5. Simplify the expression. √80x²y • √25xy^4

The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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Answer:

The length of side of patio is 11.27 feet.

Option A is correct option.

Step-by-step explanation:

Area of patio = 127 ft^2

We need to find side length of the patio.

Since the patio is square, the formula used is:

\(Area\: of\: square = l^2\)

where l is the side length of square.

Now, putting value of area we can find area of square.

\(Area\: of\: square = l^2\\127=l^2\\Switching\:sides\:\\l^2=127\\Taking\:square\:root\:on\:both\:sides\\\sqrt{l^2}=\sqrt{127} \\l=11.27\)

So, the length of side of patio is 11.27 feet.

Option A is correct option.

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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The values of BMW after 2, 4 and 8 years  according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.

Using the parameters given, we define an decreasing exponential function :

\(A = A_{0} (1 - r)^{t}\)

Where,

\(A_{0}\) = initial amount ; r = Rate ; t = time ; A = final amount

Value after 2 years :

t = 2

A = 55000(1 - 0.22)²

A = 55000(0.78)²

A = $33,462

Value after 4 years :

t = 4

A = 55000(1 - 0.22)^4

A = 55000(0.78)^4

A = $20,358.28

Value after 8 years :

t = 4

A = 55000(1 - 0.22)^8

A = 55000(0.78)^8

A = $7,535.63

Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.

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When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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It is not sensible to measure a football pitch in nanometres because they  are extremely small units of length which are typically used to measure particles or atomic structures.

Nanometres are a billion times smaller than a meter making them unsuitable for measuring macroscopic objects like a football pitch. Football pitches are typically measured in meters or yards which provide a more appropriate scale for their size.

Nanometres are better suited for measuring things on a molecular or atomic level such as the size of nanoparticles or the spacing between atoms. Attempting to measure a football pitch in nanometres would not only be impractical but also misleading as it would not accurately reflect the dimensions of the pitch in a meaningful way.

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The value of x for the given expression is 576xyz² - 960xy + 6624y + 552x²yz² - 920x²y + 5068z² - 8460y + 1152.

To find the value of x for the given expression (8x - 7)(3x - 11)(2y + 23) (3z2 - 5)(4y + 8), we need to first simplify the expression using the distributive property of multiplication.

Here's how: First, we can combine the terms inside the first set of parentheses: (8x - 7)(3x - 11) = 24x² - 104x + 77. Next, we can multiply this result by the second set of parentheses: (24x² - 104x + 77)(2y + 23) = 48xy + 552y + 46x²y + 529

Next, we can multiply this result by the third set of parentheses: (48xy + 552y + 46x²y + 529)(3z² - 5) = 144xyz² - 240xy + 1656y + 138x²yz² - 230x²y + 1267z² - 2115

Finally, we can multiply this result by the fourth set of parentheses: (144xyz² - 240xy + 1656y + 138x²yz² - 230x²y + 1267z² - 2115)(4y + 8) = 576xyz² - 960xy + 6624y + 552x²yz² - 920x²y + 5068z² - 8460y + 1152. Now, we can set this result equal to x and solve for x:576xyz² - 960xy + 6624y + 552x²yz² - 920x²y + 5068z² - 8460y + 1152 = x

Therefore, the value of x for the given expression is 576xyz² - 960xy + 6624y + 552x²yz² - 920x²y + 5068z² - 8460y + 1152.

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The coordinate matrix of x in Rn relative to the basis b' is [5, 6]. To find the coordinate matrix of x in Rn relative to the basis b', we need to express x as a linear combination of the basis vectors in b'.

Given the basis b' = {(9, 0), (0, 4)} and the vector x = (45, 24), we want to find the scalars c1 and c2 such that:

x = c1*(9, 0) + c2*(0, 4)

By solving this equation, we can determine the values of c1 and c2, which represent the coordinates of x in the basis b'.

Expanding the equation, we have:

(45, 24) = (9c1, 0) + (0, 4c2)

Equating the corresponding components, we get two equations:

45 = 9c1   (equation 1)

24 = 4c2    (equation 2)

Solving equation 1, we find c1 = 5.

Solving equation 2, we find c2 = 6.

Therefore, the coordinate matrix of x in Rn relative to the basis b' is [5, 6].

In other words, the vector x can be expressed as a linear combination of the basis vectors in b' with coefficients 5 and 6, respectively.

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By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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10; decreases

8: decreases, increases

7: increases, stays the same, increases, stays the same, increases.

9: increases, increases

I hope that this is correct and was able to help

If a translation maps H onto J, the option from the following statements which is true is:  ∠I ≅ ∠K (Option 1)

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. The four fundamental translations or transformations in geometry are:

With regard to the above answer, note that, because both triangles have the same vertex, angle HGI is equivalent to angle JGK. Angle H is parallel to angle J.

As a result, by converting angle I to angle K, their measurements will be equivalent. As a result, the angle I is congruent with angle K.

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Full Question:

If a translation maps H onto J, which of the following statements is true?

1. ∠I ≅ ∠K

2. GH = 2GJ

3. ∠G ≅ ∠K

4. HI = 2JK

The focus, directrix and axis of symmetry of the parabola \(y^{2} = 16\cdot x\) are \((x,y) = (0, 4)\), \(x = -4\) and \(y = 0\).

The equation of the parabola in standard form is defined below:

\(4\cdot a\cdot (x- h) = (y-k)^{2}\) (1)

Where:

The coordinates of the focus are \((x,y) = (0, h+a)\) and the equation of the directrix is \(x = h-a\). Lastly, the equation of the axis of symmetry is \(y = k\).

If we know that \(h = 0\), \(k = 0\) and \(a = 4\), then the focus, directrix and axis of symmetry of the parabola are:

Focus

\((x,y) = (0, 4)\)

Directrix

\(x = -4\)

Axis of symmetry

\(y = 0\)

The focus, directrix and axis of symmetry of the parabola \(y^{2} = 16\cdot x\) are \((x,y) = (0, 4)\), \(x = -4\) and \(y = 0\).

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Answer:

A: \(csc(\theta)\)

Step-by-step explanation:

Let's rewrite the expression in terms of sine and cosine, then simplify what can be simplified.:

\(sin(\theta) \cdot \frac{cos^2(\theta)}{sin^2(\theta)}\cdot \frac 1{cos^2(\theta)} =\\\frac1{sin(\theta)} = csc(\theta)\)

Hey there!☺

\(Answer:\boxed{1\frac{7}{10}}\)

\(Explanation:\)

\(3\frac{1}{2}-1\frac{4}{5}\)

Subtract the two fractions:

\(3\frac{1}{2}-1\frac{4}{5}=\frac{17}{10}\)

To get the final answer, you will have to simplify 17/10:

\(\frac{17}{10}=1\frac{7}{10}\)

1 7/10 is your answer.

Hope this helps!☺

Answer:

3/4x+3-2x= −5 /4 x+3

Step-by-step explanation:

yw <3 IMAO

Answer:

3.C

4.D

5.C..........m

Answer:

Your answer will be 14 for the value of b in Darren's equation

Answer:

it is 14

Step-by-step explanation:

The description that best defines AB¯¯¯¯¯ is:

"The set of points containing point A and point B."

AB¯¯¯¯¯ represents a line segment with endpoints A and B.

A line segment is a part of a line that connects two points, and it includes all the points that lie between the two endpoints.

Therefore, the set of all points between point A and point B is the most accurate description of AB¯¯¯¯¯.

The set of all points between point A and point B includes both endpoints A and B, as well as all the points that lie in between them. These points can be represented by the notation [A, B].

In other words, AB¯¯¯¯¯ is the line segment that starts at point A and ends at point B, and it includes all the points that lie between A and B.

This definition of AB¯¯¯¯¯ is important in geometry and other related fields. It is used in a variety of applications, including measuring the distance between two points and finding the slope of a line.

Additionally, it is an important concept in trigonometry and calculus, where it is used to define integrals and to calculate the arc length of a curve.

In summary, AB¯¯¯¯¯ is the set of all points between point A and point B, including both endpoints.

This definition is essential to many branches of mathematics and has important applications in geometry, trigonometry, and calculus.

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Answer:

x = 2

Step-by-step explanation:

3x + 4 - x = 8

Combine like terms

2x + 4 = 8

-4 from both sides

2x = 4

Divide by 2

x = 2

Answer:

x=4

Step-by-step explanation:

Add 4 to both sides of the equation

3x=8+4

add 8 and 4

3x=12

Divide each term in 3 x = 12 by 3.

3x/3 = 12/3

Cancel the common factor.

3x/3 = 12/3

Divide x by 1.

x = 12/3

 Divide 12 by 3.

Answer:

Y = -1x - 1

Step-by-step explanation:

I used desmos graphing calculator and tried until I got a line that worked.  It passes through (2, -3) and has a slope of -1

Hope this helped :)

Answer:

50 minutes left

Step-by-step explanation:

1 hour is 60 mins

60 mins+45mins=105 mins

105-55=50

50 mins left

Answer:

50 minutes remaining in the movie

Step-by-step explanation:
1 hour= 60 minutes 

+45 minutes 

----------------------

105 minutes in movie total

- 55 minutes watched 

----------------------

50 minutes remaining in the movie

Answer:

5(x+8)

5x+8x

5x+40

6q+2+3q+5

9q+7

Answer:

1. 5x + 40

to get this answer i multiplied the 5 to the variables in the parenthesis

2. 9q +7

to get this answer i added the variables that were similar., one pair has q at the end and the other does not.

Answer: X=3

Step-by-step explanation:

Answer:

Subtract 8 with 29, and that'll give you 21. Divide 7 for both and your answer will be 3.

Step-by-step explanation:

The greatest common factor of 30y⁸ +10y⁴ is 10y⁴

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.

The common factors of 30 are: 1,2,3,5,6,10,15,30

The common factors of 10 are : 1,2,5,10

therefore the greatest common factor is 10

The greatest common factor between y⁴ and y⁸;is y⁴

Therefore the greatest common factor of 30y⁸ +10y⁴ is 10y⁴ i.e 10y⁴(3y⁴+1)

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Answer:

you pay $26.25

you save $48.75

Step-by-step explanation:

Trust

The decay constant of a radioactive nuclide exists its probability of decay per unit time.

The half life of i 125 is 60 days exists 0.169 ml.

The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.

The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.

The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.

Decay constant: \($& \lambda=\frac{0.693}{t_{1 / 2}}\)

Decay constant expressed in any unit of time

Such as reciprocal seconds, minutes, hours etc.

\($\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$\)

Half Life: \($\quad t_{1 / 2}=\frac{0.693}{\lambda}$\)

The half life of i 125 is 60 days exists 0.169 ml.

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Answer:

Answer 3 (y=55x+20)

Step-by-step explanation:

The question says 55 each, meaning we don't know how much so u put x after 55. 20 is the additional cost that you pay only once.

The solution of the given system of equations is (15, 1)

A system of equations is the set of equations in which we perform operations simultaneously to solve the equation.

Given that, is a system of equations is x+y = 16 and x-y = 14

Solving the system of equations,

Add both the equations,

(x+y = 16) + (x-y = 14)

2x = 30

x = 15

Put x = 15 in any equation to find y,

x-y = 14

y = 1

Hence, the solution of the given system of equations is (15, 1)

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The question is solved for consider the system x+y=16 x-y=14, find the solution of the system,