Systems (i) and (ii) are linear, while systems (iii) and (iv) are nonlinear.
A linear system satisfies the properties of superposition and homogeneity, meaning that if the input is scaled or if multiple inputs are added together, the output will also be scaled or added together accordingly. Systems (i) and (ii) are both linear since they both satisfy these properties. However, systems (iii) and (iv) are nonlinear since they do not satisfy the properties of superposition and homogeneity. System (iii) contains a non-linear term (y(t))^2 and system (iv) contains a non-linear term (u(t))^2.
The determination of whether a system is linear or nonlinear can have important implications for the analysis and control of the system. It is important to recognize the differences between these types of systems in order to effectively model and manipulate them.
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Please help me on this.
Answer:
B No solution
Step-by-step explanation:
Must be written as an equation
Answer:
10x^2 - 40x = 10x(x - 40)
H.A. y = 1/2
V.A. x = 0, x = 40
0 1 2 3 4.10 .20 .50 .15 0.05What is the probability that at least 1 student comes to office hours on Wednesday?
The probability that at least 1 student comes is therefore 1 - 0.05 = 0.95. So the probability that at least 1 student comes is 1.00 - 0.05 = 0.95.
To calculate the probability that at least 1 student comes to office hours on Wednesday, we need to add up the probabilities of all the possible scenarios in which at least 1 student comes.
First, we can calculate the probability that no student comes, which is given by the last number in the list, 0.05.
The probability that at least 1 student comes is therefore 1 - 0.05 = 0.95.
Alternatively, we could add up the probabilities of all the scenarios where at least 1 student comes, which are given by the first 9 numbers in the list:
0.00 + 0.10 + 0.20 + 0.50 + 0.15 + 0.05 + 0.00 + 0.00 + 0.00 = 1.00
So the probability that at least 1 student comes is 1.00 - 0.05 = 0.95.
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You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as ____________.
The relevant hypotheses for this question would be:Null hypothesis (H0): The incidence of smoking among women is not significantly higher than among men in the neighborhood (μ1 ≤ μ2).
Null hypothesis (H₀): The incidence of smoking among women (population 1) is equal to the incidence of smoking among men (population 2), or p₁ = p₂.
Alternative hypothesis (H₁): The incidence of smoking among women (population 1) is greater than the incidence of smoking among men (population 2), or p₁ > p₂.
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as relevant hypothesis .
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A 12 ft ladder is leaning against a wall. It reaches up the wall a height of 4 feet. How far is the base of the ladder from the wall? Round to the nearest tenth.
The base of the ladder from the wall is 11 ft. 4 inches.
The Pythagorean theorem states that “The square of the hypotenuse is equal to the sum of the square of the sides,” or, in the parametric form,
c² = a² + b² where c is the hypotenuse and a and b are the two sides.
We create a triangle and we know that the point where the ladder touches the wall would be the unknown. Let us call the unknown height b. Knowing that the length of the ladder is 12 feet, and that it represents the hypotenuse of a triangle, it would be c. And the distance from the wall would be a, 4 feet.
Now, Solving the problem, by using Pythagorean theorem:
c² = a² + b²
Plugging all the values in above formula :
[tex]4^2=12^2+b^2[/tex]
b² = 144 - 16.
b² = 128
[tex]b = \sqrt{128}[/tex]
b = 11.3
So the answer becomes either 11.3 feet or 11 ft. 4 inches.
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bill has three one-piece jumpsuits, five pairs of work pants, and eight work shirts. he wears either a jumpsuit or pants and a shirt to work. how many different possible outfits does he have?
Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.
First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.
Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.
Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.
In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.
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a researcher at a major clinic wishes to estimate the proportion of the adult population of the united states that has sleep deprivation. how large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%?
In order to estimate the proportion of the adult population in the United States that has sleep deprivation, a researcher at a major clinic would need to determine the appropriate sample size to achieve a 99% confidence level with a 5% margin of error. This means that the researcher wants to be 99% certain that the sample proportion they obtain is within 5% of the true proportion in the population.
To calculate the necessary sample size, the researcher would need to use a formula that takes into account the confidence level, margin of error, and estimated proportion in the population. Since the researcher does not have an estimate of the true proportion, they can assume a conservative estimate of 50%, which maximizes the necessary sample size.
Using this assumption and plugging the values into the formula, the necessary sample size would be approximately 385. This means that the researcher would need to collect data from 385 adults in the United States in order to be 99% confident that the sample proportion they obtain is within 5% of the true proportion of adults with sleep deprivation in the population.
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I desperatly need this u can have all my points i rly need thisssssss
Answer: (-1,-1)
Step-by-step explanation: i just did this one on a math assignment lol
Suppose that a conservative 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 68% plus or minus 4%. Find the sample size, n, that was used to obtain this confidence interval.
The sample size used to obtain the 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is approximately 360.
To find the sample size, n, we need to use the formula:
n = (z^2 * p * q) / E^2
Where:
z = the z-score corresponding to the desired confidence level (in this case, it is 1.96 for a 95% confidence level)
p = the proportion of first-year students who played in intramural sports (given as 0.68)
q = the complement of p (q = 1 - p)
E = the margin of error (given as 0.04)
Substituting the given values into the formula, we get:
n = (1.96^2 * 0.68 * 0.32) / 0.04^2
n = 360.15
Therefore, the sample size used to obtain the 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is approximately 360.
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(Q1) The _____ will lie at the vertex of the right angle in a right triangle.
In a right triangle, one of the interior angles measures exactly 90 degrees, which is called the right angle.
This right angle is formed by the intersection of the two non-hypotenuse sides of the triangle, and it is located at the vertex where these sides meet. The "right angle vertex" or "vertex of the right angle" are other names for this vertex. The right angle vertex is an important feature of right triangles, and it is used in many geometric and trigonometric calculations. For example, the Pythagorean Theorem, which relates the lengths of the sides of a right triangle, depends on the location of the right angle vertex.
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suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. in a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes
A normal distribution centered at 0 with a standard deviation of approximately 0.05 is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions.
The difference in sample proportions between the two groups can be approximated by a normal distribution if the sample size is large enough. In this case, we have a sample size of 100 for each group, which is considered large enough.
The expected value of the difference in sample proportions is 0.25 - 0.22 = 0.03. The standard deviation of the difference can be calculated as follows:
√[(0.25 * 0.75 / 100) + (0.22 * 0.78 / 100)] = 0.0499Therefore, the most likely representation of the simulated sampling distribution of the difference between the two sample proportions is a normal distribution centered at 0 with a standard deviation of approximately 0.05.
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The complete question is:
Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, Pwomen menwas calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?
A beverage manufacturer has been accused of cheating customers by underfilling its bottles. The bottles are labeled 8 oz. , but there are reports on social media of bottles containing less. A consumer advocacy panel investigated whether the manufacturer was indeed cheating customers by underfilling the bottles; they found a random sample of bottles contained an average of 7. 83 oz.
(a) Which hypotheses should the consumer panel test?
H0:
Ha:
(b) Which value of would make it easier for the consumer panel to conclude the manufacturer is cheating its customers?
= 0. 01
= 0. 05
= 0. 10
The hypothesis used for consumer panel test are null hypothesis when μ = 8 and alternative hypothesis when μ < 8.
And α = 0.01 make it easier for consumer panel to conclude that manufacturer is cheating its customers
Bottles are label with 8 oz.
Random sample contained an average of 7.8 oz.
The consumer panel should test the following hypotheses,
Null hypothesis,
H₀: The population mean amount of liquid in the bottles is equal to 8 oz. μ = 8.
Alternative hypothesis,
Hₐ, The population mean amount of liquid in the bottles is less than 8 oz. μ < 8.
Here, H₀ represents the null hypothesis that the manufacturer is not cheating customers,
while Hₐ represents the alternative hypothesis that the manufacturer is cheating customers by underfilling the bottles.
To determine which value of α would make it easier for the consumer panel to conclude that the manufacturer is cheating its customers,
Consider the level of significance of the test.
The level of significance α is the probability of rejecting the null hypothesis when it is actually true a Type I error.
A smaller value of α makes it less likely to reject the null hypothesis and more difficult to conclude that the manufacturer is cheating customers.
Conversely, a larger value of α makes it more likely to reject the null hypothesis.
And easier to conclude that the manufacturer is cheating customers.
Given the serious nature of the accusation,
A conservative approach would be appropriate, and the consumer panel may want to use a lower value of α to minimize the risk of a Type I error.
This implies, of the three given values α = 0.01 would make it easier for consumer panel to conclude that manufacturer is cheating its customers.
As it represents the smallest value of α and the most conservative approach.
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For the best system, calculate the ratio of the masses of the buffer components required to make the buffer. Express your answer using two significant figures. Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type m(nh3)m(nh4cl)
The ratio based on the information will be 0.200 g of NH₃ per g of NH₄Cl
How to explain the informationFrom complete information, the mass ratio will be:
m(NH₃)/m(NH4Cl) =
pH = pKa + log(NH₃/NH₄Cl)
9.05 = 9.25 + log(NH₃/NH₄Cl)
(NH₃/NH₄Cl) = 10(9.05-9.25)
(NH₃/NH₄Cl) = 0.63095
Change to mass
1 mol of NH₃ = 17 g
1 mol of NH₄Cl = 53.491 g
assume a basis of 1 mol of NH4Cl
(NH₃/NH₄Cl) = 0.63095
NH₃ = 0.63095*NH4Cl
1 mol of NH₄Cl --> 0.63095 mol of NH3
mass of NH₄Cl = 53.491 g
mol of NH₃ = 0.63095*17 = 10.72615 g
ratio --> NH₃/NH₄Cl = 10.72615 /53.491 = 0.200 g of NH₃ per g of NH₄Cl
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What is the simplest form of the radical expression 3^3 sqrt 2a-6^3 sqrt 2a.
The given radical expression is 3^3√(2a) - 6^3√(2a). To find the simplest form, we can follow these steps:
1. Factor out the common terms from both parts of the expression, 2. Simplify any remaining radicals.
First, let's simplify each radical individually: 3^3 sqrt(2a) = 27 sqrt(2a), 6^3 sqrt(2a) = 216 sqrt(2a), Now we can subtract these two expressions: 27 sqrt(2a) - 216 sqrt(2a) = -189 sqrt(2a), And there you have it - the simplest form of the radical expression.
It's important to note that when simplifying radicals, we want to find a common factor between the radicands (the number inside the radical) in order to simplify the expression.
In this case, the common factor is sqrt(2a), which we can factor out and simplify the expression accordingly.
Now, we can simplify the expression inside the parentheses:
3^3 = 27
6^3 = 216
So, the expression becomes:
√(2a)(27 - 216)
Further simplification of the expression inside the parentheses:
27 - 216 = -189
Finally, the simplest form of the given radical expression is:
-189√(2a)
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amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur. if arthur carries a total of x crumbs to the anthill, how many crumbs will amy bring to the anthill, in terms of x?
If Arthur carries x crumbs to the anthill, then Amy will carry 1.5 times as many crumbs per trip. Since Amy makes twice as many trips as Arthur, the total number of crumbs that Amy will bring to the anthill can be calculated as follows:
Number of crumbs per trip for Arthur = x/ (2 * number of trips made by Arthur)
Number of crumbs per trip for Amy = 1.5 * (x / (2 * number of trips made by Arthur))
Total number of crumbs brought by Amy = Number of crumbs per trip for Amy * (2 * number of trips made by Amy)
Simplifying this expression, we get:
Total number of crumbs brought by Amy = (1.5 * x * 2) / 2
= 1.5x
Therefore, Amy will bring 1.5x crumbs to the anthill, in terms of x. This means that Amy will bring 50% more crumbs to the anthill than Arthur. Overall, this problem demonstrates how to use mathematical expressions to determine the quantity of something, based on a given set of parameters and conditions.
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Say, for example, the correlation is 0.75 between fat content (measured in grams) and cholesterol level (measured in milligrams) for 20 different brands of American cheese slices. If cholesterol level were changed to being measured in grams (where 1 gram = 1000 milligrams), what effect would this have on the correlation?
If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.
This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.
The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.
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A researcher was interested in the relationship between a swimmer’s hand length and corresponding time to complete the 100-meter freestyle. The researcher selected a random sample of twenty swimmers from all participants in a swim competition. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle?.
To investigate whether there is convincing evidence, at a 5 percent level of significance,
that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a two-sample t-test.
The independent variable is hand length, and the dependent variable is time to complete the 100-meter freestyle.
The t-test compares the mean time to complete the 100-meter freestyle for swimmers with longer hand lengths to the mean time for swimmers with shorter hand lengths.
The t-test is appropriate because the sample size is small, and the researcher is comparing two groups.
By conducting a two-sample t-test, the researcher can determine whether the observed difference in mean times is statistically significant or due to chance.
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Rewrite as an exponential equation.
In 2=y
Answer:
[tex]y = ln(2) [/tex]
[tex] {e}^{y} = 2[/tex]
3x^2 - 2x - 4 is divided by x - 3
Answer:
Step-by-step explanation:
The bases on a baseball daimond are 90 feet apart on a standard baseball field what is the distance in feet for the cacther to throw a homerun to reach second plate
The catcher needs to throw the ball approximately 190.5 feet to reach second base from home plate.
Let's call the distance between the catcher and second plate "x" and the distance between the home plate and second plate "y". Using the Pythagorean theorem, we get:
distance² = x² + y²
We know that the distance between each base is 90 feet, so the distance between the home plate and second plate is
=> 90 + 90 = 180 feet.
Therefore, we can substitute "y" with 180 feet:
distance² = x² + 180²
We want to solve for "distance", so we need to isolate it on one side of the equation. We can do this by taking the square root of both sides:
distance = √(x² + 180²)
So, if the catcher is standing at home plate, the distance he needs to throw to reach second base is the square root of x² + 180², where "x" is the distance between the catcher and second plate.
The exact value of "x" would depend on where the catcher is standing on the field, but we can assume it's around 60 feet:
Which means that x = 60, then the distance is calculated as
distance = √(60² + 180²) = √(36000) = 190.5 feet
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Create the equation of a circle that has a center at (-7, 10) and has a radius of 11 units.
What is the equation of this circle in Standard Form?
A. (x – 10)2 + (y + 7)2 = 11
B. (x + 10)2 + (y – 7)2 = 121
C. (x – 7)2 + (y + 10)2 = 11
D. (x + 7)2 + (y – 10)2 = 121
The equation of this circle in standard form include the following: D. (x + 7)² + (y - 10)² = 11².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided, we have the following parameters:
Radius, r = 11 units.Center, (h, k) = (-7, 10).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - 10)² = 11²
(x + 7)² + (y - 10)² = 11²
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the alternative hypothesis of the chi-square test states that the obtained chi-square value will be:
The alternative hypothesis of the chi-square test is that the obtained chi-square value will be significantly different from the expected chi-square value under the null hypothesis
The alternative hypothesis of the chi-square test states that the obtained chi-square value will be significantly different from the expected chi-square value under the null hypothesis. In other words, the alternative hypothesis states that there is a relationship between the variables being tested, and that the observed data is not due to chance alone. The null hypothesis, on the other hand, asserts that there is no correlation between the variables under consideration and that any differences that are seen are the result of chance.
Therefore, the alternative hypothesis of the chi-square test is that the obtained chi-square value will be significantly different from the expected chi-square value under the null hypothesis, indicating that there is a relationship between the variables being tested.
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a runner is running a 10k race. the runner completes 30% of the race in 20 minutes. if the runner continues at the same pace, what will her final time be?
we first need to figure out how long the entire 10k race will take the runner.
Since the runner has completed 30% of the race in 20 minutes, we can use that information to estimate the total time it will take the runner to complete the entire race.
To do this, we can use a proportion. If the runner completed 30% of the race in 20 minutes, we can set up the equation: 30/100 = 20/x, Here, x represents the total time it will take the runner to complete the race. To solve for x, we can cross-multiply:
30x = 100 * 20
30x = 2000
x = 2000/30
x ≈ 66.67
So, the runner will complete the entire 10k race in approximately 66.67 minutes. Next, we need to determine whether the runner can maintain the same pace for the entire race. If the runner can maintain the same pace, we can use the information we have to estimate the runner's final time.
If the runner completed 30% of the race in 20 minutes, we can use that to calculate how long it will take the runner to complete the remaining 70% of the race. To do this, we can set up the equation: 30/100 = 20/x, Solving for x, we get: x = 20 * 100 / 30, x ≈ 66.67/3, x ≈ 22.22 .
So, the runner will complete the remaining 70% of the race in approximately 22.22 minutes if she can maintain the same pace. Adding this time to the 20 minutes the runner has already completed, we get: 20 + 22.22 = 42.22,
Therefore, if the runner can maintain the same pace, her final time for the 10k race will be approximately 42.22 minutes.
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Suppose a graduate student is studying a population of bluebonnets along a roadside. The plants in this population are genetically variable. She counts the seeds produced by 100 plants and measures the mean and variance of seed number. The variance is 25. Selecting one plant, the student takes cuttings from it and cultivates them, producing many genetically identical clones. She then transplants these clones into the roadside population, allows them to grow for one year, and then counts the number of seeds produced. Thestudent finds that the variance in seed number among the cloned plants is 10. From the phenotypic variance (p) of the genetically variable and genetically identical plants, calculate thebroad-sense heritability (H) of seed number for the roadside population of bluebonnets
From the phenotypic variance (p) of the genetically variable and genetically identical plants, the value of the broad-sense heritability (H) of seed number for the roadside population of bluebonnets is equals to the 0.6.
We have, population of graduation studying students in bluebonnets along a roadside. Sample size of plants = 100
variance for plants = 25
=> standard deviations = 5
We have to determine the broad-sense heritability (H) of seed number for the roadside. Broad-sense heritability [tex]H2 = \frac{V_G }{ V_P} [/tex] ---(1)
The phenotypic variation [tex]V_P = V_G + V_E [/tex], here [tex] V_P = 25[/tex]
[tex]25 = V_G + V_E[/tex] ------(II)
In the identical population, [tex] V_G = 0[/tex] and here [tex] V_P = 10[/tex]
=> [tex]10 = 0 + V_E [/tex]
=> [tex]V_E= 10[/tex]
By substituting [tex]V_E[/tex] value in equation (II), we will determine [tex]25 = V_G + 10 [/tex]
=> [tex]V_G = 15[/tex]
Substitute the values of [tex]V_G and V_E [/tex] of the roadside population in equation (1), [tex]H²=\frac{15}{25}=0.6[/tex].
The key to the answer is assumption should be the genetic variance of the genetically identical plants is the same as the genetically variable population. In the event that we don't make this supposition, at that point our concern turns out to be very entangled in light of the fact that then we should likewise realize the genetic variance effect of the plant in its environment as well.
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Determine the total number of roots of each polynomial function using the factored form.
a. f (x) = (x + 1)
b. (x - 3)
c. (x - 4)
The total number of roots of each polynomial function is one.
The roots of a polynomial refer to the values of the variable that make the polynomial equal to zero. The number of roots of a polynomial is dependent on the degree of the polynomial.
The given polynomial functions are already in factored form.
a. f(x) = (x + 1)
The polynomial function f(x) has one root, which is -1.
b. f(x) = (x - 3)
The polynomial function f(x) has one root, which is 3.
c. f(x) = (x - 4)
The polynomial function f(x) has one root, which is 4.
Therefore, the total number of roots of each polynomial function is one.
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I need help ASAP!!!! What is the volume of the sphere? Round the answer to the nearest cubic unit.
18 cm
3,054 cm3
399 cm3
763 cm3
9,160 cm3
The volume of given sphere is 3054 cm³
Given that a sphere with diameter of 18 cm we need to find its volume,
Volume of a sphere = 4/3 × π × radius³
So,
Volume = 4/3 × 3.14 × 9³
= 9156.24 / 3
= 3053.08
≈ 3054 cm³
Hence the volume of given sphere is 3054 cm³
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To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 40 40 years and 40 40 years or older). What must be true about the randomized block design of the experiment?
In the context of your experiment comparing the effectiveness of two treatments using a randomized block design, the following must be true:
1. The subjects are divided into two blocks based on their age: under 40 years and 40 years or older.
2. Randomization is used within each block to assign subjects to one of the two treatments. This ensures that each treatment group within a block has a random mix of subjects, reducing potential biases.
3. The purpose of blocking by age is to control for any confounding variables or potential effects that age might have on the treatment outcomes. By blocking, researchers can more accurately measure the differences between the two treatments.
4. The experiment is well-designed, which means it should minimize potential sources of error, include sufficient sample size, and ensure proper randomization and data collection.
5. To analyze the results, researchers will compare the treatment outcomes within each age block and then combine the results to get an overall measure of the effectiveness of the two treatments.
By using a randomized block design in this experiment, researchers can control for age-related factors and obtain a more accurate comparison of the treatment effectiveness.
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Consider rigid-body physics in a higher or lower dimension than three. How many coordinates are required to specify the location and orientation of a rigid body:
If the space is two-dimensional?
a. 2
b. 3
c. 4
d. 5
If the space is one-dimensional?
a. 0
b. 1
c. 2
d. 3
If the space is four-dimensional?
a. 7
b. 8
c. 9
d. 10
If the space is two-dimensional: c. 4
If the space is one-dimensional: b. 1
If the space is four-dimensional: a. 7
In rigid-body physics, the location of a rigid body can be specified by three coordinates (x, y, z) in three-dimensional space. The orientation of a rigid body can be specified by three angles (roll, pitch, yaw) or by a rotation matrix.
If the space is two-dimensional, the location of a rigid body can be specified by two coordinates (x, y). The orientation can be specified by one angle or by a 2x2 rotation matrix. Therefore, the total number of coordinates required is 3.
If the space is one-dimensional, the location of a rigid body can be specified by one coordinate (x). Since there is only one dimension, there is no need to specify orientation. Therefore, the total number of coordinates required is 1.
If the space is four-dimensional, the location of a rigid body can be specified by three coordinates (x, y, z) as in three-dimensional space. The orientation can be specified by four parameters, such as quaternions, which require four coordinates. Therefore, the total number of coordinates required is 7.
So, the answers are:
If the space is two-dimensional: c. 4
If the space is one-dimensional: b. 1
If the space is four-dimensional: a. 7
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let the continuous random variables x and y be defined by the joint density function. determine e[x|y
The expected value of X given Y=y is given by 1/f(y) ∫x f(x,y) dx. This can be calculated by evaluating the integral ∫x f(x,y) dx over all possible values of X and dividing the result by f(y).
To find E[X|Y=y], we need to use the conditional expected value formula
E[X|Y=y] = ∫x f(x|y) dx
where the conditional density function of X for Y=y is denoted by f(x|y). f(x|y), the conditional density function, is defined as follows:
f(x|y) = f(x,y) / f(y)
where f(x,y) is the joint density function of X and Y, and f(x,y) is the marginal density function of Y.By integrating the joint density function across all possible values of X, given that we have the joint density function of X and Y, we may determine the marginal density function of Y:
f(y) = ∫f(x,y) dx from negative infinity to positive infinity.
Once we have the marginal density function of Y, we can then find the conditional density function of X given Y=y:
f(x|y) = f(x,y) / f(y)
Now, we can use the formula for the conditional expected value to find E[X|Y=y]:
E[X|Y=y] = ∫x f(x|y) dx
= [f(x,y)/f(y)] dx
= 1/f(y) ∫x f(x,y) dx
where the integral ∫x f(x,y) dx is over all possible values of X.
Therefore, to find E[X|Y=y], we need to evaluate the integral ∫x f(x,y) dx and divide the result by f(y). This will give us the conditional expected value of X given Y=y.
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Which one is it I know it’s not 5 or 2
The radius of circle C include the following: C. 12.
What is a circle?In Mathematics and Geometry, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
What is the chord of a circle?In Mathematics and Geometry, the chord of a circle can be defined as a line segment that typically join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two (2) separate points on a circle.
For the radius, we have the following:
Radius = diameter/2
Radius = 24/2
Radius = 12 units.
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