a loading dock is 5 feet high. if a ramp makes an angle of 25 d with the ground and is attached to the loading dock, how long is the ramp?

Answers

Answer 1

The length of the ramp is 10.7 feet high.

What is ratio of triangle ?

 The definition of the tangent (tan) of the angle is the ratio of the opposing to the neighbouring in any right triangle. The tangent's value for the red triangle is given by: tan(c) = 1 / 2 =.5. We maintain the same angle c for the blue triangle, but we have doubled the sizes of the adjacent and opposite sides.

It always helps to draw a diagram and find the right triangle.  

In this case, the triangle has the loading dock as one leg, the ramp as the hypotenuse, and the distance of the ramp from the loading dock as the other leg.

Call that distance x.  Use the tangent of 25° to find x.

=> tan(25°) = [tex]\frac{opposite }{adjacent}[/tex]

=> tan(25°) = [tex]\frac{5}{x}[/tex]

=> x = 5/ tan(25°)≈ 10.7 feet.

Hence the length of ramp is 10.7 ft.

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Related Questions


can someone please help with this geometry

Answers

Answer:

  ∠ABD = 19.5°

  ∠ABE = 160.5°

Step-by-step explanation:

Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.

Angle bisector

An angle bisector divides an angle into two equal parts, each with half the measure of the whole.

  ∠ABD = 1/2∠ABC

  ∠ABD = 1/2(39°)

  ∠ABD = 19.5°

Linear pair

The angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.

  ∠ABE = 180° -∠ABD

  ∠ABE = 180° -19.5°

  ∠ABE = 160.5°

(a) if you selected repeated samples of size twelve from the u.s. population, what would be the mean number of individuals per sample who do not exercise regularly?

Answers

The mean number of individuals per sample who do not exercise regularly = 7

According to the survey 58% of the Americans does not exercise.

Hence probability of not exercising, p = 58/100 = 0.58

Define a random variable X denoting the number of people who does not exercise.

Then X follows the binomial distribution.

If p denotes the probability of success and if n is the sample size or number of trials, then

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ gives the probability of the random variable X.

Here, the sample size, n = 12

For a binomial distribution, mean, μ = np

Therefore,  mean number of individuals per sample who do not exercise regularly = np

               = 12 x 0.58

               = 6.96

               ≈ 7

The question is not complete. Find the complete question below:

According to the Behavioral Risk Factor Surveillance System, 58% of all Americans adhere to a sedentary lifestyle (sedentary means does not exercise).

a. If you selected repeated samples of 12 from the U.S. population, what would be the mean number of individuals per sample who do not exercise regularly?

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72% of what weight is 50oz

Answers

Answer:

See below

Step-by-step explanation:

72 %  is .72 in decimal

.72 x = 50 oz     Divide both sides by .72

X = 50 / .72 = 69.44 oz     ( or 69  4/9 oz )

4 = -(x + 3) implemented as a real life problem

Answers

4=-x-3
Add 3 on both sides
7=-x
Divide both sides by negative 1
Answer: X=-7

3. A clothing store is having a sale with all clothes being 10% - 30% off the original retail price.
(CAREFUL)
What would be the possible prices for a shirt with an original price of $60?

Answers

Answer:  between $42 and $54 including both endpoints.

In symbolic form we can say [tex]42 \le p \le 54[/tex] where p is the final price after the discount is applied.

===============================================

Explanation:

10% off means you save 10% but pay the remaining 90%

Then convert 90% to decimal form to get 0.90

If the original price is $60, then the final price is 0.90*60 = 54 dollars.

In other words,

10% of 60 = 0.10*60 = 6 dollars saved

60-6 = 54 is the final price

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

If the discount is 30% then you pay the remaining 70%

0.70*60 = 42

Or you can think of it like this

30% of 60 = 0.30*60 = 18 dollars saved

60-18 = 42 dollars is the final price

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

Let's summarize with this chart:

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}[/tex]

Therefore, the final price after the discount is between $42 and $54 including both endpoints.

Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.

The Reach French Club is raising money for a trip to Strasbourg. They have some money already, and will raise $700 per month for x months.

Their fundraising progress is modeled by the function $8000 = $1200 + $700x.

What is the meaning of 1200 in this equation?

A They started with $1200.They started with $1200.
B They will raise $1200 per month.They will raise $1200 per month.
C They will save money for 1200 months.They will save money for 1200 months.
D They have a goal of $1200 total.

Answers

Function : $8000 = $1200 + $700x

They will raise $700 per month for x months -> $700x is the amount of money they raise per month.

Since $8000 is the sum in the function, it is the goal.
Therefore, $1200 in this case means they started with $1200.


Work out the volume of this cylinder.
Give your answer rounded to 1 DP.

The diagram is not drawn to scale.

Answers

The volume of a cylinder is: V = π r² h then the volume of a cylinder is 5091.43  cm²

How to estimate the volume of the cylinder?

The volume of a cylinder is:

V = π r² h

From the information provided it can be concluded that:

The height of the cylinder is, h = 20 cm

The radius of the base exists, r = 9 cm

Compute the volume of a cylinder as follows:

V = π r² h

substitute the values in the above equation, we get

= (22/7) × 9² × 20

simplifying the above equation, we get

= (22 × 81 × 20) / 7

= 5091.42857

≈ 5091.43

Therefore, the volume of a cylinder is 5091.43 cm².

The complete question is:

Calculate the volume of this cylinder, giving your answer to 1 decimal place.

20 cm

9 cm

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The table shows sets of ordered pairs that form a relation.

Does each set of ordered pairs represent a function?

Select Function or Not a Function for each set of ordered pairs.

Answers

The ordered pairs that are also functions are listed below.

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

The ordered pairs that are not functions are listed below.

3.{(-2,-3),(4,1),(4,4),(-3,2)}

A function is a relation between two sets of ordered pairs that describe that there should be only one output for each input, or that for every element in set A, there should be one and only one relation in set B.

A relation between two sets of ordered pairs can be considered a function when every X value is associated with only one Y value.

Here in the first, second, and fourth sets of ordered pairs

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

Hence, every value in X has only one single value in Y. Hence, all these relations can be considered functions.

In the third set, i.e.,

3.{(-2,-3),(4,1),(4,4),(-3,2)}

It can be seen that element 4 has two values as its output, which are 1 and 4 ((4,1),(4,4)). Hence, it cannot be considered a function.  

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18-9.2x10 to the power of -4 subtract the following in.Write your answer in standard notation

Answers

The subtraction of the numbers, involving scientific notation, is given as follows:

18 - 9.2 x 10^(-4) = 17.99908.

What is scientific notation?

A number in scientific notation is given according to the rule presented as follows:

[tex]a \times 10^b[/tex]

The base is [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

In this problem, we are given the following subtraction:

18 - 9.2 x 10^(-4).

When two numbers are subtracted, they must have the same base, hence we are going to convert 9.2 x 10^(-4) to base 0.

This means that 4 has to be added to the exponent, meaning that the base has to be divided by 10000 to compensate, then:

9.2 x 10^(-4) = 0.00092.

Then the result of the subtraction is given as follows:

18 - 9.2 x 10^(-4) = 18 - 0.00092 = 17.99908.

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Randy has $450 saved in the bank. He wants to purchase a bike for $700. He plans to save $25
per month until he has enough to buy the bike. Randy's savings plan is represented by the
equation s = 25m + 450, where (s) represents total saved and (m) represents total saved and (m) represents months.
Does the equation represent a proportional relationship? Explain.

Answers

Answer: Yes because an example of a proportional problem is 54x = 103

I am pretty sure that is the answer

What is the inverse of the function
f
(
x
)
=

1
2
(
x
+
3
)
f(x)=−
2
1

(x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis?

Answers

The inverse function of the function f(x) = 12(x+3)  is f(x) = -2x - 3

A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.

The function given is:

To find the inverse, we must perform the following procedures.

y takes the place of f(x);

y = -(x+3)/2

Change the x and y variables.

x = -(y+3)/2

Calculate y

2x = - (y + 3)

2x = -y - 3

y = -2x - 3

We get the following in inverted notation:

f(x)⁻¹ = -2x - 3

Thus the obtained inverse function is f(X) =  -2x - 3

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WILL GIVE BRAINLIST TO BEST ANSWER PLUS EXTRA POINTS
5. The cost of a ride in a taxi is $5.00 for the first half-mile plus a constant amount per half mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.

5.00, 5.75, 6.50, …

Part A: Write an Explicit Function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half miles.


Part B: What is the cost, in dollars, for an 55-mile ride in the taxi? Provide mathematical justification for your answer.

Answers

The explicit function of the relation is Tn = 4.25 + 0.75n and the cost of a 55 miles ride is $45.5

How to determine the explicit function?

The sequence of the relation is given as

5.00, 5.75, 6.50, …

In the above sequence, we can see that

The sequence have a common difference of 0.75

This means that the sequence is an arithmetic function

An arithmetic function is represented as

T(n) = a + (n - 1)d

Where

a = First term = 5.00d = common difference = 0.75n = Number of termsTn = Current term

Substitute the known values in the above equation

Tn = 5 + 0.75(n - 1)

Expand

Tn = 5 - 0.75 + 0.75n

Evaluate

Tn = 4.25 + 0.75n

The cost of a 55-mile ride

This means that

n = 55

Subsitute n = 55 in the equation Tn = 4.25 + 0.75n

So, we have

T55 = 4.25 + 0.75 * 55

Evaluate the product

T55 = 4.25 + 41.25

Evaluate the sum

T55 = 45.5

Hence, a 55-mile ride will cost $45.5

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jae has $500 to spend on video games. the video games that cost $60 each. he also wants to get game accessories that cost $45. let x be the # of games he can buy, and let y be the # of accessories he can buy.

Answers

The two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories will be 60x + 45y = 500

It is given that,

The total money that Jae has =  $500

The cost price of each video game = $60

And, the cost price for each game accessories = $45

We need to find an arithmetic equation representation which is known as equation in two variable

To do that, the question has represented both number of games and gaming accessories that Jae bought with x and y variables

It is given,

Total number of video games he an buy = x

Total number of gaming accessories he an buy = y

Now, the total expenditure that Jae will do in buying Video games and gaming accessories should not exceed $500 as this s the total money he had wit him

Therefore,

60x + 45y = 500

This is the two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories

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A used boat dealership buys a boat for $2800 and then sells it for $3800 what is the percent increase

Answers

Percent increase by 35.71%

What is Profit and Loss ?

Profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year.

Given,

cost price of a boat is = $2800

selling price of a boat is = $3800

There is profit since C.P is less than S.P.

so, Profit = S.P - C.P

               = $3800 - $2800

               = $1000

Now, find profit percent i.e, Profit% = (Profit / C.P) * 100

=> Profit % = (1000 / 2800)*100

                 = 35.71%

Therefore, Percent increase by 35.71%

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Here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: George Lucas (5500).
Steven Spielberg (3700), Oprah Winfrey (3200), Paul McCartney (1200), J. K. Rowling (1000), and Jerry Seinfeld (950)
Find the range, variance, and standard deviation for the sample data. What do the results tell us about the
population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision?

Answers

Part a: Range = 4550

Part b: Variance  = 287,034

Part c: Standard deviation =  (287,034)².

What is termed as the standard deviation?The standard deviation is just a statistic that calculates as the square root of the variance and measures the distribution of a dataset relative to its mean. The standard deviation is determined as the square root of the variance by determining the deviation of each data point from the mean.

For the given question;

The highest net worths (in millions of dollars) for 6 celebrities is shown.

George Lucas (5500).Steven Spielberg (3700), Oprah Winfrey (3200),Paul McCartney (1200), J. K. Rowling (1000), and Jerry Seinfeld (950)

Part a: calculate the range;

Range = highest value - lowest value

Range = George Lucas (5500) - Jerry Seinfeld (950)

Range = 4550

Part b: Calculated the variance;

σ = ∑X²/n - μ² =  ∑(X²- μ²)/n

σ = varianceμ = mean n = total frequency

First find the mean;

μ =  ∑X/n

μ = (5500 + 3700 + 3200 + 1200 + 1000  950)/6

μ = 7775/3

σ =  (5500² + 3700² + 3200² + 1200² + 1000²  950²)/6 - (97775/3)²

σ = 287034

Variance = 287,034

Part c:  Calculated the standard deviation;

standard deviation = σ²

σ² = (287,034)²

Thus, the standard deviation is found as (287,034)².

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Write each mixed number as an improper fraction 5 whole number and 1 3 fraction form. Can you show me how you did the problem.

Answers

Answer:

16/3.

Step-by-step explanation:

5 1/3

First multiply 5 by 3.

This gives 15.

Now add the numerator of the fraction (1) to 15

- to give 16.

The improper fraction is 16/3.

two students a and b are both registered for a certain course. assume that student a attends class 80 percent of the time, student b attends class 60 percent of the time, and the absences of the two students are independent. a. what is the probability that at least one of the two students will be in class on a given day? b. if at least one of the two students is in class on a given day, what is the probability that a is in class that day?

Answers

A)  The probability that at least one of the two students will be in class on a given day is; 0.92

B)  If at least one of the two students is in class on a given day, the probability that a is in class that day is; 0.8696

How to solve Conditional Probability?

In probability theory, the occurrence of the events may depend on its relative events which are called dependent events while the events not dependent on their relative events are referred to as independent events. For dependent events, if conditional probabilities are required , we will make use of the Baye's Theorem and the total probability theorem sometimes.

We are given;

Probability that student A attends class = 80% = 0.8

Probability that student B attends class = 60% = 0.6

A) The probability that at least one of the two students will be in class on a given day is;

P = 1 - Probability that that neither show up to class on any given day.

P(A ∪ B) = 1 - P(A∼ ∩ B∼)

Where  P(A∼ ∩ B∼) = (1 - 0.8) × (1 - 0.6)

P(A∼ ∩ B∼) = 0.08

Thus;

P(A ∪ B) = 1 - 0.08

P(A ∪ B) = 0.92

B) We want to find the probability that student A was in the class given that at least one of them was in the class.

This is obviously a case of conditional probability which will give us the formula;

P(A|A ∪ B) = P(A ∩ (A ∪ B))/P(A ∪ B)

= P(A)/P(A ∪ B)

= 0.8/0.92

= 0.8696

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Calculate the volume for each right rectangular prism 5 3/4 in high 8 1/2 in long 2 1/4width

Answers

5 3/4 = 5.75

8 1/2 = 8.50

2 1/4 = 2.25

Volume = width × height × length

? = (5.75)(8.50)(2.25)

volume = 109.96875

in fraction form = 109 31/32

-5y+6x=40
3y-8x=-46

x=

y=

Answers

Answer:

[tex]x=5, y=-2[/tex]

Step-by-step explanation:

[tex]-5y+6x=40 \implies -15y+18x=120 \\ \\ 3y-8x=-46 \implies 15y-40x=-230 \\ \\ \therefore -22x=-110 \implies x=5 \\ \\ \therefore -5y+6(5)=40 \implies y=-2[/tex]

having a half braincell moment again
attachment below

Answers

Using similarity of triangles, the length of side GH is given as follows:

GH = 18.

Similar triangles

Similar triangles have congruent angle measures, thus the measures of the side lengths are proportional.

In this problem, triangles CAD and HGD are similar, and the equivalent sides are given as follows:

AC = GH. (the measures are AC = 12 and GH = x).CD = HD. (the measures are CD = 30 and HD = 45).

Hence the following proportional relationship is established:

x/12 = 45/30

Applying cross multiplication, we can solve for x, which is the length of side GH, as follows:

30x = 45 x 12 (simplifying by 30)

x = 1.5 x 12 (multiply 1.5 and 12).

x = 18. (which is the length of side GH).

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Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

Answers

First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}[/tex]

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

A bowl contains blueberries and strawberries. There are a total of 16 berries in the bowl. The ratio of blueberries to strawberries is 3 : 1. How many of each berry are in the bowl?

Answers

Answer:

12 Blueberries and 4 Strawberries

Step-by-step explanation:

12+4 = 16 and 12:4 = 3:1

3 times the sum of a number and 12 is 56

Answers

Answer:

6.6666 or 7

Step-by-step explanation:

Use synthetic substitution to find f(−3) if f(x)=x^3+4x^2−5x+11 .

Answers

By using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

The function is defined as the relationship between the one variable and another variable. If one variable is dependent variable and another variable will be independent variable

To find the value of f(-3), first we have to substitute the value x = -3 in the given function

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

Substitute the value of x = -3

f(-3) = [tex](-3)^3+4(-3)^2-5(-3)+11[/tex]

= -27 + 36 + 15 + 11

= 35

Hence, by using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

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I’m very confused on how to solve this. Can someone please help me

Answers

Considering the average rate of change of the function, the matched pairs are given as follows:

1 - a.2 - b.3 - c.4 - d.

What is the average rate of change of a function?

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given according to the following rule:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For the interval given by item 1, between -1 and 2, we have that:

f(-1) = -2.f(2) = -17.

Hence the rate is:

r = (-17 - (-2))/(2 - (-1)) = -15/3 = -5.

Meaning that 1 matches with a.

For the interval given by item 2, between -1 and 0, we have that:

f(-1) = -2.f(0) = 3.

Hence the rate is:

r = (3 - (-2))/(0 - (-1)) = 5/1 = 4.

Meaning that 2 matches with b.

For the interval given by item 3, between 1 and 2, we have that:

f(1) = -2.f(2) = -17.

Hence the rate is:

r = (-17 - (-2))/(2 - 1) = -15/1 = -15.

Meaning that 3 matches with c.

For the interval given by item 4, between -2 and 0, we have that:

f(-2) = -17.f(0) = 3.

Hence the rate is:

r = (3 - (-17))/(0 - (-2)) = 20/2 = 10.

Meaning that 4 matches with d.

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Write

1
.
5
y
=
4
.
5
x



9
in standard form.

Answers

juhfhfufyffuufzk Liznfndjdhs

Giving Brainliest, Please help

Answers

According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

What does a function mean in the simplest terms?

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output.

What best describes a function?

A function is defined technically as a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

According to the given data:

g(n) = -n² -1 h(n) = -2n + 2

find  (g o h)(n)

We can write it as:

g o h = g  x h

         = (-n² -1) x (-2n + 2)

        = 2n³ + 2n +2n -2

       = 2n³ +4n -2

According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

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URGENT PLEASE

Zachary purchased a computer for ​$1600 on a payment plan. five months after he purchased the​ computer, his balance was ​$900. eight months after he purchased the​ computer, his balance was ​$480. What is an equation that models the balance y after x​ months

Answers

If Zachary purchased a computer for ​$1600 on a payment plan. five months after he purchased the​ computer, his balance was ​$900. eight months after  his balance was ​$480.  The equation that models the balance y after x​ months is: y = -140x + 1600.

Equation

Month    Balance

0            1600

5              900

8              480

Slopes:

(1600 - 900) / 5  = 700 / 5 = 140

(1600 - 480) / 8 = 1120 / 8 = 140

(900 - 480 ) /  - 3 = - 140

Hence,

y = -140x + 1600

Therefore the equation is y = -140x + 1600.

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so if i get a 60% on a math test and my current grade is an 80%, how much will my grade go down?

Answers

The new grade of the student will be 70% and the grade reduced by 10 percent.

Percentage

This is a rate, number, or amount in each hundred. Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

In the given question, we simply need to add the two percentage together and find the average of the value.

This can be done mathematically as

[tex]\frac{60+80}{2} = 70[/tex]

The average grade will be 70% and this shows that the grade dropped by

[tex]80\% - 70\% = 10\%[/tex]

The grade will go down by 10%.

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Graphing transformations of sine and cosine functions: Sketch function below given the domain x e [-360, 360] <-- both are in degrees

Answers

By following the steps below, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

What are trigonometric functions?

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is the following function -

y = 5 cos(2x + π/3) - 1

We have -

y = 5 cos(2x + π/3) - 1

We can sketch the function as follows -

Let y = cos(x)

The first step is Amplitude magnification -

       y = 5 cos(x)

The second step can be understand in an easy way as if we multiply [x] by 2, the frequency of the cosine wave increases i.e. the distance between consecutive crests decreases.

        y = 5 cos(2x)

Third step include shifting of graph along the [x] axis. This can be done by adding a phase value as -

        y = 5 cos(2x + π/3). This will shift the graph along the negative

        [x] - axis by π/3.

Finally, we will shift the graph by 1 unit towards the negative [y] - axis.

Therefore, by following the steps above, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

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