An airplane flies over a straight route connecting two radio beams located at 18 miles from each other. Given that the angles of depression [check the textbook, page 485 . for the definitionl are. respectivelv. 25 ∘
. and 34 ∘
. find the altitude. 22mi Hint. The altitude from the plane to the ground does not split the 22 miles distance between the beams in two equal parts. You may call the two pieces x, and y, with x+y=22. Note how they form, with the altitude, two right triangles. The relation between x and y, together with the

The correct answer for the first question is D. The data are discrete because the data can take on any value in an interval.

Quiz scores from a college level statistics course are analyzed to determine student progress. This is not a voluntary response sample because the students taking the quiz are required to participate, and their scores are collected for the purpose of analyzing their progress.

For the second question, the data described, which is the number of donations a charity receives each month, is discrete. Discrete data can only take on specific values and cannot be divided into smaller, meaningful intervals. In this case, the number of donations can only be whole numbers, such as 0, 1, 2, and so on. It cannot take on any value in an interval or be represented by fractions or decimals. Therefore, the data is discrete.

It is important to distinguish between discrete and continuous data when analyzing and interpreting data, as different statistical methods and techniques are used for each type. Discrete data is usually counted or measured in whole numbers, while continuous data can take on any value within a given range or interval.

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To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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The next pair of values in the linear function given is (4,0)

From the given pair of coordinates :

The x-values increments by a value of 2

Hence, the next x value could be :

The y-values on the other hand increments by 1

Hence, the next y value could be :

Therefore, the next ordered pair would be (4,0)

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The three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

To find the missing coordinates such that the three vectors form an orthonormal basis for R3, we need to use the concept of coordinates, vectors, and orthonormality.

First, let's define the three vectors as u = (0.6, -0.8, 0), v = (1, 0, 0), and w = (0, 0, 0.6).

To form an orthonormal basis for R3, the three vectors need to be orthogonal to each other and have a magnitude of 1.

Orthogonality means that the dot product of any two vectors is 0. So we need to find the missing coordinates of w such that:

u • v = 0
u • w = 0
v • w = 0

Since u and v are already orthogonal to each other, we only need to find the missing coordinates of w such that it is orthogonal to both u and v.

Let's start with u • w = 0:

0.6 * 0 + (-0.8) * 0 + 0 * 0.6 = 0

This equation is already satisfied, so we don't need to find any missing coordinates for w in relation to u.

Now let's look at v • w = 0:

1 * 0 + 0 * 0 + 0 * 0.6 = 0

Again, this equation is already satisfied, so we don't need to find any missing coordinates for w in relation to v.

Since both equations are satisfied, the missing coordinates of w are (0, 0).

Therefore, the three vectors that form an orthonormal basis for R3 are:

u = (0.6, -0.8, 0)
v = (1, 0, 0)
w = (0, 0, 0.6)

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The area of the regular polygon with an apothem of 15 inches will be 2338.27 square inches.

Let 'a' be the apothem and 'b' be the regular side length.

Then the area of the regular polygon will be

A = 3 × a × b

We know that each angle of the regular hexagon is 60°.

Then the base length is given as,

b = 2a tan θ

b = 2 x 15 x tan 60°

b = 51.96 in

Then the area of the regular hexagon is given as,

A = 3 × a × b

A = 3 × 15 × 51.96

A = 2338.27 square inches

The area of the regular polygon with an apothem of 15 inches will be 2338.27 square inches.

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The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

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The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

The value of blue sector area is 438 cm²(approx.).

Now we know, if the sector angle is \(\theta\), then the sector area for this sector is \($\frac{\theta}{360^{\circ}} \times \pi r^2$\) where the radius of the circle is r.

Given, the sector angle \((\theta) =256^{\circ}\) and radius (r) is 14 cm.

Now putting the value of \(\theta\) and r in the formula we get,

Area= \($\frac{256^{\circ}}{360^{\circ}} \times \pi \times (14)^2$\) cm²

=0.711111 x 3.14 x 14 x 14 cm²

=437.6462 cm² (approx.)

= 438 cm² (approx.).

So, the required area is 438 cm² (approx.).

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Answer:

- 7/24

Step-by-step explanation:

Step 1:

3/8 = r + 2/3

Step 2:

9/24 = r + 16/24

Step 3:

9/24 - 16/24 = r

Answer:

- 7/24 = r

Hope This Helps :)

Answer:

-7/24

Step-by-step explanation:

Isolate the variable, r. Note the equal sign, what you do to one side, you do to the other.

Subtract 2/3 from both sides:

3/8 (-2/3) = r + 2/3 (-2/3)

3/8 - 2/3 = r

Simplify. First, find common denominators. Note that what you do to the denominator you do to the numerator.

(3/8) x (3/3) = (9/24)

(2/3) x (8/8) = (16/24)

Subtract:

(9/24) - (16/24) = -7/24

r = -7/24

~

Answer:

0.18

Step-by-step explanation:

Answer:

I need a question, then I will help

Step-by-step explanation:

Answer:

To answer this question I need the values of the rhombus. like the p and the q.

Step-by-step explanation:

Answer:

1. True

2. True

3. False

4. True

5. False

6. True

7. False

8. True

9. True

Bonus: ∠2 = 112°, ∠4 = 112°, ∠8 = 112°, ∠1 = 68°, ∠3 = 68°, ∠5 = 68°, ∠7 = 68°

Step-by-step explanation:

1. Angles 1 and 2 are supplementary because they form a straight line (180° angle) together.

2. Angles 1 and 5 are corresponding because their places (and angle measures) match.

3. Angles 2 and 5 are not alternate exterior angles because angle 5 is not on the outside area of the parallel lines.

4. Angles 4 and 6 are alternate interior angles because they are on opposite sides of the transversal and are both in the inside area of the parallel lines.

5. Angles 7 and 2 are not corresponding because their places (and angle measures) do not match.

6. Angles 3 and 6 are interior angles on the same side of the transversal because they are both in the inside area of the parallel lines and are on the same side of the transversal.

7. Angle 3 is not congruent to angle 8 because they do not have the same angle measures.

8. Angles 3 and 7 are corresponding angles because their places (and angle measures) match.

9. Angles 8 and 2 are alternate exterior angles because they are on opposite sides of the transversal and are outside areas of the parallel lines.

Bonus: If angle 6 has a measure of 112°, then the angle that supplements it has a measure of 68° (112 + 68 = 180). It also goes for the other angles that are congruent to angle 6.

Hope this helped :)

Answer: the height of this triangle is 55.4 mm

Step-by-step explanation:

\(\displaystyle\\Area\ of\ a\ triangle:\ A =\ \frac{ah}{2} \\\\Hence,\\\)

Multiply both parts of the equation by 2:

\(2A=ah\)

Divide both parts of the equation by a:

\(\displaystyle\\\frac{2A}{a} =h\\\\Thus,\ h=\frac{2A}{a} \\\\h=\frac{2(227.14)}{8.2} \\\\h=\frac{454.28}{8,2} \\\\h=55.4\ mm\)

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The cost for renting a car can be represented by the equation: c = a + bm

The cost of renting a car can be expressed as a function of the number of miles driven. This function is typically linear, with a fixed cost component and a variable cost component. The fixed cost component represents the cost of renting the car regardless of the number of miles driven, while the variable cost component represents the additional cost per mile driven.

The equation that represents the cost of renting a car is c = a + bm, where c represents the total cost of renting the car, m represents the number of miles driven, a represents the fixed cost component, and b represents the variable cost component.

The equation shows that the cost of renting a car is dependent on the number of miles driven. As the number of miles driven increases, the cost of renting the car also increases, reflecting the additional variable cost per mile. By knowing the values of a and b, we can estimate the total cost of renting the car for a given number of miles.

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Answer:

C. The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f.

Step-by-step explanation:

It's a given that f(x) = x^2 so that means g(x) = f(x) - 9 means g(x) = x^2 - 9

in slope intercept form y = mx + b, b is the y-intercept

since g(x) is just f(x) with the y-intercept as -9 we know that the vertex of the parabola moves downwards 9 units

---

Hope this helps! :) If so, please mark my answer as brainliest

Function g(x) is the translation of function f(x). The y-intercept of the graph of g is 9 units below the y-intercept of the graph of f(x). The correct statement is C.

\(f(x)=x^{2}\).

\(g(x) = f(x) - 9.\)

From the above functions it is clear that the equation for the graph of g(x) will be,

\(g(x)=x^{2} -9\).

The equation \(y=mx+c\) is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Since The y intercept of function f(x) is zero.

Hence in the function g(x), it is 9 units below the intercept of the function f(x). Thus the correct option is C.

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After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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Answer:

x = 66.93

Step-by-step explanation:

By pythagoras theorem,

72² = 28² + y²

⇒ y² = 72² - 28²

⇒ y² = 4400

⇒ y = 66.33

sin x = opposite/hypotenuse

sin x = 66.33/72

sin x = 0.92

\(x = sin^{-1} (0.92)\)

x = 66.93

Answer: the answer is 67.1

Exponential, triangular, Weibull, beta, Erlang, gamma, and lognormal distributions are often referred to as continuous theoretical distributions.

In most simulations, a queue is important for keeping an entity when it cannot move.

Exponential, triangular, Weibull, beta, Erlang, gamma, and lognormal distributions are all examples of continuous theoretical distributions. These distributions are used to model random variables that take on continuous values, such as time, length, or volume. They are characterized by probability density functions that describe the likelihood of different values occurring within a given range.

In simulation modeling, a queue is an important construct used to manage entities or objects that need to wait or be processed in a specific order. When an entity cannot move or proceed further in the simulation, it is typically placed in a queue until the conditions allow it to progress. Queues are commonly used in various simulation scenarios, such as modeling service systems, production lines, or network traffic.

Global variables and attributes are generally used to store and manage data within a simulation, but they do not specifically address the concept of keeping an entity when it cannot move. Resources, on the other hand, are entities that are required or consumed by other entities in the simulation, such as equipment or personnel, but they do not directly handle the situation of entities being unable to move.

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Answer:

1 < x < 6

Step-by-step explanation:

6 < x + 5 < 11

You want x alone, and 5 is being added to x, so subtract 5 from all three sides of the compound inequality.

6 - 5 < x + 5 - 5 < 11 - 5

1 < x < 6

Answer:

1<x<6

hope this helps :D

The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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Option 2 has a lower NPV and thus should be chosen as it results in less total payment and better savings. Hence, you would choose option 2 as the Net Present Value of choosing option 2 is -9,903,615.48.

Given:

Purchase price = 12.5 million baht

Down payment = 15%30-year mortgage

We have to calculate the option which is best for us.

Option 1: Mortgage rate = 7.25%

Option 2:Mortgage rate = 6.75%

(a) Monthly Payment of Option 1:

Loan Amount = 12.5 * (100-15)%

= 10,625,000 baht

n = 30 * 12

= 360

i = 7.25%/12

= 0.006042857

Yearly Interest Paid = i * 10,625,000

= 64,515.48 baht

Monthly Interest Paid = 64,515.48 / 12

= 5,376.29 baht

EMI =\([P x R x (1+R)^n] / [(1+R)^n-1]\)

where P = Loan Amount, R= Interest Rate per month, n= total number of payments.

EMI = \([10,625,000 x 0.006042857 x (1+0.006042857)^360] / [(1+0.006042857)^360-1]\)

EMI = 69,677.31 baht

(b) Monthly Payment of Option 2:

Loan Amount = 12.5 * (100-15)%

= 10,625,000 baht

n = 30 * 12 = 360

i = 6.75%/12 = 0.005625

Yearly Interest Paid = i * 10,625,000

= 59,765.63 baht

Monthly Interest Paid = 59,765.63 / 12

= 4,980.47 baht

Point cost = 4% of Loan Amount

= 10,625,000 x 4/100

= 425,000 baht

Loan Amount after Deducting Points = 10,625,000 - 425,000

= 10,200,000 baht

EMI = \([P x R x (1+R)^n] / [(1+R)^n-1]\)

where P = Loan Amount, R= Interest Rate per month, n= total number of payments.

EMI =\([10,200,000 x 0.005625 x (1+0.005625)^360] / [(1+0.005625)^360-1]\)

EMI = 66,128.92 baht

(c) We have to calculate the NPV of the payments to decide which option is better.

We use the formula to calculate NPV:-

NPV = - \([B + (PMT / i) * (1 - (1 + i)^-n)] / ((1 + i)^t)\)

Where B = amount borrowed, PMT = monthly payment, i = interest rate, n = total number of payments, t = year.

NPV =\(- [10625000 + (69677.31 / 0.006042857) * (1 - (1 + 0.006042857)^-360)] / ((1 + 0.006042857)^30)\)

= -9,892,571.85 baht

NPV = \(- [10200000 + (66128.92 / 0.005625) * (1 - (1 + 0.005625)^-360)] / ((1 + 0.005625)^30)\)

= -9,903,615.48 baht

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

21.7 in^2

Step-by-step explanation:

A = 6a^2 =6 · 1.9^2 = 21.66in²

Round: 21.7 in^2

0.6 KL = 600 grams

you can always use the ladder method

5 kilograms (kg) is equivalent to 11.0231 pounds (lbs). The conversion from kilograms to pounds is a common one, as these units are used for measuring weight or mass in different parts of the world.

To convert kilograms to pounds, we can use the formula

pounds = kilograms x 2.20462

This formula is based on the fact that there are 2.20462 pounds in one kilogram. Therefore, to convert 5 kg to pounds, we can simply multiply 5 by 2.20462:

5 kg x 2.20462 = 11.0231 lbs

Therefore, 5 kilograms is equivalent to 11.0231 pounds. This conversion is often used in applications such as international travel, where luggage weight limits may be specified in either kilograms or pounds. It is also used in scientific and medical fields, where accurate measurement of weight or mass is critical to diagnosis and treatment.

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The equation used to find the answer is 26 -14 -6 =

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

number of flowers picked by the girl = 14

number of flowers already with her = 6

number of flowers picked by her grand mother = 26

so her grandmother picked 26 - 14 - 6 flowers more than her. so then equation becomes 26 -14 -6 = ?

In conclusion, the equation that best describes the above is 26 -14 -6 = ?

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