what fraction of an hour is 15 minutes pls help

It is proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

The problem is based on Complex Analysis.

Let U CC be a region containing D(0; 1) and let f be a meromorphic function on U, which has no zeros and no poles on aD(0; 1).

If f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), we need to prove that f has a pole in D(0; 1).

We know that f is meromorphic function on U and we are given that it has a zero at 0. So, we can write the Laurent expansion of f around 0 as: f(z) = anzn+ ... + a1z + a0 + b1z + ... where an ≠ 0 and the expansion is valid in a deleted neighborhood of z=0. This implies that f(z) has a pole of order m at 0 where m is the largest non-negative integer such that am ≠ 0.

Suppose that m = 0 and f(z) has a removable singularity at 0 then by Riemann’s theorem f(z) is bounded in some deleted neighborhood of z = 0 which implies that Ref(z) ≤ M, a contradiction to Ref(z) > 0 for every ze aD(0; 1).

Hence, f(z) has a pole at 0. Therefore, f has a pole in D(0; 1). Hence, we have proved that if f has a zero at 0 and if Ref(z) > 0 for every ze aD(0; 1), then f has a pole in D(0; 1).

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Answer:

x - 3 > 10

There were more than

13

board games in Anne's cabinet to start.

Step-by-step explanation:

The variable x represents how many board games were in Anne's cabinet to start. Since she has already picked out 3 board games to bring, the expression x–3 represents how many board games are still in the cabinet.

And, since Anne has more than 10 board games still in her cabinet, x–3 must be greater than 10.

This inequality shows the relationship.

x–3>10

Now, solve for x.

x–3

> 10

x–3+3

> 10+3 Add 3 to both sides

x

> 13 Simplify

So, there were more than 13 board games in Anne's cabinet to start.

The data set is the most clustered around its mean is

A.4, 10, 8, 6

To determine which data set is the most clustered around its mean, we can calculate the mean and the standard deviation for each data set.

calculate the mean and standard deviation for each data set

Data Set A: 4, 10, 8, 6

Mean: (4 + 10 + 8 + 6) / 4 = 28 / 4 = 7

Standard Deviation: √[(4-7)^2 + (10-7)^2 + (8-7)^2 + (6-7)^2] / 4 ≈ 1.58

Data Set B: 11, 3, 10, 4

Mean: (11 + 3 + 10 + 4) / 4 = 28 / 4 = 7

Standard Deviation: √[(11-7)^2 + (3-7)^2 + (10-7)^2 + (4-7)^2] / 4 ≈ 3.87

Data Set C: 2, 9, 13, 4

Mean: (2 + 9 + 13 + 4) / 4 = 28 / 4 = 7

Standard Deviation: √[(2-7)^2 + (9-7)^2 + (13-7)^2 + (4-7)^2] / 4 ≈ 4.27

Data Set D: 11, 2, 9, 6

Mean: (11 + 2 + 9 + 6) / 4 = 28 / 4 = 7

Standard Deviation: √[(11-7)^2 + (2-7)^2 + (9-7)^2 + (6-7)^2] / 4 ≈ 3.27

Comparing the standard deviations, we find that data set A has the smallest standard deviation of approximately 1.58. this indicates that the data points in Data Set A are the closest to the mean, making it the most clustered around its mean.

Therefore, the answer is A. 4, 10, 8, 6.

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Answer:

The f(x) domain is the set of all values for the function and the function spectrum is the set of all values for which f is defined.

Step-by-step explanation:

Answer:

Domain = all real numbers

Range = y ≥ -4

Step-by-step explanation:

Domain is the x-values, and for parabolas it is almost always all real numbers.

Range is the y-values, and the lowest it gets is -4.

Answer: Online discussions have a better portrayal of other cultures

Step-by-step explanation:

Unless you are very antisocial then the only good thing that an online group shares is being able to stay safe from corona virus and the ability to speak with each other from different perspectives. Lets say hypothetically I was in a bear watching group where everybody took pictures and discussed bears. If I lived in North Michigan I would see black bears and brown bears. If I lived in more of an arctic region I would see polar bears. You can see how this would throw in a little more content to discuss. Which bears are bigger? Which bears live longer? Which bears have heavier coats? This obviously does not only apply to bears. Books, sports, video games, cars, and more all have different miniature cultures in different states or countries.

Answer:

Facilitating an online conversation may require even more work, so that participants continue engaging with one  another online.

Step-by-step explanation:

Answer:

$1,324

Step-by-step explanation:

$8.50 * 65 = $552.50. $601.50 - $552.50 = $49. So the flat fee would be $49.

$8.50* 150 = $1,275. With the flat fee it would be $1,275+$49 = $1,324.

Answer:

nth term: n+6

Step-by-step explanation:

a1 gives -7 and a2 gives -1. Let's compare these two numbers. From -7 to -1, we need a +6. Since -7 + 6 = -1.

a2 to a3, -1 + 6 = 5

a3 to a4, -5 + 6 = 11

Answer:

x + y [tex]\leq 6[/tex]

Step-by-step explanation:

The amount of Oranges (x) and the amount of Mangoes (y) will add up to be less than or equal to 6.  

This condition is represented by the inequality x + y ≤ 6

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

In this case, Trish wants to buy x oranges and y mangoes, and she intends to carry them in her bag.

Her bag can hold a maximum of 6 fruits.

Since she wants to buy both types of fruit, the total number of fruits must be less than or equal to 6.

The inequality to represent this situation is:

x + y ≤ 6

This inequality represents that the sum of the number of oranges and mangoes Trish buys should be less than or equal to 6, which is the maximum number of fruits her bag can hold.

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Answer:

A

Step-by-step explanation:

-y = -2x+5

y = 2x-5

3x+2(2x-5)= -3

Answer:

Step-by-step explanation:

the first one cant be a triangle

im pretty sure the second one can

the third one can

im pretty sure the fourth one cant

Answer:

A.

Step-by-step explanation:

The first question equals 729 and it is the highest, I reccomend using photomath.

Answer:

Step-by-step explanation:

The degree of f(x) is 0.

Its leading coefficient is 13 and the type is constant. Because the function is constant,

f(x = 13 when x --> -∞ and

f(x) = 13  when x --> ∞ .

(How? Because I'm smart like that!! :D)

The probability that a randomly dealt 6-card hand contains all hearts is approximately 0.0000844, or about 0.00844%.

To calculate the probability of a randomly dealt 6-card hand containing all hearts, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Favorable outcomes: A 6-card hand containing all hearts consists of 6 hearts from the deck.

There are 13 hearts in a standard deck of 52 cards, so we can choose 6 hearts from the 13 available. This can be calculated using combinations:

Number of favorable outcomes = C(13, 6) = 13! / (6! × (13 - 6)!) = 13! / (6! × 7!) = 1716

Total number of possible outcomes: The total number of 6-card hands that can be dealt from a standard deck of 52 cards is C(52, 6):

Number of possible outcomes = C(52, 6) = 52! / (6! × (52 - 6)!) = 52! / (6! × 46!) = 20358520

Therefore, the probability of a randomly dealt 6-card hand containing all hearts is:

Probability = Number of favorable outcomes / Number of possible outcomes = 1716 / 20358520 ≈ 0.0000844

So, the probability is approximately 0.0000844, or about 0.00844%.

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The probability of winning at least one prize when buying one ticket each month for 5-months is (c) 0.44.

In order to calculate the probability of winning at least one prize when buying one ticket each month for five months, we use the complement rule. The complement of winning at least one prize is not winning any prize.

The probability of not winning any prize in a single month is 1 - 0.11 = 0.89 (because the probability of winning a prize is given as 0.11),

Since the events of not winning a prize in each month are independent, the probability of not winning a prize in all five months is (0.89)⁵,

So, the probability of winning at least one prize is 1 - (0.89)⁵ ≈ 1 - 0.5570 ≈ 0.443 ≈ 0.44,

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is 0.11. If you buy one ticket each month for five months,

What is the probability that you will win at least one prize?

(a) 0.55

(b) 0.50

(c) 0.44

(d) 0.45

(e) 0.56

Answer:

C

Step-by-step explanation:

All you do is take the number choices and plug it into the equation. For example if you take A and plug it in the equation would look like -5(-5) < 25 and -5 times -5 is 25 so you know 25 is equal to 25 not less than.

If you plug in C you get -5(-4) < 25 and -5 times -4 is 20 and 20 is indeed less than 25

The amount of sales tax is $87.79.

Given a total purchase price of a sofa as $1,254.07 and state taxes of 7%.

We are required to calculate the amount of sales tax.

The amount of sales tax can be calculated by multiplying the purchase price by the sales tax rate.

Let's represent the sales tax rate by `r`.

Therefore, the sales tax formula is expressed as:

Sales tax = r * purchase price

In this case, the rate of the sales tax `r` is 7%.

Therefore, we have:r = 7% = 0.07

Now we substitute the values given into the formula:

Sales tax = 0.07 * $1,254.07= $87.79

Therefore, the amount of sales tax is $87.79.

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Answer: 26ft

Step-by-step explanation:

Answer:

I honestly am very confused

Step-by-step explanation:

The average cost AC when x = 90 is $1, and the derivative C'(x) when x = 90 is $0.41.

The average cost function AC and the derivative of the total cost function C'(x) can be found using the given total cost function C(x) = 0.01x + 0.4x + 50, where x represents the number of units produced and sold.

To find the average cost AC, we divide the total cost C(x) by the quantity x:

AC = C(x) / x

Substituting the given total cost function C(x) = 0.01x + 0.4x + 50, we have:

AC = (0.01x + 0.4x + 50) / x

Simplifying, we get:

AC = (0.41x + 50) / x

When x = 90, we substitute this value into the equation:

AC = (0.41 * 90 + 50) / 90

AC = (36.9 + 50) / 90

AC = 86.9 / 90

AC ≈ $0.97 ≈ $1 (rounded to two decimal places)

To find the derivative C'(x), we differentiate the total cost function C(x) with respect to x:

C'(x) = d/dx (0.01x + 0.4x + 50)

C'(x) = 0.01 + 0.4

C'(x) = 0.41

When x = 90, we substitute this value into the equation:

C'(90) = 0.41

Therefore, the derivative C'(x) when x = 90 is $0.41.

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Answer:

6 feet tall.

Step-by-step explanation:

The boy is 4 ft tall, but he casts a 6 ft long shadow. You need to find how long a shadow would be if a person/thing was just 1 ft tall.

To do this, you would need to divide 4 by 4, and 6 by 4 as well.

6/4 is 1.5, or 1 and a half.

If a person (or a thing) is 1 foot tall, the statue will cast 1 and a half feet long shadow.

The statue casts a 9 ft long shadow.

Since we already figured out 1 ft = 1 and 1/2 ft shadow, and since the statue casts a 9 foot long shadow, you need to divide 9 by 1.5.

(You'll get 6.)

This means that the statue is 6 feet tall, and it casts a 9 foot long shadow.

(a) To prove that B\A = (AB)* using only the above equations and equivalences, we need to show that B\A is equivalent to (AB)*.

First, we will show that B\A is a subset of (AB)*.

Let x be an element of B\A. Then, x is in B and x is not in A. Therefore, x is in AB and not in A. This means that x is in (AB)*. Thus, we have shown that B\A is a subset of (AB)*.

Next, we will show that (AB)* is a subset of B\A.

Let x be an element of (AB)*. Then, x is in AB or x is not in AB.

If x is in AB, then x is in B and x is in A. Therefore, x is not in B\A.

If x is not in AB, then x is not in A or x is not in B. Therefore, x is not in A and x is in B. This means that x is in B\A.

Thus, we have shown that (AB)* is a subset of B\A.

Since we have shown that B\A is a subset of (AB)* and (AB)* is a subset of B\A, we can conclude that B\A = (AB)*.

(b) To prove that B* A* = (AB)*, we need to show that B* A* is a subset of (AB)* and (AB)* is a subset of B* A*.

First, we will show that B* A* is a subset of (AB)*.

Let x be an element of B* A*. Then, x is in (B*) and x is in (A*).

If x is in B*, then x is in B or x is not in B.

If x is in A*, then x is in A or x is not in A.

If x is in B and x is in A, then x is in AB.

If x is not in B and x is not in A, then x is not in AB.

If x is in B and x is not in A, then x is in B\A.

If x is not in B and x is in A, then x is in A\B.

Therefore, we have shown that x is in (AB)*.

Next

The family members were 3 adults and 2 children.

We have given that the,

A family of 10 purchased tickets to the county fair.

Tickets for adults cost $6 and tickets for children cost $3

Total cost is $42.

We have to determine how many family members were adults and children

(3 x 10) + (2 x 6)

30+12=42

Therefore we get 3 adults and 2 children.

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The center of the sphere can be found by taking the average of the coordinates of points A and B, and the radius of the sphere is half the distance between points A and B.

Let's denote point A as (2, 1, 5) and point B as (6, 2, 22). We want to find the set of points P such that the distance from P to A is twice the distance from P to B.

We can express this condition mathematically as:

|PA| = 2|PB|

Using the distance formula, we can rewrite this equation as:

[tex]\sqrt{(x - 2)^2+ (y - 1)^2 + (z - 5)^2} = 2\sqrt{(x - 6)^2 + (y - 2)^2 + (z - 22)^2}[/tex]

Simplifying the equation, we have:

[tex](x - 2)^2 + (y - 1)^2 + (z - 5)^2 = 4((x - 6)^2 + (y - 2)^2 + (z - 22)^2)[/tex]

Expanding and combining like terms, we get:

[tex]3x^2 + 3y^2 + 3z^2 - 28x - 10y - 96z = 273[/tex]

This equation represents the equation of a sphere. The center of the sphere can be found by taking the average of the coordinates of points A and B, which gives us the center (4, 1.5, 13.5). The radius of the sphere is half the distance between points A and B, which is the square root of 273 divided by 2.

Therefore, the set of all points satisfying the given condition is a sphere with center (4, 1.5, 13.5) and radius √(273/2).

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Answer:

[tex]3n + 7 = 52 \\ 3n = 52 - 7 \\ 3n = 45 \\ n = \frac{45}{3} \\ n = 15[/tex]

Graph is not inserted.

Answer:

The answer is A. (an even number)

Step-by-step explanation:

2 x 27 is equivalent to 54 and 54 is an even number.

Sum of two interiors =Exterior

Use simple way

Angle beside x

Measure of x

Answer:

x = 44°

Step-by-step explanation:

According to the Exterior Angle Theorem of a triangle, the external angle is equal to the sum of the two interior opposite angles of a triangle.  

This is because the interior angles of a triangle sum to 180° and angles on a straight line sum to 180°.

⇒ x = ∠CAB + ∠BCA

⇒ x = 14° + 30°

⇒ x = 44°

Proof

Interior angles of a triangle sum to 180°

⇒ ∠CAB + ∠ABC + ∠BCA = 180°

⇒ 14° + ∠ABC + 30° = 180°

⇒ ∠ABC = 180° - 14° - 30°

⇒ ∠ABC = 136°

Angles on a straight line sum to 180°

⇒ ∠ABC + x = 180°

⇒ 136° + x = 180°

⇒ x = 180° - 136°

⇒ x = 44°

Answer: The answer is: 693 ft^3 or 693ft cubed

Given:

The function is:

[tex]f(x)=x^2-16[/tex]

To find:

The inverse of the function.

Solution:

We have,

[tex]f(x)=x^2-16[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=x^2-16[/tex]

Step 2: Interchange x and y.

[tex]x=y^2-16[/tex]

Step 3: Isolate y.

[tex]x+16=y^2[/tex]

[tex]\pm \sqrt{x+16}=y[/tex]

[tex]y=\pm \sqrt{x+16}[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex]

Therefore, the inverse function of the given function is [tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex].