7
Answer:
(28-16)
Step-by-step explanation:
x=7
4x-16
If x is 7
then it is 4x7 = 28
Therefore we can say 28-16 is our final answer.
Thank you.
theoretically, you could determine the value of the pre-exponential factor, a, from the same plot you use to determine the activation energy. what graphical feature would you use to determine this value?
The Arrhenius plot can be used to determine the value of the pre-exponential factor.
The slope of the Arrhenius plot can be used to find the activation energy. The Arrhenius plot can also be used by extrapolating the line back to the y-intercept to obtain the pre-exponential factor. The Arrhenius equation is k = Ae^(-Ea/RT), where A is the frequency or pre-exponential factor and e^(-Ea/RT) represents the fraction of collisions that have enough energy to overcome the activation barrier at temperature T.
In chemical kinetics, the pre-exponential factor is the pre-exponential constant in the Arrhenius equation, an empiorical relationship between temperature and rate coefficient. The pre-exponential factor is a constant that can be derived experimentally or numerically. It is also called frequency factor.
In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, plotted against reciprocal of the temperature. Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. Arrhenius plots show that reaction rates are inversely proportional to temperature changes.
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Study abroad. A survey on 1,509 high school seniors who took the SAT and who completed an optional web survey between April 25 and April 30, 2007 shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. 34 (a) Is this sample a representative sample from the population of all high school seniors in the US? Explain your reasoning (b) Let's suppose the conditions for inference are met. Even if your answer to part (a) indicated that this approach would not be reliable, this analysis mays be interesting to carry out (though not report). Construct a 90% confidence interval for the proportion of high school seniors (of those who took the SAT) who are fairly certain they will participate in a study abroad program in college, and interpret this interval in context (c) What does "90% confidence" mean? (d) Based on this interval, would it be appropriate to claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college?
No, this sample is not representative of all high school seniors in the US as the sample is selected by an optional web survey, which is not a good sampling technique as non-response bias is introduced.
90% confidence interval for a population proportion.
= 0.55 ± 1.645 * √0.55(1-0, 55)/1509
= 0.55 ± 0.0211
= (0.5289, 0.5711)
We are 90% confident the true proportion of high school seniors who are fairly certain they will participate in a study abroad program in college lies between 52.89% to 57.11%b
90% confidence means if we select 100 samples, 90 of them will have their sample statistic within the 90% confidence interval. Or otherwise, we can be 90% certain that the population parameter will fall within the 90% confidence interval.
Yes, as the lower limit of the confidence interval is greater than 50%, there is strong evidence to support the claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college.
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johnny is designing a rectangular poster to contain 12 in2 of printing with a 1-in margin at the top and bottom and a 3-in margin at each side. what overall dimensions will minimize the amount of paper used?
the dimensions will minimize the amount of paper used is with length 4 inch and a width 12 inch.
What is the area of the rectangle?
The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.
We have given
Johnny is designing a rectangular poster to contain 12 in² of printing with a 1-in margin at the top and bottom and a 3-in margin at each side.
Let,
l be the length and w be the width.
Area is A = l * w
Johnny is designing a rectangular poster to contain 12 in² of printing
i.e. Area of the inner printed section 12 = lw .........(1)
A 1-in margin at the top and bottom and a 3-in margin at each side.
i.e. l'=l+2 and w'=w+6
The total Area of the Poster is
A = (l+2) + (w+6) ...........(2)
Substitute the value of l from (1) in (2),
A = (12/w + 2) (w + 6)
A = 12 + 72/w + 2w + 12
A = 24 + 72/w + 2w
Differentiate w.r.t w,
A' = -72/w² + 2
For critical value put A'=0,
-72/w² + 2 = 0
2 = 72/w²
w² = 72/2
w² = 36
w = 6
Differentiate again w.r.t w,
A''(w) = 2(72/w²)
A''(6) = 2(72/(6)²)
A''(6) = 2(72/36)
A''(w) = 2*2 = 4>0
It is minimum at w=6.
Substitute in (1),
12 = lw
l = 2
The dimensions required are
l' = l + 2
= 2+2
= 4 inch
w'=w + 6
= 6 + 6
= 12 inch
Hence, the dimensions will minimize the amount of paper used is with a length 4 inch and a width 12 inch.
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Select the expression that have a value of 40 when x = 10.8.
The expression that has a value of 40 when x = 10.8. is (C) (x² ÷ 18) + 33.52
How to determine the expressions that fit the given category?The complete question is added at the end of this solution
From the question, we have the following expressions that can be used in our computation:
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
The value of x is given as
x = 10.8
So, we evaluate the expressions at this value of x
Expression A: 4,320 ÷ x
4,320 ÷ 10.8 = 400 --- false
Expression B 288/x + 16:
288/10.8 + 16 = 42.7 --- false
Expression C (x² ÷ 18) + 33.52:
(10.8² ÷ 18) + 33.52 = 40 --- true
Expression D (1,752 ÷ x) – 162/29:
(1,752 ÷ 10.8) – 162/29 = 156.6 --- false
Expression F x/12 + 36:
10.8/12 + 36 = 36.9 --- false
Hence, the only expression is (x² ÷ 18) + 33.52
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Complete question
Select all the expressions that have a value of 40 when x = 10.8.
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
3.
(07.04)
1 over 3b = 4 over 5 . Which of the following equals b in this equation? (4 points)
1 over 4
1 1 over 8
2 2 over 5
2 over 5
Answer:
c) 2 2 over 5 = 2 2/5
Step-by-step explanation:
Forming the equation,
→ (1/3)b = 4/5
Now the value of b will be,
→ (1/3)b = 4/5
→ b = (4/5) ÷ (1/3)
→ b = (4/5) × (3/1)
→ b = (4 × 3)/(5 × 1)
→ b = 12/5
→ [ b = 2 2/5 ]
Hence, value of b is 12/5.
PLEASE HELPPPPPPPPP QUICKKKK
WILL MARK BRAINLEST
please look in down below all in there
The letters that form the word
MATHEMATICS are placed in a bowl. Are the
odds favorable or unfavorable that he will
choose a letter that is a vowel followed by a
"T"?
Answer:
Step-by-step explanation:
The odds arent favorable its a 2/11 chance of happening
If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b].
True
False
If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b] then it is a true statement
What is an absolute maximum?
An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.
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we want to estimate the population proportion of people in new jersey who are in favor of legalizing marijuana. a 95% confidence interval within 5% of the true value is wanted. what size sample is needed?
In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.
The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
This can be calculated using the formula:
n = (z^2 * p * (1-p)) / (e^2)
where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).
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Ingrid competed in a triathlon that requires her to run, swim and bike. If she swam at a rate of 3 mph for 1 and a half hour, biked at 12 mph for 3 hours and ran for 6 mph for 4 hours, find the distance of the triathlon.
The distance of the triathlon, given the time Ingrid spent swimming, biking, and running, is 61.5 miles
How to find the distance?To find the distance of the triathlon, find the distance of the individual events which are the running, swimming, and biking. Then sum these distances up to find the triathlon distance that Ingrid ran.
The distance for swimming:
= Rate x Number of hours
= 3 x 0.5 hours
= 1.5 miles
The distance for biking:
= 12 x 3
= 36 miles
The distance for running:
= 6 x 4
= 24 miles
The triathlon distance is:
= 1.5 + 36 + 24
= 61.5 miles
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can someone answer this?
The value of y in the intersected lines is 80.
How to find the angles in the intersected line?When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles, angles on a straight line etc.
Therefore, the value of y in the angles can be found as follows:
10y - 12 = 3x + 29 (vertically opposite angles)
vertically opposite angles are congruent.
Hence,
10y - 12 = 3x + 29
10y - 3x = 41
6x - 3 + 10y - 12 + 37 = 180 (sum of angles on a straight lines)
6x + 10y = 180 + 3 + 12 - 37
6x + 10y = 158
combine the equation
10y - 3x = 41
10y + 6x = 158
9x = 117
x = 117 / 9
x = 13
6(13) + 10y = 158
10y = 158 - 78
10y = 80
y = 80 / 10
y = 8
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MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write an
equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a
vertical line. Who is correct? Explain.
O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.
O Your cousin. You may need more than two points to write an equation in slope-intercept form.
O Your friend. If f is a function, then the line is not vertical.
O Your cousin. If the line is vertical, it will not have a slope.
Answer:
O Your friend. If f is a function, then the line is not vertical.
Step-by-step explanation:
If you are given that the equation is a linear function, it can't have any undefined values.
Answer:
Your friend. If ƒ is a function, then the line is not vertical.
Step-by-step explanation:
I just had this question, and I solved it and got it right, see the picture
HELP HELP HELP FFHFJFHDHDHDHD
Answer:
y ≈ 15.9 cm
Step-by-step explanation:
using the tangent ratio in the right triangle
tan53° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{12}[/tex] ( multiply both sides by 12 )
12 × tan53° = x , that is
x ≈ 15.9 (to 1 decimal place )
=-7x+y=-19
-2x+3y=-9
The system of equation - 7x + y = 19 and - 2x + 3y = - 9 have solution at
(-101/9, -3318/19).
What is linear system of equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given, A system of equations - 7x + y = 19 and - 2x + 3y = - 9.
Now, multiplying eqn(i) by 2 and eqn(ii) by 7 we get,
- 14x + 2y = 38...(iii) and - 14x + 21y = - 63...(iv)
Now, subtracting eqn(iii) from eqn(iv) we get,
(- 14x + 21y = - 63)
- (- 14x + 2y = 38)
_______________
19y = - 101.
y = - 101/19
and putting the value of y in eqn(iv) we get x = - 3318/19.
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Which graph best represents the function f(x) = (x + 1)(x − 1)(x − 4)? (4 points) Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 10 and 15. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 2, and 3. The graph intersects the y axis at a point between 15 and 20. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, 1, and 3. The graph intersects the y axis at a point between 5 and 10. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.
A graph which best represents the polynomial function f(x) = (x + 1)(x − 1)(x − 4) is: D. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.
What is a polynomial function?In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can reasonably and logically deduce that the zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and these include the following on a graph:
Zeros = (-1, 0)
Zeros = (1, 0)
Zeros = (4, 0)
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Polygon P is dilated from the origin by a scale factor other than 1 to create polygon P′.
Determine whether each statement is true or false. Select True or False for each statement.
A. Polygon P is similar to polygo
n P′. TrueFalse
B. Polygon P is congruent to polygon P′. TrueFalse
C. The side lengths of polygon P are equal to the corresponding side lengths of polygon P′. TrueFalse
D. The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′. TrueFalse
The correct options are: Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′
What is dilation of figure?The dilation of a figure is enlargement or reduction of its original image to final image by a certain scale factor.
Given that, Polygon P is dilated from the origin by a scale factor other than 1 to create polygon P′
We know that, in dilation, both figures are similar not congruent, because they get enhanced or reduced by a certain scale factor, if scale factor is 1 then they can be congruent also.
Since, both figure are similar, therefore, their corresponding angles are congruent.
Hence, correct options are ; Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′.
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What is the value of x in the equation 3x-4y=65, when y=4?
Answer: The answer is 27
Answer:
27
Step-by-step explanation:
I hope its helpful to you.
Please answer this ASAP.
Answer:
y = 0.8x
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts
Bottom line slope can be found by noting that it passes through points
(0, -3.2) and (4,0)
Then find the difference in y values which is called the rise
Find the corresponding difference in x values called the run
rise/run = slope
For the bottom line
Rise = 0 - (-3.2) = 3.2
Run = 4 - 0 =4
So slope m = 3.2/4 = 0.8
Slope of top line is also 0.8
Since it passes through origin there is no y-intercept
So equation of top line is simply
y = 0.8x
it takes a hose 3 minutes to fill a rectangular aquarium 12 inches long, 13 inches wide, and 14 inches tall. how long will it take the same hose to fill an aquarium measuring 21 inches by 28 inches by 35 inches? minutes round your answer to the nearest minute
The hose will take 28.27 minutes to fill the second aquarium.
Given,
Rectangular Aquarium - 1
Length = 12 inches
Width = 13 inches
Height = 14 inches
Time taken by a hose to fill the aquarium = 3 minutes
Rectangular Aquarium - 2
Length = 21 inches
Width = 28 inches
Height = 35 inches
We have to find the time taken by the same hose to fill the aquarium 2.
Volume of Aquarium 1 = length × width × height
= 12 × 13 × 14 = 2184 inch³
To fill 2184 inch³, the hose will take 3 minutes.
Now,
Volume of Aquarium 2 = length × width × height
= 21 × 28 × 35 = 20580 inch³
Here,
The time taken by the hose to fill a volume of 20580 inch³;
= 3 × 20580 / 2184 = 28.27 minutes
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logic operators are operators that compare two numbers and produce a true or false result. for example, a > b contains such an operator that compares the numbers in variables a and b if the value in a is greater than the value in b, then this operator returns a true result. otherwise, the operator returns a false result.
The operator used in the statement a > b is a comparison operator. In this case, true will be returned if the value of a is greater than the value of b, whereas false if the value of a is less than the value of b.
What are Comparison Operators?Code decisions require comparison operators. Comparison operators are used in the statement a > b. Using a and b as variables, it compares their values, returning true if a is greater than b, and false otherwise.
By comparing the values of two variables, the program can make decisions. Coders should understand how comparison operators work since they are used frequently in programming.
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3. Suppose U and V are conformally equivalent. Prove that if U is simply con- nected, then so is V. Note that this conclusion remains valid if we merely assume that there exists a continuous bijection between U and V.
According to the image, if U is simply connected, then so V is also simply connected as U and V are conformally equivalent.
What is meant by conformally equivalent?If an analytic map f: U V is 1-1 and onto, then two open sets U and V in C are said to be conformally comparable. A conformal equivalence between U and V is the name given to such a f. The conformal equivalence between V and U is then f1(w). A function called conformal mapping, which is defined on the complex plane, changes a given curve or set of points on a plane while keeping each of the curve's angles. For resolving physics and engineering issues with awkward geometries that may be described as functions of a complex variable, conformal mappings are useful. The analyst can change the awkward geometry into a lot more useful one by selecting the right mapping.
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