Is this graph a function?

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.

Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.

let \(p_{1}\) be the probability that commercial cars have rear license plates and \(p_{2}\) be the probability that connected trucks have rear license plates.

                         Cars                     Trucks                         Total

Total                  2049                    334                             2383

x                          239                      45                                284

p                        0.1166                   0.1347                          0.1191

α=0.05

Hypothesis will be  :

\(H_{0}:p_{1} =p_{2}\)

\(H_{1} :p_{1} < p_{2}\)

It is a left tailed test at 0.05 significance.

Standard errors of p=\(\sqrt{p(1-p)/n}\)

=\(\sqrt{(0.1191*0.8809)/2383}\)

=\(\sqrt{0.1049/2383}\)        

=0.0066

Test statistic Z=p difference/standard error

=(0.1166-0.1347)/0.0066

=-0.0181/0.0061

=-2.967

p value=0.001505<5%

Since p is less than 5% we reject null hypothesis.

We cannot calculate standard deviation so  we cannot calculate confidence interval.

Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

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The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Total fixed cost is $6. The value of AFC is $6 / Q. Productive efficiency is greatest at Q = 4.5. Diminishing returns begin when Q = 3. The total fixed cost (TFC) does not change because it is fixed.

a) Total fixed cost is $6

b) We can obtain the average fixed cost function (AFC) from the total fixed cost (TFC) by dividing it by output (Q) as follows: AFC = TFC / Q. So, the value of AFC is $6 / Q.

c) The AVC function is calculated by dividing total variable cost (TVC) by output (Q).

STC = TFC + TVC6 + 9Q - 3Q2 + (1/3)Q3TVC = 9Q - 3Q2 + (1/3)Q3AVC = TVC / QAVC = (9Q - 3Q2 + (1/3)Q3) / QAVC = 9 - 3Q + (1/3)Q2

d) The MC function is derived by taking the first derivative of the STC function with respect to output (Q). The derivative of the STC function is: MC = dSTC / dQMC = 9 - 6Q + Q2

e) As Q approaches infinity, the denominator of AFC becomes larger and larger. So, AFC approaches zero as Q gets very large. This implies that fixed costs per unit decrease as production quantities get larger.

f) We can find the value of Q at which AVC is a minimum by taking the first derivative of the AVC function and setting it equal to zero. The first derivative of AVC is: AVC = 9 - 3Q + (1/3)Q2

dAVC / dQ = -3 + (2/3)Q= 0

Q = 4.5

g) Productive efficiency is greatest when AVC is at its minimum. Therefore, productive efficiency is greatest at Q = 4.5.

h) We can demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum by plugging Q = 4.5 into both the AVC and MC functions. AVC = 9 - 3(4.5) + (1/3)(4.5)2AVC = 7.125MC = 9 - 6(4.5) + 4.52MC = 7.125

Since SMC = MC, we can conclude that SMC equals AVC at the value of Q where AVC is a minimum.

i) In the short run, the total fixed cost (TFC) does not change because it is fixed. Therefore, the derivative of the STC function with respect to output (Q) is equal to the derivative of the TVC function with respect to output (Q). This means that dSTC / dQ = dTVC / dQ.

j) Increasing returns to scale cease when the marginal cost (MC) is equal to average total cost (ATC). Diminishing returns to scale begins when MC exceeds ATC. ATC is calculated by dividing the total cost (TC) by output (Q). TC is calculated by adding total fixed cost (TFC) and total variable cost (TVC).

ATC = TC / QATC = (6 + 9Q - 3Q2 + (1/3)Q3) / Q

Now, we can find the level of Q where increasing returns to scale cease by calculating the first derivative of ATC and setting it equal to zero.

ATC = (6 + 9Q - 3Q2 + (1/3)Q3) / QdATC / dQ = (6 - 6Q + Q2) / Q2= 0

Q = 3

Now, we can calculate the marginal cost function and find the level of Q where diminishing returns begins. We know that diminishing returns begin where the marginal cost is at its minimum.

MC = 9 - 6Q + Q2MC = 9 - 6(3) + 32MC = 3

So, diminishing returns begin when Q = 3.

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Answer:

Area=\(\frac{13(6)}{2}\)

        =\(\frac{78}{2}\)

       =39

Step-by-step explanation:

Answer:

39 ft

Step-by-step explanation:

use the formula for the area of the triangle (base*height)/2

(13*6)/2=78/2= 39 ft

The extreme values of the function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1 are approximately ±0.235

To find the extreme values of the given function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1, we can use the method of Lagrange multipliers.

First, we write down the Lagrangian function L(x, y, λ) as follows:

L(x, y, λ) = xy(2y^2 x^4 − y^4) + λ(x^2 + y^2 − 1)

Then, we take the partial derivatives of L with respect to x, y, and λ and set them equal to zero:

∂L/∂x = y(2y^2 x^4 − y^4) + 2λx = 0

∂L/∂y = x(6y^3 x^4 − 4y^3) + 2λy = 0

∂L/∂λ = x^2 + y^2 − 1 = 0

Simplifying the first two equations, we get:

2y^5 x^4 − y^5 + 2λxy = 0

6y^4 x^4 − 4y^4 + 2λxy = 0

Dividing these equations, we obtain:

3x^4 = 2y^2

Substituting this back into the equation x^2 + y^2 = 1, we get:

3x^4 + x^2 = 1

This is a quartic equation in x^2. We can solve it using numerical methods to get the two possible values of x:

x ≈ ±0.681

y ≈ ±0.732

Plugging these values into the equation 3x^4 = 2y^2, we get:

y ≈ ±0.524

Now we can calculate the corresponding values of the function f(x, y) = xy(2y^2 x^4 − y^4):

f(x, y) ≈ ±0.235

Therefore, the extreme values of the function f(x, y) on the circle x^2 + y^2 = 1 are approximately ±0.235, and they are attained at the points (±0.681, ±0.732) and (±0.732, ±0.681).

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The acceleration vector a(t) is (-9 cos 3t)i + (-2 sin t)j.

If r(t) is the position vector of a particle in the plane at time t, and r(t) = (cos 3t) i + (2 sin t) j, you want to find the acceleration vector.

First, find the velocity vector by taking the derivative of the position vector with respect to time:

v(t) = dr(t)/dt = (-3 sin 3t) i + (2 cos t) j

Next, find the acceleration vector by taking the derivative of the velocity vector with respect to time:

a(t) = dv(t)/dt = (-9 cos 3t) i + (-2 sin t) j

The acceleration vector a(t) is (-9 cos 3t)i + (-2 sin t)j.

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To maintain the CG and balance in the system, the third box weighing 20 pounds should be placed 4 feet forward of the CG.  The CG is the point where the weight of the object is evenly distributed, and it is crucial for maintaining balance.

First, let's calculate the total weight of the system. We have two boxes weighing 15 pounds and 10 pounds, and a third box weighing 20 pounds. The total weight is 15 + 10 + 20 = 45 pounds.
Next, we need to find the moment caused by the two boxes already placed. The moment is the product of the weight and its distance from the CG.
For the 15-pound box, the moment is 15 pounds * 4 feet = 60 pound-feet.
For the 10-pound box, the moment is 10 pounds * 2 feet = 20 pound-feet.

To keep the CG unchanged, the total moment of the system must be zero. This means that the moment caused by the third box must balance out the moments of the other two boxes.

Let's denote the distance from the CG to the third box as 'x' feet. The moment caused by the third box is 20 pounds * x feet.
So, to maintain balance, the equation becomes:
60 pound-feet + 20 pound-feet = 20 pounds * x feet.
Simplifying this equation, we get:
80 pound-feet = 20x feet.
To solve for 'x', we divide both sides by 20:
4 = x.
Therefore, the third box should be placed 4 feet forward of the CG to maintain balance.

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Answer:

the product is equal to the number. When a positive whole number is multiplied by a fraction greater than 1. When a positive whole number is multiplied by a fraction between 0 and 1, the product is less than the whole number.

Step-by-step explanation:

The value of \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) is \(e^z\cos y\).

The gradient is a vector operation that transforms a scalar function into a vector with a magnitude equal to the highest rate of change of the function at the gradient's point and a direction pointing in the same direction.

To find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\), we need to calculate the divergence of the gradient of the function ϕ.

The gradient of ϕ is given by:

\(\bar{\nabla} \phi\) = (∂x/∂ϕ​, ∂y/∂ϕ, ∂z/∂ϕ)

Let's calculate the partial derivatives of ϕ with respect to each variable:

\(\frac{\partial \phi}{\partial x}=e^{z}\sin y\)

\(\frac{\partial \phi}{\partial y}=xe^{z}\cos y\)

\(\frac{\partial \phi}{\partial z}=xe^{z}\sin y\)

Now, we can find the divergence of \(\bar{\nabla} \phi\) by taking the sum of the partial derivatives:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) =  \(\frac{\partial}{\partial x}(e^z\sin y)+\frac{\partial}{\partial y}(xe^z\cos y)+\frac{\partial}{\partial z}(xe^z\sin y)\)

Simplifying each partial derivative:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\) + \((-xe^z\sin y)\) + \((xe^z\sin y)\)

Combining like terms, we find:

\(\bar{\nabla} \cdot(\bar{\nabla} \phi)\) = \(e^z\cos y\)

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The complete question is:

Given that \(\phi(x, y, z)=x e^{z} \sin y\) Find \(\bar{\nabla} \cdot(\bar{\nabla} \phi)\).

Answer:

96

Step-by-step explanation: -6x2= -12

-12x-8= 96 :)

Answer: 96 is the answer I multiplied and got 96 use pemdas

Hope this helped you :-)

Answer:

\(\frac{61}{8}\)

Step-by-step explanation:

If a polynomial p(x) is divided by a factor (x + h ) then the remainder is

f(- h)

Here p(x)is divided by (x - \(\frac{1}{2}\) ) thus evaluate p(\(\frac{1}{2}\) ) for remainder

p(\(\frac{1}{2}\) )

= (\(\frac{1}{2}\) )³ - 2(\(\frac{1}{2}\) )² + 8

= \(\frac{1}{8}\) - \(\frac{1}{2}\) + 8

= \(\frac{61}{8}\)

The sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl. The test statistic is 50 and then the p-value is 32.93

Mean is the ratio of the sum of all observations to the number of observations. Standard deviation is the measure in which it shows how much the variation such as spread, dispersion,  from the mean exists and the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

For the study of jordanian children in exercise 64, the sample mean hemoglobin level was 11.3 mg/dl and the sample standard deviation was 1.6 mg/dl.

Given that, exercise n =64

mean  = 11.3 mg/dl

standard deviation = 1.6mg/dl

The test statistic is 50

the p-value is calculated by, (n-mean) / (standard deviation)

(64 - 11.3) / (1.6)

32.93

Therefore, the p-value in which it obtains a more precise value is 32.93

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Answer:

x ≈ 8.7

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 5² = 10²

x² + 25 = 100 ( subtract 25 from both sides )

x² = 75 ( take square root of both sides )

x = \(\sqrt{75}\) ≈ 8.7 ( to the nearest tenth )

Answer:

g(x) = 2x-8

Step-by-step explanation:

To translate down

y = f(x) + C   C < 0 moves it down

So we need to subtract 2 from the function

f(x) -2

f(x) = 2x-6  -2

f(x) = 2x-8

The new function is 2x-8

Answer:

Fx=2x-6. Fx/x=2x-6/x. F=2x-6/x answer: f=2x-6/x

So it D

Step-by-step explanation: Hope this help

Answer:6

Step-by-step explanation:

Since each batch of bagels takes 2/4 of an hour to make. This means that in one hour, 2 batches would be made.

Therefore, in 3 hours, the number of batches that would be made will then be:

= 2 × 3

= 6

Therefore 6 batches can be made before opening

Answer:

a and c

Step-by-step explanation:

im just a god like that

Answer:

y+0

As y=0 represent x-axis whose slope is 0 and intersects y-axis at the origin.

The equations are solved to w = 0 and z = -2. Option B

From the information given, we have the simultaneous equations as

3w-4z=8

2w+3z=-6

Make w the subject from equation 1

w = 8 + 4z/3

Substitute the value into equation 2, we have that;

2(8 + 4z/3) + 3z = -6

expand the bracket, we get;

16 + 8z/3 + 3z = -6

find the LCM, we have;

16 + 8z + 9z/3 = -6

cross multiply

16 + 17z = - 18

add the values

19z = -34

Make 'z' the subject

z =-2

Substitute the value

3w - 4z = 8

3w = 8 - 8

w = 0

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The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Answer:

-4.29

Step-by-step explanation:

The computation of the z score is shown below:

data provided in the question

Average minutes = 16 minutes

Standard deviation = 1.4 minutes

Amount of advertising time = 8 minutes

Based on the above information, the z score is

\(= \frac{x-m}{\sigma} \\\\ = \frac{8-14}{\1.4} \\\\ = \frac{-6}{1.4}\)

= -4.29

Hence, the z score is -4.29. It is come by considering the above formula

The first statement, "lim f(x) = infinity as x approaches 2," means that as x gets closer and closer to 2, the function f(x) gets larger and larger without bound. Essentially, there is no finite limit to how big f(x) can get as x approaches 2.

The second statement, "f(x) = [infinity]," means that f(x) approaches infinity as x approaches some point (the statement doesn't specify which point). This means that there is no upper bound on how large f(x) can get.

Finally, the third statement says that the values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) -2. In other words, if you pick a really small number (like 0.0001), you can find an x value that is very close to -2 that will make f(x) smaller than that number. However, the statement also says that f(x) can get arbitrarily large by taking x sufficiently close to -2 (but not equal to it), so f(x) is not necessarily bounded.

Here are the meanings of each term:

1. lim f(x) = infinity as x -> 2: This means that as the value of x approaches 2 (but does not equal 2), the function f(x) approaches infinity. In other words, the function grows without bound when x is very close to 2.

2. f(x) = [infinity]: This notation is used to emphasize that the function f(x) is taking on very large values or growing without bound, similar to the concept of infinity.

3. Values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) -2: This means that as the value of x approaches -2 (but does not equal -2), the function f(x) approaches 0. In other words, the function gets closer and closer to 0 as x gets closer to -2.

4. Values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) -2: This means that as the value of x approaches -2 (but does not equal -2), the function f(x) approaches infinity. In other words, the function grows without bound when x is very close to -2.

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Answer:

Answer: √49

___________

√49 = 7

Step-by-step explanation:

The area of a square is equal to the square of its side or the product of its side and its side.

A = s², because the sides of a square are congruent.

a) The expected number of people to die before their 71st birthday is given as follows: 128.

b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:

0.025679 x 5000 = 128.

The probability for item b is given as follows:

0.016798/0.018925 = 0.8876 = 88.76%.

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Answer:

the value of p is 7

Step-by-step explanation:

Given function;

f(x) = 2x³ - 7px + (p - 12)

factor of the given function = x - 5

Apply remainder theorem to solve for p

f(x - 5) = 0

x - 5 = 0

x = 5

f(5) = 2(5)³ - 7p(5) + (p - 12) = 0

        2(125) - 35p  + p - 12 = 0

         250 - 34p  - 12 = 0

        238  - 34p = 0  

           34p  = 238

                p = 238/34

                 p = 7

Therefore, the value of p is 7

Answer:

-20, I believe is the answer.