A boat is heading towards a lighthouse, where Dominic is watching from a vertical distance of 114 feet above the water. Dominic measures an angle of depression to the boat at point � A to be 6 ∘ ∘ . At some later time, Dominic takes another measurement and finds the angle of depression to the boat (now at point � B) to be 32 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.

Answer:

[tex]2 \sqrt{2(6 + \sqrt{3} )} [/tex]

Step-by-step explanation:

There's your answer.

The point (2,2) may be considered an anomaly and should be investigated further to determine if it is a valid data point or if it should be excluded from the analysis.

The relation of the point (2,2) to the line of best fit can be determined by analyzing the residual value of this point. The residual value is the difference between the actual y-value and the predicted y-value based on the line of best fit. If the residual value is close to zero, then the point lies on the line of best fit. If the residual value is positive, then the actual y-value is higher than the predicted y-value, and if the residual value is negative, then the actual y-value is lower than the predicted y-value.

Unfortunately, the data necessary to determine the residual value of the point (2,2) is not provided in the question. Therefore, it is impossible to determine the exact relation of this point to the line of best fit.

However, we can make some generalizations based on the location of the point relative to the trend of the data.

If the point (2,2) lies close to the line of best fit, with a residual value close to zero, then it can be said that the point follows the trend of the data and is a typical data point. However, if the point lies far away from the line of best fit, with a large positive or negative residual value, then it can be said that the point is an outlier and does not follow the trend of the data.

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The flagpole is approximately 16.27 meters tall.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

We can solve these equations simultaneously to find h. First, we can rearrange the first equation to get:

x = h / tan(50)

Then, we can substitute this expression for x into the second equation and simplify:

tan(20) = h / (h / tan(50) + 7)

tan(20) = h / (h / 1.1918 + 7)

h(1 - 0.8393 tan(20)) = 7 tan(20)

h = 7 tan(20) / (1 - 0.8393 tan(20))

Using a calculator, we can evaluate this expression to get:

h ≈ 16.27 meters

Therefore, the flagpole is approximately 16.27 meters tall.

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The percentage of rents between $1,300 and $1,720 is 34.13%.

To calculate this, we need to use the z-score formula to convert the rent range into a z-score range. The z-score formula is (x-μ)/σ, where x is the rent range, μ is the mean rent and σ is the standard deviation.

To calculate the lower z-score, the formula becomes (1300-1510)/210 = -1.19.

To calculate the higher z-score, the formula becomes (1720-1510)/210 = 1.14. The z-score of -1.19 to 1.14 corresponds to 34.13% according to the z-table. Therefore, 34.13% of rents are between $1,300 and $1,720.

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Answer:

=(x+9)(x+5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked:

Jason's hours = 14/3

Sheldon's hours = 25/6

Jason's hours - Sheldon's hours = (14/3) - (25/6)

To subtract fractions, we need to have a common denominator, which in this case would be 6:

(14/3) - (25/6) = (28/6) - (25/6) = 3/6

Simplifying the result, we get:

3/6 = 1/2

Therefore, Jason worked 1/2 more hours than Sheldon.

Jason worked 1/3 more hours than Sheldon.

To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked.

Jason worked for 14/3 hours, which can be simplified to 4 and 2/3 hours. Sheldon worked for 25/6 hours, which can be simplified to 4 and 1/6 hours.

Subtracting the hours Sheldon worked from the hours Jason worked, we get: 4 and 2/3 - 4 and 1/6 = 2/3 - 1/6 = 1/3.

Therefore, Jason worked 1/3 more hours than Sheldon.

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Answer:9.22

Step-by-step explanation:

You dont need the left side of this triangle to figure out the answer. You can use the fact that the remaining side to find is of a right triangle and use pythagorean theorem to solve.

Since 11 is the hypotenuse, and the pythagorean theorem states that a^2 +b^2 = c^2, the hypotenuse being c, you can reverse the equation like this:

11^2-6^2=rt^2

if you plug this in, you get that rt is exactly equal to 9.21954445729

Since you asked for it rounded to the nearest hundredth, you can round it to 9.22

Answer:

k - 6

Step-by-step explanation:

I'm not sure if this is a mistake or not, or if you pressed enter a little too early, but for example:

let k = 16

6 [the number provided] less than 16 [k] is not 6 - 16, as that would be 16 less than 6. You can read the math problem from right to left, and 16 - 6 would read out as "six less than sixteen".

Honestly, you don't really need this, and it isn't a good way to do it, there are many better ways.

Therefore  the range of the quadratic function with vertex (-3, -1) is y ≥ -1 and the domain is all real number and the Domain is real numbers .

A quadratic function's vertex form is given by:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the parabola's vertex. In this instance, we have:

[tex]h = -3, k = -1[/tex]

So the quadratic function's equation is:

[tex]y = a(x + 3)^2 - 1[/tex]

To determine the function's range, we must first determine the minimum value of y. Because the squared term's coefficient is positive, the parabola opens upwards and the vertex is a minimum point. As a result, the range is:

Range: y ≥ -1

To determine the function's domain, we must first determine the set of all x-values for which the function is defined. Due to the fact that a quadratic function is defined for all real numbers, the domain is:

Domain: All real numbers

So the domain of the quadratic function with vertex (-3, -1) is all real numbers, and its range is y -1.

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Answer:

$32.50

Step-by-step explanation:

20% * y = 6.5 =>

y =6.5 ÷ 20% =

6.5 ÷ (20 ÷ 100) =

(100 × 6.5) ÷ 20 =

650 ÷ 20 =

32.5

Percentage of 20% of what number = 6.5?

20% × ? = 6.5

20% of 32.5 = 6.5

Answer:

2963*100,000 that's the answer for that question

There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.

To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.

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Therefore , the solution of the given problem of graphs comes out to be a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

Graphs are used by theoretical coordinate points physicists to analytically and graphically present assertions rather than values. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of pas de container construction composed of groups and lines. The borders, also known as the channels, should be joined with glue.

Here,

According to Kepler's third law, one can determine the connection between a planet's orbital period and its separation from a star by:

=> P² = (4π² / GM) * a³

where P denotes the orbit's duration in years, a denotes the semi-major axis in astronomical units (AU), G denotes gravity's constant, and M denotes the star's mass in solar masses.

If we rewrite this equation, we obtain:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

We can rewrite this equation as follows since our goal is to estimate the distance from the sun in AU based on the mass of the planet in relation to the sun:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

where Mp is the mass of the planet in relation to the sun and Ms is the mass of the sun.

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Odd coefficients of the polynomial are obtained by multiplying both odd integers.

Even coefficients of the polynomial are obtained by multiplying both even integers.

Even and odd coefficients of the polynomial are obtained by multiplying both odd integers.

Lets take two integer m and n,

If both 'm' and 'n' are odd integers, then the coefficients of the polynomial obtained by multiplying out will be odd.

If both 'm' and 'n' are even integers, then the coefficients of the polynomial obtained by multiplying out will be even.

If one of 'm' and 'n' is even and the other is odd, then the coefficients of the polynomial obtained by multiplying out will be even and odd.

There are no other cases.

The general form of the polynomial obtained by multiplying out a binomial is:

[tex](a+b)^n = nC_0a^n + nC_1a^{(n-1)}b + nC_2a^{(n-2)}b^2 + .....+ nC_n-1ab^{(n-1)} + nC_nb^n[/tex]

where [tex]nC_k[/tex] is a binomial coefficient.

In general, for a polynomial [tex](a+b)^n[/tex], the coefficient of the term of degree k is [tex]nC_k[/tex].

The binomial coefficients are defined as:  [tex]nC_k = n! / (k!\times(n-k)!)[/tex]

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Answer:

The answer to your problem is 53 in ^2

Hope it helps

Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

It is a numerical value that runs from 0 to 1, with 0 denoting the impossibility of an event and 1 denoting its certainty. The probability of an event A is expressed mathematically as P(A), where P(A) is the number of possible ways that event A could happen divided by the total number of outcomes.

given

The final choice is the long-term study: "An intelligence test is given to a class of kindergarteners. During 30 years, they are retested every other year."

In a longitudinal study, a group of individuals are followed over a lengthy period of time, frequently years or even decades. A longitudinal study's goal is to look at how people change or grow over time and to pinpoint any potential contributing elements.

Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

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The theoretical probability of not drawing an "o" is 3/4.

We have,

Each of the letters of the word Colorado are written on a piece of paper and then put into a bag.

Here, The word "Colorado" has 8 letters, including 2 "o"s.

Therefore, the probability of drawing an "o" is,

P = 2/8

P = 1/4

Hence, The probability of not drawing an "o" is the complement of this probability is,

1 - 1/4 = 3/4.

Therefore, the theoretical probability of not drawing an "o" is 3/4.

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Step-by-step explanation:

[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]

Step-by-step explanation:

hope this will help u

Amy is picking her fall term classes, including probability 101, 102, and 103 so,

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

a) the probability that she will get 101

P = [tex]\frac{^1C_1*^1^9C_2}{^2^0C_3}[/tex]

= 171/1140

P = 0.15

probability that she will get 101 = 0.15.

b) the probability that she will get 101 and 102.

P = [tex]\frac{1*1*18}{20!*3!(20-3)!}[/tex]

P = 18/1140

= 0.0158

probability that she will get probability 101 and probability 102 is 0.0158.

c) the probability she will get all three probability courses

P = [tex]\frac{^3C_3}{^2^0C_3}[/tex]

= 1/1140

P = 0.0009

The probability she will get all three probability courses is 0.0009.

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Complete question:

Amy is picking her fall term classes. She needs to fill three time slots, and there are 20 distinct courses to choose from, including probability 101, 102, and 103. She will pick her classes at random so that all outcomes are equally likely.

(a) What is the probability that she will get probability 101?

(b) What is the probability that she will get probability 101 and probability 102?

(c) What is the probability she will get all three probability courses?

The line-plot of the the given data 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 that displays the lengths of the books on the booom shelf is attached.

What is line plot?

A line plot is a type of graph that represents the kind of data representation. It is line plot or a line chart shows the data in a visual form or visual representation. The graph is plotted with help of straight lines and points or dots. The x-axis is represented by straight lines or the it is labelled about the data. The y-axis is represented by the dots or frequency of the data. It is generally used to represent the small data set. This graph uses symbols to show or represent the frequency of the observations.

The data represented here is 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2

we can make the frequency table using the above values, after which it can be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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Attached is a line-plot of the given data showing the lengths of the books on the book shelf: 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2.

An example of a graph that shows this sort of data representation is a line plot. The data is presented visually in the form of a line plot or a line chart. With the aid of straight lines, points, or dots, the graph is drawn. Straight lines or labels that describe the data are used to depict the x-axis. The dots or frequency of the data are used to depict the y-axis. It often serves as a representation for a tiny group of data. The frequency of the observations is shown or represented by symbols on this graph.

9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2 are the numbers shown.

Using the aforementioned variables, we can create the frequency table, which can then be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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To check if the line drawn is diameter it should be intersected at centre and it must be equidistant from the centre of the circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To determine if the line Neil drew is an actual diameter of the circle and not just a smaller chord, he can use the following method -

Extend the line on both sides to create two lines that intersect at a point outside the circle.

Use a compass to draw a circle with the same center as the original circle, and with a radius that is greater than half the length of the line Neil drew.

Check if the two lines intersect the circle at two points that are equidistant from the center of the circle.

If they do, then the line Neil drew is an actual diameter of the circle.

If they do not, then the line Neil drew is just a chord.

This method works because a diameter of a circle is the longest chord that passes through the center of the circle.

By extending the line Neil drew and creating two lines that intersect outside the circle, we can compare the distance from the center of the circle to each of the two intersection points with the radius of the circle we drew.

If the distances are equal, then the line Neil drew must be a diameter of the circle.

Therefore, the method to find the actual diameter is explained.

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The probability that Emme answers exactly 3 questions correctly is 0.1961.

Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:

P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6

Using a calculator, we get:

P(X = 3) = 0.1961

Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.

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Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

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The expression 75 + 1.45x represents the total cost of a training session with Terrell

Let x be the distance (in miles) that Terrell must drive to and from the training session.

Then the total cost C of the training session, in dollars, can be expressed as:

C = 75 + 1.45x

Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.

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The answer this riddle is time as it is always in a hurry, constantly moves forward and waits for no one. And time is often represented as being in a high position, such as on a clock or a calendar.

A riddle is a type of puzzle or question that is designed to challenge and engage the mind. It usually presents a seemingly paradoxical or enigmatic situation or description, and the goal is to figure out the hidden meaning or answer through careful thought and analysis.

Riddles can take many different forms, but they often involve wordplay, metaphor, or clever misdirection to lead the solver towards the solution. Riddles have been used for entertainment, education, and even as a means of passing on cultural knowledge and wisdom from one generation to the next.

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Answer:

[tex]2 \sqrt{61} \: in[/tex]

Step-by-step explanation:

Use the Pythagorean theorem (assume, that the length of hypotenuse is x):

[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]

Answer:

95/63 or 1 32/63

Step-by-step explanation:

turn the fraction into a mixed number/improper fraction

65/9-40/7

find a common denominator which in this case is 63

so, the first fraction you will multiply the numerator and denominator by 7 to get

455/63

then the second fraction multiply the numerator and the denominator by 9

360/63

then you would subtract the two numerators KEEP THE DENOMINATOR THE SAME

455/63-360/63=95/63

The sampling method used in the study where the sample is chosen by separating all cars by size, and selecting 10 of each size grouping is known as stratified random sampling.

Stratified random sampling is a method of sampling that involves dividing the population into smaller sub-groups known as strata. In this method, each stratum is composed of elements that have similar characteristics.

The strata could be based on demographic characteristics such as age, sex, education, and so on. Once the strata have been created, the next step is to select a sample from each of the strata to make up the final sample. The selection is done randomly, and the number of elements selected from each stratum is proportional to the size of the stratum. This ensures that the sample is representative of the entire population in terms of the different characteristics of the population.

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