Find the equation of the hyperboloid of one sheet passing through the points (±5,0,0),(0,±2,0) and (±10,0,3),(0,±4,3) =1

Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

We have:

∫30∫3ysin(x^2) dxdy

To reverse the order of integration, we need to express the limits of integration as inequalities of x and y:

3y ≤ x^2 ≤ 9y

√(3y) ≤ x ≤ √(9y)

0 ≤ y ≤ 1

So, we have:

∫30∫√(9y)√(3y)sin(x^2) dxdy

Integrating with respect to x first, we get:

∫√(9y)√(3y) [-cos(x^2)/2] |_0^(√(3y)) dy

= ∫30 [-cos(3y)/2 + cos(y)/2] dy

= [-sin(3y)/6 + sin(y)/2] |_0^3

= (-sin(9)/6 + sin(3)/2) - (0 - 0)

= (-sin(9)/6 + sin(3)/2)

Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

Note: We can also check the answer by evaluating the original integral and comparing it with the answer obtained by reversing the order of integration.

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Answer:

not a right triangle

Step-by-step explanation:

you can use the pythagorean theorem to prove whether not this is a right triangle

if this triangle is a right triangle then the following equality should be true

a²+b²=c²

(9.75)²+(3.45)²=(10.24)²

(95.06)+(11.90)=(104.86)

106.96≠104.86

since the following equality is not true, this is not a right triangle.

Answer:

156

Step-by-step explanation:

f(x)= 4^(2x) -100

Let x =2

f(2)= 4^(2*2) -100

   = 4^4 - 100

   = 256 -100

   = 156

Answer:

Greatest:8 2/5  

least:3/26

Step-by-step explanation :Hope im right:)But if im wrong try listening to your teacher you might understand if you do that:)

Answer:

1/3

Step-by-step explanation:

(4/6) - (1/3)

The denominators need to be the same, so let's convert the second term to (2/6), which is the same as (1/3)

(1/3)*(2/2) = (2/6)

Now we can wite:

(4/6) - (2/6)

This is equal to 2/6 or 1/3

Hello!

The equation \(\frac{4}{6} - \frac{1}{3}\) simplified is \(\frac{1}{3}\).

Step-by-step explanation:

Begin by giving both equations common denominators in this case we will use 18.

For the first set of fractions we multiply 4 by 3 to get 12 and for the second set of fractions we multiply 1 by 6 to get 6.

Our new set of fractions will look like this \(\frac{12}{18}\)\(- \frac{6}{18}\)

Now we can subtract the numerators since our denominators match.

\(12-6=6\) so the new answer will be \(\frac{6}{18}\)

It's time to simplify both sets of fractions before we can completely solve the equation. (divide by 2, then 3)

\(\frac{6}{18}\) ÷ \(2=\frac{3}{9}\) ÷ \(3=\frac{1}{3}\)

Since 3 is larger than 1 we are done reducing, time to solve for the final answer.

\(\frac{4}{6} -\frac{1}{3} =\frac{1}{3}\)

Hope this helps!

Answer:c the third one

Step-by-step explanation: because i did it!

Answer:

-11 - 13i.

Step-by-step explanation:

(12) — (23 + 13i)

= 12 - 23 - 13i

= -11 - 13i.

Answer:

m puq

Step-by-step explanation:

Answer: the bus is going 27mph

Step-by-step explanation: 40km is 27 miles

The average speed of the bus will be 80 km per hour.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

If a bus travels 40 km in 30 minutes. Then the average speed of the bus is given as,

Average speed = 40 / 30

Average speed = 1.33 km per minute

Average speed = 1.33 x 60

Average speed = 80 km per hour

The average speed of the bus will be 80 km per hour.

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Answer:

umm...im not funny tho.......

Step-by-step explanation:

The probability model for X is: X 0 1 2P(X) 0.49 0.33 0.18 .The probability model for X can be found by computing the probabilities associated with each value of X. X can take on the values 0, 1, or 2 because there are only two games.

Let's compute the probability that Mill Valley wins both games: P(X = 2) = P(win 1) × P(win 2 | win 1) = (0.3) × (0.6)

= 0.18

Let's compute the probability that Mill Valley wins one game. There are two ways to win one game: win the first game and lose the second, or lose the first game and win the second.

We can calculate these probabilities separately.

P(win 1) × P(lose 2 | win 1) = (0.3) × (0.4) = 0.12P(lose 1) × P(win 2 | lose 1)

= (0.7) × (0.3)

= 0.21

So, the probability of winning one game is P(X = 1) = 0.12 + 0.21

= 0.33

Probability of winning no games

Let's compute the probability that Mill Valley wins no games. This is the complement of the probability of winning at least one game.

So, P(X = 0) = 1 − P(X ≥ 1)

= 1 − P(X = 1) − P(X = 2)

= 1 − 0.33 − 0.18

= 0.49

Therefore, the probability model for X is: X 0 1 2P(X) 0.49 0.33 0.18

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Answer:

ytyt

Step-by-step explanation:

tyt5667

Using the law of exponent again, \(7^21/7^18\) is equal to\(7^(21-18)\), which is equal to\(7^3.\) Thus, the value of the expression\(7^12x7^9/(7^6)^3 is 7^3,\) which is equal to 343.

The expression\(7^12x7^9/(7^6)^3\) is asking to calculate the value of 7 to the power of 12 multiplied by 7 to the power of 9 divided by (7 to the power of 6) to the power of 3. This can be written as \(7^(12+9)/7^(6*3)\). Using the law of exponent, \(7^(12+9)/7^(6*3)\)can be simplified to\(:7^21/7^18\).Finally, using the law of exponent again,\(7^21/7^18\) is equal to\(7^(21-18)\), which is equal .Thus, the value of the expression\(7^12x7^9/(7^6)^3 is 7^3\), which is equal to 343.

\(7^12 x 7^9 / (7^6)^3= (7^12 x 7^9) / (7^18)= (7^21) / (7^18)= 7^3= 343\)

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

L=12, W=6

Step-by-step explanation:

L=2W

(L+2L)=36

3L=36

2L=12

L=6

The probability that exactly 7 of the captured small monsters are phlogiston subtypes is approximately 0.2083 or 20.83%.

To calculate the probability that exactly 7 of the captured small monsters are phlogiston subtypes, we can use the binomial probability formula. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

- P(X = k) is the probability of exactly k successes,

- n is the number of trials (31 in this case),

- k is the number of successful trials (7 in this case),

- p is the probability of success for each trial (27% or 0.27 for phlogiston subtype),

- (n choose k) is the binomial coefficient, calculated as n! / (k! * (n - k)!)

Let's plug in the values and calculate the probability:

P(X = 7) = (31 choose 7) * (0.27)^7 * (1 - 0.27)^(31 - 7)

Calculating the binomial coefficient:

(31 choose 7) = 31! / (7! * (31 - 7)!)

            = 112,385,013

Now let's calculate the probability:

P(X = 7) ≈ (112,385,013) * (0.27^7) * (0.73^24)

        ≈ 0.2083 (rounded to four decimal places)

Therefore, the probability that exactly 7 of the captured small monsters are phlogiston subtypes is approximately 0.2083 or 20.83%.

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Answer:

36

Step-by-step explanation:

because if 6x6=36

Answer: A  streetlight casts a shadow 15 feet long. At the same time, a 18-foot flag pole casts a shadow 10 feet long. How tall is the tree? | Socratic A tree casts a shadow 15 feet long.

Answer: the common factor is 1

Step-by-step explanation:

Answer:

\(5^{16}\)

Step-by-step explanation:

Exponential rules: add the exponents

Answer:

13√ 2

Step-by-step explanation:

√ 26*(26/2)

=√ 26*13 = √ 338 = 13√ 2

The length of the segment  cut from the line by the two other sides of the triangle is \(13\sqrt{2\)

The length of the side is given as:

L= 26 inches

The length (d) of the line that divides the segment is calculated as:

\(d = \sqrt{(L/2)^2 + (L/2)^2\)

So, we have:

\(d = \sqrt{(26/2)^2 + (26/2)^2\)

Evaluate the quotients

\(d = \sqrt{13^2 + 13^2\)

Rewrite the expression as:

\(d = \sqrt{13^2* 2\)

Take the square root

\(d = 13\sqrt{2\)

Hence, the length of the segment is \(13\sqrt{2\)

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The constant of proportionality for the work done when lifting an object is given as follows:

k = 14.78.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted, hence the equation is given as follows:

W = khm.

The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules, the the constant is given as follows:

150k = 2216.8

k = 2216.8/150

k = 14.78.

The problem asks for the constant of the proportional relationship.

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The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is y<2/7x-5.

Here,

Put (x, y)=(21, 0) in the given inequality, we get

0<2/7(21)-5

0<1

So, it is solution

Put (x, y)=(6, -4) in the given inequality, we get

-4<2/7(6)-5

-4<12/7-5

-4<1.7-5

-4<-3.3

So, it is solution

Put (x, y)=(0, -5) in the given inequality, we get

-5<2/7(0)-5

-5<-5

Which is not true, it is not a solution

Put (x, y)=(7, -3) in the given inequality, we get

-3<2/7(7)-5

-3<-3

Which is not true, it is not a solution

Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

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An increase in the tax rate (T) will result in a lower equilibrium interest rate (i) and a lower equilibrium output level (Y). It's important to note that these effects depend on various assumptions and the specific functional forms of the equations in the IS/LM model.

A. To calculate the effect of the change in government spending (G) on the equilibrium interest rate (i) and output level (Y), we need to analyze the IS/LM model.

In the IS/LM model, the equilibrium is determined by the intersection of the IS curve (goods market equilibrium) and the LM curve (money market equilibrium).

Effect on the equilibrium interest rate (i):

An increase in government spending (G) will shift the IS curve to the right. This is because higher government spending increases aggregate demand, leading to higher output and income. As a result, there is upward pressure on the interest rate.

The shift in the IS curve will cause the equilibrium interest rate (i) to increase.

Effect on the equilibrium output level (Y):

With the increase in government spending (G), the IS curve shifts to the right, indicating higher aggregate demand. This leads to an increase in the equilibrium output level (Y). The increase in government spending directly contributes to the increase in output through the autonomous component of aggregate demand (G).

In summary, an increase in government spending (G) will result in a higher equilibrium interest rate (i) and a higher equilibrium output level (Y).

B. To calculate the effect of the change in the tax rate (T) on the equilibrium interest rate (i) and output level (Y), we again analyze the IS/LM model.

Effect on the equilibrium interest rate (i):

A change in the tax rate (T) affects disposable income (YD) and, consequently, consumption (C). An increase in the tax rate reduces disposable income, leading to a decrease in consumption. This decrease in consumption reduces aggregate demand and shifts the IS curve to the left. The shift in the IS curve will cause the equilibrium interest rate (i) to decrease.

Effect on the equilibrium output level (Y):

The decrease in consumption resulting from the increase in the tax rate (T) reduces aggregate demand, which in turn leads to a decrease in the equilibrium output level (Y). The decrease in consumption directly affects the aggregate demand component related to consumption (C), resulting in a lower equilibrium output level (Y).

In summary, an increase in the tax rate (T) will result in a lower equilibrium interest rate (i) and a lower equilibrium output level (Y).

It's important to note that these effects depend on various assumptions and the specific functional forms of the equations in the IS/LM model.

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1. Objective Function and Constraints:

Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

2. Using Excel Solver, find the optimal allocation of funds.

3. The maximum value of the objective function is reported by Excel Solver.

We have,

Objective Function and Constraints:

Let:

x1 = amount spent on food

x2 = amount spent on shelter

x3 = amount spent on entertainment

Objective Function:

Maximize: 2x1 + 3x2 + 5x3 (since each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5)

Constraints:

Subject to:

x1 + x2 + x3 ≤ $1,500 (maximum disposable income)

x1 + x2 ≤ $1,100 (amount spent on food and shelter combined must not exceed $1,100)

x2 ≤ $800 (amount spent on shelter alone must not exceed $800)

x3 ≤ $400 (entertainment cannot exceed $400)

Using Excel Solver:

In Excel, set up a spreadsheet with the following columns:

Column A: Variable names (x1, x2, x3)

Column B: Objective function coefficients (2, 3, 5)

Column C: Constraints coefficients (1, 1, 1) for the first constraint (maximum disposable income)

Column D: Constraints coefficients (1, 1, 0) for the second constraint (amount spent on food and shelter combined)

Column E: Constraints coefficients (0, 1, 0) for the third constraint (amount spent on shelter alone)

Column F: Constraints coefficients (0, 0, 1) for the fourth constraint (entertainment limit)

Column G: Right-hand side values ($1,500, $1,100, $800, $400)

Apply the Excel Solver tool with the objective function and constraints to find the optimal allocation of funds.

Once the Excel Solver completes, it will report the maximum value of the objective function, which represents the optimal satisfaction value achieved within the given budget constraints.

Thus,

Objective Function and Constraints: Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

Using Excel Solver, find the optimal allocation of funds.

The maximum value of the objective function is reported by Excel Solver.

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The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the \(\mu_0\) is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

\((\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})\)

\((6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})\)

\((6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})\)

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

\(n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}\)

\(n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}\)

\(n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}\)

\(n=2.6097^2\frac{2.12^2}{0.5^2}\)

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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Answer:

probably y= 1/2x + 1

Step-by-step explanation:

could also be y= 2x + 1

The given error function E(z), with its z-transform E(z) = 3z³ / (z³ - 9z² + 27z - 27), can be expressed as the product of two z-transform equations E₁(z) and E₂(z), where E₁(z) and E₂(z) are fractional polynomials of z with first-order numerators.

To express E(z) as the product of two z-transform equations E₁(z) and E₂(z), we factorize the denominator of E(z):

E(z) = 3z³ / (z³ - 9z² + 27z - 27)

The denominator can be factored as follows:

z³ - 9z² + 27z - 27 = (z - 3)(z - 3)(z - 3)

Now, we define E₁(z) = 3z / (z - 3) and E₂(z) = z - 3. Multiplying them together, we obtain:

E₁(z) x E₂(z) = (3z / (z - 3)) x (z - 3) = 3z³ / [(z - 3)(z - 3)(z - 3)]

This expression is equal to E(z), as shown by the factored denominator. Therefore, we have proven that E(z) can be written as the product of two z-transform equations E₁(z) and E₂(z), where E₁(z) has a first-order numerator 3z and E₂(z) has a first-order numerator z - 3.

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