Find the exact values of each of the following trigonometric ratios using the given triangle.

cos A
cos B

sin A
sin B

tan A
tan B

What is the relationship between each of the values you found and why?

Answer:

a strong and almost perfect positive linear correlation.

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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9514 1404 393

Answer:

  x = 48

Step-by-step explanation:

It looks like your proportion is ...

  y = k√x

Then k can be found as ...

  k = y/√x = 25/√3

__

For y = 100, the value of x can be found from ...

  100 = (25/√3)√x

  4√3 = √x . . . . . . . . . . multiply by √3/25

  48 = x . . . . . . . . . . . . . square both sides

Proofreading refers to the checking for errors in a text before it is published or shared. It is the last stage of the writing process. One correct minor spelling and punctuation mistakes.

The following are the symbols in proofreading;

lc - lowercase a letter

bf - set in boldface

ital - set in italics

sp - spell out

cap - change from lowercase to uppercase/ capital letter

here, we have,

lc

so, we get,

Therefore, the correct answer is option C. Lowercase a letter.

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Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).

To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.

Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.

Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.

The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.

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Expressing In(422) as ln(422) without using fractions or exponents. Solving for r in an equation and obtaining r=1. Finding the difference quotient for f(x)=3x^2. Solving an equation with ln(x-3) to obtain x=3e+3.

Problem 1: To rewrite the expression In(422) without using fractions or exponents, we can express it as ln(422).

Problem 2: To solve for r, we need to rewrite the equation as V1+2=4-1 → r + 2 = 3 → r = 1.

Problem 3: For f(x) = 3x^2, the difference quotient is given by [(f(x + h) - f(x))/h]. Plugging in the function, we get [(3(x + h)^2 - 3x^2)/h].

Problem 4: Given ln(x - 3) = ln(4 - 1) + 1, we can rewrite it as ln(x - 3) = ln(3) + 1. To solve for x, we use the property ln(a) - ln(b) = ln(a/b). We get ln((x - 3)/3) = 1. Now, we can exponentiate both sides: (x - 3)/3 = e^1 → x - 3 = 3e → x = 3e + 3.

Problem 5: The inequality 2r + 1 - 15 > 0 can be simplified to 2r - 14 > 0. Divide by 2, we get r - 7 > 0 → r > 7. The solution in interval form is (7, ∞).

I hope this helps! If you have any more questions or need further clarification, feel free to ask.

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Answer:

A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept, according to Kennesaw State University. ... However, Newton's law doesn't explain what gravity is, or how it works.

Step-by-step explanation:

Answer:

law is federal

Step-by-step explanation:

ik

Answer:

3.92*10^3mm

Step-by-step explanation:

In the diagram it gives you 7900mm. There is a figure which was given underneath written 900mm. use 7900 to subtract 900 you will get 7000. Then you can use the Pythagoras theorem to solve it, with a= height, b=5800mm and c=7000mm where, a^2+b^2=c^2.

Answer:

3919 mm

Step-by-step explanation:

Length of hypotenuse = 7900 - 900 = 7000 mm

Base = 5800 mm

Let the height of the triangle be h mm

Therefore, by Pythagoras theorem:

\( h = \sqrt{7000^2 - 5800^2} \)

\( h = \sqrt{49000000- 33,640,000} \)

\( h = \sqrt{15,360,000} \)

\( h = 3,919.18359\: mm\)

\( h = 3,919\: mm\)

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Answer:

=−2p+4

Step-by-step explanation:

i hope this help

Answer:

Step-by-step explanation:

7p - 1 - 9p + 5

-2p + 4

Answer:

Option D

Step-by-step explanation:

Fractions are considered to be rational numbers because they are decimals that can be written as a fraction and since it's already wrote as a fraction but can be converted back to a decimal it is a rational number. The fraction is considered to be a real number because all rational numbers are real numbers and since we just proved that 5/8 is a rational number it is therefore a real number. Which means your answer is option D or "rational numbers, real numbers."

Hope this helps.

The supplied rectangle is a square, a unique variety of rectangles with equal lengths on all sides.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.

Because a square is a quadrilateral with all four angles at right angles, every square is also a rectangle.

To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.

So, plot the given coordinates as follows:

(Refer to the graph attached below)

Now, we can observe that it is a square which is a special type of rectangle with all sides equal.

Therefore, the supplied rectangle is a square, a unique variety of rectangles with equal lengths on all sides.

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Answer:

Triangle ABC is congruent to triangle DFE.

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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In order to calculate the new divisor for a 3-for-4 reverse stock split, we must first calculate the new share price for Able. Since 3/4 of the shares are being replaced with just 1/4 of the old shares, the new price for Able will be $111 (3 x $37 = $111).

The divisor is used to calculate the new index value by dividing the sum of the new share prices by the divisor. Therefore, the new divisor will be 1.33 ($111 + $312 + $94 = $517 / 1.33 = $389.28). This is because the new share prices will total $517 and when you divide that by the divisor, the index value will be $389.28.

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To find how long each station was originally supposed to last, we can set up an equation based on the given information.

Let's assume that each station was supposed to last for "x" minutes. Since there were 6 stations, the total time for the field day without the fire drill would be 6 times "x", which is 6x minutes.

However, due to the fire drill, they lost 30 minutes, so the total time available for the field day became 90 minutes.

We can set up the equation as follows:

6x - 30 = 90

To solve for "x", we can add 30 to both sides of the equation:

6x = 120

Finally, we can divide both sides by 6 to isolate "x":

x = 20

Therefore, each station was originally supposed to last for 20 minutes.

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The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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Answer:

C

Step-by-step explanation:

Triangle = 180

100+62.7+18=180.7

180.7 is not a triangle

Answer:

C     100.3, 62.7, 18

Step-by-step explanation:

Angles inside of a triangle add up to 180 degrees

Option A

25+85+70=180

Option B

11.6+91+77.4=180

Option C

100.3+62.7+18=181

Option D

60+60+60=180

Option C is the answer as it is the only option that does not add up to 180 degrees

The probability of selecting three packages that are satisfactory is 0.729.

we need to find the probability of selecting three packages that are satisfactory from the given satisfactory weight probability. P(satisfactory) = 90.0/100 = 0.9So, the probability of selecting the first satisfactory package is 0.9, for the second package is also 0.9, and for the third package is also 0.9.

∴ The probability of selecting three packages that are satisfactory P(3 satisfactory) = P(Satisfactory) × P(Satisfactory) × P(Satisfactory)P(3 satisfactory) = (0.9)³P(3 satisfactory) = 0.729.

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

2.50 or 2.5

Step-by-step explanation:

1/4=.25 so 25% of a number=5/8=0.625

So we multiply .625*4 to get the number. Since it's 25% and we want 100% to get it back to the original number

.625*4=2.50 or 2.5

Answer:

15

Step-by-step explanation:

5x3 = 15 It's Simple Hope it helps

Answer:

24 weeks

Explanation:

Let w represent the number of weeks Maribeth has been saving.

If she saves $25 per week and has saved a total of $600, we can find w as follows;

Answer:

12/13

Step-by-step explanation:

     \(\sf Cos \ x = \dfrac{adjacent \ side \ to \ \angle x}{hypotenuse}\\\\\)

              \(\sf = \dfrac{XY}{ZX}\\\\=\dfrac{36}{39}\\\\=\dfrac{36 \div3}{39 \div 3}\\\\=\dfrac{12}{13}\)

your anwer would be 12/13 love

Each party basket will have 73 pieces of candy

Felicia has 4.5 bags of candy for her party basket

Each bag has 146 pieces of candy

She has 9 party baskets, the number of candies in each party basket can be calculated by multiplying 4.5 by 146 and dividing the result by 9

4.5 × 146/9

= 657/9

= 73

Hence there are 73 pieces of candy in each basket

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Answer:

No

Step-by-step explanation:

Using a graph typing in 9x and looking at the table, (2,1) is not on the table, so (2,1) is not a solution to 9x

Answer:

No

Step-by-step explanation:

to determine if (2, 1 ) is a solution, substitute the x- coordinate into the equation and if the result is equal to the y- coordinate then it is a solution.

y = 9x ( substitute x = 2 )

y = 9 × 2 = 18 ≠ 1

then (2, 1 ) is not a solution to the equation.

Given:

The expression is

\(x+4x-3+3x^2-2x\)

To find:

The value of given expression when x=5.

Solution:

We have,

\(x+4x-3+3x^2-2x\)

Substituting x=5 in the above expression, we get

\(=(5)+4(5)-3+3(5)^2-2(5)\)

\(=5+20-3+3(25)-10\)

\(=5+20-3+75-10\)

On further simplification, we get

\(=(5+20+75)+(-3-10)\)

\(=100+(-13)\)

\(=100-13\)

\(=87\)

Therefore, values of the given expression at x=5 is 87.