Find all numbers that are not in the domain of the given expression. Then, give the domain in set notation. (x)/(x-7)

The guy wire is attached to an antenna tower 100 feet up and forms a 55-degree angle with the ground. We need to determine the length of the wire.

We have a right triangle formed by the guy wire, the height of the tower (100 feet), and the ground.

Let's denote the length of the guy wire as "w."

Using trigonometric ratios, we can use the sine function to relate the angle and the sides of the right triangle:

sin(angle) = opposite/hypotenuse

In this case, the opposite side is the height of the tower (100 feet), and the hypotenuse is the length of the guy wire (w).

sin(55 degrees) = 100/w

To solve for w, we can rearrange the equation:

w = 100/sin(55 degrees)

Using a calculator, we can calculate the value of sin(55 degrees) ≈ 0.8192.

Substituting this value into the equation, we have:

w ≈ 100/0.8192 ≈ 122.16

Therefore, the length of the guy wire is approximately 122.16 feet.

Answer: The length of the wire is approximately 122.16 feet.

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Answer:

the second graph is likely the continuous one because the first graph stops on the x-axis

Answer:

(36,25)

Step-by-step explanation:

We want to find where the two lines intersect

We know the x value is about 1/2 way between 30 and 40 and the y value is close to 25

The closest value is (36,25)

Step-by-step explanation:      I GOT YOU

The point at which the prices are the same would be at (36, 25)

I know this to be true because that's when the lines touch each other (intersect) on the graph. After 36 minutes go by the cost is 25 dollars for both lines. Also the sides have names, cost on the left, and time on the bottom. And the lines stand for the store prices over time. In summary, just look at the number on the side and bottom and see where the lines intersect.

Answer:

4.5

Step-by-step explanation:

Answer:

x = 9

y = 9√2

Step-by-step explanation:

We can use the properties of an isosceles right triangle (45-45-90) to solve for x and y.

The legs of an isosceles triangle are congruent, so x = 9.

The hypotenuse of an isosceles right triangle is equal to one of the legs multiplied by the square root of 2. Therefore,

y = 9 · √2 = 9√2

Answer:

x = 9 , y = 9\(\sqrt{2}\)

Step-by-step explanation:

the triangle is a 90- 45- 45 , isosceles right triangle, with congruent legs

then x = 9

using Pythagoras' identity in the right triangle

y² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )

y = \(\sqrt{162}\) = \(\sqrt{81(2)}\) = \(\sqrt{81}\) × \(\sqrt{2}\) = 9\(\sqrt{2}\)

The time it will take for Helen and Reid to meet is given as follows:

3/7 of an hour = 26 minutes.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the time is obtained as follows:

7 = 3/t

7t = 3

t = 3/7 of an hour = 26 minutes.

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The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).

\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.

In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.

Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

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-10

Step-by-step explanation:

-17 + y = -27

+17        +17

y=-10

Answer: 10

Step-by-step explanation: y will be 10 i hope so it is -17 + 10 = -27

If we solve the given equation for t we get that t=-2

The equation given,

9t+5(t+3) = -(t+13) +t

⇒9t + 5t + 15 = -t -13 +t

⇒14t + 15 = -13                    (∵-t+t=0)

⇒14t = -13-15                       (bringing 15 from left hand side to right hand      side the sign is flipped and 15 becomes -15)

⇒14t = -28

⇒\(t=\frac{-28}{14}\)                            (dividing both sides by 14)

⇒t = -2

Thus on solving the equation we get t = -2

Your question was incomplete but most probably your full question was

Solve for t when this equation is given, 9t+5(t+3) = -(t+13) +t

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The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).

Given,

\(\frac{11x}{55^{2}+22k }\)  We have to simplify in rational expression

The common factor is 11. So, we have to pick the common factor from the equation.

= \(\frac{11x}{55^{2}+22k }\)

= \(\frac{1}{5x + 2}\)

Therefore the simplification of given equation is 1/(5k+2).

Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.

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Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.

c = 45 ft

a = 27 ft

b² = c² - a²

b² = (45 ft)² - (27 ft)²

b² = 2025 - 729

b² = = 1296

b = 36 ft

If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.

Using Pythagorean theorem, determine how far up the ladder is on the side of the house.

c = 45 ft

b = 39 ft

a² = c² - b²

a² = (45 ft)² - (39 ft)²

a² = 2025 - 1521

a² = 504

a = 6√14

a = 22.45 ft

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The best upper bound on the probability that the grade of the student is at most 50 is 1/50.

Since the average grade in the class is 95 out of 100, we can use the Chebyshev's inequality to obtain an upper bound on the probability of a student's grade being below a certain threshold. Chebyshev's inequality states that for any non-negative random variable, the probability that it deviates from its mean by k or more standard deviations is at most 1/k^2.

Let X be the grade of the randomly chosen student. We want to find c and a non-negative random variable g(X) such that the event {X ≤ 50} can be expressed as {g(X) ≥ c}. In this case, we can choose g(X) = 100 - X and c = 50. Therefore, the event {X ≤ 50} is equivalent to {g(X) ≥ 50}.

Now, applying Chebyshev's inequality, we have:

P(g(X) ≥ 50) ≤ 1/k^2

Since we want to find the best upper bound, we want to minimize k. In this case, k represents the number of standard deviations the grade of the student can deviate from the mean. To maximize the upper bound, we want k to be as small as possible.

We know that the minimum value that X can take is 0, and the maximum value it can take is 100. Therefore, the standard deviation of X is at most 100/2 = 50. We can set k = 1, as it gives the smallest possible value.

P(g(X) ≥ 50) ≤ 1/1^2 = 1

Thus, the best upper bound on the probability that the grade of the student is at most 50 is 1/1 = 1.

Conclusion: The best upper bound on the probability that the grade of the student is at most 50 is 1, indicating that it is guaranteed that the student's grade is at most 50.

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The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is,

\(x^{2} +4x+y^{2} +6y-3=0\)

Given that,circle with a center at (–2, –3)

diameter of circle is  8 units

To find

the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.

Radius of the Circle is,

The diameter of the circle is 8 units. therefore,

\(radius=\frac{d}{2}=\frac{8}{2} =4\)

Equation of a circle

The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units.

\((x-h)^{2} +(y-k)^{2} =R^{2}\)

Substituting the values,

\((x-(-2))^{2} + (y-(-3))^{2} =4^{2}\)

\((x+2)^{2} + (y+3)^{2} =4^{2}\\\)

\(x^{2} +4x+4+y^{2} +6y+9=0\)

\(x^{2} +4x+y^{2} +6y-3=0\)

Therefore, the option C is correct.

The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is

\(x^{2} +4x+y^{2} +6y-3=0\)

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Greetings from Brasil....

Every rational number is written as:

A/B   where A ∈ ℤ and B ∈ ℤ* (B ≠ 0)

So in our case, 2/9 is a rational number, because we have the division of 2 by 9 and 2 ∈ ℤ and 9 ∈ ℤ*

43% of eighth graders claim to spend more than an hour every day on social media.

A ratio written as a fraction of 100 is what is referred to as a percentage.

Students were asked in a survey if they thought they used social media more or less than an hour every day.

Added to Less

7th 12 14

8th 20 26

The number of students who responded "more" must be divided by the total number of 8th-grade students polled, and the result must then be multiplied by 100 to get the percentage of students who said they spend more than an hour a day on social media.

20 out of 46 students (20+26) responded "more," or roughly 43.48%.

As a result, 43% of eighth graders believe they spend more than an hour every day on social media.

The Complete Question.

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It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.

Answer: knvsvvs

Step-by-step explanation:

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Answer:

D

Step-by-step explanation:

The sum of the areas of the shaded regions will be 14 square units as the big outside square has an area of 84, and the dots are all equally spaced, forming smaller squares.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

The required area will be,

=1*1+1*9+0.75*4+0.25*4

=14 square units

Because the big outside square has an area of 84 square units and the dots are all evenly spaced, forming smaller squares, the total area of the shaded regions will be 14 square units.

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A confidence interval for a population mean  is option  B. Estimates a likely interval for a population mean.

A statistical method known as a confidence interval is utilized to predict a plausible interval within which the actual population mean may exist. This offers a set of values that we can credibly estimate the probable range for the actual mean of the population.

The process of constructing a confidence interval involves utilizing a set of sample data to make an approximation of the population mean and to determine the margin of error.  Expressed as a percentage (for instance, 95%), the confidence level indicates the likelihood that the interval calculated includes the genuine average of the population.

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A confidence interval for a population mean __________.

A. Estimates the population range

B. Estimates a likely interval for a population mean

C. Estimates likelihood or probability

D. Estimates the population standard deviation

The theater will sell approximately 930 tickets for each of its 5 songs.

To determine the approximate number of tickets the theater will sell for each of its 5 songs, we need to divide the total number of seats in the theater by the number of songs.

Total number of seats: 4650

Number of songs: 5

To find the approximate number of tickets sold per song, we divide the total number of seats by the number of songs:

4650 seats / 5 songs = 930 tickets per song (approximately)

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Answer:

Kylie drove at a speed of 60 miles per hour going to the soccer game.

Step-by-step explanation:

Let us assume that Kylie drove at speed x miles per hour going to the soccer game. On the way back, she had to drive at a speed of (x-10) miles per hour. We are given that the trip took 1 hour longer on the way back, which means that the time taken on the way back was greater than the time taken going to the soccer game. We can form an equation using the distance formula:

300/x = 300/(x-10) + 1

Simplifying this equation by cross multiplication, we get:

300(x-10) = 300x + x(x-10)

Simplifying further, we get:

300x - 3000 = 300x - 10x

Solving for x, we get:

x = 60

Therefore, Kylie drove at a speed of 60 miles per hour going to the soccer game.

Considering the piece-wise function for the snow depth, it is found that:

a) The graph of the function is given at the end of the answer.

b) The snow is deepest in the month of February, at 26 inches.

c) The snow begins in October and ends in April.

A piece-wise function is a function that has different definitions based on the input x of the function.

For this problem, the functions has three definitions, given as follows:

For all these cases, the function is a linear function, composed by two segments connecting the numeric values of the end-points of each interval.

The maximum point of the graph is of:

(4,26).

Hence the maximum depth of snow is of 26 inches in the month of February.

The snow begins in October, as the graph starts to increase between x = 0 and x = 1, still representing October, and ends in April, as the x-intercept at x = 6.5 represents the month of April.

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Answer:

Sure, let's break down each part step by step.

Part A:

To calculate how much fabric is needed to make 3 aprons, we need to multiply the amount of fabric needed for one apron by 3.1 apron requires

1 1/2 yards of fabric for the front and 1/8 yards of fabric for the tie.1 1/2 yards + 1/8 yards = 15/8 yards (Adding fractions with a common denominator)

Now we can multiply the total fabric needed for one apron by 3 to get the fabric needed for 3 aprons:

3 * 15/8 yards = 45/8 yards (Multiplying by a whole number)

So, the total fabric needed to make 3 aprons is 45/8 yards.

Part B:

If Susan originally has 7 yards of fabric and she uses 45/8 yards to make 3 aprons, we can subtract the amount used from the original amount to find out how much fabric is left over.

7 yards - 45/8 yards = 56/8 yards - 45/8 yards (Subtracting fractions with a common denominator)

= 11/8 yards (Subtracting fractions)

So, after making the aprons, Susan will have 11/8 yards of fabric left over.

Part C:

To determine if Susan has enough fabric left to make another apron, we need to compare the amount of fabric left (11/8 yards) with the amount of fabric needed for one apron (1 1/2 yards + 1/8 yards = 15/8 yards).

Since 15/8 yards is greater than 11/8 yards, Susan does not have enough fabric left to make another apron. She is short by 4/8 yards (or 1/2 yard) of fabric.

Hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

Answer:

1200 people do they expect to attend on opening day.

Step-by-step explanation:

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

$750$ people attended the county fair on an opening day last year. Organizers of the fair expect a $60\%$ increase in attendance this year on opening day.

As there is a 60% Increase in attendance..

60% more ppl would attend than last year..

so this year's attendance would be

750 + 60% of 750 ..

=750 + 450 ..

=1200 people.

Hence, 1200 people do they expect to attend on opening day.

Answer:

1,200 people.

Step-by-step explanation:

-60% of 750 is 450.

i.e 60/100 x 750/1=450

-Add 450 to 750.

i.e 450+750= 1,200.

Answer:

r(180°,0) is a rotation of 180° degrees over the origin.

Notice that this rotation moves our figure to the opposite quadrant (so a translation of two quadrants).

Then this is equivalent to:

A reflection over the x-axis followed by a reflection over the y-axis.

Or.

A reflection over the y-axis followed by a reflection over the x-axis.

There is another possible reflection, but it depends on where is our figure.

If the figure is in the first or third quadrant, a reflection over the line y = -x is equivalent to the rotation.

If the figure is in the second or third quadrant, then the reflection over the line y = x is equivalent to the rotation.

We can combine those two and write:

A reflection over the line y = (-1)^n*x.

Where n is the number associated with the quadrant where the figure is in.

As a backpack designer at a sportswear company, my team has been assigned the task of creating a smaller toddler size backpack and a larger teen size backpack based on our already popular kids model. In addition to designing these new backpacks, we will also create accessories that can be sold alongside them.

For the smaller toddler size backpack, our focus will be on ensuring a comfortable fit for young children while incorporating fun and age-appropriate designs. We will consider using lightweight and durable materials to make it easier for toddlers to carry. The backpack will have adjustable straps to accommodate their smaller frames and promote proper weight distribution. As for accessories, we can design detachable safety harnesses, featuring playful characters or animal shapes, to help parents keep their toddlers close in crowded places.

For the larger teen size backpack, we will prioritize functionality and style to cater to the needs and preferences of teenagers. The backpack will have ample storage compartments to accommodate textbooks, laptops, and other school essentials. We will also consider incorporating features like padded laptop sleeves, water bottle pockets, and headphone ports to enhance convenience and usability. To complement the backpack, we can design coordinating accessories such as pencil cases, lunch bags, and keychain attachments that match the overall design aesthetic.

Throughout the design process, we will ensure that both the toddler and teen size backpacks maintain the high quality and attention to detail that our brand is known for. Our team will carefully select fabrics, hardware, and zippers that are durable and long-lasting, considering the wear and tear expected in different age groups. We will also focus on ergonomic design principles to prioritize comfort and proper weight distribution for both the smaller and larger backpacks.

By expanding our backpack line to include smaller toddler and larger teen sizes, along with the accompanying accessories, we aim to provide functional, stylish, and age-appropriate options for a broader range of customers.

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Answer:

It’s d

Step-by-step explanation: