the volume of the solid whose base is bounded by the circle x²y² = 4 is 0.
The equation of a circle in the coordinate plane can be written as(x - a)² + (y - b)² = r², where the center of the circle is (a, b) and the radius is r.
The equation x²y² = 4 can be rewritten as:y² = 4/x².
Therefore, the graph of x²y² = 4 is the graph of the following two functions:
y = 2/x and y = -2/x.
The line connecting the points where y = 2/x and y = -2/x is the x-axis.
We can use the washer method to find the volume of the solid obtained by rotating the area bounded by the graph of y = 2/x, y = -2/x, and the x-axis around the x-axis.
The volume of the solid is given by the integral ∫(from -2 to 2) π(2/x)² - π(2/x)² dx
= ∫(from -2 to 2) 4π/x² dx
= 4π∫(from -2 to 2) x⁻² dx
= 4π[(-x⁻¹)/1] (from -2 to 2)
= 4π(-0.5 + 0.5)
= 4π(0)
= 0.
Therefore, the volume of the solid whose base is bounded by the circle x²y² = 4 is 0.
To know more about coordinate visit:
https://brainly.com/question/22261383
#SPJ11
3.18 steph curry is a 91ree-throw shooter. he decides to shoot free throws until his first miss. what is the probability that he shoots exactly 20 free throws (including the one he misses)
The required answer is P(X=20) = 0.0919
To find the probability that Steph Curry shoots exactly 20 free throws (including the one he misses), we can use the binomial distribution formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- X is the number of successes (made free throws)
- k is the specific number of successes we are interested in (20)
- n is the total number of trials (free throws attempted)
- p is the probability of success (making a free throw)
Since Steph Curry is a 91% free-throw shooter, we know that p = 0.91. We also know that he will keep shooting free throws until he misses, which means that the number of trials is not fixed. However, we can still use the formula by setting n = 20 (the maximum number of free throws he could make before missing).
A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive events (events with no common results, such as the events {1,6}, {3}, and {2,4}), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events
Now, we just need to calculate P(X=20):
P(X=20) = (20 choose 20) * 0.91^20 * (1-0.91)^(20-20)
P(X=20) = 0.0919
So the probability that Steph Curry shoots exactly 20 free throws (including the one he misses) is approximately 0.0919, or 9.19%.
We are given that Steph Curry is a 91% free-throw shooter, which means he has a 91% chance of making each free throw and a 9% chance of missing one. We want to find the probability that he shoots exactly 20 free throws, including the one he misses.
probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events
In uniform probability distributions, the likelihood of each possible outcome happening or not is the same. This property means that, for any given trial, the probability that an event will be successful does not change
Step 1: Calculate the probability of making the first 19 free throws. Since each free throw has a 91% chance of success, the probability is 0.91^19.
Step 2: Calculate the probability of missing the 20th free throw. This is a 9% chance or 0.09.
Step 3: Multiply the probability of making the first 19 free throws by the probability of missing the 20th one to find the overall probability. This is (0.91^19) * 0.09.
The probability that Steph Curry shoots exactly 20 free throws, including the one he misses, is approximately 0.0357 or 3.57%.
To know more about probability. Click on the link.
https://brainly.com/question/30034780
#SPJ11
What is the solution to –2(8x – 4) < 2x + 5? x > x is greater than StartFraction 1 Over 6 EndFraction. x < x is less than StartFraction 1 Over 6 EndFraction. x > 6 x < 6
Answer:
x > 1/6.
Step-by-step explanation:
–2(8x – 4) < 2x + 5
-16x + 8 < 2x + 5
-18x < -3
x > 1/6.
The solution to the inequality expression is x > 1/6
Given the inequality expression
–2(8x – 4) < 2x + 5
Expand the parenthesis
-16x + 8 < 2x + 5
Subtract 5 from both sides
-16x + 8 - 5 < 2x + 5 - 5
-16x + 3 < 2x
-16x - 2x < -3
-18x < -3
Divide both sides by -18
-18x/-18 > -3/-18
x > 1/6
Hence the solution to the inequality expression is x > 1/6
Learn more on inequality here: https://brainly.com/question/24372553
the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n. true or false
The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.
In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.
On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.
The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.
Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.
To know more about statistical notation refer here:
https://brainly.com/question/28171663#
#SPJ11
A rectangular tank measuring 50cm by 50cm by 42cm was 2/3 filled with water.when a stone was placed in the tank, the tank became 3/4 full.(a) Find the capacity of the tank in cubic centimeters.(b) Find the volume of the stone.
ok
Volume of the tank = 50 x 42 x 50
= 105000 cm^2
Volume of 2/3 of the tank = 2/3 x 105000
= 70000 cm^3
Volume of 3/4 of the tank = 3/4 x 105000
= 78750 cm^3
a) Capacity of the tank = 105000 cm^3
b) Volume of the stone = 78750 - 70000
= 8750 cm^3
20/100 + 4/10 =20/100 + x = x move a fraction to make the equation true
Answer:
remove 4/10
20/100=20/100= 1 which is x
Step-by-step explanation:
Mrk ME BRAINLIEST PLZZZZZZZZZZ
Help fast I will do anything
Mercy participates in a bowling league on a team with her friends. The cost of
ordering team shirts can be represented by f(x) = 12.75x + 3.50, where the total
cost is a function of x, the number of shirts ordered Mercy's team must have a
minimum of 6 players and a maximum of 10 players. Which is a reasonable
range for the situation?
a. All real numbers
b. 80 SXS 131
C. {80, 92.75, 105.5, 118.25, 131}
d. y > 80
Find the area of each triangle to the nearest tenth
the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring. true/false
The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.
The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:
P(A or B) = P(A) + P(B) - P(A and B)
On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the conditional probability of B given that A has occurred.
It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.
In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.
In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.
To learn more about probability click on,
https://brainly.com/question/30648713
#SPJ4
Ms. J has been practicing her factoring skills. She factored the following problem by grouping,
but made a mistake.
Example 1: 4x2 + 20x - 3xy - 15y
Ms. J's work:
Step 1: 4x2 + 20x - 3xy - 15y
Step 2: 4x(x + 5) - 3y(x - 5)
Step 3: (x+5)(4x - 3y)
a. What was the mistake?
b. How can she fix the mistake?
Answer:
a) She did mistake in Step 2
b) when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)
Step-by-step explanation:
We need to find problem in Ms J solution.
Ms J solution:
\(Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5) - 3y(x - 5)\\Step \ 3: (x+5)(4x - 3y)\)
She did mistake in Step 2 when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)
Correcting the mistake:
\(Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5)\mathbf{- 3y(x +5)}\\Step \ 3: (x+5)(4x - 3y)\)
Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts. (-5,0), (5,0) opens upward f(x)=x²+x-5 X opens downward f(x)=x²-x+5
We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.
For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:
f(x) = a(x + 5)(x - 5)
where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:
f(x) = a(x^2 - 25)
To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:
f(x) = x^2 - 25
For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:
g(x) = a(x + 5)(x - 5)
where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:
g(x) = a(x^2 - 25)
To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:
g(x) = -x^2 + 25
For such more questions on quadratic
https://brainly.com/question/1214333
#SPJ8
we note that c is a positively-oriented, smooth, simple closed curve. green's theorem tells us that in this situation, if d is the region bounded by c, then p dx q dy c = ∂ ____ /∂x - ∂ ____ /∂y) dA
We note that c is a positively-oriented, smooth, simple closed curve. Green's theorem tells us that in this situation, if d is the region bounded by c, then p dx + q dy = (∂q/∂x - ∂p/∂y) dA
Based on the given information, we can apply Green's Theorem, which states that for a positively-oriented, smooth, simple closed curve c and the region d bounded by c, the line integral of the vector field (p, q) over c is equal to the double integral of the curl of (p, q) over d.
Green’s theorem is mainly used for the integration of the line combined with a curved plane. This theorem shows the relationship between a line integral and a surface integral.
It is related to many theorems such as Gauss theorem, Stokes theorem.
Green’s theorem is used to integrate the derivatives in a particular plane. If a line integral is given, it is converted into a surface integral or the double integral or vice versa using this theorem.
Green’s theorem is one of the four fundamental theorems of calculus, in which all of four are closely related to each other.
Green’s theorem defines the relationship between the macroscopic circulation of curve C and the sum of the microscopic circulation that is inside the curve C. Using the notation for the partial derivatives, we can express this as:
p dx + q dy = (∂q/∂x - ∂p/∂y) dA
Therefore, the missing terms in the equation would be q and p, respectively:
p dx + q dy = (∂q/∂x - ∂p/∂y) dA
p dx + q dy = (∂q/∂x - ∂p/∂y) dA
p dx + q dy = (∂q/∂x - ∂p/∂y) dA
Learn More About Green's Theorem: https://brainly.com/question/23265902
#SPJ11
nails cost $12.99 per box, and screws cost $14.99 per box. a carpenter must buy both nails and screws and can spend no more than $60. which system of inequalities represents this situation, where n represents the number of boxes of nails and s represents the number of boxes of screws?
The cost of nails can be represented as 12.99n, and the cost of screws can be represented as 14.99s.
The cost of buying nails and screws can be represented by a system of inequalities where "n" represents the number of boxes of nails and "s" represents the number of boxes of screws.
The cost of one box of nails is $12.99 and the cost of one box of screws is $14.99. Hence, the cost of "n" boxes of nails is represented by 12.99n and the cost of "s" boxes of screws is represented by 14.99s. The carpenter has a budget of $60 and can spend no more than that.
Therefore, the combined cost of buying nails and screws must be less than or equal to $60. This requirement can be represented by the inequality 12.99n + 14.99s <= 60.
To make the calculation easier, we can also express the inequality as n + s <= 4.62, where 4.62 is obtained by dividing $60 by $12.99. This system of inequalities represents the carpenter's budget constraint and helps to determine the number of boxes of nails and screws that can be purchased within the budget.
You can learn more about system of inequalities at
https://brainly.com/question/9290436
#SPJ4
I’m not sure what the answer is
Answer:24200
Step-by-step explanation:
I=PxRxT
20000x.07x3=4200
20000+4200=24200
Maria orders 8 pizzas for 24 people coming to her party.
a) How many people can be fed
b) How many pizzas would she need if 33 people come to the party.
Using the arithmetic operation of division -
a) 3 people can be fed by 1 pizza.
b) Maria would need 11 pizzas for 33 people.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of pizzas ordered = 8
The number of people are = 24.
Number of people that can be fed if 1 pizza was there =
Number of people = Number of people that came/ Number of pizza
Use the arithmetic operation of division -
Number of people = 24/8
Number of people = 3
Therefore, 3 people can be fed.
Now, the number of people = 33
Number of pizzas required for 33 people can be obtained as -
Use the arithmetic operation of division -
Number of pizzas = Number of people/ Number of people fed by 1 pizza
Number of pizzas = 33/3
Number of pizzas = 11
Therefore, Maria will require 11 pizzas.
To learn more about arithmetic operation from the given link
https://brainly.com/question/20628271
#SPJ1
PLEASEEWWE HELPPP!! Select each transformation that carries a square onto Itself.
1.) a reflection over one of the square's sides
2.) a reflection over one of the square's diagonals
3.) a rotation of 90° clockwise about the square's center
4.) a rotation of 180'clockwise about one of the square's vertices
5.) a rotation of 180' clockwise about the square's center
A C D
Step-by-step explanation:
Turn this equation into a sentence: 5x - 8 - 7
Answer:
5 times x minus 8 minus 7
Step-by-step explanation:
whenever you see an x right next to a number, it means that it's being multiplied for that number. For example: 2x mean 2 times x
This symbol - is a minus symbol. So when it's in front of a number, you say "minus" and then the number. For example: 4 - 3 means, Four minus three.
Dominic took a 20-question online quiz. He received 5 points for every correct answer. For every
question he answered incorrectly, he lost 2 points. The quiz also had a 20-point bonus for
finishing in one hour or less. Since Dominic finished the quiz in less than one hour, his score S is
determined by x, the number of questions answered correctly.
Drag and drop expressions into the function to correctly define S(2).
Х
X + 20
X-20
20 - x
2
5
20
S(x) = 5
-2
+
Answer:
X+20=2 i think this is a little above my head
4
Chaman's truck weighs 35 tons. The truck pulls a trailer
5
1
that weighs 4= tons. How heavy are the truck and trailer
5
together? Simplify the answer if possible.
Answer:
39 tons
Step-by-step explanation:
35 + 4 = 39
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Hence, when \(n=10\) the given inequality is true.
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.
So,
\(2(n + 2) < 5(n-1)\)
When
\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)
Hence, when \(n=10\) the given inequality is true.
To know more about the inequality
https://brainly.com/question/23575974
#SPJ1
Write the complex number in rectangular form. 6( cos 225 + i sin 225) The complex number is (Simplify your answer, including any radicals. Type your answer in the form a +bi. Use integers
Answer:
The rectangular form of the complex number is -3√2 - 3√2i.
To see why, recall that cos(225°) = -sin(45°) = -√2/2 and sin(225°) = -cos(45°) = -√2/2.
So we have:
6(cos 225 + i sin 225)
= 6(-√2/2 - i√2/2)
= -3√2 - 3√2i
A product or service which benefits everyone in the community but often is not feasible or efficient to provide without the collective effort of the community is a (n)
A product or service which benefits everyone in the community but often is not feasible or efficient to provide without the collective effort of the community is a public good.
What are public goods?
A public good is a good or service that is non-excludable and non-rivalrous. Non-excludability ensures that everybody in the community may benefit from the good or service.
Non-rivalry, on the other hand, ensures that consumption of the good or service by one person does not reduce its availability for others to enjoy without limitation.
A product or service which benefits everyone in the community but often is not feasible or efficient to provide without the collective effort of the community is a public good.
Public goods and services include a variety of things, such as schools, bridges, and parks, that everyone can use and benefit from without having to pay.
To learn more about public goods visit:https://brainly.com/question/14975509
#SPJ11
What are the opportunity costs involved in either decision?
Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”
The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.
Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.
Learn more about opportunity costs to visit this link
https://brainly.com/question/13036997
#SPJ4
At a party, the amount of people who ate lasagna was 15 less than 2/3 of the total number of people. The number of people who ate lasagna was 21. Write and solve an equation to find the number of people at the party. Let x represent the number of people at the party. Use pencil and paper. Write a one-step equation that has the same solution.
Based on the information given, it can be seen that the total number of people at the party is 54.
Solving an equationLet the total number of people at the party be represented by x.
Therefore, based on the information given, the equation will be:
(2/3 × x) - 15 = 21
2/3x - 15 = 21
2/3x = 21 + 15
2/3x = 36
x = 36/0.667
x = 54
Therefore, the total number of people at the party is 54.
Learn more about equations on:
https://brainly.com/question/13763238
PLEASE HELP I AM BEING TIMED!!
Assume line M and line N are parallel line cut by the transversal line L.
Find the value of X.
Options: X=18.2
X=-0.2
X=1.2
X=2
Answer:
X=1.2
Step-by-step explanation:
i just did that
Answer:x is 1.2
Step-by-step explanation:
Caclator
Ophelia works as a lifeguard to earn extra money. Last week, Ophelia worked for 14 hours and earned a total of $350. This situation is represented by the equation 14y = 350.
Which is the best definition of the variable y?
A. The variable y represents the number of kids in the pool during Ophelia’s time at work.
B. The variable y represents the number of hours Ophelia worked.
C. The variable y represents the amount of money Ophelia earns per hour.
D. The variable y represents the total amount of money Ophelia earned this week.
Option C i.e. the variable y represents the amount of money Ophelia earns per hour is the best definition of the variable y. The solution has been obtained by using concept of linear equation.
What is a linear equation?
One is the degree of the linear equation. As a result, it is clear that linear equations with exponents greater than one are void of variables. Such an equation on the graph yields a straight line.
We are given that Ophelia works as a lifeguard to earn extra money.
Last week, Ophelia worked for 14 hours and earned a total of $350 which is represented by 14y = 350.
So, from this we get that the variable y represents the amount of money Ophelia earns per hour as the equation gives us the total earnings.
Hence, option c is the best definition of the variable y.
Learn more about linear equation from the given link
brainly.com/question/30092358
#SPJ1
What is the slope-intercept equation of the line below?
Answer:
C
Step-by-step explanation:
y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.
What is the slop of the line y=4
Answer:
Undefined
Step-by-step explanation:
If the line is y=4 the slope is undefined meaning thst it cannot be found.
Answer:
0
Step-by-step explanation
y = m(x) + b
m = 0 Plug it in
y = 0(1x) + 4
1 * 0 = 0
y = 0 + 4
y = 4
This means it is undefined.
I hope this is right. If not, I apologize in advance.
How can i learned maths hardly?
Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.
Some tips that may help you learn maths quickly and efficientlyStart with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.
Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.
Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.
Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.
Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.
Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.
Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.
Read more about learning maths here:
https://brainly.com/question/30346704
#SPJ1
Please help me respond this question
Check the picture below.
Answer:
14.1
Step-by-step explanation:
You add all of your numbers up, and then you divide by how many numbers you have.
A music group expects to sell a new compact disc (CD) at the rate R(t)=20,000e−0.12t CDs per week, where t denotes the number of weeks since the CD was first released. To the nearest thousand, how many CDs are expected to be sold during the first 12 weeks after the release?
Answer:
4739 CDs
Step-by-step explanation:
Given the function that models the rate at which the disc is sold expressed as;
R(t)=20,000e^−0.12t
t is the number of weeks since the CD was first released
We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;
R(t)=20,000e^−0.12t
R(12)=20,000e^−0.12(12)
R(12)=20,000e^−1.44
R(12)=20,000(0.2369)
R(12) = 4738.56
Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs
Answer:
127,000
Step-by-step explanation:
you take the integral from 0 to 12 of R(t)