Baird Airlines is a small airline that occasionally carries overload shipments for the overnight delivery company Never-Fail, Inc. Never-Fail is a multimillion-dollar company started by Wes Never immediately after he failed to finish his first accounting course. The company’s motto is “We Never-Fail to Deliver Your Package on Time.” When Never-Fail has more freight than it can deliver, it pays Baird to carry the excess. Baird contracts with independent pilots to fly its planes on a per-trip basis. Baird recently purchased an airplane that cost the company $4,940,000. The plane has an estimated useful life of 24,700,000 miles and a zero salvage value. During the first week in January, Baird flew two trips. The first trip was a round trip flight from Chicago to San Francisco, for which Baird paid $300 for the pilot and $250 for fuel. The second flight was a round trip from Chicago to New York. For this trip, it paid $250 for the pilot and $125 for fuel. The round trip between Chicago and San Francisco is approximately 4,900 miles and the round trip between Chicago and New York is 2,000 miles. Required Select if the costs mentioned below are direct or indirect. Determine the total cost of each trip.

Answer:

142 square meters

Step-by-step explanation:

To find the Surface Area of a Cylinder you have to use the formula [tex]A= 2\pi rh+2\pi r^2[/tex]

Plug in the radius, height, and pi to get

[tex]A=(2*3.14*2.6*6.1)+(2*3.14*2.6^2)\\A= (99.6008)+(42.4528)\\A= 142.0536\\[/tex]

You can round the answer to 142

The root of this given equation is 2, -3.

What is a quadratic equation?

Any equation that can be written in standard form as where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.

Here, we have

Given:  x³ - x² - 8x + 12 = 0

We have to solve this equation and find the roots.

x³ - x² - 8x + 12 = 0

= (x-2)(x²+ x - 6) = 0

= (x-2)(x² + 3x - 2x - 6)

= (x-2)(x(x+3)-2(x+3))

= (x-2)(x+3)(x-2) = 0

x = 2, -3

Hence, the root of this given equation is 2, -3.

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After solving  [tex]x^3 - x^2 - 8x + 12 = 0[/tex] we get x = 1,  x = √8, and x = -√8.

The equation[tex]x^3 - x^2 - 8x + 12 = 0.[/tex]

Identify the given equation.

The given equation is [tex]x^3 - x^2 - 8x + 12 = 0.[/tex]

Look for possible factorization.

In this case, we can factor the equation by grouping:

[tex]x^3 - x^2 - 8x + 12 = (x^3 - x^2) + (-8x + 12)[/tex]

Factor out the common terms in each group.

[tex]x^3 - x^2 - 8x + 12 = x^2(x - 1) - 8(x - 1)[/tex]

Factor out the common binomial.

[tex]x^3 - x^2 - 8x + 12 = (x^2 - 8)(x - 1)[/tex]

Solve the factors for x.

Set each factor to zero and solve for x:

[tex]x^2 - 8 = 0[/tex] and x - 1 = 0

[tex]x^2 = 8[/tex], x = 1

x = ±√8

The solutions to the equation [tex]x^3 - x^2 - 8x + 12 = 0[/tex] are x = 1, x = √8, and x = -√8.

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The statement "S′H′ is parallel to S′Q′" is true.

To find the image of the square after reflection across the x-axis, we need to flip each point of the square over the x-axis. The coordinates of the reflected points will have the same x-coordinate, but the y-coordinate will have the opposite sign.

The coordinates of the original square are:

S(−3,0)

H(2,0)

A(2,5)

Q(−3,5)

The coordinates of the reflected square are:

S′(−3,0)

H′(2,0)

A′(2,−5)

Q′(−3,−5)

Now, we can find the slopes of the sides of the reflected square to determine which sides are parallel.

S′H′¯¯¯¯¯¯¯¯¯¯¯: The slope of S′H′¯¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.

S′Q′¯¯¯¯¯¯¯¯¯¯: The slope of S′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, S′Q′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.

H′A′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′A′¯¯¯¯¯¯¯¯¯¯¯ is undefined, since the two points have the same x-coordinate. Therefore, H′A′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.

H′S′¯¯¯¯¯¯¯¯¯¯¯: The slope of H′S′¯¯¯¯¯¯¯¯¯¯¯ is also undefined, since the two points have the same x-coordinate. Therefore, H′S′¯¯¯¯¯¯¯¯¯¯¯ is parallel to the y-axis.

A′Q′¯¯¯¯¯¯¯¯¯¯: The slope of A′Q′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, A′Q′¯¯¯¯¯¯¯¯¯¯ is parallel to the x-axis.

Q′S′¯¯¯¯¯¯¯¯¯¯: The slope of Q′S′¯¯¯¯¯¯¯¯¯¯ is 0, since both points have the same y-coordinate. Therefore, Q′S′¯¯¯¯¯¯¯¯¯¯ is also parallel to the x-axis.

Based on these calculations, we can see that S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯ (both are parallel to the x-axis). Therefore, the statement "S′H′¯¯¯¯¯¯¯¯¯¯¯ is parallel to S′Q′¯¯¯¯¯¯¯¯¯¯" is true.

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Answer:$386,711.70

Step-by-step explanation:

To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value

PMT = payment per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

First, we need to find the number of compounding periods and the interest rate per quarter:

n = 4 (quarterly compounding)

r = 0.12 / 4 = 0.03 (3% quarterly interest rate)

Next, we can plug in the values:

PMT = $500

n = 4

r = 0.03

t = 30

FV = $500 x [(1 + 0.03/4)^(4*30) - 1] / (0.03/4)

FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075

FV = $500 x [6.3207 - 1] / 0.0075

FV = $500 x 773.4234

FV = $386,711.70

Therefore, if you save $500 quarterly into an account that pays 12% compounded quarterly from your 21st to your 51st birthday, you will have approximately $386,711.70 in the account.

If Fran and Jill made a new years resolution to ride bikes.  it will take 3 weeks for Fran and Jill to have ridden the same number of miles..

Let's assume that it takes "x" number of weeks for Fran and Jill to ride the same number of miles.

In the first week, Fran rides 40 miles, and Jill rides 70 miles.

In the "x"th week, Fran will have ridden a total of 40 + 55x miles.

In the "x"th week, Jill will have ridden a total of 70 + 45x miles.

For Fran and Jill to ride the same number of miles in "x" weeks, we need to solve the following equation:

40 + 55x = 70 + 45x

Simplifying this equation, we get:

10x = 30

x = 3

Therefore, it will take 3 weeks for Fran and Jill to have ridden the same number of miles.

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The possible values of a and the corresponding values of b are; a= -3, 2 and b= -18, 12.

Expanding the left-hand side of the equation:

(a + 3√5)² + a - b√5 = a² + 6a√5 + 45 + a - b√5

Combining like terms:

2a² + (2a - b)√5 + 45 = 51

Simplifying further:

2a² + (2a - b)√5 = 6

Now, since √5 is irrational, the only way the left-hand side can equal 6 is if both the rational and irrational parts are equal to 0. Therefore two equations:

2a² + 2a - b = 0 (Equation 1)

2a - b = 0 (Equation 2)

Solving Equation 2 for b:

b = 2a

Substituting this into Equation 1:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, a = 0 does not satisfy the original equation, since the left-hand side would be 45, which is not equal to 51. Therefore, we can divide both sides of Equation 1 by 2a to get:

a + 1 - b/2a = 0

Multiplying both sides by 2a:

2a² + 2a - b = 0

Substituting b = 2a:

2a² + 2a - 2a = 0

Simplifying:

2a² = 0

Thus, a = 0 is a solution. However, as noted above, a = 0 does not satisfy the original equation. Therefore, we must consider the case where a ≠ 0. Dividing both sides of Equation 2 by 2:

a - b/2 = 0

Solving for b:

b = 2a

Substituting into the original equation:

(a + 3√5)² + a - 2a√5 = 51

Expanding:

a² + 6a√5 + 45 + a - 2a√5 = 51

Combining like terms:

a² + 7a√5 - 6 = 0

Using the quadratic formula:

a = (-7√5 ± √(7²√5² - 4(1)(-6))) / 2(1)

Simplifying:

a = (-7√5 ± 13) / 2

Therefore, the possible values of a are -3 and 2. For each value of a, we can use b = 2a to find the corresponding value of b. Thus, the possible values of b are -18 and 12.

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The difference between the means of the two data sets is 4.

Statistical measures are used to describe, analyze, and interpret data. There are several measures that are commonly used in statistics, such as mean, median, mode, standard deviation, etc.

The mean, also known as the average, is the sum of all the values in a dataset divided by the total number of values. It represents the central tendency of the data.

The difference between the means of the two data sets is:

difference between the means = (Class 2 mean) - (Class 1 mean)

difference between the means = 24 - 20 = 4

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First, 90 + 90 = 180

Second, 320 - 180 = 140

Third, 140 / 2 = 70.

|                                90 * 70 = 6,300
|
|
| 90
|
|____________

         70

The slope of BC is 1/2, since the slope of AD is 1/2. This is because the rise and run of the two bases are the same.

The slope of a line is defined as the ratio of the vertical change (the rise) to the horizontal change (the run).

In the case of an isosceles trapezoid, the two bases (AD and BC) are parallel and of equal length. Therefore, the slope of the two bases is the same.

Given that the slope of AD is 1/2, the slope of BC is also 1/2.

This is because the rise and run of the two bases are the same. Therefore, the ratio of rise to run is the same and the slope of both bases is 1/2.

To understand this better, let us consider the rise and run of the two bases:

AD: Rise = y² − y1, Run = x² − x1

BC: Rise = y² − y1, Run = x² − x1

Therefore,

Slope of AD = (y² − y1)/(x² − x1)

Slope of BC = (y² − y1)/(x² − x1)

Since the rise and run of the two bases are the same, the slope of the two bases is also the same.

Therefore, the slope of BC is 1/2, since the slope of AD is 1/2.

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After simplifying the given expression we can write answer using positive exponent [tex]7^3 * 6^30[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, variables, and symbols that are grouped together to represent a mathematical relationship or quantity. It can be a single term, or a combination of terms separated by mathematical operations such as addition, subtraction, multiplication, and division.

When we raise a power to another power, we need to multiply the exponents. So we can simplify the expression as follows:

[tex]7^3(6^6)^5 = 7^3 * 6^(6*5) = 7^3 * 6^30[/tex]

so we write the answer using positive exponents as:

[tex]7^3 * 6^30[/tex]

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Step-by-step explanation:

The probability of Meikel wearing khakis and sandals is

3 ÷ 12 which will give us

1/4

Step-by-step explanation:

You need the line in y = mx + b form:

y = -12x + 765        where x = minutes     y = height in feet

a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet or 1.5 miles. b)  1000 feet or 1 mile. c)  2000 feet or 2 miles. d) 2500 feet or 2.5 miles.

Distance is the measurement of how far apart two points are on a surface.

a) The distance from the Bumper Cars to the Ferris Wheel is 3 squares or 1500 feet. To calculate this, we can count the number of squares (3) from the Bumper Cars to the Ferris Wheel. Each square represents 500 feet, so the total distance is 1500 feet or 1.5 miles.

b) The distance from the Water Slide to the Rollercoaster is 2 squares or 1000 feet.

To calculate this, we can count the number of squares (2) from the Water Slide to the Rollercoaster. Each square represents 500 feet, so the total distance is 1000 feet or 1 mile.

c) The distance from the Bumper Cars to the Restrooms is 4 squares or 2000 feet.

To calculate this, we can count the number of squares (4) from the Bumper Cars to the Restrooms. Each square represents 500 feet, so the total distance is 2000 feet or 2 miles.

d) The direct distance from the Water Slide to the Ferris Wheel is 5 squares or 2500 feet.

To calculate this, we can count the number of squares (5) in a straight line from the Water Slide to the Ferris Wheel. Each square represents 500 feet, so the total distance is 2500 feet or 2.5 miles.

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Answer: The answer is C.

Step-by-step explanation:

The equation that could represent a rational function is answer C.

I hope this helped! A brainilist would be amazing! <3

Using Bayes theorem, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0.059 or 5.9%.

We can solve this problem using Bayes' theorem. Let A be the event that the person received a speeding ticket, and Bi be the event that the radar trap was set at location Li, for i = 1, 2, 3, or 4. Then we want to find the conditional probability of B22 given A, which is:

[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)[/tex]

We can compute each of the probabilities on the right-hand side using the given information.

First, we have:

[tex]P(B_1) = 0.4, P(B_2) = 0.2, P(B_3) = 0.3, P(B_4) = 0.4[/tex]

Next, we have:

[tex]P(A | B_1) = 0.3, P(A | B_2) = 0.1, P(A | B_3) = 0.4, P(A | B_4) = 0.2[/tex]

Finally, we have:

[tex]P(A) = P(A | B_1) * P(B_1) + P(A | B_2) * P(B_2) + P(A | B_3) * P(B_3) + P(A | B_4) * P(B_4)\\= (0.3 * 0.4) + (0.1 * 0.2) + (0.4 * 0.3) + (0.2 * 0.4)\\= 0.34[/tex]

Plugging these values into Bayes' theorem, we get:

[tex]P(B_2 | A) = P(A | B_2) * P(B_2) / P(A)\\= (0.1 * 0.2) / 0.34\\= 0.059\\[/tex]

Therefore, the probability that the person passed through the radar trap located at L2 given that she received a speeding ticket is 0..059 or 5.9%.

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Answer: 33.34

Step-by-step explanation: first we have to cut this shape up like you would a pizza

2 triangles and 1 rectangle, we know that the rectangle is 10 by 3 cm, but we don't have all the measurements for the triangle.

Find the last side using this equation:
3.2 squared = 10.24
3 squared = 9
subtract
1.24
square root of 1.24 = 1.11

Area of rectangle:
10 x 3 = 30
Area of triangle:
1.11 x 3 ≈ 1.67

Final Area:
30 + 1.67x2 = 33.34

The number of ounces in solution A= 16, and the number of ounces in the solution B = 104

let x be the number of ounces of solution A

let y be the number of ounces of solution B

x+y=120

Substitute the value of y,

y=120-x

Solution A is 70% salt and B is 95% salt,

then

0.7x+.95y=.75(120)

0.7x+.95y=90

multiply both sides of the equation by 100 to remove the decimal points,

70x+95y=900

70x+95(120-x)=900

70x+1140-95x=900

-15x=900-1140

15x=240

x=16

and y=120-16

y=104

The number of ounces in solution A= 16

and the number of ounces in solution B = 104

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Answer:

The number of times the tire will have to turn in travelling the length of the street is 30.9 times.

To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.  

Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 1.7m and π = 3.14

∴ C = 3.14 × 1.7

C = 5.338 m

Therefore, the circumference of the tire is 5.338 m

Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 165 m ÷ 5.338 m

Number of times the tire will have to turn = 30.91045 times

Number of times the tire will have to turn ≅ 30.9 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 30.9 times

The length segment of the circle indicated is 6 units.

A circle is a round-shaped figure that has no corners or edges. Therefore, let's find the length segment of the circle.

Therefore, the diameter of a circle is the line that passes through the centre and meets the circumference at opposite ends.

Therefore, the radius of a circle is the distance from the centre of the circle to any point on it's circumference.

The radius is half of a diameter.

Therefore, the length x is the radius of the circle and it is 6 units.

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The maximum number of homes that can be placed on the street is 11.

first we need to divide the total length of the street by the width of each home.

The length of the street is 345 feet and the width of each home is 30 feet. Therefore, the number of homes that can be placed on the street is:

345 feet / 30 feet per home = 11.5 homes

Since we cannot have a fraction of a home, we need to round down to the nearest whole number.

Therefore, the maximum number of homes that can be placed on the street is 11.

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Answer:

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

Angle with the measure of 130° forms a vertical angle pair with the sum of x and 107° angle.

Since vertical angles are congruent we have:

The two angles, x and 2x together form a right angle, since they form a linear pair with another angle, marked as right angle. Therefore, x and 2x are complementary angles:

The probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.

(To find the probability that exactly 250 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.

Then, we can standardize the value of 250 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.

z = (250 - 225) / 10.42 ≈ 2.4

Using a standard normal table or calculator, we find that the probability of z being less than or equal to 2.4 is approximately 0.9918.

Therefore, the probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.

(b) To find the probability that no more than 220 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.

Then, we can standardize the value of 220 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.

z = (220 - 225) / 10.42 ≈ -0.48

Using a standard normal table or calculator, we find that the probability of z being less than or equal to -0.48 is approximately 0.3146.

Therefore, the probability that no more than 220 of those surveyed feel the state of morals is poor is approximately 0.3146.

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Yes, 5:10 and 15:30 are equivalent ratios because they simplify to the same ratio of 1:2.

Ratios represent the relationship between two or more quantities or values. When two ratios have the same simplified form, they are considered equivalent because they represent the same relationship between the quantities being compared.

In the given example, the ratios 5:10 and 15:30 can be simplified to the same ratio of 1:2. This means that both ratios represent the same relationship between the quantities being compared. Specifically, both ratios represent a comparison between two quantities where the second quantity is twice as large as the first quantity.

To simplify a ratio, we divide both the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both the numerator and denominator. In this case, the GCF of 5 and 10 is 5, and the GCF of 15 and 30 is 15. Dividing both ratios by their respective GCFs results in a simplified ratio of 1:2 for both ratios.

Therefore, 5:10 and 15:30 are equivalent ratios because they represent the same relationship between quantities, and have the same simplified form.

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Amount Due at Maturity a. $102,000, b. $30,100, c. $62,620, d. $42,930, e. $40,700.

Interest is the cost of borrowing money, typically expressed as a percentage of the borrowed amount, called the principal. It is the amount charged by a lender to a borrower for the use of money over a certain period of time. Interest can also refer to the amount earned on money that is invested, such as in a savings account or a bond. The rate of interest depends on factors such as the level of risk associated with the loan, the length of the loan period, and the market rate of interest at the time of borrowing. The amount of interest paid or earned can be calculated using various formulas, including simple interest and compound interest.

To determine the due date and amount of interest due at maturity for each note, we can use the following formula:

Interest = Principal x Rate x Time

where Principal is the face amount of the note, Rate is the annual interest rate, and Time is the time in years (based on a 360-day year).

a. January 5, $100,000, 6%, 120 days

Due Date: May 5

Time: 120/360 = 1/3 year

Interest = $100,000 x 0.06 x 1/3 = $2,000

Amount Due at Maturity = Principal + Interest = $100,000 + $2,000 = $102,000

b. February 15, $30,000, 4%, 30 days

Due Date: March 17 (assuming non-leap year)

Time: 30/360 = 1/12 year

Interest = $30,000 x 0.04 x 1/12 = $100

Amount Due at Maturity = Principal + Interest = $30,000 + $100 = $30,100

c. May 19, $62,000, 8%, 45 days

Due Date: July 3

Time: 45/360 = 1/8 year

Interest = $62,000 x 0.08 x 1/8 = $620

Amount Due at Maturity = Principal + Interest = $62,000 + $620 = $62,620

d. August 20, $42,400, 5%, 90 days

Due Date: November 18

Time: 90/360 = 1/4 year

Interest = $42,400 x 0.05 x 1/4 = $530

Amount Due at Maturity = Principal + Interest = $42,400 + $530 = $42,930

e. October 19, $40,000, 7%, 90 days

Due Date: January 17

Time: 90/360 = 1/4 year

Interest = $40,000 x 0.07 x 1/4 = $700

Amount Due at Maturity = Principal + Interest = $40,000 + $700 = $40,700

Therefore, the due date and amount of interest due at maturity for each note are as follows:

a. Due Date: May 5, Interest: $2,000, Amount Due: $102,000

b. Due Date: March 17, Interest: $100, Amount Due: $30,100

c. Due Date: July 3, Interest: $620, Amount Due: $62,620

d. Due Date: November 18, Interest: $530, Amount Due: $42,930

e. Due Date: January 17, Interest: $700, Amount Due: $40,700

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After answering the prοvided questiοn, we can cοnclude that As a result, the sοlutiοn tο the inequality is p greater than 32.

In mathematics, an inequality is a nοn-equal relatiοnship between twο expressiοns οr values. As a result, imbalance leads tο inequality. In mathematics, an inequality cοnnects twο values that are nοt equal. Inequality is nοt the same as equality. When twο values are nοt equal, the nοt equal sign is cοmmοnly used ().

Different inequalities, nο matter hοw small οr large, are used tο cοntrast values. Many simple inequalities can be sοlved by mοdifying the twο sides until οnly the variables remain. Hοwever, a number οf factοrs cοntribute tο inequality: Negative values are divided οr added οn bοth sides. Exchange left and right.

We must isοlate the variable p οn οne side οf the inequality sign in οrder tο sοlve it.

-16 negative οne-half p

When bοth sides οf the inequality are multiplied by -2 (and the inequality sign is reversed because we are multiplying by a negative number), we get:

p > 32

As a result, the sοlutiοn tο the inequality is p greater than 32.

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Total area of garden after adding rectangular piece will be 55 ft² i.e. B.

What exactly is a rectangle?

A rectangle is a two-dimensional geometric shape that is characterized by having four sides and four right angles. Opposite sides of a rectangle are parallel and equal in length, while opposite angles are equal. The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is the sum of the lengths of all its sides. Rectangles are commonly used in many fields, such as architecture, engineering, and mathematics.

Now,

The rectangle has a length of |-21 - (-23)| = 2 and a width of |7 - 12| = 5. Therefore, the area of the new rectangular piece is 2 x 5 = 10 square feet.

Adding this to the area of the existing garden gives a total area of 45 + 10 = 55 square feet.

Therefore, the answer is (B) 55 ft².

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Answer:

7:22

Step-by-step explanation:

Given: 2 hours and 22 minutes

5:00 + 2 hours

5 + 2 = 7

7:00 + 22 minutes

7:22

21. The trainer raised the end of the treadmill from the floor by 0.62 ft or 7.4 in.

22. The ramp needs to be 1.19 ft tall at the highest point.

23. The springboard is 6.21 in long.

Trigonometric ratio is the ratio of two sides of a right triangle to each other, or the ratio of the sine, cosine, or tangent of an angle in a right triangle.

21: Incline = 7°

Length of walking surface = 5 ft

We need to calculate the change in height of the treadmill.

Let x be the height of the end of the treadmill from the floor.

We can use the trigonometric ratio, tangent (tan), to solve the problem.

tan(7°) = Opposite/Adjacent

=> x/5 = tan(7°)

=> x = 5tan(7°)

=> x = 5×0.124

=> x = 0.62 ft

22: Angle = 20°

Length of board = 3.5 ft

We need to calculate the height of the ramp at the highest point.

Let y be the height of the ramp at the highest point.

We can use the trigonometric ratio, sine (sin), to solve the problem.

sin(20°) = Opposite/Hypotenuse

=> y/3.5 = sin(20°)

=> y = 3.5sin(20°)

=> y = 3.5×0.342

=> y = 1.19 ft

23: Angle = 14.5°

Length of springboard coils = 6 in

We need to calculate the length of the springboard.

Let z be the length of the springboard.

We can use the trigonometric ratio, cosine (cos), to solve the problem.

cos(14.5°) = Adjacent/Hypotenuse

=> 6/z = cos(14.5°)

=> z = 6/cos(14.5°)

=> z = 6/0.966

=> z = 6.21 in

For more questions related to trigonometric ratio

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