You are 60 feet from a radio tower and the angle of elevation from the ground to the top of the tower is 69°. Find the height of the radio tower.​

Answer:

------------------------

Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.

Total surface area includes a square base and four triangular faces and the measure of it is:

The matching choice is B.

Consider concert tickets as a long-term savings objective.Therefore, the answer is A.

Savings refers to anything that existing at any given moment, a stock variable, whereas saving refers to an action occurring over period, a flow variable. Even seasoned economists and financial experts frequently refer to "saving" for "savings" due to the widespread misunderstanding of this distinction.\

Saving for a concert is not a long-term savings goal because it is a short-term financial goal. Long-term savings goals typically involve saving money for events or expenses that will occur several years or even decades in the future, such as college, a down payment on a house, or retirement. Saving for a concert is unlikely to take more than a few months or a year, so it is not a long-term goal.

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The value of x in the given triangle is 36.87°.

One of the six functions in mathematics is the trigonometric function (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) In trigοnοmetry, sin cοs and tan values are the primary functiοns we cοnsider while sοlving trigοnοmetric prοblems. These trigοnοmetry values are used tο measure the angles and sides οf a right-angle triangle. Apart frοm sine, cοsine and tangent values, the οther three majοr values are cοtangent, secant and cοsecant.

According to Trigonometric function,

Tan θ = Opposite side/Adjacent side

Therefore,

Tan θ = 6/8

θ = arctan(6/8)

θ ≈ 36.87°

This is simplest way to calculate, there is no other way to calculate.

Thus, the value of x in the given triangle is 36.87°.

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There are 350 different lineups that can be created.

The question here is regarding the possibility of different lineups given that there are two groups of players available - guards and forwards/centers. The coach wants to choose 2 of her guards and 3 of her forwards/ centers. To avoid an unbalanced lineup, she places the names of her 5 guards in one hat and the names of her 7 forwards/centers in a second hat. Then, she will randomly select 2 guards from the first hat and 3 forwards/ centers from the second hat.

In order to get the different possibilities of lineups, we need to calculate the total number of ways we can select the guards and the forwards/centers separately.

Total number of ways to select guards =[tex]5C_2 = (5 \times 4) / (2 \times 1) = 10[/tex]

Total number of ways to select forwards/centers = [tex]7C_3 = (7 \times 6 \times 5) / (3 \times 2 \times 1) = 35[/tex]

Thus, the total number of ways the lineup can be created is 10 × 35 = 350.

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Cos G therefore equals 4/5 since we must use mathematics to express cos G as a fraction in the simplest words.

A closed, two-dimensional triangle in geometry is a shape having three straight sides and three angles. Triangles can be categorized according to the size of their angles and the length of their sides. In three locations known as vertices, a triangle's three sides come together. An angle is the place where two triangle sides intersect, and the angle that faces a given side is known as the opposing angle. A triangle's three angles can never add up to more than 180 degrees.

given

We may use the cosine rule to find cos G:

(E2 + F2 - G2) / cos G (2EF)

Inputting the values provided yields:

[tex]cos G = (20^2 + 25^2 - 15^2) / (2 * 20 * 25)[/tex]

= (400 + 625 - 225) / 1000 = 800 / 1000 \s= 4 / 5

Cos G therefore equals 4/5 since we must use mathematics to express cos G as a fraction in the simplest words.

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Answer:

Step-by-step explanation:

The function f(x) = 15x² is increasing over the interval x > 0.

To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.

The function f(x) is decreasing over the interval x < 0.

To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.

This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).

The coordinates of E can be found by taking the average of the x and y coordinates of points A and B.  This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).  To find the coordinates for these points, we use the formula [tex](x1 + x2)/2, (y1 + y2)/2[/tex].  For example, to find the x coordinate for E, we would use (-2 + 4)/2 = 1, and for the y coordinate of E, we would use (3 + 5)/2 = 4.  We can then use this formula to find the coordinates for all of the midpoints.Step 1: Find coordinates of E, F, G, and H E: (1, 4) F: (7, 2) G: (9, - 5) H: (3, - 6) Step 2: Calculate the perimeter of the quadrilateral ABCD,Perimeter = |AB| + |BC| + |CD| + |DA = |(-2, 3) - (4, 5)| + |(4, 5) - (10, -1)| + |(10, -1) - (8, -9)| + |(8, -9) - (-2, 3)| = (6 + 14 + 18 + 10) = 48

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Answer: Yes

Step-by-step explanation:

To determine if Mindy's estimate is reasonable, we need to consider the context of the movie theater and the audience it serves. Generally, movie theaters offer tickets to various categories of customers, such as adults, children, and seniors. Seniors usually receive discounted tickets to encourage their attendance.

Mindy estimates that out of 400 tickets sold on a Friday evening, about 100 of them will be senior tickets. This means that she is estimating that 25% of the tickets sold are senior tickets (100 senior tickets / 400 total tickets = 0.25 or 25%).

While it's difficult to know the exact proportions of ticket categories sold without more information, a 25% estimate for senior tickets may be reasonable if the movie theater attracts a diverse audience and offers films or events that appeal to seniors. The actual proportion of senior tickets might vary depending on the location of the theater, the movies being shown, and the demographics of the surrounding community.

It would be helpful to gather more data on the actual distribution of ticket sales across different categories or to compare Mindy's estimate with industry averages to determine if her estimate is reasonable.

a) The maximum error in the calculated area of the disk =  23.87 cm²

b) The relative error is: 0.0211 and the percentage error is 2.11%

Let us assume that r represents the radius of the circular disk and A represents the area.

Here, the radius of a circular disk is given as 19 cm

So, r = 19 cm

and the radius has a maximum error in measurement of 0.2 cm.

So, dr = 0.2

The area of the circular disk would be,

A = πr²            ..........(1)

A = π × 19²

A = 361π cm²

Differentiating equation (1) with respect to r,

dA = 2πr × dr

dA = 2 × π × 19 × 0.2

dA = 7.6π

dA = 23.87 cm²

So, the maximum error in the calculated area is: 23.87 cm²

Now we find the relative error.

R = dA/A

R = 7.6π / 361π

R = 0.0211

And the percentage error would be:

P = relative error × 100

P = 0.0211 × 100

P = 2.11%

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Answer:

.............

Step-by-step explanation:

.............

The constant percent rate of change in the exponential function [tex]f(x) = 2(3)^x[/tex] is 200%, indicating a doubling of the output value for each unit increase in the input value.

The equation [tex]f(x) = 2(3)^x[/tex] represents an exponential function. Exponential functions have a constant percent rate of change, which means that the percent change between any two points on the graph of the function is the same.

In this case, we can find the percent rate of change by calculating the ratio of the output values for any two input values that differ by 1. For example, if we compare the output value when x=1 to the output value when x=0, we get:

[tex]f(1) = 2(3)^1 = 6[/tex]

[tex]f(0) = 2(3)^0 = 2[/tex]

The percent change from x=0 to x=1 is:

percent change = (f(1) - f(0)) / f(0) x 100%

= (6 - 2) / 2 x 100%

= 200%

This means that the output value increased by 200% when the input value increased by 1. We can also express this as a constant percent rate of change by dividing the percent change by the change in input value:

constant percent rate of change = percent change / change in input value

= 200% / 1

= 200%

Therefore, the equation [tex]f(x) = 2(3)^x[/tex] has a constant percent rate of change of 200%.

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Owen will have $116.60 in one year. The same principal amount is used for the calculation every period, and the interest earned each period will be the same.

Principal amount is the total amount of money borrowed or invested, excluding any interest, fees or other charges.

This can be calculated using the formula for simple interest, where

I = P x R x T, where P is the principal (the initial investment), R is the interest rate expressed as a decimal, and T is the time.

In this case, the principal (P)= $110,

the interest rate (R) = 0.056,

and the time (T)= 1 year.

Therefore, I = 110 x 0.056 x 1

= 6.16.

When this is added to the original principal of $110, we get $116.16.

This is happening because simple interest is calculated on the principal amount only.

It is not compounded, so the interest is not added to the principal and then used to calculate the interest in the next period.

Therefore, the same principal amount is used for the calculation every period, and the interest earned each period will be the same.

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Answer:

11.16

Step-by-step explanation:

there are two methods

100%+5.6%=

105.6

%

105.6%

Whole balance before interest = 100%, then add on interest

105.6% of the current balance means

105.6

100

of it.

105.6% of the current balance means  

100

105.6

​

 of it.

"Percent" literally means "out of 100."

105.6

100

=

100

105.6

​

=

1.056

1.056

To find 105.6% of the current balance, multiply by  1.056:

To find 105.6% of the current balance, multiply by 1.056:

$110

×

1.056 = $110 × 1.056 =

$116.16

$116.16

method 2

Find the interest, 5.6% of $110:

Find the interest, 5.6% of $110:

5.6

100

=

100

5.6

​

=

0.056

0.056

$

110

×

0.056

=

$110×0.056=

$

6.16

$6.16

Add the interest to the current balance:

Add the interest to the current balance:

$

110

+

$

6.16

=

$110+$6.16=

$

116.16

$116.16

​

​

The score obtained by Lara is less than the score obtained by Pei, which can be modeled by this inequality 30,065 < 30,408.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided about the scores (points) scored by Lara and Pei after playing the same game;

Lara = thirty thousand sixty five points = 30,065 points.

Pei = thirty thousand four hundred eight points = 30,408 points.

In conclusion, we can logically deduce that 30,408 points is greater than 30,065 points or 30,065 points is less than 30,408 points.

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Answer:

a. vertical angles

b. supplementary angles

c. complementary angles

The answer is , (a)  the length of AD is approximately 7.62 meters. (b) the size of angle DCB is approximately 59.04° degrees. 3. the angle of depression of the pedestrian from the man is approximately 38° degrees.

The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle (a triangle with one angle measuring 90 degrees), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. (a) To calculate the length of AD, we can use the Pythagorean theorem,

In triangle ABD, we have:

AB² + BD² = AD²

Substituting the given values, we get:

7² + 3² = AD²

49 + 9 = AD²

58 = AD²

Taking the square root of both sides, we get:

AD ≈ 7.62 m

Therefore, the length of AD is approximately 7.62 meters.

(b) To calculate the size of angle DCB, we can use the trigonometric function tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In triangle DBC, we have:

tan(DCB) = opposite/adjacent = BC/BD = 5/3

Using a calculator, we can find the inverse tangent of 5/3, which gives us:

DCB ≈ 59.04°

Therefore, the size of angle DCB is approximately 59.04° degrees.

3. Let's call the height of the building "h" and the angle of depression "θ".

From the man's point of view, we can draw a right triangle with the hypotenuse being the line of sight from the man to the pedestrian, and the opposite side being the height of the building "h". The adjacent side is the distance from the man to the pedestrian, which is 48 meters.

Similarly, we can draw another right triangle from the pedestrian's point of view, with the hypotenuse being the line of sight from the pedestrian to the top of the building, and the opposite side being the distance from the pedestrian to the foot of the building, which is 34.5 meters.

Now, we can use trigonometry to solve for the angle of depression "θ". We have:

tan(θ) = opposite/adjacent = h/48

tan(θ) = adjacent/opposite = 34.5/h

Solving for "h" in the second equation, we get:

h = 34.5/tan(θ)

Substituting this value of "h" in the first equation, we get:

tan(θ) = h/48 = 34.5/(48*tan(θ))

Simplifying this equation, we get:

tan²(θ) = 34.5/48

Taking the square root of both sides, we get:

tan(θ) = √(34.5/48) = 0.7975

Now, we can find the angle of depression "θ" by taking the inverse tangent (arctan) of this value:

θ = arctan(0.7975) = 38.3 degrees (rounded to the nearest degree)

Therefore, the angle of depression of the pedestrian from the man is approximately 38 degrees.

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The solution set for the stated system of linear inequalities;

y ≥ -2x + 4 and y ≥ x - 2  is the dark area below represents the intersection of a two solutions ranging upto +∞.

The collection of all solutions makes up the solution set for an inequality. Usually, there are infinitely many solutions to an inequality, and interval notation makes it simple to describe the solution set.

The group of values that fulfil a certain inequality is known as a solution set. This indicates that every single value with in solution set will fulfil the inequality, and not one other value will do so.

By utilising the equations to locate certain locations and drawing a line to reflect the point in two dimensions, you can draw the lines produced by the two equations.

y ≥ -2x + 4 and y ≥ x - 2

The coloured area thus provides the answer to this problem.

Putting together the two solutions, the intersection of both solutions, as seen in the dark zone below, reveals the answer to the system of inequality,  ranging upto +∞.

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The solutions to the quadratic equation 4x2 = 64 are:  x= -4 and x = 4 therefore, Option (C) is correct.

The Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph).

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation) Just plug in the values of a, b and c, and do

the calculations.

Given,

4x2 = 64

We need to solve the quadratic equation.

To solve this quadratic equation,We can rewrite the equation as:

4x2 - 64 = 0

Dividing both sides by 4x2 - 16 = 0x2 = 16

Taking square root on both sides,x = ±4

Hence,The solutions to the quadratic equation 4x2 = 64 are:

x= -4 and x = 4Option (C) is correct.

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Therefore, the principal is $654.50 when rate of interest is 10% and time period is 16 months.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics.

Here,

The Interest Formula is:

I = P * R * T

where I is the interest earned, P is the principal (initial amount of money), R is the interest rate, and T is the time period.

We can rearrange the formula to solve for P:

P = I / (R * T)

Substituting the given values, we have:

P = 1047.20 / (0.10 * 16)

= $654.50

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The volume of metal that we have in the hollow bar is 180 cubic inches.

For a prism of length L, width W, and height H, the volume is:

V = L*H*W

Here we need to take the volume of the larger prism, and subtract the volume of the hole, then the volume of metal that we have is:

Volume = 5in*6in*10in - 3in*4in*10in

Volume = 300in³ - 120in³

Volume = 180 in³

The bar has 180 cubic inches of metal.

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Step-by-step explanation:

1) area= 2.4^2×3.14=18.0864

rounded=18ft^2

circumference= 4.8×3.14=15.072

rounded= 15ft

2) area= 6^2×3.14=113.04

rounded= 110ft^2

circumference= 12×3.14=37.68

rounded= 38ft

3) area= 32^2×3.14=3215.36

rounded=3220ft^2

circumference= 64×3.14=200.96

rounded=200ft

The probability of a birth occurring before 245 days, which is the probability of a newborn baby being premature.

To do this, we need to calculate the area under the normal distribution curve that represents the probability of a birth occurring before 245 days.

We can use a standard normal distribution table or an appropriate applet to find this probability. Using the applet, we can enter the mean, standard deviation, and the value of 245 days to find the probability.

In mathematical terms, we can write this as:

P(birth before 245 days) = probability of a randomly selected newborn baby being premature

= P(X < 245), where X is the random variable representing pregnancy length

Using the normal distribution table or applet, we can find P(X < 245) by calculating the area under the normal distribution curve to the left of 245 days.

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Answer:    scalene triangle

Step-by-step explanation:

can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.

Answer:

scalene triangle is the triangle

the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²). To find the derivative of y = sec⁻¹(1/x), we will use the chain rule of differentiation. Let's start by using the definition of the inverse secant function:

sec⁻¹(θ) = cos⁻¹(1/θ)

Then we can rewrite the given function as:

y = cos⁻¹(x)

Using the chain rule, the derivative of y with respect to x is:

dy/dx = d/dx [cos⁻¹(x)]

= -1/√(1 - x²) * d/dx [x]

= -1/√(1 - x²)

Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

We can check this result by taking the derivative of y using the definition of the inverse secant function:

y = sec⁻¹(1/x)

sec(y) = 1/x

cos(y) = x

-sin(y) dy/dx = 1

dy/dx = -1/sin(y)

Using the Pythagorean identity sin²(y) + cos²(y) = 1, we can solve for sin(y) as:

sin(y) = √(1 - cos²(y)) = √(1 - x²)

Substituting this expression into the derivative, we get:

dy/dx = -1/√(1 - x²)

which is the same result we obtained using the chain rule. Therefore, we have confirmed that the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

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Using division, we can find that he must sell 2123 pairs to get a profit of $69840.

One of the four fundamental operations in mathematics is division, along with addition, subtraction, and multiplication. The splitting of a large group into smaller groups so that each group contains an equal number of items is a straightforward definition of division. It is a mathematical process used for equitable grouping and distribution.

Here,

Profit by selling one pair of shoes = $80.

Now, expenses = $100,000

Total profit he wants = $69,840.

So, total revenue to be generated = 100000 + 69840

= $169840.

Let x be the total pairs sold.

So, x = 169840/80

= 2123.

Therefore, he must sell 2123 pairs to get a profit of $69840.

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The graph of each function from a to d are attached below

Graphs of nonlinear functions are graphs of functions that do not have a constant rate of change or a linear relationship between the input and output values. Nonlinear functions include quadratic, exponential, logarithmic, trigonometric, and many other types of functions.

The shape of the graph of a nonlinear function can vary greatly depending on the specific type of function. For example:

The graph of a quadratic function (y = ax^2 + bx + c) is a parabola, which is a symmetric U-shaped curve.

The graph of an exponential function (y = a^x) is a curve that increases or decreases rapidly, depending on whether the base a is greater than or less than 1.

The graph of a logarithmic function (y = log_a(x)) is a curve that approaches a vertical asymptote as x approaches zero.

The graph of a trigonometric function (y = sin(x) or y = cos(x)) is a periodic wave that oscillates between a maximum and minimum value.

Nonlinear functions can exhibit complex and interesting behaviors, such as multiple intercepts, asymptotes, and singularities. The graphs of these functions can be used to model a wide range of real-world phenomena, such as population growth, radioactive decay, and the motion of objects under the influence of gravity.

The graphs of the functions given are attached below

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Step-by-step explanation:

(a) The slope of the equation y = 9x + 15 is 9, and the y-intercept is 15.

(b) The rate of change or slope of the equation y = 9x + 15 is 9, which represents the constant rate at which the workers are picking oranges. For every hour of work, they pick 9 more oranges. The initial amount or y-intercept of 15 represents the number of oranges they would have picked if they had started working from the beginning of time. However, since this is not possible, it can be interpreted as the number of oranges they picked before starting to work for the period of time that is being measured.

The equation for the number of baskets is an illustration of a linear function.

The function is given as:

[tex]\bold{y=9x+15}[/tex]

(a) The slope and the y-intercept

A linear function is represented as:

[tex]\bold{y=mx+b}[/tex]

Where:

m represents the slope, and b represents the y-intercept

By comparison, the slope is 9, and the y-intercept is 15

(b) The rate of change and the initial amount

The rate of change is the slope, and the initial amount is the y-intercept

By comparison, the rate of change is 9, and the is 15

The solution to the given inequality expression is: x ≥ -8 and it is shown on the number line attached

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle. An open circle shows it does not include the value. A closed circle shows it does include the value.

We are given the inequality expression as:

8x - 4 ≥ -68

Add 4 to both sides to get:

8x ≥ -64

Divide both sides by 8 to get:

x ≥ -8

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