Let F : ]0, +[infinity][ × R → R be the function F(x, y)=y(e**y +x)-ln(x).
Show: there exists a neighborhood I ⊂ R of the point x0 = 1 and a unique function f :I →R such that.
(1) f(1) = 0 and f ∈ C1(I),
(2) F(x, f(x)) = 0 for all x ∈ I.
( f ∈ C1(I), means that f is differentiable and that the derivative is continuous. )

Answer:

x=19

Step-by-step explanation:

First, you place the numbers in place of the variables in their relative positions using the pythagorean theorem:

\(15^{2} +x^{2}=24^{2}\)

Then you square the numbers that you currently have:

\(225+x^{2}=576\)

Then subtract 225 from both sides to isolate the x:

\(x^{2} =576-225\)

This gives you the equation:

\(x^{2} =351\)

Then take the square root of both sides which gives you:

\(x=18.7349939952\)

Then round to the nearest whole number which gives you x=19

Answer: Y = 21

Step-by-step explanation:

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

The value of x, to the nearest tenth, is approximately 4.96. The steps involved using the tangent ratio and solving for the unknown side in a right triangle.

In a triangle, the angle opposite to the side x as angle A, and the side opposite to the angle 33° as side B, and the largest side as side C. So we have:

Angle A = 90° - 33° = 57° (since the sum of angles in a triangle is 180°)

Side B = 8

Side C = 15

Side x = ?

Write the formula for the tangent ratio in terms of the sides of the triangle. For angle A, we have:

tangent(A) = opposite/adjacent

Substitute the known values into the formula and solve for the unknown side. Substituting the values we have, we get

tangent(33°) = x/8

Multiplying both sides by 8, we get:

x = 8 * tangent(33°)

Use a calculator to find the value of the tangent of 33 degrees. We get:

tangent(33°) ≈ 0.6494

Substitute the value of the tangent into the formula we obtained in step 3 and solve for x. We get

x ≈ 8 * 0.6494

x ≈ 5.1952

Round the answer to the nearest tenth, since the question asks for the value of x to the nearest tenth. We get

x ≈ 4.96

Therefore, the value of x, to the nearest tenth, is approximately 4.96.

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The probability that the absolute value of the running tally never equals 3 is approximately 0.718, or 71.8%. In this scenario, the running tally can only change by 1 each time the coin is tossed, either increasing or decreasing. It starts at 0, and we need to calculate the probability that it never reaches an absolute value of 3.

To find the probability, we can break down the problem into smaller cases. First, we consider the probability of reaching an absolute value of 1. This happens when there is either 1 head and no tails or 1 tail and no heads. The probability of this occurring is 1/2.

Next, we calculate the probability of reaching an absolute value of 2. This occurs in two ways: either by having 2 heads and no tails or 2 tails and no heads. Each of these possibilities has a probability of (1/2)² = 1/4.

Since the running tally can only increase or decrease by 1, the probability of never reaching an absolute value of 3 can be calculated by multiplying the probabilities of not reaching an absolute value of 1 or 2. Thus, the probability is (1/2) * (1/4) = 1/8.

However, this calculation only considers the case of the first coin toss. We need to account for the fact that the coin can be tossed multiple times. To do this, we can use a geometric series with a success probability of 1/8. The probability of never reaching an absolute value of 3 is given by 1 - (1/8) - (1/8)² - (1/8)³ - ... = 1 - 1/7 = 6/7 ≈ 0.857. However, we need to subtract the probability of reaching an absolute value of 2 in the first coin toss, so the final probability is approximately 0.857 - 1/8 ≈ 0.718, or 71.8%.

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Answer:

Yes because, we'll technically but then we get yur answer

Answer:

x = 7

Step-by-step explanation:

Step 1: Write everything out

-3 - (-8) - (-2) = x

Step 2: Switch signs

x = -3 + 8 + 2

Step 3: Combine

x = 10 -3

x = 7

Answer:

7u-4v/8

Step-by-step explanation:

u+6u=7u

-v+(-3v)=-v-3v=-4v

7u-4u/8

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

{-22, -14, -6, 2, 18}

Step-by-step explanation:

f(-4)=4(-4)-6=-22

f(-2)=4(-2)-6=-14

f(0)=4(0)-6=-6

f(2)=4(2)-6=2

f(6)=4(6)-6=18

The probability that someone exiting the tavern is either a gnome or a goblin can be found by dividing the number of gnomes and goblins by the total number of individuals in the tavern. In this case, there are 3 gnomes and 5 goblins, so the total number of gnomes and goblins is 3 + 5 = 8. The total number of individuals in the tavern is 6 + 3 + 4 + 5 + 1 = 19. Therefore, the probability is 8/19.

To calculate the probability, we consider the total number of favorable outcomes (gnomes and goblins) and divide it by the total number of possible outcomes (all individuals in the tavern). In this scenario, there are 8 favorable outcomes (3 gnomes and 5 goblins) and 19 possible outcomes (6 humans, 3 gnomes, 4 dwarves, 5 goblins, and 1 elf). By dividing 8 by 19, we find that the probability of someone exiting the tavern being either a gnome or a goblin is approximately 0.421 (rounded to three decimal places).

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Answer:

Slope = 2 6/11

Step-by-step explanation:

Formula: \( \frac{y2}{x2} - \frac{y1}{x1} = m\)

m = slope.

Substitute the given points into the formula:

\( \frac{35}{16} - \frac{7}{5} = m\)

Solve:

\( \frac{35}{16} - \frac{7}{5} = \frac{28}{11} = 2 \frac{6}{11} \)

Answer: Either A or B because you have to add the amount you have to get the total amount she spent.

Step-by-step explanation:

Answer:

y = -4x + 1

Step-by-step explanation:

Okay, one way we can find the equation is to plug the x and y values into y = mx + b

We m (slope) is -4 so

y = -4x + b

We want to find b so we plug in x and y (-2 and 9)

9 = -4 (-2) + b

9 = 8 + b

In this case, b is 1

Now we plug this to make our equation,

y = -4x + 1

Hi there!

The question is asking us to find the equation of the line, given that it has a slope of 4, and it passes through (-2,9).

I will go about solving this by using point-slope:

\(\sf{y-y_1=m(x-x_1)}\)

\(\sf{y-9=-4(x-(-2)}\)

\(\sf{y-9=-4(x+2)}\\\sf{y-9=-4x-8}\\\sf{y=-4x-8+9}\\\sf{y=-4x+1}\)

Therefore, the line's equation is y = -4x + 1.

Have a fantastic day!

Answer:

Step-by-step explanation:

Given the following DE = 4X-2

EF = 3x+2

FG 5x-3

GD = 2x+5

Since DE is parallel to GF, this means that the sides are equal hence;

4x - 2 = 5x - 3

4x - 5x = -3 + 2

-x = -1

x = 1

Hence the value of x is 1

Answer:

4.2L=4200^3<this one Is a I think

0.35km=350m<This one ik

Step-by-step explanation:

Answer:

A- 6 weeks

B-18 trailers

C-3 trailers

D- the mean is 3

Step-by-step explanation:

Answer:

9 cm²

Step-by-step explanation:

the area = ½× 3√2 × 3√2 = ½×18 = 9

Answer:

93

Step-by-step explanation:

This question is on Arithmetic sequence, and we can find the 16th term using the Arithmetic sequence formula below;

aₙ= a₁ + (n-1)d

Where n= nth term in that particular sequence.

n₁= first term in the particular sequence.

d= common sequence between the terms.

Given:

d=6

a₁ =3.

Using the formula above,

a₁₆= 3 + (16-1)6

= 3+(15)6

=3+90

=93

Hence, the the 16th term of the arithmetic sequence is 93

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where V is the volume and r is the radius of the sphere.

We are given that the volume of the sphere is 36π cm^3, so we can write:

36π = (4/3)πr^3

Simplifying:

r^3 = (36/4) * 3

r^3 = 27

r = 3

Therefore, the radius of the sphere is 3 cm.

The circumference of a great circle on a sphere is given by the formula:

C = 2πr

where r is the radius of the sphere.

So, the circumference of the great circle is:

C = 2π(3) = 6π

Therefore, the circumference of the great circle of the sphere is 6π cm.

Answer:

The volume of the parallelepiped is 247 cubic units.

Step-by-step explanation:

The volume of the parallelepiped formed by the column vectors of a matrix A is given by the absolute value of the determinant of A. Therefore, we need to compute the determinant of the matrix A:

det(A) = (1)(5)(-4) + (-3)(-3)(-3) + (2)(-3)(2) - (-27)(5)(2) - (3)(-4)(1)(-3)

      = -20 - 27 - 12 + 270 + 36

      = 247

Since the determinant is positive, the absolute value is the same as the value itself.

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The probability that their score is at least  P(X> 555.3) = 0.8275

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Let x denotes the score of a man.

standard deviation (σ) = 104

mean (μ) = 507

If 1 of the men is randomly selected, find the probability that his score is at least 553.5 will be :-

P(X > 553.5) = 1 - P(X ≤ x)

= 1 - P{((x - μ)/σ) ≤ (553.5 - 507/104)}

= 1 - P(z ≤ 0.447)

= 1 - 0.1725

= 0.8275

Hence, the probability that their score is at least  P(X> 555.3) = 0.8275

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Answer:

11+11= 22 answer is $ 22.03

At 0.01 level of significance, we cannot conclude that the population mean SAT score for graduates of the course is greater than 538.

To determine if we can conclude that the population mean SAT score for graduates of the course is greater than 538, we can conduct a one-sample t-test.

Provided information:

- Sample size (n) = 80

- Sample mean (xbar) = 542

- Population mean (μ) = 538

- Standard deviation (σ) = 35

- Significance level (α) = 0.01

The null hypothesis (H₀) assumes that the population mean SAT score for graduates of the course is equal to or less than 538:

H₀: μ ≤ 538

The alternative hypothesis (H₁) assumes that the population mean SAT score for graduates of the course is greater than 538:

H₁: μ > 538

We'll calculate the test statistic and compare it to the critical value to make our conclusion.

First, calculate the standard error of the mean (SEM):

SEM = σ / √n

SEM = 35 / √80

SEM ≈ 3.92

Next, calculate the t-value:

t = (xbar - μ) / SEM

t = (542 - 538) / 3.92

t ≈ 1.02

Now, we need to determine the critical value. Since the alternative hypothesis is one-tailed (greater than), we'll use the upper critical value for a t-distribution at the provided significance level.

Looking up the critical value in a t-table or using a statistical software, at α = 0.01 with 79 degrees of freedom (n - 1), we obtain the critical value to be approximately 2.623.

Since the calculated t-value (1.02) is less than the critical value (2.623), we fail to reject the null hypothesis.

Therefore, based on the provided information, we cannot conclude that the special preparation course significantly improves the population mean SAT score.

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1. Definition of Congruence:∠ RSU ≅ ∠ VST

2. Definition of Congruence: m∠ RSU = m∠ VST

3. Angle Addition Postulate: m∠ RSU + m∠ USV = m/RSV

4. Angle Addition Postulate: m∠ VST + m∠  USV = m∠ UST

5. Transitive Property: m∠ RSU + m∠ USV = m∠ UST

6. Substitution Property: m∠ RSV = m∠ UST

7. Definition of Congruence: ∠ RSV ≅ ∠ UST

In mathematics, a relation R on a set X is said to have a transitive property if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.

This is shown in the case of number 6 where :

m∠ RSU + m∠ USV = m∠ UST

The transitive property is also shown in  equality states where all values of a, b, and c, if a = b, and b = c, then a = c.

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The probability that all 5 servers are working, given that the game is not shut down, is 0.59049 or approximately 0.59.

To find the probability that all 5 servers are working, given that the game is not shut down, we need to use conditional probability. We know that if two or fewer servers are working, the game will shut down. Therefore, we are interested in finding the probability that more than two servers are working.

Since the servers are assumed to be independent, the probability that a single server is working is 0.9, and the probability that it is not working is 1 - 0.9 = 0.1.

To find the probability that more than two servers are working, we can calculate the complement of the event "two or fewer servers working." The complement is the event "three or more servers working." We can calculate this probability using the binomial probability formula:

\(P(X \geq k) = 1 - P(X < k)\)

In this case, k = 3 (since we want three or more servers working), n = 5 (total number of servers), and p = 0.9 (probability of a server working).

Using the formula, we get:

\(P(X \geq3) = 1 - P(X < 3)\\ = 1 - P(X = 0) - P(X = 1) - P(X = 2)\\ = 1 - (0.1^5) - (5 * 0.1^4 * 0.9) - (10 * 0.1^3 * 0.9^2)\\ \approx 0.59049\\\)

Therefore, the probability that all 5 servers are working, given that the game is not shut down, is approximately 0.59049 or 59%.

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The volume of the balloon is increasing at a rate of 800π cubic inches per second when the radius is 10 inches.

Using the volume of a sphere formula, V = (4/3)πr³, where V is the volume and r is the radius, we can determine how quickly the balloon's volume is growing.

We are given that the radius is increasing at a rate of 2 inches per second, so dr/dt = 2.

We need to find dV/dt, the rate at which the volume is changing with respect to time. To do this, we can differentiate the volume formula with respect to time using the chain rule:

dV/dt = dV/dr × dr/dt

First, let's find dV/dr. Differentiating the volume formula with respect to the radius gives us:

dV/dr = d/dt ((4/3)πr³) = 4πr²

We can now enter the supplied values into the equation as follows:

dV/dt = (4πr²) × (dr/dt) = (4π(10)²) × (2)

Calculating this expression gives us the rate of change of the volume:

dV/dt = 800π cubic inches per second

So, when the radius is 10 inches, the volume of the balloon is increasing at a rate of 800π cubic inches per second.

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Answer:

x = 69

Step-by-step explanation:

Knowns:

y = 69

Problem Workout

180 - z = 2y

180 - z = 2 (69)

180 - z = 138

-z = -42

z = 42

Since there is no picture, I am guessing x is the third angle.

x = 180 - (y + z)

x = 180 - (69 + 42)

x = 180 - 111

x = 69