The power of -1 to a function, or ((f^-1)(x)), means...

a) The conjugate of the denominator is given as follows: 2 - 14i.

b) The division has the result given as follows: 0.375 - 1.15i.

A complex number is a number that is composed by a real part and an imaginary part, as follows:

z = a + bi.

In which:

The division for this problem is given as follows:

(16 - 3i)/(2 + 14i).

For the conjugate of the denominator, we keep the real part, changing the sign of the imaginary part, hence it is given as follows:

2 - 14i.

Hence we can solve the division multiplying by the conjugate, considering that i² = -1, as follows:

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (32 - 224i - 6i + 42)/(4 + 196)

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (74 - 230i)/200

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = 0.375 - 1.15i.

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Answer:

1) -4<x<-2

2) x<-7 or x75

3) 2<x<7

4) x<-5 or x<6

5) x<-8 or x74

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

45°-45°-90° triangles are Special Right Triangles. There are some super helpful shortcuts you can learn for a 45°-45°-90° triangle.

The two legs of the triangle are always the same. The longest side, the hypotenuse, is:

hypot = leg•sqrt2

The leg in your problem is sqrt2.

You are asked to find the hypotenuse, k.

hypot = leg•sqrt2

k = leg•sqrt2

k = sqrt2•sqrt2

k = 2

k is 2. Don't be sidetracked by the direction that says "Write your answer in simplest radical form". If there was a radical in your answer, we would simplify it, but there isn't...it's just plain 2.

In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.
The volume of a cone is given by the formula V = (1/3)πr²h here r is the radius of the base and h is the height of the cone.

Now we have differentiate this formula concerning t to get
dV/dt = (1/3)πr²dh/dt + (2/3)πrh²dr/dt.

It is given to us  that water is coming out a giant cone shaped funnel at a rate of 15 cubic inches per second, then we  can say that
dV/dt = -15 cubic inches per second

Therefore the funnel has a maximum radius of 40 inches and a height of 75 inches. We need to evaluate  dh/dt
If h = 15 inches.

In order to find dh/dt,
we need to evaluate  dr/dt and place it in  equation for dV/dt.

Therefore, to find dr/dh = r/h.
Given
when h = 75 inches,
r = 40 inches.
Therefore, dr/dh
= 40/75.

Staging this into the equation for dV/dt,

-15 = (1/3)π(40²)(dh/dt) + (2/3)π(40)(15)²(40/75)

Here simplification takes place


dh/dt = -0.4π/3
≈ -0.42 cubic inches per second
In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.


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The mean of a binomial probability distribution with p = 0.32 and n = 150 is 48

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success, denoted by p. In the case of a binomial distribution with n trials and probability of success p, the mean, or expected value, is equal to the product of the number of trials and the probability of success, which is np.

In this case, the problem provides the values of p and n, which are p = 0.32 and n = 150, respectively. Therefore, the mean can be calculated by multiplying these two values

μ = np = 150 x 0.32 = 48

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Answer:

parallelogram and rectangle

Step-by-step explanation:
the shape can’t be a rhombus or a square, because all sides of it are not the same length. it’s a parallelogram, because all 4 sides are parallel to each other, and it’s a rectangle, because it’s a parallelogram and all of its sides aren’t equal.

Therefore , the solution of the given problem of angles comes out to be  

x = 7 is the answer to the equation (16x + 17) = 129° for the variable x.

A skew greatest and smallest walls are located where the roads leading to its ends meet. A crossroads could be where two paths converge. Angle is another outcome of two things interacting. They mimic dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various ways between their endpoints.

Here,

The steps below can be used to find x in the equation (16x + 17) = 129°:

To find the term with x on one side of the equation, first subtract 17 from both sides of the equation:

=> 16x + 17 - 17 = 129 - 17

=> 16x = 112

Step 2: To find x, multiply both sides of the equation by 16:

=> 16x / 16 = 112 / 16 x = 7

Thus, x = 7 is the answer to the equation (16x + 17) = 129° for the variable x.

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The volume of the solid formed by rotating the region is 26.95 cubic units.

To find the volume of the solid formed by rotating the region enclosed by y = [tex]e^{4x}[/tex] + 1, y = 0, x = 0, and x = 0.3 about the x-axis, we can use the formula for the volume of a solid of revolution:

V = ∫[a, b] π * f(x)^2 dx

where a and b are the limits of integration, and f(x) is the distance from the x-axis to the curve being rotated.

In this case, a = 0 and b = 0.3, and f(x) = e^4x+1. Therefore, we have:

V = ∫[0, 0.3] π * [tex](e^{4x}+1)^{2}[/tex] dx

To evaluate this integral, we can use u-substitution with u = 4x + 1, du/dx = 4, and dx = du/4. Making this substitution, we get:

V = ∫[5, 6.2] π * [tex](e^{u} )^{2}[/tex] * (1/4) du

Simplifying, we get:

V = (π/4) * ∫[5, 6.2] [tex]e^{2u}[/tex] du

Using the power rule of integration, we get:

V = (π/8) * [[tex]e^{2u}[/tex] /2] |_[tex]5^{6.2}[/tex]

Substituting back in for u and simplifying, we get:

V = (π/8) * ([tex]e^{12.4} - e^{10}[/tex] )

Therefore, the volume of the solid formed by rotating the region enclosed by y =  [tex]e^{4x}[/tex] +1, y = 0, x = 0, and x = 0.3 about the x-axis is approximately 26.95 cubic units.

Correct Question :

Find the volume of the solid formed by rotating the region enclosed by y = e^4x+1 , y = 0 , x = 0 , x = 0. 3 about the x -axis.

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Answer:

the event would be independent.

Step-by-step explanation:

because the penny and dime are two seperate variables

a)  $155.61 is deducted from Violet's paycheck for her 401(k).

b) $19.05 is deposited into Violet's retirement plan each day.

A) To calculate how much is deducted from Violet's paycheck for her 401(k), we need to find her biweekly gross income and then calculate 7% of it.

Violet's biweekly gross income can be found by dividing her annual income by the number of biweekly pay periods in a year, which is 26:

Biweekly gross income = $57,903 / 26 = $2,223

Now, we can calculate the amount that is deducted from Violet's paycheck for her 401(k):

401(k) deduction = 7% of $2,223 = 0.07 x $2,223 = $155.61

Therefore, $155.61 is deducted from Violet's paycheck for her 401(k).

B) To calculate how much is deposited into Violet's retirement plan each day, we need to first find out how much is deposited each pay period.

Violet contributes 7% of her biweekly gross income to her 401(k), which is $155.61 as calculated above. Her employer matches up to 5% of her contribution, so the total contribution to her retirement plan each pay period is:

Total contribution = Violet's contribution + employer's contribution

= $155.61 + (5% of $2,223)

= $155.61 + $111.15

= $266.76

There are 14 days in a biweekly pay period, so we can calculate how much is deposited into Violet's retirement plan each day:

Daily deposit = Total contribution / number of days in pay period

= $266.76 / 14

= $19.05

Therefore, $19.05 is deposited into Violet's retirement plan each day.

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The Central Limit Theorem can also be used to investigate unusual events. An unusual event is one that occurs with a probability of less than 1%

The Central Limit Theorem can be used to investigate unusual events by calculating the probability of a sample mean being a certain number of standard deviations away from the population mean.

If we assume that the population is normally distributed, then we can use the normal distribution to calculate the probability of observing a sample mean that is a certain number of standard deviations away from the population mean.

An unusual event is typically defined as an event that occurs with a low probability, usually less than 5% or 1%. So, if we observe a sample mean that is more than 2 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 5%. Similarly, if we observe a sample mean that is more than 3 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 1%.

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On solving the provided question we can say that As a result, the surface area of the rectangular prism with 3 cm, 9 cm, and 6 cm dimensions is [tex]198 cm^2.[/tex]

The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional object (a three-dimensional shape contains height, breadth, and depth).

The surface area of a rectangular prism is given by the formula:

SA = 2(lw + lh + wh),

where l, w, and h are the rectangular prism's length, width, and height.

SA = 2(3×9 + 3×6 + 9×6)

= 2(27 + 18 + 54)

= 2(99)

= 198 cm²

As a result, the surface area of the rectangular prism with 3 cm, 9 cm, and 6 cm dimensions is [tex]198 cm^2.[/tex]

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The quadratic equation in the given graph is:

y = -3(x - 1)^2 + 4

How to write the quadratic.

Look at the vertex, is it at (1, 4), then we can write the general quadratic equation in the vertex form (with a leading coefficient a) as follows:

y = a(x - 1)^2 + 4

Now the function passes through (0, 1) then we can replace these values in the equation above to get.

1 = a(0 - 1)^2 + 4

1 = a + 4

1 - 4 = a

-3  =a

The quadratic equation is:

y = -3(x - 1)^2 + 4

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3/10 of Max's money was left after he spent 3/5 of his money in the first shop and 1/4 of the remainder in the second shop.

Let's assume Max had $100 to start with (we can use any amount for this problem, but $100 is a convenient round number).

If Max spent 3/5 of his money in the first shop, he spent:

3/5 x $100 = $60

This means he had $40 remaining. If he then spent 1/4 of this remaining amount in the second shop, he spent:

1/4 x $40 = $10

So Max has spent a total of $60 + $10 = $70. Therefore, the amount of money Max has left is:

$100 - $70 = $30

So Max has $30 left out of his original $100. To express this as a fraction, we can write:

$30 / $100 = 3/10

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Answer:

Step-by-step explanation:

B appears to be the only answer to this problem as the rest are perfect squares meaning their roots will terminate, while there is no guarantee for 8.

B is the correct answer

The quadratic equation that has solutions of 3 and -4 and includes f(7) = 88 is f(x) = 2(x - 3)(x + 4).

A quadratic equation is a second-degree polynomial equation that can be written in the general form:ax^2 + bx + c = 0

where x represents the variable, and a, b, and c are coefficients that represent real numbers, with a ≠ 0. The highest power of x in a quadratic equation is 2, and it typically forms a parabolic shape when graphed on a coordinate plane.

According to the given information:

A quadratic equation is typically written in the form:

f(x) = ax^2 + bx + c

where a, b, and c are coefficients.

Given that the solutions of the quadratic equation are 3 and -4, we can write the equation in factored form as:

f(x) = a(x - 3)(x + 4)

where (x - 3) and (x + 4) are the factors corresponding to the solutions 3 and -4, respectively.

Now, we are given that f(7) = 88. We can substitute x = 7 and f(x) = 88 into the equation above to obtain:

88 = a(7 - 3)(7 + 4)

Simplifying the expression inside the parentheses, we get:

88 = a(4)(11)

88 = 44a

Dividing both sides by 44 to solve for a, we get:

a = 88 / 44

a = 2

So, the value of a is 2.

Substituting the value of an into the factored form of the equation, we get:

f(x) = 2(x - 3)(x + 4)

Therefore, the quadratic equation that has solutions of 3 and -4 and includes f(7) = 88 is: f(x) = 2(x - 3)(x + 4)

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On solving the provided question we can say that As a result, the sequence's ninth term is -781250.

A sequence is a collection of numbers, sometimes known as "terms." Terms like 2, 5, and 8 are examples. Some sequences may be made infinitely long by utilising a specific pattern they follow. To continue the process, take the example of 2,5,8 and add 3. There are formulae that show where to search in a series for words. In mathematics, a sequence (or event) is a collection of items that are in some order. It is similar to a set in that it comprises parts (also known as elements or terms). The length of a series is defined as the total number of ordered items, which may be infinite. The act of arranging two or more elements in a logical sequence.  

To discover the nth term in a series, we must first figure out what pattern or rule guides the sequence.

In this situation, each term in the series may be generated by multiplying the previous term by -5. So the pattern or rule for this sequence is as follows:

an = -5 * an-1

where a1 = -2

[tex]a^9 = -5 * a8\\= -5 * (-2 * (-5)^7)\\= -781250\\[/tex]

As a result, the sequence's ninth term is -781250.

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The question of which is better, a romance book or a storybook, is subjective and depends on individual preferences. But in my opinion, story book is better.

A romance book typically centers around a romantic relationship between two characters and is focused on emotional and personal development. In contrast, a storybook can cover a broad range of genres, including adventure, mystery, sci-fi, fantasy, etc. They can also have romance as a subplot but are not limited to it.

When it comes to the question of which is better, it ultimately depends on individual preferences. Romance books may be more appealing to readers who enjoy exploring the intricacies of relationships, while storybooks may be more suitable for those who prefer diverse storytelling.

In terms of how a storybook can be better than a romance book, one reason is the sheer variety of genres and styles that storybooks can offer. Readers who are looking for a thrilling adventure or a thought-provoking mystery may find a storybook more engaging than a romance novel, which often follows a similar formula.

Additionally, storybooks can introduce readers to new worlds, characters, and ideas, making them not just entertaining but also educational. This can provide a more enriching experience for readers, as they can learn and expand their knowledge while enjoying a good story.

Overall, the question of which is better, a romance book or a storybook, is subjective and depends on individual preferences. Both can offer unique and engaging experiences, and readers should choose the one that suits their tastes and interests.

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If ethan threw away 16 Paris of solid-coloured socks and 16 Paris of patterned socks, Ethan had 140 pairs of patterned socks at first.

Let's start by assuming that Ethan had x pairs of patterned socks. According to the problem statement, Ethan had 3/4 as many solid-coloured socks as patterned socks. Therefore, the number of solid-coloured socks he had can be represented as 3/4*x.

Ethan threw away 16 pairs of solid-coloured socks and 16 pairs of patterned socks. So, after the clean-up, he had (3/4*x)-16 pairs of solid-coloured socks and (x-16) pairs of patterned socks.

The problem states that 1/5 of his socks were now solid-coloured socks. So, we can set up an equation:

(3/4x-16) = (1/5)(3/4*x + x - 32)

Simplifying and solving for x, we get:

x = 140

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In the given equation g - h = h - g, where g & h are real-numbers and LHS will be equal to RHS only when values of g & h are equal in magnitude & sign so that LHS & RHS becomes zero..

Natural numbers are used to count things or objects, whereas rational numbers can be used to represent or indicate fractions, irrational numbers are used to calculate or evaluate a number's square root, integers are used to measure temperature, and so on. Real numbers are a collection of several forms of numbers, such as whole, natural, integers, fractions, etc. Integers, both positive and negative, fractions, and irrational numbers are examples of rational numbers that are combined to form real numbers. R's symbol for or representation of the set of real numbers.

Given that g - h = h - g

On simplifying the equation we get:

g - h = h - g

g + g = h + h

2g    = 2h

g      = h

g & h can take any values, but both must be equal in order to satisfy the given condition.

For e.g, let g=h=12

g - h = h - g

12 - 12 = 12 - 12

       0  = 0

Both LHS & RHS can only be zero.

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Answer: Thomas swims 50,000 meters in 5 weeks.

Step-by-step explanation: To determine the total distance swam by an individual over a period of 5 weeks, the product of their weekly swim distance can be calculated by multiplying said distance by 5.

The accumulated distance covered within a period of five weeks by an individual with a weekly average of 10,000 meters amounts to a total distance of 50,000 meters.

Thomas swims 50,000 meters in 5 weeks.

Thomas swims 10 kilometers each week. To convert kilometers to meters, we multiply by 1,000 because there are 1,000 meters in a kilometer.

10 km * 1,000 meters/km = 10,000 meters

Thomas swims 10,000 meters each week. Now, to find out how many meters he swims in 5 weeks, we multiply the weekly distance by the number of weeks:

10,000 meters/week * 5 weeks = 50,000 meters

Answer:

B

Step-by-step explanation:

The overall mean number of hours worked can be determined by calculating the weighted average of the means for males and females, taking into account the sample size as weights.

Given:

X₁ = 6 (mean number of hours worked for males)

X₂ = 9 (mean number of hours worked for females)

n₁ = 30 (sample size for males)

n₂ = 20 (sample size for females)

The overall mean number of hours worked, denoted as X, can be calculated as follows:

X = (X₁ * n₁ + X₂ * n₂) / (n₁ + n₂)

Plugging in the given values:

X = (6 * 30 + 9 * 20) / (30 + 20)

X = (180 + 180) / 50

X = 360 / 50

X = 7.2

If diameter 6 cm and height 16 cm, the volume of the right circular cylinder is 144π cubic cm.

The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height. In this case, the diameter is given as 6 cm, so the radius is half of the diameter, which is 3 cm. The height is given as 16 cm.

Substituting these values into the formula, we get:

V = π(3 cm)^2(16 cm)

V = π(9 cm^2)(16 cm)

V = 144π cubic cm

A right circular cylinder is a three-dimensional object with a circular base and straight sides that are perpendicular to the base. The volume of a cylinder is the amount of space that it occupies and is calculated by multiplying the area of the base by the height.

In this case, the base of the cylinder is a circle with radius 3 cm, so its area is π(3 cm)^2 = 9π square cm. The height of the cylinder is 16 cm, so the volume is 9π x 16 = 144π cubic cm.

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11. The area difference between them is 96 square units (192 - 96).

12. The trough stands 4 feet tall.

11. The area of Figure A is 96 square units (12 x 8) and the area of Figure B is 192 square units (16 x 12). The difference in their areas is 96 square units (192 - 96).

12. Let the height of the trough be h. The volume of the trough is given by the formula:

Volume = base area x height

Substituting the given values:

96 = 24h

Dividing both sides by 24:

h = 4

Therefore, the trough is 4 feet tall.

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The total volume of the wedding tent is approximately 13146.7 cubic feet.

The volume of a rectangular prism is expressed as;

V = w × h × l

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where w is the width, h is height and l is length

To find the total volume of the wedding tent, we need to find the volumes of the rectangular prism and the rectangular pyramid and add them together.

Given that: the dimensions of the rectangular prism are 34 ft by 40 ft by 8 ft.

Therefore, the volume of the rectangular prism is:

V_prism = w × h × l

V_prism = 34ft × 40ft × 8ft

V_prism = 10880 ft³

Next, we find the volume of the rectangular pyramid.

Note that: the dimensions of the base of the rectangular pyramid are the same as the dimensions of the rectangular prism, which are 34 ft by 40 ft.

Hence:

The volume of rectangular pyramid is expressed as;

V_pyramid  = (1/3) × l × w × h

V_pyramid  = (1/3) × 34ft × 40ft × 5ft

V_pyramid  = 2266.7ft³

Now we can find the total volume of the tent by adding the volume of the rectangular prism and the volume of the rectangular pyramid:

V_total = V_prism + V_pyramid

V_total = 10,880 + 2266.7

V_total = 13146.7 ft³

Therefore, the total volume of the tent is 13,146.7 ft³

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Answer:

I'm guessing A

Step-by-step explanation:

175 is the only multiple of 5 so it has to be that also there's no option for zero