Q: 3
^Ignore above^

Just help me again please

The statement that f has a simple zero at z=0 and vanishes nowhere else in |z|≤1 implies that the function f is non-vanishing and has a derivative that does not vanish at z=0.

From this, we can use the Implicit Function Theorem which states that if f is holomorphic in a neighborhood of a point (a,b) and f(a,b)=0 and ∂f/∂y(a,b)≠0, then there exists an open neighborhood U of a and a unique holomorphic function g:U→R such that g(a)=b and (x,g(x)) is a solution of the equation f(x,y)=0 for all x in U.

In this case, since f(z) has a simple zero at z=0 and f'(0)≠0, by the Implicit Function Theorem, there exists an open neighborhood U of 0 and a unique holomorphic function h:U→C such that h(0)=0 and f(h(ϵ))=0 for all ϵ in U. Hence, fϵ(z) has a unique zero in |z|≤1.

Also, since f and g are holomorphic in a region containing the disc |z|≤1 and ϵ is continuous, it follows that fϵ is holomorphic in the same region. Thus, by the holomorphicity of fϵ and h, the mapping ϵ↦zϵ is continuous.

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Step-by-step explanation:

\( \sin(60) = \frac{y}{10} \\ y = 5 \sqrt{3} \)

Answer:

frequency of nuts based on another relative frequency. What might

she be doing

nuts:3/30=15%

The exponential function that is equivalent to f(x) = x^5/6 * x^11/6 is g(x) = x^(8/3).

Given, the exponential function f(x) = x^5/6 * x^11/6To find which exponential function is equivalent to the given function, we have to simplify it. Let's simplify the given exponential function: We know that, when we multiply two numbers with same base, then we add their exponents. So, x^5/6 * x^11/6 = x^[(5/6)+(11/6)] x^(16/6) = x^(8/3)Hence, the exponential function that is equivalent to f(x) = x^5/6 * x^11/6 is g(x) = x^(8/3).

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A predetermined formula known as "Functions" that performs computations using specified values inside a particular arrangement or structure.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

Thus, a predetermined formula known as "Functions" that performs computations using specified values inside a particular arrangement or structure.

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Answer:

(c) negative

Step-by-step explanation:

hope this helps

Answer:

Two solutions: -0.12 and 1.75.

Step-by-step explanation:

The quadratic formula is:

\(\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}\). Assuming that the x² term is a, the x term is b, and the constant is c, we can plug the values into the equation.

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {8^2 - 4\cdot-4.9\cdot1} }}{{2\cdot-4.9}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {64 + 19.6} }}{{-9.8}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {83.6} }}{{-9.8}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {9.14} }}{{-9.8}}} \end{array}\)

\(\frac{-8 + 9.14}{-9.8} = -0.12\)

\(\frac{-8-9.14}{-9.8} =1.75\)

Hope this helped!

Answer:

Shai received $192 while Mara received $288.

Step-by-step explanation:

Let u be 1 unit.

5u=$160

u=$160÷5

=$32

6u=$32×6

=$192

9u=$32×9

=$288

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

(2, 7) is not an ordered pair for the function.

Step-by-step explanation:

For frequency table: a) Each number appears 10 times b) Table not given c) Data not provided d) Dice is not fair

a) If the dice is fair, it means each of the eight sides has an equal probability of being rolled, which is 1/8. So, if you roll the dice 80 times, you would expect each number to appear 1/8 * 80 = 10 times.

b) I don't have access to the actual table you're referring to, but I can help guide you on how to complete it. For each number 1 to 8, you'll need to count how many times it appears in the 80 rolls, and then divide that count by the total number of rolls (80) to get the relative frequency. Then, round your answer to three significant figures.

c) To determine the combined relative frequency for each possible outcome, you can simply add the relative frequencies you calculated in part b for each number (1 to 8). Note that since you didn't provide the actual data, I cannot calculate this for you.

d) To conclude if the dice is fair, compare the relative frequencies you calculated in part b with the expected frequency (1/8 or 0.125) for a fair dice. If the relative frequencies are very close to the expected frequency, you can conclude that the dice is likely fair. However, if there are significant deviations, it might indicate that the dice is not fair.

Remember that this is a probability-based conclusion and not a guarantee, as even a fair dice can show variations in frequencies over a limited number of rolls.

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Answer:

7 laps

Step-by-step explanation:

4n = 28

n = 7

hope this helps :)

1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

Answer:

The correct answer is D

Step-by-step explanation:

-190 + -100 = -290

190 + -100 = 90

-10 + -100 = -110

10 + -100 = 90

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Answer:  the answer is U hoppe this helpsss

Step-by-step explanation:

f(x) = 1 + 7x + 49x^2/2! + 343x^3/3! + ...

The Taylor series for f(x) = e^7x (centered at c = 0) is given by the above equation.

The Taylor series formula is a way of expressing a function as an infinite sum of terms. This sum can be made up of the derivatives of the function evaluated at a single point.

The formula for Taylor series is as follows:

f(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + ... where c is the center of the series and f', f'', f''', and so on, represent the first, second, third, and so on, derivatives of the function f(x).

For f(x) = e^7x and c = 0, we will first find the derivatives of f(x):

f(x) = e^7x

f'(x) = 7e^7x

f''(x) = 49e^7x

f'''(x) = 343e^7x

...

and so on.

Evaluating these derivatives at c = 0:

f(0) = e^0 = 1

f'(0) = 7e^0 = 7

f''(0) = 49e^0 = 49

f'''(0) = 343e^0 = 343

...

and so on.

Substituting these values into the Taylor series formula:

f(x) = 1 + 7x + 49x^2/2! + 343x^3/3! + ...

The Taylor series for f(x) = e^7x (centered at c = 0) is given by the above equation.

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The truth value of this wff of a. (thereexists x)A(x), b. (thereexists x)[A(x) logicaland B(x)], c. (forall x)[A(x) rightarrow B(x)] is true.

(thereexists x)A(x) The truth value of this wff depends on whether there exists at least one integer x such that x < 5. Since the domain consists of integers, there are integers such as 0, 1, 2, 3, and 4 that satisfy this condition. Therefore, the truth value of this wff is true.

(thereexists x)[A(x) logicaland B(x)] The truth value of this wff depends on whether there exists at least one integer x such that x < 5 and x < 7. Since x < 5 is a stronger condition than x < 7, any integer x that satisfies x < 5 also satisfies x < 7. Therefore, the truth value of this wff is true.

(forall x)[A(x) rightarrow B(x)] The truth value of this wff depends on whether every integer x that satisfies A(x) also satisfies B(x). Since A(x) is true for integers less than 5 and B(x) is true for integers less than 7, it follows that every integer x that satisfies A(x) also satisfies B(x). Therefore, the truth value of this wff is true.

(forall x)[B(x) rightarrow A(x)] The truth value of this wff depends on whether every integer x that satisfies B(x) also satisfies A(x). Since A(x) is true for integers less than 5 and B(x) is true for integers less than 7, it follows that not every integer x that satisfies B(x) also satisfies A(x). For example, there are integers such as 5 and 6 that satisfy B(x) but not A(x). Therefore, the truth value of this wff is false.

The truth value of the wff of a, b and c is true.

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The space remaining in the glass after the gοlf ball is placed in it is:

502 - 452.39 - 33.51 ≈ 16.1 cm³

Vοlume is the amοunt οf space that an οbject οccupies in three-dimensiοnal space. It is a measure οf hοw much a cοntainer can hοld οr hοw much material an οbject cοntains.

The space remaining in the glass after the gοlf ball is placed in it is equal tο the vοlume οf the glass minus the vοlume οf water already in the glass and the vοlume οf the gοlf ball.

The diameter οf the glass is 8 cm, sο its radius is 4 cm. The height οf the glass can be calculated using the fοrmula fοr the vοlume οf a cylinder:

Vοlume οf cylinder = π * radius² * height

Substituting the given values, we get:

502 = π * 4² * height

Simplifying and sοlving fοr height:

height = 502 / (π * 4²) ≈ 9.99 cm

The vοlume οf water in the glass is equal tο the vοlume οf a cylinder with radius 4 cm, height 8.99 cm, and depth οf 1 cm:

Vοlume οf water = π * 4² * 8.99 - π * 3² * 1 ≈ 452.39 cm³

The vοlume οf the gοlf ball can be calculated using the fοrmula fοr the vοlume οf a sphere:

Vοlume οf gοlf ball = (4/3) * π * (2²) ≈ 33.51 cm³

Sο, the space remaining in the glass after the gοlf ball is placed in it is:

502 - 452.39 - 33.51 ≈ 16.1 cm³

Putting the gοlf ball in the glass οf water will cause the water tο οverflοw since the space remaining in the glass after adding the gοlf ball is less than the vοlume οf water displaced by the gοlf ball.

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Answer:

  f'(x) = -2/√(x³)

Step-by-step explanation:

You want the derivative of f(x) = 4/√x.

The power rule for derivatives is ...

  \(\dfrac{d}{dx}(x^n)=nx^{(n-1)}\)

Applied to the given function, we have ...

  \(f(x)=\dfrac{4}{\sqrt{x}}=4x^{-\frac{1}{2}}\\\\f'(x)=4(-\frac{1}{2}x^{-\frac{3}{2}})\\\\\boxed{f'(x)=-\dfrac{2}{\sqrt{x^3}}}\)

__

Additional comment

The first attachment shows a calculator gives the same result.

The second attachment shows the derivative curve matches the one described by the function we found.

sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

this is to hard

Step-by-step explanation:

7, 8 ,9 ,0 10

Answer:

850m^2

Step-by-step explanation:

Look at the formula SA=L*W*H. And plug in the numbers pertaining the question! hints on to what to add is stuff like "long" for length, "wide" for width, and "high" for height! And use a calculator, or scetch it out to find your total answer!

Hope this helps!

Answer:

Find the domain for

y

=

√

x

−

1

so that a list of

x

values can be picked to find a list of points, which will help graphing the radical.

Tap for more steps...

Interval Notation:

[

1

,

∞

)

Set-Builder Notation:

{

x

|

x

≥

1

}

To find the radical expression end point, substitute the

x

value

1

, which is the least value in the domain, into

f

(

x

)

=

√

x

−

1

.

Tap for more steps...

0

The radical expression end point is

(

1

,

0

)

.

(

1

,

0

)

Select a few

x

values from the domain. It would be more useful to select the values so that they are next to the

x

value of the radical expression end point.

Tap for more steps...

x

y

1

0

2

1

3

1.41

image of graph

Step-by-step explanation:

Answer:

0.85x + 1.29y < 5

Step-by-step explanation:

0.85x of potatoes

1.29 y of grapes

0.85x+1.29y<5 is required equation

Inequality represents purchase of x pounds of potatoes for \($0.85\) per pound and y pounds of grapes for \(\$1.29\) per pound with  total cost was less than \(\$5\) is equal to \(0.85x + 1.29y < 5.\)

" Linear inequality is defined as the relation between variables with highest exponent one is related with sign of inequality >, < , ≤, ≥."

According to the question,

'x' pounds represents the weight of potatoes

'y' pounds  represents the weight of grapes

Cost of potatoes per pound = \(\$0.85\)

Cost of grapes per pound = \(\$1.29\)

Total cost used to purchase the items = \(\$5\)

Substitute the values to represents the relation of linear inequality,

\(0.85x + 1.29y < 5\)

Hence, linear inequality represents Dan purchase is \(0.85x + 1.29y < 5.\)

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