For the company to practice price discrimination, there should not be any resale of its product, is not true if a public utility company is considered a monopolist. This is because price discrimination involves charging different prices to different groups of customers based on their willingness to pay. Resale of the product can actually facilitate price discrimination as it allows different customers to buy the product at different prices and then resell it to others. The other options are true for a monopolist, such as having upward sloping demand and supply curves, charging a price higher than its marginal revenue, and determining profit maximizing quantity at the point where marginal revenue equals marginal cost.
Let's analyze each statement:
A. The company's demand curve and supply curve are upward sloping.
This statement is NOT true for a monopolist. A monopolist faces a downward sloping demand curve, which means that they can increase the quantity sold by lowering the price. The supply curve does not apply in the traditional sense for monopolists, as they have the power to set both the price and quantity produced.
B. Its price must be higher than its marginal revenue.
This statement is true for a monopolist. Under a monopoly, the price charged by the company is higher than its marginal revenue due to the downward-sloping demand curve.
C. For the company to practice price discrimination, there should not be any resale of its product.
This statement is true. In order for a monopolist to successfully engage in price discrimination, they must prevent the resale of their product, ensuring that consumers cannot undercut the monopolist's pricing strategy.
D. Its profit maximizing quantity is determined where its marginal revenue equals its marginal cost.
This statement is true. A monopolist maximizes its profit by producing the quantity where marginal revenue equals marginal cost, and then setting the price based on the demand curve at that quantity.
So, the statement that is NOT true for a public utility company considered as a monopolist is: A. The company's demand curve and supply curve are upward sloping.
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his cold-water supply system serves a bathroom in a multistory building. The architect
directed the piping to be installed in the wall cavities with the main branch above ceiling
level. The supply pipe construction is 4 type-L copper. The building supply is capable of
maintaining a flow rate of 10 gallons per minute. The walls contain a 6-inch cavity, and the
ceilings contain a 12-inch cavity. Consider the installation to be centered in the available
cavity space.
If the cold-water supply pressure to the floor represented in the drawing measures 50 psi
and the flush-valve manufacturer specifies a minimum working pressure of 25 psi, how many
stories can be constructed before friction losses prevent proper valve operation?
A. None including this floor
B. This floor and one more story
C. This floor and two more stories
D. This floor only
Answer: D
Step-by-step explanation:
To determine the maximum number of stories that can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure loss due to friction as the water flows through the piping to each floor.
Using the Hazen-Williams formula, which is commonly used for sizing water supply systems:
P = (4.52Q1.85L10.67/C1.85)d4.87
where:
P = pressure loss due to friction (psi)
Q = flow rate (gpm)
L = length of pipe (feet)
C = Hazen-Williams coefficient (dimensionless)
d = inside diameter of pipe (inches)
Assuming the flow rate is 10 gpm, the length of pipe from floor to floor is the height of the building divided by the number of stories, and the inside diameter of the pipe is 4 inches (since 4 type-L copper corresponds to a 4-inch nominal diameter), the pressure loss for each story can be calculated using a Hazen-Williams coefficient of 130 for copper piping:
P = (4.52 x 10^1.85 x (1 story height/number of stories)10.67/1301.85)4.87
P = 3.3 x (1/number of stories)^1.85
For example, for a 2-story building, the pressure loss would be:
P = 3.3 x (1/2)^1.85
P = 1.6 psi
To ensure that the minimum working pressure of 25 psi is maintained at each flush valve, the pressure loss for each story cannot exceed 25 - 50 = -25 psi (since lower pressures can cause valve malfunctions).
Solving for the maximum number of stories:
3.3 x (1/number of stories)^1.85 <= -25
(1/number of stories)^1.85 <= -25/3.3
1/number of stories <= (-25/3.3)^0.54
number of stories >= 1/(-25/3.3)^0.54
number of stories >= 6.7
Therefore, the maximum number of stories that can be constructed before friction losses prevent proper valve operation is D. This floor only.
What two numbers multiply to 4 and add up to -4?
WILL GIVE 100 POINTS
Answer:
-2 and -2
Step-by-step explanation:
2 numbers need to multiply to get a positive 4.
2 numbers added up to get a negative 4.
This means that both numbers have to be 2 or -2, as they need to multiply to get 4.
-2 x -2 = 4
-2 + -2 = -4
Hope this helps! :)
Answer:
Step-by-step explanation:
The two numbers that multiply to 4 and add up to -4 are -2 and -2.
Question 6: Find the inverse of f(x)=3*
Answer:3xf
Step-by-step explanation:
you just reverse the 40∞•§ with the 589€¢¨•§•ª¶¶ which gives you 3xf
two six-sided dice are rolled. what is the size of the sample space that corresponds to the event that both dice are odd?
When rolling a single six-sided die, there are three odd numbers: 1, 3, and 5, and three even numbers: 2, 4, and 6. Since we are rolling two dice, each with six possible outcomes, there are a total of $6 \times 6 = 36$ possible outcomes.
To find the sample space corresponding to the event that both dice are odd, we need to determine all possible outcomes in which both dice land on odd numbers. There are three odd numbers on each die, so there are three possibilities for the first die and three possibilities for the second die, for a total of $3 \times 3 = 9$ outcomes where both dice are odd.
Therefore, the size of the sample space that corresponds to the event that both dice are odd is 9.
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agnetic field b = 1 t goes out of the plane of the page. a straight wire carries a current 1 a from right to left. find the direction of force acting on the wire. A) out of the page
B) into the page
C) left, in the plane of the page
D) right, in the plane of the page
E) up, in the plane of the page
According to the right-hand rule for the force on a current-carrying wire in a magnetic field, the direction of the force is perpendicular to both the direction of the current and the direction of the magnetic field.
The direction of the force acting on the wire can be determined using the right-hand rule for the force on a current-carrying wire in a magnetic field. According to the right-hand rule:
Point the fingers of your right hand in the direction of the current (from right to left).
Curl your fingers towards the direction of the magnetic field (out of the page).
Your thumb will now point in the direction of the force.
Therefore, the direction of the force on the wire will be upwards, perpendicular to both the current and the magnetic field.
Since the force is perpendicular to the plane of the page, the answer would be (E) up, in the plane of the page.
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Differentiate The Function. H(X)=43(X5−3x3+7)8 H′(X)=
The differentiation of H(X)=43(X5−3x3+7)⁸ is H′(x) = 344(x^5 - 3x^3 + 7)^7(5x^4 - 9x^2)
To find the derivative of the function H(x) = 43(x^5 - 3x^3 + 7)^8, we need to use the chain rule of differentiation. The chain rule states that if we have a function f(g(x)), then its derivative is given by f'(g(x)) * g'(x). In this case, our function g(x) is (x^5 - 3x^3 + 7), and our function f(x) is (43x^8). So, using the chain rule, we get:
H′(x) = f'(g(x)) * g'(x)
H′(x) = 43(8)(x^5 - 3x^3 + 7)^7 * (5x^4 - 9x^2)
Simplifying the expression, we get:
H′(x) = 344(x^5 - 3x^3 + 7)^7(5x^4 - 9x^2)
Therefore, the derivative of the function H(x) = 43(x^5 - 3x^3 + 7)^8 is H′(x) = 344(x^5 - 3x^3 + 7)^7(5x^4 - 9x^2).
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in a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts what is the sampling method? simple random systematic stratified cluster convenience
The sampling method used in this study is a simple random sample. This is because each person's name has an equal chance of being selected when the darts are blindly thrown at the dartboard.
The sample is also random because there is no predetermined criteria or grouping used in selecting individuals.
The other sampling methods such as systematic, stratified, and cluster involve pre-determined groups or criteria that the individuals must meet, which is not the case with the dartboard method.
Additionally, convenience sampling involves selecting individuals based on their availability or accessibility, which is not applicable in this scenario as the individuals are selected randomly without any biases or preferences.
Overall, the study is using a simple random sampling method to select individuals for the sample.
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which of the following give chart elements a realistic, three-dimensional look?A. axisB. chart areaC. legendD. plot area
The option that gives chart elements a realistic, three-dimensional look is D. Plot Area.
The option that gives chart elements a realistic, three-dimensional look is the plot area. The plot area is the portion of the chart that displays the data points and is typically the main focus of the chart. Adding shading and depth to the plot area, can give the chart a more lifelike appearance and make the data more visually engaging. Additionally, three-dimensional charts can also be created by using specialized charting software that allows for the creation of 3D visualizations. These types of charts can be useful for highlighting patterns and trends in the data, especially when dealing with large datasets.
In a chart, the plot area is the space where the actual data points, bars, lines, or pie slices are displayed. By applying three-dimensional effects to the plot area, you can make the chart elements appear more realistic and visually appealing. This can enhance the viewer's understanding of the data being represented and make the chart more engaging.
In summary, to give chart elements a realistic, three-dimensional look, you should focus on the plot area (Option D). The axis (Option A), chart area (Option B), and legend (Option C) do not directly contribute to creating a three-dimensional appearance for the chart elements.
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Indicate below whether the equation in the box is true or false
Answer:
False
Step-by-step explanation:
In order to compare fractional terms both sides, you have to make sure that both sides are equal in denominator. In this case, our denominators are 3 and 12. To equalize the denominator of both sides, find the LCM of 3 and 12 which is 12.
Therefore, we multiply 2/3 by 4/4. Therefore:
[tex]\displaystyle{\dfrac{2\cdot 4}{3\cdot 4} = \dfrac{9}{12}}\\\\\displaystyle{\dfrac{8}{12} = \dfrac{9}{12}}[/tex]
The equation is false since 8/12 does not actually equal 9/12. You can also try cutting the pieces into 12 pieces total and compare both shaded regions; you'll see that both are not equivalent at all.
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9. What is the savings after 6 months?
Months Savings
0 $200
1 $250
2 $300
3 $350
All of the students in the sixth-grade class went on a field trip to an amusement park. *40% bought a pass to ride an unlimited number of rides. *75 students paid for each ride individually. How many students are in the sixth grade?
There are 187 students in the sixth grade.
We can start by using the information that 40% of the students bought a pass to ride an unlimited number of rides. This means that 60% of the students did not buy a pass and paid for each ride individually.
Let's assume that the total number of students in the sixth grade is "x". Then, 40% of the students bought a pass, which is 0.4x. The remaining 60% paid for each ride individually, which is 0.6x.
We also know that 75 students paid for each ride individually. Therefore, we can set up an equation:
0.6x = 75
Solving for x, we get:
x = 75 / 0.6
x = 125 / 0.4
x = 187.5
Since we can't have half a student, we round up to the nearest whole number. Therefore, there are 187 students in the sixth grade.
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angles
find a when B and C is 52 degrees and the outside is 308 degrees
Check the picture below.
let's recall, twin sides make twin angles.
The domestic violence study conducted in 1984 by Sherman and Berk had an ethical concern in that: O They financially profited from the research. O They did not adhere to special protections for vulnerable populations. O They potentially withheld a beneficial treatment. O They deceived their subjects.
In the 1984 domestic violence study conducted by Sherman and Berk, the ethical concern was that they potentially withheld a beneficial treatment.
The domestic violence study conducted by Sherman and Berk in 1984 raised an ethical concern in that they financially profited from the research. This raises the question of whether their motives were purely altruistic or whether they were driven by financial gain. Additionally, the study did not adhere to special protections for vulnerable populations such as women and children who may have been victims of domestic violence. This raises concerns about the validity and generalizability of the study's findings. Furthermore, the study potentially withheld a beneficial treatment, which raises questions about the ethical responsibility of researchers to ensure that their subjects receive the best possible care. Finally, there are also concerns that the researchers may have deceived their subjects, which raises questions about the integrity and transparency of the research process. In conclusion, the ethical concerns raised by this study highlight the need for researchers to carefully consider the impact of their research on vulnerable populations and to ensure that they adhere to the highest ethical standards.
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on the package of a certain snack, the nutrition facts label states that the protein content in one serving is 4 grams. the company wants to check this claim and takes a simple random sample of five servings of the snack from their factory. their lab obtains these measurements (in grams): 3.88 4.04 3.97 3.90 3.94 all but one of these measurements is under 4 grams. can this be due to chance error in the measurements?
the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements
To determine whether the discrepancy between the sample mean and the claimed protein content of 4 grams can be due to chance error in the measurements, we can perform a hypothesis test.
The null hypothesis, H0, is that the true mean protein content is equal to 4 grams. The alternative hypothesis, Ha, is that the true mean protein content is less than 4 grams.
Using a one-tailed t-test with a significance level of 0.05 and four degrees of freedom (n-1=5-1=4), we calculate the t-value to be -1.386. The critical t-value for a one-tailed test at a significance level of 0.05 and four degrees of freedom is -2.132.
Since our calculated t-value of -1.386 is greater than the critical t-value of -2.132, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true mean protein content is less than 4 grams. Therefore, it is possible that the discrepancy between the sample mean and the claimed protein content is due to chance error in the measurements.
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Brenda is solving the system of equations A, shown in the table, by using the elimination method. She produced system of equations B as her first step in the solution method. Which of the following statements justifies the two systems being equivalent?
Option D is correct as it justifies the two systems being equivalent
How to get the correct optionMultiply by 2 the first equation A
2 (X + 2Y ) = 6
This would give us the first part of the equation B
= 2x + 4y = 12
Then the second equation
Multiply by 5 to get B
5(2/5x - y ) = 3
= 2x - 5y = 15
Hence the last option is the correct answer
Therefore we would say that Option D is correct as it justifies the two systems being equivalent
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need this for geometry
The value of the missing leg using Pythagoras theorem is 12.5.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
To calculate the missing leg, we use Pythagoras theorem.
a² = b²+c²..................... Equation 1Where:
a = 16b = 10 c = Missing legSubstitute these values into equation 1 and solve for c
16² = 10²+c²c² = 16²-10²c² = 256-100c² = 156c = √156c = 12.5Learn more about Pythagoras theorem here: https://brainly.com/question/28981380
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show your work pleasee
The range of values in the upper 15.85% of the distribution is given as follows:
x > 19.4.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 16, \sigma = 3.4[/tex]
The value of interest is Z with a p-value of 1 - 0.1585 = 0.8415 = 1, hence the value of x is obtained as follows:
1 = (x - 16)/3.4
x - 16 = 3.4
x = 19.4.
Hence the interval is:
x > 19.4.
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Identify the correct cross section of the regular square pyramid.
The value of correct cross section of the regular square pyramid is a Square as shown in Option C.
We have to given that;
A pyramid is shown in figure.
Since, We know that;
In a given pyramid, the cross section is shown by blue figure.
And, The blue figure is shown a square.
Thus, The value of correct cross section of the regular square pyramid is a Square as shown in Option C.
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Jada bought a used car for $6000. The value of the car is expected to depreciate at a uniform rate of 30% per year. What will be the approximate value of the car in 3 years? Use the formula =^-kt
The approximate value of the car in 3 years is $1648.37.
We have,
To calculate the approximate value of the car in 3 years, we can use the formula for exponential decay:
V = Vo e^(-kt)
where V is the value of the car after t years, Vo is the initial value of the car, k is the decay rate (in this case, 0.3), and e is the mathematical constant e (approximately equal to 2.718).
Substituting the given values.
V = 6000 x e^(-0.33)
V = 6000 x e^(-0.9)
V ≈ $1648.37
Therefore,
The approximate value of the car in 3 years is $1648.37.
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f(θ) = 2 cos(θ) + cos2(θ), 0 ≤ θ ≤ 2π
To find the maximum and minimum values of the given function f(θ), we need to find its critical points and endpoints.
First, we take the derivative of f(θ) with respect to θ:
f'(θ) = -2 sin(θ) - 2 cos(θ) sin(θ)
Setting f'(θ) = 0, we get:
-2 sin(θ) - 2 cos(θ) sin(θ) = 0
Simplifying and factoring out -2 sin(θ), we get:
-2 sin(θ) (1 + cos(θ)) = 0
This gives us two critical points: θ = 0 and θ = π.
Next, we need to evaluate the function at the endpoints of the given interval [0, 2π]:
f(0) = 2 cos(0) + cos2(0) = 3
f(2π) = 2 cos(2π) + cos2(2π) = 3
Now we compare the values of f(θ) at the critical points and endpoints to find the maximum and minimum values:
f(0) = 3 (endpoint)
f(π) = 1 (critical point)
f(2π) = 3 (endpoint)
Therefore, the maximum value of f(θ) is 3 and the minimum value is 1.
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This is the second part pls answer. in case you can't see anything notify me
Answer:
K = 2cm
Step-by-step explanation:
The figure are similar by AA similarity theorem
A-A similarity theorem was deals with at least the two angles are congrunt then we said that figure is similar.
So in the given figure ∆SRT ~ ∆QPT and if the two triangles are dimilar their coresponding side ratio are equal and their angles are congrunt .
Now our question is to find the scale factor . let it be K
K = QP/SR = PT/RT = QT/ST
K = 4cm/2cm = 6cm/3cm= 6cm /3cm
K = 2cm = 2cm = 2cm ... so the scale factor is 2cm.
Find the critical value tc for the confidence level c=0.99 and sample size n=21.
The critical value tc for the confidence level c=0.99 and sample size n=21 is 2.845.
To find the critical value tc for the confidence level c = 0.99 and sample size n = 21, we can use the t-distribution table or a statistical software package.
t-distribution critical value formula is: tc = t(α/2, n-1)
For a confidence level of 0.99, the significance level α is:
α = 1 - c = 1 - 0.99 = 0.01
Using a t-distribution table with 20 degrees of freedom (n-1), we can find the t-value with a cumulative probability of 0.005 in the upper tail, since we are interested in the critical value at the two-sided 99% confidence level.
The t-value with a cumulative probability of 0.005 and 20 degrees of freedom is 2.845.
Therefore, the critical value tc for the confidence level c = 0.99 and sample size n = 21 is:
tc = t(α/2, n-1) = t(0.005, 20) = 2.845
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Julian is making barbecue sauce that he will put into jars. He uses 15 cups of tomato sauce, 2 cups of white vinegar, How many quart jars can he fill?
Julian can fill 4 quart jars with the barbecue sauce, with a little bit remaining (0.25 quart) that won't fill a full jar.
To determine how many quart jars Julian can fill, we need to convert the total volume of the barbecue sauce to quarts. Since there are 4 cups in 1 quart, we can divide the total volume of the sauce in cups by 4 to get the equivalent volume in quarts.
Julian uses 15 cups of tomato sauce + 2 cups of white vinegar, which gives a total of 17 cups of sauce. Now, we divide 17 cups by 4 to convert it to quarts:
17 cups ÷ 4 = 4.25 quarts.
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The figure above shows the graphs of the circles x^2 + y^2 = 2. What is the radius of the larger circle?
a) √2 b) 2 c) √4 d) 4
The figure above shows two circles, one inside the other. The equation x^2 + y^2 = 2 represents the smaller circle, while the larger circle is not explicitly defined in the question.
However, we can see from the graph that the center of both circles is at the origin (0,0) and that the larger circle has a radius twice as big as the smaller circle.
Therefore, the radius of the larger circle is 2 times the radius of the smaller circle, which is the square root of 2. So the answer is (a) √2.
The given equation of the circle is x^2 + y^2 = 2. To find the radius of this circle, we can rewrite the equation in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
In this case, the equation is already in the standard form with h = 0, k = 0, and r^2 = 2. Therefore, the radius of the larger circle is r = √2. So, the correct answer is a) √2.
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Use the expression 3x^2 + 4y - 5x + y + 11 to match the vocabulary terms with their "parts" of the given expression. constant, greatest common factor, number of terms in the polynomial, coefficient of the leading term, exponent of the leading term. DRAG & DROP THE ANSWER 4 11 1 3 2 6 5
Answer:
Constant: 11Greatest common factor: 1Number of terms in the polynomial: 5Coefficient of the leading term: 3Exponent of the leading term: 2Step-by-step explanation:
In order to solve this, we need to know the definitions of the vocabulary terms and how to identify them in a polynomial expression. Here are the definitions:
A constant is a term that has no variable. For example, 11 is a constant. It's also a prime number, but don't let that get to its head.A greatest common factor (GCF) is the largest number or expression that divides evenly into all the terms of a polynomial. For example, the GCF of 3x² + 4y - 5x + y + 11 is 1, because 1 is the only number that divides evenly into all the terms. It's also the loneliest number, but don't let that make you sad.The number of terms in a polynomial is the number of separate parts that are added or subtracted. For example, 3x² + 4y - 5x + y + 11 has five terms: 3x², 4y, -5x, y, and 11. It's also the number of fingers on one hand, but don't let that limit your counting.The coefficient of the leading term is the numerical factor of the term with the highest degree (the highest exponent of the variable). For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its coefficient is 3. It's also the number of sides on a triangle, but don't let that make you obtuse.The exponent of the leading term is the power of the variable in the term with the highest degree. For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its exponent is 2.To match the vocabulary terms with their “parts” of the given expression, you need to drag and drop the correct numbers from the options. Here are the matches:
Constant: 11Greatest common factor: 1Number of terms in the polynomial: 5Coefficient of the leading term: 3Exponent of the leading term: 2Cuántas diagonales tiene un polígono de 33 lados
Answer: 527
Step-by-step explanation:
As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices.
Screenshot 2023-05-01 at 19.09.51
The circumference of the circle is given as follows: C = 109.9 in.
The relationship between the diameter of a circle and it's circumference is presented in this problem.
We have,
The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:
r = 0.5 x 35
r = 17.5 in.
Then the circumference of the circle is given as follows:
C = 2 x pi x 17.5
C = 109.9 in.
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Missing Information
The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.
Which measure of central tendency is not resistant to extreme values in a numeric data set? A. Parameters B. Mean C. Median D. Mode
B. Mean is not resistant to extreme values in a numeric data set. The mean is affected by outliers or extreme values in a dataset because it takes into account all the values in the dataset, including the extreme values.
Central tendency is a measure that is used to find the central or typical value of a set of data. The most common measures of central tendency are mean, median, and mode. These measures provide different ways of summarizing the data, depending on the nature of the dataset and the research question.
The mean is calculated by adding up all the values in a dataset and dividing by the number of values. The mean is often considered to be the most common measure of central tendency because it takes into account all the values in the dataset. However, the mean is not resistant to extreme values or outliers. An outlier is an observation that is significantly different from other observations in the dataset.
When a dataset contains extreme values or outliers, the mean is often affected, resulting in a value that does not represent the central tendency of the dataset. This is because the mean is influenced by every value in the dataset, including the outliers, and is not a robust measure of central tendency. In contrast, the median and mode are resistant to extreme values and provide better estimates of central tendency when a dataset contains outliers.
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how many different ways can president, vice president, treasurer, and secretary be chosen from a class of 40 students?
There are 91,390,400 different ways to choose president, vice president, treasurer, and secretary from a class of 40 students.
To find the number of different ways to choose president, vice president, treasurer, and secretary from a class of 40 students, we need to use the formula for permutations. This formula is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being chosen. In this case, n = 40 and r = 4, so we have equations:
40P4 = 40! / (40 - 4)!
40P4 = 40! / 36!
40P4 = (40 x 39 x 38 x 37) / (4 x 3 x 2 x 1)
40P4 = 91,390,400
Therefore, there are 91,390,400 different ways to choose president, vice president, treasurer, and secretary from a class of 40 students. This means that each person in the class has a 1 in 91,390,400 chance of being chosen for all four positions.
It's important to note that this calculation assumes that each person can only hold one position, and that the order in which the positions are filled matters. If these assumptions are changed, then a different formula would need to be used.
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Let X1,... ,X7 be independent normal random variables and X, be distributed as N(μ1,o₁ 2) for i = 1,.,7. Find P(X < 14) when μ₁ =.... =μ= 15 and o₁2 = ... = o2/7 = 7 (round off to second decimal place).
The probability P(X < 14) when μ₁ =.... =μ= 15 and o₁2 = ... = o2/7 = 7 is 0.
Let X1, ..., X7 be independent normal random variables, each distributed as N(μ1, o₁²) for i = 1,...,7. Given that μ₁ = ... = μ = 15 and o₁² = ... = σ²/7 = 7, you want to find P(X < 14) rounded to the second decimal place.
To solve this problem, follow these steps:
1. Calculate the mean and variance of the sum of the random variables.
Since X1, ..., X7 are independent and identically distributed, the mean of their sum is the sum of their means, and the variance of their sum is the sum of their variances. Thus, for the sum S = X1 + ... + X7, we have:
Mean of S = 7 * μ = 7 * 15 = 105
Variance of S = 7 * σ²/7 = 7 * 7 = 49
2. Calculate the standard deviation of the sum.
The standard deviation is the square root of the variance, so:
Standard deviation of S = √49 = 7
3. Calculate the z-score for X < 14.
The z-score is calculated as:
z = (X - Mean) / Standard deviation
Since we want to find probability P(X < 14), we need to find the z-score for X = 14:
z = (14 - 105) / 7 = -91 / 7 = -13
4. Find the probability P(X < 14) using the z-score.
Using the z-score of -13, you can look up the corresponding probability in a standard normal distribution table or use a calculator that provides this functionality. A z-score of -13 is extremely far from the mean, so the probability P(X < 14) is very close to 0.
To the second decimal place, the probability P(X < 14) is approximately 0.00.
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