find a formula for the described function. a rectangle has perimeter 24 m. express the area a (in m2) of the rectangle as a function of the length, l, of one of its sides.
a. the larger of n 1 - 1 or n 2 - 1
b. n 1 + n 2 - 2
c. the smaller of n 1 - 1 or n 2 - 1
d. n 1 + n 2 - 1

The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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Answer:

The extraneous solution is x = -5/6

Length = 4 ft

Width = 5 ft

Step-by-step explanation:

Length = 3x - 5 ft

Width = 2x - 1 ft

Height = 2 ft

Volume = 40 ft^3

Volume = length × width × height

40 = (3x - 5)(2x-1)(2)

40 = (6x^2 - 3x - 10x + 5)(2)

40 = 12x^2 - 6x - 20x + 10

12x^2 - 26x + 10 - 40 = 0

12x^2 - 26x - 30 = 0

Divide through by 2

6x^2 - 13x - 15 = 0

Solve using factorization method

(6x + 5) (x - 3) = 0

6x + 5 = 0

6x = -5

x = -5/6

Or

x - 3 = 0

x = 3

The extraneous solution is x = -5/6

Length = 3x - 5 ft

= 3(3) - 5

= 9 - 5

= 4 ft

Width = 2x - 1 ft

= 2(3) - 1

= 6 - 1

= 5 ft

The correct answer in this scenario is a) The courts are likely to consider ChromaLite Builders's performance as a substantial performance, and Jessica will have to pay something but not the full amount; i.e. she is entitled to monetary damages.

This is because ChromaLite Builders did not fully comply with the contract by installing grade A carpeting instead of grade A+ carpeting, but the difference may not be significant to most people. As a result, the courts are likely to consider this a minor breach of contract and award Jessica some monetary damages but not the full cost of the contract.

It is important to note that if the difference between the two grades of carpeting was significant and clearly stated in the contract, Jessica may have had a stronger case for refusing to pay. However, in this scenario, it seems that the breach of contract was not significant enough to justify a complete refusal to pay.

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when multiplying two matrices A and B with m>n, the product AB will always result in a square matrix with linearly dependent rows or columns, causing its determinant to be 0.

To explain why the product of matrices A and B has det(AB)=0 when m>n, let's first understand the basics of matrix multiplication and determinants.
Matrix multiplication: If A is an m by n matrix and B is an n by m matrix, then their product AB is an m by m square matrix. To calculate the product, the number of columns in A (n) must be equal to the number of rows in B (n).
Determinants: The determinant is a scalar value that can be computed for any square matrix (i.e., the number of rows and columns are equal). The determinant is used to understand certain properties of the matrix, such as invertibility. If the determinant is 0, the matrix is singular and not invertible.
Example 1 (m < n): Let A be a 2x3 matrix and B be a 3x2 matrix. Their product AB is a 2x2 square matrix. The determinant can be calculated for AB, but not for A or B, as they are not square matrices.
Example 2 (m > n): Let A be a 3x2 matrix and B be a 2x3 matrix. Their product AB is a 3x3 square matrix. Since m > n in this case, the resulting product matrix will have linearly dependent rows or columns, which implies that its determinant will be 0.

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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Answer:

Step-by-step explanation:

Answer:

x=7?

Step-by-step explanation:

(x-9)(3x-9)

3x²-9x-27x+81

3x²-36x+81

sry mate it's binomial.

The given equation that should be in the standard form should be like a 4.5 x 10¹¹.

The equation in standard form:

Since

The equation is (5 x 10³) x (9 x 10⁷)

Now here we use the commutative property

So,

45 x (10³ x 10⁷)

45 x 10¹⁰

4.5 x 10¹¹

Here, we multiply the number in the 1st bracket, then add, it, and then finally in standard form.

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Answer:

Step-by-step explanation:

(5*10^3)*(9*10^7)

(5*1000)*(9*10000000)

5000*90000000

450000000000

Answer:

12 square centimeters

Step-by-step explanation:

Not sure what formula you are using here. The standard one is A=1/2 b h, where b is the base and h is the height.

base=4

height=6

A= 1/2 x 4 x 6

A=1/2 x 24

A=12 cm^2

Answer:

Sum is

Step-by-step explanation:

Answer:

All students have to take at least one math class and one language class. Twenty students take calculus, and thirty students take statistics.

Answer: An incline, a slant up or down.

Step-by-step explanation:

Fragment free frame processing method causes a switch to wait until the first 64 bytes of the frame have been received before forwarding the frame to the destination device

An advanced type of cut-through switching is fragment-free (runtless switching). Before making a switching choice, switches engaged in cut-through switching merely read the Ethernet frame's destination MAC address field.

The latency in fast-forward mode is calculated between the first bit received and the first bit delivered. The most common cut-through switching technique is fast-forward switching. Switching without fragments: The switch stores the first 64 bytes of the frame in fragment-free switching before forwarding.

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Answer:

\(2x + 10 = 28 \\ 2x = 28 - 10 \\ 2x = 18 \\ 2x \div 2 = 18 \div 2 \\ x = 14\)

Step-by-step explanation:

If triangle ABC is a right angle, it will allign with Pythagoras theorem where a² = b² +c²

A will be the longest side (hypotenuse)

10² = 6² + 8²

100 = 36 + 64

100 = 100

A is square root of 100 on both sides

It is a right angle triangle

The estimated pressure needed to raise a column of water to the same height as a 35m tall tree is approximately 343,350 N/m² or Pascal (Pa).

The given calculation is partially correct, but there are some errors in the final equation. Let's correct and complete the calculation:

We need to calculate the pressure needed to raise a column of water to the same height as a 35m tall tree.

Given:

h = 35 m (height of the tree)

φ = 1000 kg/m³ (density of water)

g = 9.81 m/s² (acceleration due to gravity)

The pressure can be calculated using the formula: P = h * φ * g

P = (35)(1000)(9.81)

P = 343,350 N/m²

So, the estimated pressure needed to raise a column of water to the same height as a 35m tall tree is approximately 343,350 N/m² or Pascal (Pa).

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Answer:

(3, 50) and (14,303)

Step-by-step explanation:

Given the system of equations;

y=23x–19 ....1

x²–y= – 6x–23 ...2

Substitute 1 into 2;

x²–(23x-19)= – 6x–23

x²–23x+19= – 6x–23 .

x²-23x + 6x + 19 + 23  = 0

x² - 17x + 42 = 0

Factorize;

x² - 14x - 3x + 42 = 0

x(x-14)-3(x-14) = 0

(x-3)(x-14) = 0

x = 3 and 14

If x = 3

y = 23(3) - 19

y = 69-19

y = 50

If x = 14

y = 23(14) - 19

y = 322-19

y = 303

Hence the coordinate solutions are (3, 50) and (14,303)

Answer:

D

Step-by-step explanation:

hope this helps with your work

Answer:

D

Step-by-step explanation:

8-(7+5m)

8-7-5m (distributive property)

To have no solution for the given system of linear equations, the value of B must make the slopes of the two equations different. Specifically, if B is equal to -8/4 or any value that is not equal to -2, the system will have no solution.

The system of linear equations is:
3x + 4y = 8
6x + By = 2
To determine the value of B that would result in no solution, we need to examine the slopes of the two equations. In equation 1, the coefficient of y is 4, which means the slope is -3/4. In equation 2, the coefficient of y is B, so the slope is -6/B.
For the system to have no solution, the slopes of the two equations must be different. This means that -3/4 must not be equal to -6/B. Solving this inequality, we have:
-3/4 ≠ -6/B
Cross-multiplying, we get:
-3B ≠ -24
Dividing both sides by -3, we find:
B ≠ 8
Therefore, any value of B that is not equal to 8, such as -8/4 or -2, would result in no solution for the given system of linear equations.

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Answer:

A, D, F.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

D

Step-by-step explanation: The slope is 1/3x, and that means it would pass through (-2,1) if the slope was there. Hope this helps  (:

To find the equation of the tangent line to the graph of the function p(t) = t ln(t) at t = 2, we need to determine the slope of the tangent line and the point of tangency.

Find the derivative of p(t):

p'(t) = ln(t) + 1

Evaluate the derivative at t = 2:

p'(2) = ln(2) + 1

Calculate the value of p(2):

p(2) = 2 ln(2)

Use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Plug in the values:

y - p(2) = p'(2)(x - 2)

Simplify the equation:

y - 2 ln(2) = (ln(2) + 1)(x - 2)

Convert the equation to a more standard form:

y = (ln(2) + 1)(x - 2) + 2 ln(2)

Now, round the coefficients and constants to three decimal places to obtain the final equation of the tangent line.

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Answer:

3x² +6

Step-by-step explanation:

(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions

... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses

... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms

... = 3x² +6

True. The HMAC-based one-time password algorithm uses a mathematical algorithm to generate a unique password for each login attempt.

This algorithm combines a secret key and a counter to produce a one-time password that is difficult to guess or duplicate. The algorithm is designed to be secure and reliable, providing an additional layer of protection for user accounts. By using a different password for each login attempt, the algorithm helps prevent attackers from gaining access to a user's account even if they manage to intercept the password. Overall, the HMAC-based one-time password algorithm is an effective way to enhance the security of online accounts and protect against unauthorized access.

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a) The inverse of the function f(x), which we can denote as f^-1(x) is y = (5x + 6)/(4x - 5)

b) The domain of f is (-∞, 5/4) U (5/4, ∞), the range of f is (-∞, 5/4) U (5/4, ∞), the domain of f^-1 is (-∞, ∞) \ {5/4}, and the range of f^-1 is (-∞, 5/4) U (5/4, ∞).

(a) To find the inverse of the function f(x), we need to switch the roles of x and y and then solve for y:

x = (5y + 6)/(4y - 5)

Multiplying both sides by (4y - 5), we get:

x(4y - 5) = 5y + 6

Expanding and rearranging, we get:

4xy - 5x = 5y + 6

Bringing all the y terms to one side, we get:

(4x - 5)y = 5x + 6

Dividing both sides by (4x - 5), we get:

y = (5x + 6)/(4x - 5)

This is the inverse of the function f(x), which we can denote as f^-1(x).

To check our answer, we can verify that f(f^-1(x)) = x and f^-1(f(x)) = x for all values of x in the domain of f and f^-1.

(b) The domain of f is all real numbers except x = 5/4, where the denominator becomes zero. The range of f is also all real numbers except -∞ and 5/4, which are not in the range.

The domain of f^-1 is the range of f, which is all real numbers except -∞ and 5/4. The range of f^-1 is the domain of f, which is all real numbers except x = 5/4.

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The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).

\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.

In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.

Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

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Answer:

1 3/4

Step-by-step explanation:

Answer: Option D

Step-by-step explanation: Explanation:

7/4 is an improper fraction. Let's take the numerator and divide it by the denominator.

Divide 7 by 4. The quotient digit is 1.

Multiply the quotient digit 1 by the divisor 4.

Subtract 4 from 7.

The result of 7 divided by 4 is 1 with a remainder of 3.

Thus, 7/4 as a mixed number can be written as 1 3/4.