Find and sketch the domain of the function: F(x, y) = ln(2 - x)/1 - x^2 - y^2
Answers
The domain of a function represents the set of all valid input values for which the function is defined. To determine the domain of the given function, we need to known about natural logarithm and conditions.
To find the domain of the function F(x, y), we consider the following restrictions:
The natural logarithm ln(2 - x) is only defined for values of (2 - x) > 0. Therefore, we have the condition 2 - x > 0, which implies x < 2.
The denominator (1 - x^2 - y^2) should not be equal to zero, as it would lead to division by zero. Therefore, we have the condition 1 - x^2 - y^2 ≠ 0, which can be rewritten as x^2 + y^2 ≠ 1.
Combining these conditions, we find that the domain of F(x, y) is the set of all points (x, y) such that x < 2 and x^2 + y^2 ≠ 1. This can be visualized as the shaded region in the xy-plane where x is less than 2 and outside the unit circle centered at the origin.
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Related Questions
10) An architect is considering bidding for the design of a new shopping mall. The cost of drawing plans
and submitting a model is $10,000. The probability of being awarded the bid is 0.09, and anticipated
profits are
$100,000, resulting in a possible gain of this amount minus the $10,000 cost for plans and a
model. What is the expected value in this situation? Answers without any work shown will
receive no credit.
A) $8000
B) $9000
C) -$1000
D) $8100
Answers
Answer:
-$1000
Step-by-step explanation:
Given that:
Possible gain = 100,000 - 10,000 = 90,000
Loss =. 10,000 = cost of model submission
P(being awarded) = 0.09
P(not being awarded). = 1 - 0.09 = 0.91
X : 90000 _____ - 10,000
P(x) : 0.09 _______ 0.91
Expected value :
Σx*p(x) = (90000*0.09) + (-10,000 * 0.91)
= 8100 - 9100
= - 1000
PLEASE HELP I NEED HELP PLEASE HURRY (GIVING BRAINLIEST)
-5x-4x-1=8 and -8(x+4)+5=13
what is the value of x for each equation ?
Answers
Answer:
−5x−4x−1=8 = X= -1
−8(x+4)+5=13= X= -5
Step-by-step explanation:
During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Amos's free-throw shooting percentage is lower and is only 52.5%. After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points Amos makes when he shoots two free-throw shots.
Answers
I’m not entirely sure but i believe it’s 1.05
At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to continue to spin the wheel until they win a prize. Define x = the number of spins a child takes until they win a prize. Which, if any, of the following requirements for x to be a binomial random variable is violated in this setting?.
Answers
In this scenario, the following conditions for X to be a binomial random variable are broken:
(A) There will be a set number of trials.
(E) This environment satisfies all standards.
What is a binomial random variable?The binomial distribution with parametric n and p is the discrete random variable distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure.
It is used in probability theory and statistics.
So, a player will spin the wheel here till a prize is won.
The letter "X" indicates how many spins a youngster must complete before winning a prize.
Currently, let's go over each of the options in turn:
Option (a): It isn't true, as it has already been stated in the question, that they can keep spinning the wheel until they win a prize.
Option (b): It is legitimate because no trial depends on any other trial.
Option (c): It is legitimate because the wheel can only produce one of two results: WIN or LOOSE.
Option (d): It is legitimate because there are only two possible results when the wheel is spun, hence the odds of winning and losing are equally equal to half.
Because Option (a) does not satisfy the criterion, Option (e) is invalid.
Therefore, in this scenario, the following conditions for X to be a binomial random variable are broken:
(A) There will be a set number of trials.
(E) This environment satisfies all standards.
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Complete question:
At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to continue to spin the wheel until they win a prize. Define X = the number of spins a child takes until they win a prize.
Which, if any, of the following requirements for X to be a binomial random variable is violated in this setting?
a) The number of trials is fixed.
b) Each trial is independent of other trials.
c) There are two possible outcomes for each trial.
d) The probability of "success" is the same for each trial.
e) All requirements are met in this setting.
In how many ways can 5 different novels, 3 different mathematics books, and 1 biology book be arranged on a bookshelf if the mathematics books must be together and the novels must be together
Answers
In how many ways can 5 different novels, 3 different mathematics books, and 1 biology book be arranged on a bookshelf if the mathematics books must be together and the novels must be together?
To find the number of ways, in which 5 different novels, 3 different mathematics books, and 1 biology book can be arranged on a bookshelf if the mathematics books must be together and the novels must be together, we can use the concept of permutation formulae.
Permutation formulae is the formula used to find out the number of ways in which a set of things can be arranged or ordered without repetition of the arrangement. Here, the mathematics books must be together and the novels must be together. Therefore, we can group the mathematics books together as one book and the novels together as one book. That is, we have two groups, one of size 3 (mathematics books) and one of size 5 (novels).
Therefore, the problem now reduces to finding the number of ways in which two groups of books can be arranged on a shelf. This can be done by using the permutation formulae as follows:
First, we find the number of ways to arrange the two groups on the shelf, ignoring the order within the groups. There are two ways to arrange the two groups: either the mathematics books can come first or the novels can come first.
Second, we find the number of ways to arrange the mathematics books within their group. There are 3! = 6 ways to arrange the 3 mathematics books within their group.
Third, we find the number of ways to arrange the novels within their group. There are 5! = 120 ways to arrange the 5 novels within their group.
Therefore, the total number of ways to arrange the books is given by the product of the number of ways to arrange the two groups, the number of ways to arrange the mathematics books within their group, and the number of ways to arrange the novels within their group.
Thus, the number of ways to arrange the books is:2 x 6 x 120= 1440.
Answer: 1440 words
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state whether each of the following can expressed as a ratio: 3 oz and 30 inches
Answers
3 oz and 30 inches cannot be expressed as a ratio because the ounce is a unit of mass, while inches are a measure of length. Then, 3 oz and 30 inches cannot be expressed in the same unit.
Which of the following numerical expressions has the least value?
A) 2 x 3 x 4 + 5
B) (2 x 3) + (4 x 5)
C) (2 + 3 + 4) x 5
D) 2 X (3 + 4) x 5
Answers
Step-by-step explanation:
A Will be 29
B Will be 26
C Will be 45
D Will be 70
So B
fastt
13. Calculate the compound interest of an annuity due of BD400 paid each 4 months for 6.2 years if the nominal rate is 3% thirdly? (3 Points)
Answers
Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.
Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)
whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as
:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1
(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,
the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:
A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17
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ASAP There are 25 female performers in a dance recital. The ratio of men to women is 3:5. How many men are in the dance recital?
Answers
Answer:
15
Step-by-step explanation:
I WILL GIVE U BRAINLYIST FIRST TO ANSWER RIGHT
Answers
Answer:
D
Step-by-step explanation:
Its D because thebsample of 2 is noticed
Mr. Autry bought a hat for $99.90. He also bought a pair of boots for $89.90. What was the total cost of the hat and boots including an 8% sales tax
Answers
Answer:
$204.98
Step-by-step explanation:
Step 1: Add both item cost
\(99.90 + 89.90 = 189.80\)
Step 2: Find the sales tax of the result
\(\frac{8}{100}\times 189.8 = 15.184\)
Step 1: Convert 8% to fraction\(8\%= \frac{8}{100}\)Simplify\(\frac{8}{100} = \frac{2}{25}\)Step 2: Convert 189.80 to a fraction\(189.80 = \frac{189.8}{1}\)Step 3: Set it up\(\frac{2}{25}\times \frac{189.8}{1}\)Step 4: Cross divide\(189.80 \div 25 = 7.592\\2 \div 1 = 2\)Step 5: Multiply the result\(7.592 \times 2 = 15.184\)Step 3: Add the result from the total cost of both items
\(189.80 + 15.184 = 204.98\)
The total cost of the hats and boots including sales tax is 204.98 dollars
i need someones help with this question
Answers
Can someone explain please? Q= find the perimeter L=2x W=10 + x i dont understand can you guys explain?
Answers
Answer:
Q = 6x + 20
Step-by-step explanation:
L=2x
W=10 + x
Perimeter of a rectangle, Q= 2(L+ W)
2(2x + 10 + x)
2(3x + 10)
Q = 6x + 20
Find the following limit. Is the function continuous at the point being approached? lim sec (ysec²y- tan²y-1) y→ 1 lim sec (y sec²y-tan ²y-1)- (Simplify your answer.) y→ 1
Answers
The limit of sec(y sec²y - tan²y - 1) as y approaches 1 is undefined. The function is not continuous at the point being approached.
Explanation: To evaluate the limit, we can first simplify the expression inside the secant function using the trigonometric identity:sec²θ - tan²θ = 1/cos²θ - sin²θ/cos²θ = (1 - sin²θ)/cos²θ = cos²θ / cos²θ = 1Substituting this expression back into the limit, we get:lim sec(y sec²y - tan²y - 1)y→1= lim sec(y - 1)y→1As y approaches 1, the argument of the secant function approaches 0, which means that the secant function approaches infinity. Therefore, the limit is undefined.Since the limit is not defined, the function is not continuous at the point being approached. A function is continuous at a point if and only if the limit of the function as x approaches that point exists and is equal to the value of the function at that point. In this case, since the limit does not exist, the function is not continuous at y = 1.
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I need help with this question asap please
Answers
-3 * 2 * a + 5(-7b) + (12 * c * 4)
* = multiplication
7th Grade Math
Pls help I’m dumb
Answers
Answer: Let's simplify step-by-step.
(((−3x)(2))(x))(a)+5(−7b)+12xcx(4)
=−6ax2+−35b+48cx2
Answer:
=−6ax2+48cx2−35b
Hope I helped?
Write an expression for the perimeter of the triangle shown below: (4 points)
A triangle is shown with side lengths labeled 0.5x plus 9, 3x, and negative 3.4x minus 25.
A 6.9x − 16
B 6.9x + 16
C 0.1x − 16
D 0.1x + 16
Answers
Answer:
The expression of the perimeter of the triangle is 0.1x - 16 ⇒ C
Step-by-step explanation:
The perimeter of a triangle is the sum of the lengths of its sides
Let us solve the problem
∵ The lengths of the sides of a triangle are:
0.5x + 93x-3.4x - 25∵ The perimeter of the triangle = sum of lengths of its sides
∴ The perimeter = (0.5x + 9) + (3x) + (-3.4x - 25)
→ Add the like terms
∵ The perimeter = (0.5x + 3x - 3.4x) + (9 + -25)
→ Remember (+)(-) = (-)
∴ The perimeter = (3.5x - 3.4x) + (9 - 25)
∴ The perimeter = 0.1x + -16
∴ The perimeter = 0.1x - 16
The expression of the perimeter of the triangle is 0.1x - 16
Answer:
C.
Step-by-step explanation:
0.1x − 16
What is the volume of the right triangular prism shown?
for brainlist
Answers
Answer: C
Step-by-step explanation:
Answer:
V = 567 yd³
Step-by-step explanation:
\(V = \frac{1}{2} ach\)
\(V = \frac{1}{2}(9)(6)(21)\)
V = 567 yd³
What is the prime factorization of 64? Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17.
Answers
The prime factorization of 64 :
64 divided by 2 = 32
32 divided by 2 = 16
16 divided by 2 = 8
8 divided by 2 = 4
4 divided by 2 = 2
2 divided by 2 = 1
So,
64 = 2 x 2 x 2 x 2 x 2 x 2
4 What is the equation of a line parallel
to y = x + 6 that passes through (-4, 1)?
Carnegie Learning.
Answers
The equation of the parallel lines is y = x + 2.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.
The slope of two parallel lines are equal.
The equation of the given line is:
y = x + 6
here, the slope of the line is 1.
So, the slope of the new line is 1.
The new line has the coordinates (-4, 1).
Using the point-slope form we have:
y - y1 = m (x - x1)
y - 1 = 1 (x + 1)
y - 1 = x + 1
y = x + 2
Hence, the equation of the parallel lines is y = x + 2.
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Bridget, Jim and Krutika share some sweets in the ratio 4:3:1. Bridget gets 45 more sweets than Krutika. How many sweets are there altogether?
Answers
Answer:
120 sweets
Step-by-step explanation:
Bri:Jim:Kru
4: 3: 1
find the difference in the ratio of Bridget and Krutika
4-1=3
ratio 3 is equivalent to 45 sweets
total ratio(4+3+1)--------> ?
total no. of sweets= 8x45
3
=120sweets
Assume that each year the IRS randomly audits 30% of the tax returns. If a married couple has filed separate returns, answer the following questions. (a) What is the probability that both the husband and the wife will be audited? (b) What is the probability that only one of thern will be audited? (c). What is the probabkity that neither one of them will be audited? (d) What is the probability that at least one of them will be audited?
Answers
The problem entails calculating the probability for a scenario in which the IRS audits 30% of tax returns at random and a married pair has filed separate returns. Calculate the chances of both husband and wife being audited, just one of them being audited, neither of them being audited, and at least one of them being audited.
a) Probability that both the husband and the wife will be audited: (0.3)² = 0.09 or 9%
b) Probability that only one of them will be audited:
Probability of the husband being audited and the wife not being audited: (0.3)(0.7) = 0.21 or 21%Probability of the wife being audited and the husband not being audited: (0.7)(0.3) = 0.21 or 21%The probability that only one of them will be audited is the sum of the two probabilities which equals 0.42 or 42%.c) Probability that neither one of them will be audited: (0.7)² = 0.49 or 49%
d) Probability that at least one of them will be audited: This is the complement of the probability that neither one of them will be audited. So, the probability that at least one of them will be audited is 1 - 0.49 = 0.51 or 51%.
The relevant terms in this question are probability and statistics. To solve for the probability of each scenario, we used the formulas for independent probabilities and complements.
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a compound that dissociates weakly is exposed to an electric current attached to a light bulb what do you expect will happen
Answers
Answer:
https://www.letsanswers.com/a-compound-that-dissociates-dissolves-to-form-ions-weakly-is-exposed-to-an-electric-current-attached-to-a-light-bul/
Step-by-step explanation:
link for the information
In this question, you will compute the variance of a geometric distribution with parameter p. (1) Recall the following Taylor expansion. "=1+r+ ir -1
Answers
To compute the variance of a geometric distribution with parameter p, we first need to understand the geometric distribution itself.
The geometric distribution represents the number of trials required for the first success in a sequence of Bernoulli trials, where each trial has a success probability of p.
The variance of a geometric distribution with parameter p can be calculated using the formula:
Variance = (1 - p) / p^2
Please note that the Taylor expansion "=1+r+ ir -1" you mentioned does not seem to be relevant to the calculation of the variance of a geometric distribution. The correct formula for the variance is provided above.
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Help me out please an thank you
Answers
Answer:
Eg would be 10.6 because its the same length as EF
Answer:
8.6?
Step-by-step explanation:
if it's a right angle an the exact same thing on the other side, than wouldn't you just add 4.3 + 4.3?
determine weather it is no solution many solutions or one solutions
3(6-4m)=2(9-6m)
Answers
Answer:
Many solutions
Step-by-step explanation:
What values of x make this true?
(x^2–3x+2)/(x –1) = x – 2
Answers
Answer:
Any value of x makes the equation true. All real numbers Interval Notation: ( − ∞ , ∞ )
Hope This Helps!!!
Does dy/dx in a graph mean the value of f'(x), or the slope of f'(x) at the point?
Answers
Find the average value of the function f(x) = (x + 2) on the interval [0, 3].
![Find the average value of the function f(x) = (x + 2) on the interval [0, 3].](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/P5zl0SIYRlJ5Lz5JinzKHjLeHoS5AWmn.png)
Answers
The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.
Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:
= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3
= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]
= (1/3) × [(9/2 + 6) - 0]
= (1/3) × (21/2)
= 7/2
Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
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when f(x)=2x-2 what is the domain?
Answers
Answer:
d: x3R
Step-by-step explanation:
Step 1: What is asked
A domain is for what values of x in the graph is defined such as when y = 2, x is equal to 2.
Step 2: Solve
Since this is a linear equation the domain would be every x value do it would be: d: x3R (x belongs to all real numbers)