The gradient of the chord PQ is 2h + 8
What is the gradient of the chord?Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.
Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).
Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).
The gradient of the chord PQ is given by:
(m) = Δy /Δx
(m) = (2h^2+8h+9 - 9) / (2+h - 2)
(m) = (2h^2+8h) / (h)
(m) = 2h + 8
As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.
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I need help on 10 and 11
Answer:
x = +8
x = -8
That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.
Step-by-step explanation:
5x + 6x - 10 + 12 = 90
11x = -88
x = -8
or
x = 8
In monopolistic competition, the end result of entry and exit is that firms end up with a price that lies a. on he upward-slopning porion of he average cost curve. b. at the very bottom of the AC curve. c. at the very top of the AC curve. d. on the downward-sloping portion of the average cost curve
In monopolistic competition, the end result of entry and exit is that firms end up with a price that lies on the downward-sloping portion of the average cost curve.
Monopolistic competition is a market condition in which many small firms compete with each other by selling slightly varied, but essentially comparable goods or services at somewhat different prices. These companies enjoy some market power, but they are not monopolies because their products or services are close substitutes for each other.
The equilibrium price in a monopolistically competitive market is a long-run, but not a short-run, outcome of entry and exit. Because the market is monopolistic, entry and exit do not have an immediate impact on the price; it simply alters the number of producers operating in the market. Over time, the entry and exit of producers in the industry will increase or decrease the number of substitutes available, driving demand curves and resulting in the price of the commodity settling on the down-sloping portion of the average cost curve in the long run.
Therefore, it can be concluded that the end result of entry and exit in monopolistic competition is that companies end up with a price that lies on the downward-sloping portion of the average cost curve.
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A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
What is circle graph?A circle graph, also known as a pie chart, is a type of chart that displays data as a circular diagram, divided into slices to represent proportions of a whole. Each slice of the circle represents a percentage of the total data being represented, and the entire circle represents 100% of the data.
According to question:Based on the circle graph, the percentage of students who prefer documentaries is 16% (as the percentage for documentaries is missing from the given options, we need to calculate it).
To find out the actual number of students who prefer documentaries, we need to multiply this percentage by the total number of students in the sample:
16% of 500 = (16/100) x 500 = 80
Therefore, 80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
Circle graphs are commonly used to show proportions or percentages of different categories within a dataset. They are useful for displaying data in a way that is easy to understand, and they are often used in business and finance, as well as in education and research.
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what is the z-score for the 25th percentile of the standard normal distribution?A. -0.625
B. 0.50 C. 0.60 D. -0.50 E. 0.00
The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.
To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.
So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.
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The Table shows different geologic time periods: Period Number of Years Ago Jurassic 2. 08 ⋅ 108 Silurian 4. 38 ⋅ 108 Tertiary 6. 64 ⋅ 107 Triassic 2. 45 ⋅ 108 Order the time periods from oldest to youngest
The oldest and youngest the
time periods are Silurian and Tertiary respectively. Order the time periods from oldest to youngest is equals to
Silurian--> Triassic --> Jurassic -->Tertiary.
We have a table which shows different geologic time periods.
Period Number of Years Ago
Jurassic 2.08 × 10⁸
Silurian 4.38× 10⁸
Tertiary 6.64× 10⁷
Triassic 2.45× 10⁸
We have to order the time periods from oldest to youngest. Time period is the length of time during which an activity occurs and geologic time period showing the geologic eons, eras, periods, epochs, and associated. Now, we check the time periods and put in order.
So, 2.08 × 10⁸ = 2,08000,000
4.38× 10⁸ = 4,38000,000
6.64× 10⁷ = 6,6400,000
2.45× 10⁸ = 2,45000,000
Here, longest or oldest time period
= 4,38000,000
Youngest time period = 6,6400,000
Therefore, the order of time periods is Silurian --> Triassic -->Jurassic -->Tertiary. Hence, required time periods are Silurian and Tertiary.
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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A dairy made 98.38 ounces of yogurt. Then a local market bought 86.2 ounces of the yogurt.
How much yogurt does the dairy have left?
The amount of yoghurt left is 12. 18 ounces
How to determine the numberThe algebraic expressions are defined as those expressions that are made up of variables, terms, constants, factors and coefficients.
The expressions are also composed of some arithmetic or mathematical operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplicationFrom the information given,
Let the total number of ounces of yoghurt be x
Let the number of ounces of yoghurt sold be y
We have that;
The number left= x - y
= 98.38 - 86.2
= 12. 18 ounces of yoghurt
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Given:
The inequality is
[tex]-3(2x - 5) < 5(2 - x)[/tex]
To find:
The correct representations of the given inequality.
Solution:
We have,
[tex]-3(2x - 5) < 5(2 - x)[/tex]
Using distributive property, we get
[tex]-3(2x)-3(-5) < 5(2)+5(-x)[/tex]
[tex]-6x+15 < 10-5x[/tex]
Therefore, the correct option is C.
Isolate variable terms.
[tex]15-10 < 6x-5x[/tex]
[tex]5 < x[/tex]
It means, the value of x is greater than 5.
Since 5 is not included in the solution set, therefore, there is an open circle at 5.
So, the graphical represents of the solution is a A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Therefore, the correct option is D.
The function is defined by the following rule.
f(x) = -x-1
Complete the function table.
x
-3
-2
0
2
X
0
0
5
Answer:
Step-by-step explanation:
[tex]f(-3)=-(-)3-1=2\\\\f(-2)=-(-2)-1=1\\\\f(0)=-0-1=-1\\\\f(2)=-2-1=-3\\\\f(4)=-4-1=-5\\\\f(x)=5\rightarrow 5=-x-1\rightarrow6=-x \rightarrow x=-6[/tex]
Please help!
(x, y)→(x + 130, y + 105 )
Graph
So the transformed rectangle has vertices A'(40, 160), B'(40, 130), C'(80, 130), and D'(80, 160).
What is transformation rule?In mathematics, a transformation rule (also known as a transformation function, transformation formula, or simply a transformation) is a mathematical rule or formula that describes how to map or transform a set of points in one coordinate system to another set of points in a different coordinate system. Transformations can be applied to various mathematical objects, such as points, lines, curves, shapes, or functions, and can be used to achieve various purposes, such as to change the size, shape, position, or orientation of an object, to create a mirror image or a rotation of an object, or to change the coordinate system of an object.
Here,
There appears to be an error in the coordinates of points B and D that you provided, as they are both (-90,25). I will assume that the correct coordinates of point D are (-50,55) to form a rectangle ABCD.
To apply the given transformation rules to each of the four vertices of the rectangle, we add 130 to the x-coordinate and 105 to the y-coordinate. Therefore, the coordinates of the transformed rectangle are:
A' = (-90 + 130, 55 + 105) = (40, 160)
B' = (-90 + 130, 25 + 105) = (40, 130)
C' = (-50 + 130, 25 + 105) = (80, 130)
D' = (-50 + 130, 55 + 105) = (80, 160)
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Complete question:
Please help! The transformation rules says: (x, y)→(x + 130, y + 105 )
Given rectangle ABCD with A(-90,55) B(-90,25) C(-50,25) D(-50,25).
Find the coordinates of transformed rectangle.
the primary purpose of statistical analysis is to: group of answer choices transform information into data.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
What is statistical analysis?Statistical analysis is the method of using statistical techniques to collect and analyze data, evaluate its reliability and determine its statistical significance. The following are the primary purposes of statistical analysis:Provide summaries and descriptions of data: One of the most important applications of statistical analysis is to present data in a clear and concise manner. Summarizing the data can assist people in making sense of the data and drawing inferences from it.
For example, data can be summarized using graphs, charts, or tables. Identify patterns and relationships: The goal of statistical analysis is to identify any patterns or relationships that exist within the data. For example, statistical analysis can be used to determine if a product's sales are correlated with a specific time of year.
Test hypotheses and draw conclusions: Statistical analysis is used to test hypotheses and draw conclusions about a population or phenomenon. This is accomplished by using statistical techniques to determine whether or not the data supports a particular hypothesis. Statistical analysis can also be used to determine the probability of an event occurring in the future.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
The complete question is as follows:
The primary purpose of statistical analysis is to:
a)transform information into data.
b)select samples and make inferences about populations
c)convert data into useful desicion-making information
d)perform statistical computations
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Marie had 10 ½ feet of ribbon to make bows. Each bow required ¾ foot of ribbon. She used the following steps to find the number of bows she could make with the ribbon.
Step 1: 10 ½ ÷ ¾
Step 2: 21/2 ÷ ¾
Step 3: ??????
Step 4: 84/6
Step 5: 14
Which expression best represents the expression Marie should have used in Step 3?
*
A 2/21 ÷ 4/3
B 2/21 ÷ ¾
C 21/2 × 4/3
D 21/2 × ¾
Therefore, the expression Marie should have used in Step 3 is option B: 2/21 ÷ ¾, which represents the division of the fraction 21/2 by 3/4.
What do you mean by fraction?A fraction is a way of expressing a quantity that represents a part of a whole or a ratio between two quantities. It is usually written as one number (the numerator) over another number (the denominator), separated by a horizontal line or slash. For example, the fraction 2/3 represents two parts out of three equal parts of a whole, or a ratio of two to three. Fractions can be expressed in various forms, such as proper fractions (where the numerator is smaller than the denominator), improper fractions (where the numerator is greater than or equal to the denominator), and mixed numbers (where a whole number and a proper fraction are combined). Fractions are an important concept in many areas of mathematics, including arithmetic, algebra, geometry and calculus.
by the question.
To solve this, Marie can use the following steps:
Step 1: 10 ½ ÷ ¾
Step 2: 21/2 ÷ ¾
Step 3: (21/2 ÷ 3/4) (finding the quotient of two fractions)
Step 4: (21/2) × (4/3) (dividing by a fraction is the same as multiplying by its reciprocal)
Step 5: 14
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Zach bought 200 shares of Goshen stock years ago for $21. 35 per share. He sold all 200 shares today for $43 per share. What was his gross capital gain?
B. $ 8,600
C. $ 4,000
A. $4,270
D. $4,330
The gross capital gain is option (D) $4330
Gross capital gain is the total amount of profit that an investor makes when they sell an asset, such as stocks, real estate, or other investments, for a higher price than the purchase price.
Zach's gross capital gain is the difference between the selling price and the purchase price of the shares.
Purchase price of 200 shares = 200 x $21.35 = $4,270
Selling price of 200 shares = 200 x $43 = $8,600
Therefore, the gross capital gain is
= $8,600 - $4,270
Subtract the numbers
= $4,330
Therefore, the correct option is (D) $4,330.
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1. it is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $380 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?
The probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6827.
Here the given data are
mean [tex]\mu = $380[/tex],
standard deviation [tex](\sigma) = $50[/tex]
Let X be the random variable which denotes the amounts of money spent on clothing in a year by college students. The distribution of X is normal distribution.
We need to find the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year. If we have the standard normal distribution, we can easily calculate the probability from the normal distribution table. Otherwise, we have to use the standard normal distribution and convert the values to standard units. This process is called standardization. We will use the z-score formula for standardization.
Let’s standardize the given values.
Lower value [tex](X_1) = $300[/tex]
Upper value [tex](X_2) = $400[/tex]
Population mean [tex](\mu) = $380[/tex]
Population standard deviation [tex](\sigma) = $50z_1 = (X_1 - \mu) / \sigma z_1 = ($300 - $380) / $50z_1 = -1.6z_2 = (X_2 - \mu) / \sigma z_2 = ($400-$380)/$50z_2 = 0.4[/tex]
Now we need to find the area between these two z-scores using the standard normal distribution table.The probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is
[tex]P(-1.6 < Z < 0.4).P(-1.6 < Z < 0.4) = P(Z < 0.4) - P(Z < -1.6)\\P(Z < 0.4) = 0.6554\\P(Z < -1.6) = 0.0548\\P(-1.6 < Z < 0.4) = 0.6554 - 0.0548 = 0.6006[/tex]
Therefore, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6006 (approx.) or 0.6827 (approx.).
Hence, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is 0.6827.
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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?
Answer: Xavier will receive $3.21 in change.
Step-by-step explanation:
To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:
Change = $10 - $6.79 = $3.21
Therefore, Xavier will receive $3.21 in change.
At cheap more super market,1 litre of fruit juice costs R25 and 1,5 litres cost R34 Which juice is cheaper. Show your calculation
The 1.5 liters of fruit juice is cheaper per liter compared to the 1 liter of fruit juice.
For the 1 liter of fruit juice, the cost per liter is R25/1 liter = R25/liter.
For the 1.5 liters of fruit juice, the cost per liter is R34/1.5 liters = R22.67/liter.
A supermarket is a large retail store that offers a wide range of food and household items to consumers. These stores are typically designed to be a one-stop shop for customers, allowing them to purchase everything they need in one convenient location. One of the primary advantages of shopping at a supermarket is the ability to choose from a wide variety of products at competitive prices.
Supermarkets usually have multiple departments, including a fresh produce section, a meat and seafood section, a bakery, and a deli. In addition to food items, supermarkets also offer a variety of household goods, such as cleaning supplies, personal care products, and pet food. Many supermarkets also offer loyalty programs, coupons, and other incentives to help customers save money.
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Solve the inequalities 1/3x-1/4(x+2)>3x-4/3
Answer: x < -46/17
Step-by-step explanation:
To solve the inequality:
1/3x - 1/4(x + 2) > 3x - 4/3
First, we simplify the left-hand side by finding a common denominator:
4(1/3x) - 3/4(x + 2) > 3x - 4/3
4/3x - 3/4x - 9/2 > 3x - 4/3
Next, we simplify the equation:
7/12x - 9/2 > 3x - 4/3
To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:
7/12x - 3x > 9/2 - 4/3
-17/12x > 23/6
Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:
x < (23/6) ÷ (-17/12)
x < -46/17
Therefore, the solution to the inequality is:
x < -46/17
The body of a cent in caterpillar is made up of five spherical parts, 3 of which are yellow and 2 are green. What is the greatest possible number of different types of this caterpillar that could exist?
The greatest possible number of different types of this caterpillar that could exist is 120.
What is the greatest possible number of the caterpillar?
If we assume that the order of the parts does not matter and that all caterpillars with the same color arrangement are considered identical, we can use combinations to find the number of different types of caterpillars that could exist.
First, we need to choose 2 out of the 5 parts to be green, which can be done in 5 choose 2 ways:
5 choose 2 = (5!)/(2!(5-2)!) = 10
For each green-yellow arrangement there are;
3! ways to permute the yellow parts and
2! ways to permute the green parts.
Therefore, the total number of different types of caterpillars is:
10 × 3! × 2! = 10 × 6 × 2 = 120
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(5,-8) and (-3, -1)
Answer:
5-8=-3
Step-by-step explanation:
-3-1=-4
Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
Please help me I will give the person with the right answer brainiest
Answer:
3. Yes because it is the same thing. (short answer just elaborate more)
4. No, a trapezoid cannot be a parallelogram. Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.
5. see last sentence in 4
6. group 1: the diamond and the square tilted, and the square.
group 2: the second one, the cup like shape, the cup shape but taller(the last one)
7. hard to see
8. hard to see
Step-by-step explanation:
A randomly generated list of integers from 1 to 5 is being used to simulate an
event, with the numbers 1 and 2 representing a success. What is the
estimated probability of a success?
A. 40%
B. 50%
C. 20%
D. 30%
The estimated probability of a success is 40% since the numbers 1 and 2 represent a success out of the integers 1 to 5. Therefore, the success outcomes (1 and 2) make up 2 out of 5 possible outcomes, or 40%.
To find the estimated probability of a success, we need to determine the proportion of successes in the generated list.
Out of the numbers 1 to 5, two numbers represent success (1 and 2). Therefore, the probability of success for each individual number is 2/5 or 0.4.
Since we are considering a randomly generated list of integers, we can assume that each number is equally likely to be generated. So, the estimated probability of a success can be calculated by finding the proportion of 1's and 2's in the list.
Let's assume that the list has n elements. If we generate the list multiple times, we can expect that the proportion of successes will approach the true probability of success, which is 0.4.
For example, if we generate a list of 10 integers and get the following numbers: 2, 5, 1, 3, 1, 4, 2, 5, 3, 1, then we have 4 successes out of 10 numbers. So, the proportion of successes in this list is 4/10 or 0.4, which matches the true probability of success.
Therefore, the answer is A. 40%.
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Ramona is climbing a hill with a 10 incline and wants to know the height of the rock formation. She walks 100 ft up the hill and uses a clinometer to measure the angle of elevation to the top of the formation. What is the height h of the rock formation?
The height of the rock formation is approximately 17.45 feet (rounded to two decimal places).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding missing sides or angles, determining distances or heights, and more. Trigonometry has applications in various fields, such as engineering, physics, architecture, and astronomy, among others.
In the given question,
We can use trigonometry to solve this problem. Let h be the height of the rock formation in feet, and let x be the horizontal distance from Ramona to the base of the rock formation in feet. Then, we have:
tan(10) = h/x
Rearranging this equation, we get:
h = x * tan(10)
We need to find the value of h, so we need to find the value of x. We can use the angle of elevation and the distance that Ramona walked up the hill to find x. We have a right triangle with height h, base x, and hypotenuse 100 ft. The angle opposite the height h is 10 degrees. So, we have:
tan(10) = h/x
sin(10) = h/100
Rearranging the second equation, we get:
h = 100 * sin(10)
Substituting this into the first equation, we get:
x * tan(10) = 100 * sin(10)
Dividing both sides by tan(10), we get:
x = 100 * sin(10) / tan(10)
Plugging this value of x into the equation for h, we get:
h = x * tan(10) = (100 * sin(10) / tan(10)) * tan(10) = 100 * sin(10)
Therefore, the height of the rock formation is approximately 17.45 feet (rounded to two decimal places).
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write re(e^(1/z)) in terms of x and y. why is this function harmonic in every domain that does not contain the origin?
The formula for the real portion of a complex function can be used to write re(e(1/z)) in terms of x and y: f(z) + f(z*) = re(f(z)) / 2
How is a harmonic function determined?where z* denotes z's complex conjugate.
By applying this formula to the provided function, we obtain:
re(e(1/z)) = (e(1/z) + e(1/z*)) / 2
re(e(1/z)) = (e(x-iy) + e(x+iy)) / 2
re(e(1/z)) = (ex (cos y + I sin y) + ex (cos y - I sin y)) /2
As a result, re(e(1/z)) can be represented as ex cos y in terms of x and y.
Because it fulfills Laplace's equation, which asserts that the total of a function's second-order partial derivatives is equal to zero, this function is harmonic in every domain excluding the origin.
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please help solve: 8x=64
Answer:
X=8
Bcuz 8x=64
64÷8=8
So that the answer is 8
Answer:
[tex]\bf x=8[/tex]
Step-by-step explanation:
[tex]\bf 8x=64[/tex]
Divide both sides by 8:
[tex]\bf \cfrac{8x}{8}=\cfrac{64}{8}[/tex]
Simplify:-
[tex]\bf x=8[/tex]
______________________
Hope this helps!
A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to
The 95% confidence interval for the population mean is equal to (30.4,39.6).
A confidence interval is a range of values that surrounds the point estimate, such as a sample mean, and provides a sense of the precision of the estimate. The confidence interval (CI) contains the estimated parameter at a given level of confidence, usually 95% or 99%.
The 95% confidence interval for the population mean is given by:
x(bar) ± Zα/2 * σ/√n
Where,
x(bar) = 35σ = 100n = 25Zα/2 = Z0.025 = 1.96
Substituting the values, we get:
CI = 35 ± 1.96 * 100/√25
CI = (30.4,39.6)
Hence, the 95% confidence interval for the population mean is (30.4,39.6).
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Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)
Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.
Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.
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Does anyone know how to solve this question with a method pls.
Answer:
(a) AC = 4√2 cm
(b) AM = 2√2 cm
(c) EM = √41 cm
(d) EF = 3√5 cm
Step-by-step explanation:
You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.
Right trianglesEach right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.
Right triangles of interest here are ...
ADC . . . . for finding AC and AM (isosceles right triangle)
CME . . . . for finding EM
FME . . . . for finding EF
(a) ACAC is the hypotenuse of ∆ADC, so ...
AC² = AD² +DC²
AC = √(4² +4²)
AC = 4√2 . . . . cm
(b) AMM is the midpoint of AC, so ...
AM = AC/2 = (4√2)/2
AM = 2√2 . . . . cm
(c) EMFM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.
CE² = CM² +EM²
EM = √(CE² -CM²) = √(7² -(2√2)²)
EM = √41 . . . . cm
(d) EFEF is the hypotenuse of ∆EMF.
EF² = EM² +FM²
EF = √(EM² +FM²) = √(41 +2²) = √45
EF = 3√5 . . . . cm
A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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By selling a camera for Rs 60,000 there is a loss 20%. At what price should it be sold to get 12% profit? Find it.
Answer:
Rs 84000----------------------------------
Let the cost price of the camera be x.
When the selling price is 60000 there is a loss of 20%. Let's show this as equation and find the cost price:
x - 20% of x = 60000x - 0.2x = 600000.8x = 60000x = 60000/0.8x = 75000The cost price is Rs 75000, and we need a profit of 12%, it gives us the selling price of:
75000 + 12% = 75000 + 0.12*75000 = 75000 + 9000 = 84000