I will give brainliest to the correct answer!

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

$76.5

Step-by-step explanation:

93.5÷5.5=17

17×4.50=76.5

Therefore the answer is 76.5.

Answer:

around 46%-48% because 9 pitchers would be 50% and the players that are not pitchers are about 48%

The compound inequality correctly shows the amount of money, m, the teacher can spend if the monthly budget for transportation is between 15% and 20% is $462.50 ≤ m ≤ $616.66

Given:

The average bi-weekly net pay of the high school teacher is $1,541.65.

To find the monthly budget for transportation, we need to multiply this amount by 2 to get the monthly net pay and then multiply the result by the percentage of the budget for transportation, which is between 15% and 20%.

The compound inequality that correctly shows the amount of money, m, the teacher can spend on transportation is:

$1,541.65 × 2 × 0.15 ≤ m ≤ $1,541.65 × 2 × 0.20

This simplifies to:

$462.495 ≤ m ≤ $616.66

$462.50 ≤ m ≤ $616.66

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The graph attached represents a non proportional function

Like the name goes, a Linear graph is a straight line graph that represents a linear relationship with the equation of the form

y = mx + c

A relationship is proportionate if its graph is a line or ray that passes through the origin. in this case c = 0

It is not proportional if the line or graph does not go through the origin.

Additionally, if anything is not linear, it is not proportional.

The attached graph passed through point (0, 1) which is not the origin (0, 0) hence the graph is not a proportional relationship

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The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)

To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:

|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)

So, a unit vector perpendicular to the plane determined by A and B is:

(-4k + 2i + 6j) / sqrt(56)

which simplifies to:

(-2i + 3j - k) / sqrt(14)

Therefore, the answer is (-2i + 3j - k).

To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.

A = -2i + 4j
B = i + j - k

Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k

Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k

Step 3: Simplify the expression:
C = -4i + 2j - 6k

Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56

Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k

So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

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The inverse Laplace transform of (-5s - 36) / ((s + 2)(s²+ 9)) is \(-4e^{-2t}\)+ (-cos(3t) + 8sin(3t))/3.

To find the inverse Laplace transforms of the given expressions, we can use partial fraction decomposition and known Laplace transform pairs. Let's solve each one step by step:

To find the inverse Laplace transform of (-2s² - 3s - 2) / (s(s + 1)²):

Step 1: Factorize the denominator:

s(s + 1)² = s(s + 1)(s + 1)

Step 2: Perform partial fraction decomposition:

(-2s² - 3s - 2) / (s(s + 1)²) = A/s + (B/(s + 1)) + (C/(s + 1)²)

Multiplying through by the common denominator, we get:

-2s² - 3s - 2 = A(s + 1)² + B(s)(s + 1) + C(s)

Expanding and equating coefficients, we find:

-2 = A

-3 = A + B

-2 = A + B + C

Solving these equations, we find: A = -2, B = 1, C = 0.

Step 3: Express the inverse Laplace transform in terms of known Laplace transform pairs:

\(L^{-1(-2s^{2} - 3s - 2) }\)/ (s(s + 1)²) = \(L^{-1(-2/s)}\) + \(L^{-1(1/(s + 1)) }\)+ \(L^{-1(0/(s+1)^{2} }\)

= -2 + \(e^{-t}\)+ 0t\(e^{-t}\)

Therefore, the inverse Laplace transform of (-2s² - 3s - 2) / (s(s + 1)²) is -2 + \(e^{-t}\).

To find the inverse Laplace transform of (-5s - 36) / ((s + 2)(s² + 9)):

Step 1: Factorize the denominator:

(s + 2)(s² + 9) = (s + 2)(s + 3i)(s - 3i)

Step 2: Perform partial fraction decomposition:

(-5s - 36) / ((s + 2)(s² + 9)) = A/(s + 2) + (Bs + C)/(s² + 9)

Multiplying through by the common denominator, we get:

-5s - 36 = A(s² + 9) + (Bs + C)(s + 2)

Expanding and equating coefficients, we find:

-5 = A + B

0 = 2A + C

-36 = 9A + 2B

Solving these equations, we find: A = -4, B = -1, C = 8.

Step 3: Express the inverse Laplace transform in terms of known Laplace transform pairs:

\(L^{-1(-5s - 36)}\) / ((s + 2)(s² + 9)) = \(L^{-1(-4/(s + 2))}\) + \(L^{-1((-s + 8)/(s^2 + 9)}\))

= \(-4e^{-2t}\) + (-cos(3t) + 8sin(3t))/3

Therefore, the inverse Laplace transform of (-5s - 36) / ((s + 2)(s²+ 9)) is \(-4e^{-2t}\)+ (-cos(3t) + 8sin(3t))/3.

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Answer:

B - 18

Step-by-step explanation:

149 total minutes minus 5 for the introductions leaves 144.

144/5=18

Answer: The first one 5/10 is 0.5 or 50% 5÷10. The second one 5/100 is 0.05 or 500%. The third one 5/1000 is 0.005 or 5000%.

Step-by-step explanation:

All you have to do is divide and you do that for all of them. Also did you know quotient means the answer to a division question. Wow! Also, if you see that all I did was add another zero in the middle of the decimals is because That is Decimal Place value. Here is a picture of that just in case.  The last answer for the very bottom one is what I just said about decimal place value so here is the reflection: When dividing by tens using decimals always be sure to use place value. Thank you I was happy to help!

If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

Answer:

=25x-7

Step-by-step explanation:

Answer:

Slope= -7/9

rise= 7

run=-9

Step-by-step explanation:

Answer

Slope= -7/9 rise= 7 run=-9

step explanation:

Step-by-step explanation:

Question 3) there's 60 minutes in a hour

3 times 60 = 180 books in 1 hour

3 times 180 = 540 books in 3 hours

540 + 180 + 180 = 900 books in 5 hours

The difference between those numbers : 900-540= 360 and 540-180= 360 so every 2 hours 360 books is done each time so just add 360 books each time for every 2 hours added

Answer:

8.6

Step-by-step explanation:

Mean = Sum of numbers/amount of numbers

= (11+13+8+9+4+8+7)/7

= 60/7

= 8.6

A total of 8,000,000 seven-digit phone numbers that can be formed if the first digit cannot be 0 or 1 and one digit can be repeated.

There are 8 possible choices for the first digit (2-9), and each of the other six digits can have 10 possible choices (0-9). Therefore, 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 possible seven-digit phone numbers.

To better understand this, let's break it down further. For the first digit, there are 8 possible choices since 0 and 1 are not allowed. For the second digit, there are 10 possible choices since any digit (0-9) can be used. For the third digit, there are 10 possible choices again since any digit (0-9) can be used.

The same holds true for the fourth, fifth, sixth, and seventh digits, giving us 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000 seven-digit phone numbers.

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-6 + x = -7

+6        +6        add 6 to both sides, 6's cancel out on the left.

________

x = -1, is the answer.

Hope this helps! Let me know if you have any other questions related to this problem. :)

Answer:

x= -1

Step-by-step explanation:

-6+x = -7

x = -7+6

x= -1

The number of possibilities in the given scenario are 144. The solution has been obtained by using permutations.

What is permutation?

Mathematical calculations are used to determine the number of different configurations for a given set, and this procedure is referred to as permutation. A permutation is a phrase that, simply put, refers to the variety of alternative configurations or orders. When employing permutations, the sequence of the arrangement is crucial.

We are given that a team of 12 lacrosse players need to choose a captain and co-captain.

This means that n is 12 and r is 2.

Using permutations, we get

⇒ Total possibilities = \(n^{r}\)

⇒ Total possibilities = \(12^{2}\)

⇒ Total possibilities = 144

Hence, the number of possibilities in the given scenario are 144.

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Answer:

1.) y = 4x - 3

2.) y = -3x + 2

Step-by-step explanation:

I'm not really sure how to explain it super well, but I do know the answers

Answer:

67,914

Step-by-step explanation:

Let x = total employees.

18.7% of x = 12,700

0.187x = 12,700

x = \(\frac{12700}{0.187}\) = 67914.438 → 67,914

I disagree with Eva. The pool will be full at 11:45 pm thus option (D) will be correct.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given table,

The pool filled out 1000 gallons every 15 minutes.

In 1 hour = 1000 x 4 = 4000 gallons,

To fill out a full pool of 15000 gallons,

15000/4 = 3 + 2000/3

3 hour + (15 + 15 + 15) minutes

⇒ 3 hours and 45 minutes

Since, it begins at 8:00 am thus 8 + 3 + 45 minutes = 11:45 am.

Hence "I don't concur with Eva. At 11:45 p.m., the pool will be filled".

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The total distance travelled by the car is 80 miles.

Speed is the ratio of total distance to total time. It is given by the formula:

Speed = distance / time

From the graph:

Distance = speed * time

Total distance = 20 mph * 1 hour + (30 mph * (90 - 60)/60 hour) + (50 mph * (120 - 90)/60 hour) + (40 mph * (135 - 120)/60 hour) + (20 mph * (150 - 135)/60 hour) + (10 mph * (180 - 150)/60 hour) = 80 miles

The total distance travelled by the car is 80 miles.

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Answer:

Step-by-step explanation:

1. Write your formula

2. Plug it in

3. Solve

these steps will help you out with all of your surface area problems.

Like this

Since it is a diameter you have to divide the diameter by 2. That will get you your radius. Then you write your formula for a cylinder. Your formula is...

V = Bh                            (Pie is also known as 3.14)

your big (B) is (pie times r squared) Then you add your height.

so your formula will look like this...

V = pie times r squared...

the full formula will be...

V = (3.14) times (2.5 squared) times the height which in this case is (12)

everything together will be...

V = (3.14) (2.5^2) (12)

all you have to do is multiply all of that and you will get your answer.

The answer is...

V = 236 inches ^2                        (Just a tip, the ^ sign means to the power of)

In the n-Firm Cournot Model, where there are n≥2 firms, each firm determines the quantity it produces in a Cournot oligopoly. The aggregate production level, denoted as Q, is the sum of the quantities produced by all the firms (q1+⋯+qn).

To represent this game as a static game with complete information, we can use the normal-form representation. In the normal-form representation, we describe the strategies and payoffs of each firm.

Let's go through the steps to create the normal-form representation of this game:

1. Identify the players: In this case, the players are the n firms participating in the Cournot oligopoly.

2. Determine the strategies: Each firm chooses the quantity it will produce, denoted by qi, where i represents the firm number. The quantity produced by each firm is the strategy of that firm.

3. Define the payoff function: The payoff for each firm depends on the market price, which is determined by the aggregate production level Q. The market price, P(Q), is given by the demand function P(Q) = a - Q.

4. Calculate the payoff for each firm: The payoff for each firm depends on the quantity it produces and the market price determined by the aggregate production level. The payoff can be calculated using the formula πi = P(Q) * qi, where πi represents the payoff for firm i.

5. Construct the normal-form representation: The normal-form representation is typically presented as a matrix, where each row represents a strategy profile (combination of quantities produced by the firms) and each column represents a player's strategy (quantity produced by a single firm). The entries in the matrix represent the payoffs for each firm.

For example, let's consider a 3-firm Cournot oligopoly with demand function P(Q) = a - Q. Firm 1, 2, and 3 have the strategies q1, q2, and q3, respectively. The payoffs can be calculated as follows:

- Payoff for firm 1: π1 = (a - Q) * q1
- Payoff for firm 2: π2 = (a - Q) * q2
- Payoff for firm 3: π3 = (a - Q) * q3

The normal-form representation matrix would look like this:

| Firm 1\2\3 | q1     | q2     | q3     |
|------------|--------|--------|--------|
| q1         | π1,1   | π1,2   | π1,3   |
| q2         | π2,1   | π2,2   | π2,3   |
| q3         | π3,1   | π3,2   | π3,3   |

Each entry in the matrix represents the payoff for each firm based on the combination of quantities produced by the firms.

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Answer:

A[2,3],(2,4),(2,5),(2,6)