The steepness, or grade, of a highway or railroad is expressed as a percent. In the photo of the cog railway at Pike’s Peak, in Colorado, the grade is 18%. Thus, for every 100 ft of horizontal run, the train rises 18 ft. Find the angle of the inclination of the railway.

Answers

Answer 1
The angle of inclination is 10.2°.

The angle of inclination will be between the hypotenuse of the triangle and the bottom leg.  The bottom leg is the 100 ft run.  The rise of 18 feet will be the other leg, which is opposite this angle.  

This gives us the sides opposite and adjacent the angle we are looking for; opposite/adjacent is the ratio for tangent:

tan x = 18/100

We can solve this using inverse tangent:
tan⁻¹ x = tan ⁻¹(18/100) 
x = 10.2°

Related Questions

YO!NEED THIS!!!!!POINTS!!!!!!WILL GIVE THE BRAIN!!!!

Answers

The graph is falling on the left hand side and rising on the right hand side.

Since the two ends of graph are in opposite direction, the exponent of variable has to be odd. For an even exponent of leading term, the two ends are in same direction.

Since the graph is falling on left and rising on right, this indicates that the coefficient of leading term is positive.

So, the leading term must have:
1) Odd exponent
2) Positive Coefficient

Thus, option Fourth is the correct answer


A boy spent 2/3 money on book store,1/3 money on craft store and has left $8. How much money he has at first?

Answers

1/3 of 12 dollars is 4 minus twelve is the 8

2/3s of 26 is 24 minus 36 is 12

so at first He would have to have $36

In​ March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost ​$1327. They start with ​$120. At the beginning of each month they plan to deposit 20​% more than the previous month. Will they have enough money for their​ trip? If​ not, how much more do they​ need? Select the correct answer below​ and, if​ necessary, fill in the answer box within your choice.

Answers

Deposited money:

March: 120
April: 120+(120×20)/100=120+24=144
May: 144+(144×20)/100=144+18,8=162,8
June: 162,8+(162.8×20)/100=162,8+32.56=195.36
July: 195.36+(195.36×20)/100=195.36+23.87=219.23
August: 219.23+(219.23×20)/100=219.23+43.85=263.08

120+144+162.8+195.36+219.23+263.08=1105.19
So the answer is no.

A gardener wants to plant 122500 trees in his field in such a way that the number of trees in a row is equal to the number of rows .How many trees will he plant in each row?

Answers

Given that the gardener wants the number of trees in each raw to be equal to the number of rows, then let the number of in each row be x this means that the number of rows will be x.
Thus the total number of trees will be:
Total=(number of rows)*(number of trees in each row)
hence:
122500=x×x
122500=x²
hence
x=√122500
x=350
thus the number of rows will be 350 and the number of trees in each row will be 350

Another question for math. ill give mad points, the question is in attachment

Answers

For this case we have the following points:
 y = (- 2, 5)
 z = (1, 3)
 Therefore, the vector yz is given by:
 yz = z - y = (1, 3) - (-2, 5)
 yz = ((1 - (- 2)), (3-5))
 yz = ((1 + 2), -2)
 yz = (3, -2)
 Then, the magnitude is given by:
 lyzl = root ((3) ^ 2 + (-2) ^ 2)
 lyzl = root (9 + 4)
 lyzl = root (13)
 Answer:
 
yz = (3, -2)
 lyzl = root (13)
 option A

Part A: Factor 5x2b2 + 14xb2 − 3b2. Show your work.
Part B: Factor x2 − 18x + 81. Show your work.
Part C: Factor x2 − 121. Show your work.

Answers

Part A:
 
We have the following expression:
 5x2b2 + 14xb2 - 3b2
 Rewriting we have:
 b2 (5x2 + 14x - 3)
 b2 (5x-1) (x + 3)

 Part B:
 We have the following expression:
 x2 - 18x + 81
 Rewriting we have:
 (x-9) (x-9)
 (x-9) ^ 2

 
Part C:
 
We have the following expression:
 x2 - 121
 Rewriting we have:
 (x-11) (x + 11)

15 Points!

Describe how to transform the graph of f into the graph of g.

A) Shift the graph of f left 3 units.
B) Shift the graph of f right 7 units.
C) Shift the graph of f right 3 units.
D) Shift the graph of f left 7 units.

Answers

[tex]f(x)=\sqrt{x-2}\\\\g(x)=\sqrt{x+5}=\sqrt{x+7-2}=\sqrt{(x+7)-2=f(x+7)[/tex]

Answer:
D) Shift the graph of f left 7 units.


Look at the picture.

A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?

Answers

Final answer:

The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.

Explanation:

The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.

Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.

Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.

Learn more about Normal Distribution here:

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Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4. A) (6, 6) B) (2, 56 5 ) C) ( 24 5 , 42 5 ) D) ( 42 5 , 24 5 )

Answers

 Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.A)(6, 6)B)(2, 565)C)(245, 425)D)(425, 245)
Your Answer Is D 42/5 ,  24/5

Group A represents males on the football team at Grizzly High School. Group B represents the men’s cross country team at Grizzly High School. Both teams are played during the same season. What can you conclude about the groups A and B?


A.
There are not any students who play in either football or run cross country.
B.
There are not any students who run only cross country .
C.
There are not any students who play only football..
D.
There are not any students who are in both sports, football and cross country.

Answers

You have to eliminate A. If there are no students in either sport, you actually can't field a team.

You actually can't tell if their is a team with no one and the other team has players. B and C are wrong for the same reason A was wrong..

Your answer from this bunch is D but it's not clear that it is right. One team could practice on Tuesdays and Thursdays and the other on Mondays and Wednesdays. I don't know what you'd do on game day. But schools have worked that problem out, I'm sure. There would not be a conflict.

<<<<<<< answer

Answer:

D.

There are not any students who are in both sports, football and cross country.

Step-by-step explanation:

John is weighing his jars of coins. His jar of pennies weighs 84.96 ounces, and his jar of nickels weighs 3.11 kilograms. There are 0.0283495 kilograms per ounce. Which jar weighs more, and how many more pounds does it weigh?

Answers

The correct answer is 1.55 lbs.

Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

Answers

The number of essays graded varies directly with the number of hours worked, with a constant rate of 6.25 essays per hour. Therefore, it will take approximately 5.6 hours for a teacher to grade 35 essays at this rate.

The scenario presented describes a situation where the number of essays graded is directly proportional to the number of hours worked. This means that as the number of essays increases, the hours required to grade them also increase, assuming the grading speed (rate) is constant. To find the constant of variation (or rate of grading), we divide the number of essays by the number of hours.

If a teacher grades 25 essays in 4 hours, the rate would be 25 essays÷4 hours = 6.25 essays per hour. To find out how long it will take to grade 35 essays at this rate, we divide the number of essays by the rate:

35 essays ÷ (6.25 essays per hour) = 5.6 hours.

So, it will take the teacher approximately 5.6 hours to grade 35 essays given the constant grading speed.

Find the volume of each sphere or hemisphere. Round to the nearest tenth.

sphere: circumference of a great circle = 26m

Answers

we know that
volume of a sphere=(4/3)*pi*r³

in this problem
circumference=26 m
circumference=2*pi*r
so
26=2*pi*r----------> r=26/(2*pi)----> 4.14 m

volume of a sphere=(4/3)*pi*(4.14)³---> 297.08 m³------> 297.1 m³

the answer is
volume of a sphere is equal to 297.10 m³


One thousand tickets were sold for a baseball game there were one hundred more adult tickets sold than student tickets, and there were fou times as many tickets sold to students as to children. how many of each type of ticket were sold.

Answers

500 Adult tickets
400 Student tickets
100 Children tickets

Let x = adults
Let y = Students
Let z = children

Then set up this system of equations

x +y + z = 100
y - 4z = 0
x - y = 100

Solve using elimination and combination. 

what is the area of the circle if DF=20 in.

Answers

we know that

DF is the diameter of the circle
so
radius r=DF/2----->20/2-----> r=10 in

area of the circle=pi*r²------> pi*10²-----> 100*pi in²-----> 314 in²

the answer is

100*pi in² or 314 in²

An insect flies 20 feet in 1 second. how fast does the insect fly in miles per hour?

Answers

[tex] \frac{20 ft}{sec} ( \frac{60 sec}{min} )( \frac{60 min}{hr})( \frac{1 mi}{5280 ft}) [/tex]

All of the units cancel other than miles divided by hours which is what we need.

Now we do (20 * 60 * 60 * 1) / 5280 which is 13.636363 (repeating) or 13.6364 miles per hour. 

Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents. Would this study be biased Why or why not?

Answers

Answer:

Yes, it will be a biased study.

Step-by-step explanation:

Given is that -

Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents.

This study will be biased and it will produce biased results.

Firstly, few people at ball game do not represent the whole population of the city and it is not necessary that all the people at ball park will respond to the question in the survey.

Answer:

Yes, it is biased. The sample of people at the ball park is not representative of Star City’s residents.

The answer is D.

What is the y-intercept of x^2+2x+6

Answers

The y-intercept occurs when x = 0.
y = x^2 + 2x + 6
Let x = 0
y = 0^2 + 2 * 0 + 6
y = 6
Answer: 6
y-intercept is a point when x=0,
so
y=x²+2x+6=0²+2*0+6=6
y=6
So y-intercept is (0,6)

A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.

Answers

let the length be x and the width be w

The perimeter will be:
2x+3w=1500

thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x

The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²

The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.

Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m

The width will be 250 m

Akikos dogs has three puppies. They weigh 2.6pounds, 2.74 pounds, and 3.1 pounds. How much more does the heaviest puppy weigh than the lightest puppy?

Answers

the answer is 0.5 pounds                 

You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed of 0.6r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.

Answers

Final answer:

This high school physics problem deals with relative velocity and vector addition by describing a journey in a kayak under varying speeds amidst a river current. To solve such a problem, the total time taken is found by adding the individual times for each part of the journey, each calculated by dividing the distance by the speed of the kayak.

Explanation:

The subject matter of this question involves understanding of the concept of relative velocity, a topic usually taught in high school physics. The student is navigating a kayak in the river with varying speeds relative to different sections of the journey, demonstrating the behavior of an object in a current or wind. In essence, the motion of the kayak is a combination of its own propelled movement and the movement of the river current.

To solve the mathematical aspect of such a problem, you would typically find the total time taken for each segment of the journey by dividing the distance of that segment by the speed at which the kayak is moving. Adding these times together will give the total time taken for the whole journey. Finally, you should understand this as an example of vector addition, where the total velocity of the kayak is the vector sum of its velocity relative to the water and the water's velocity relative to the riverbank.

Learn more about Relative Velocity here:

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use the formulas to find the lateral area and the surface area of the given prism round your answer to the nearest whole number 5.39m 26m 5m 2m
the choices for the answer is
322m2 327m2
296m2 342m2
296m2 332m2
322m2 332m2

Answers

The Answer is 296m2 342m2

Answer:

for connexus 322m^2, 332m^2

Step-by-step explanation:

A number is mutiplied by 10. Then 32 is added to the product. This sum is then devised by 4. The answer is 28. What was the original number?

Answers

The Answer is 8 because you take 28 and multiply 4, then you subtract 32, and lastly, you divide by 10 and you get 8.
8 is your original number.

I went in a did the opposite of what it said (so I multiples 28 by 4, subtracted 32, and then divided by 10). Hope this helps!

Use graphs and tables to find the limit and identify any vertical asymptotes of the function.

Answers

Lim x→8- [1/(x-8)]=1/(8-8)=1/(-0)→Lim x→8- [1/(x-8)]=-Infinite

Vertical asymptote: x=8

Answer:

The limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1}{x-8}[/tex]

We need to find the value of

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}[/tex]

The graph of the function f(x) is attached below.

From the graph it is clear that the function approaches to -∞ as x approaches to 8 from left. So, by the graph we can say that

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]

The table of values is attached below. From the table it is clear that the value of f(x) decreasing as the value of x is closed to 8 from left. So, by the table we can say that

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]

To find the vertical asymptotes equate denominator, equal to 0.

[tex]x-8=0[/tex]

[tex]x=8[/tex]

Therefore the limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.

A circular mirror has a diameter of 12 inches. part a what is the area, in square inches, of the mirror?
a. 6 π
b. 12 π
c. 36 π
d. 72 π part b a circular frame that is 3 inches wide surrounds the mirror. what is the combined area, in square inches, of the circular mirror and the frame?
a. 9 π
b. 18 π
c. 54 π
d. 81 π

Answers

1st part is c
2nd part is d 

I BELIEVE

Final answer:

The area of the circular mirror is 36π square inches, and the combined area of the mirror and frame is the difference between the total area with the frame (81π square inches) and the mirror alone, resulting in 45π square inches.

Explanation:

Part A: Area of the Circular Mirror

To find the area of the circular mirror, we use the formula for the area of a circle, which is A = πr², where r is the radius of the circle. Since the diameter of the mirror is given as 12 inches, the radius would be half of that, which is 6 inches. Plugging the radius into the formula, we get:

A = π(6 inches)² = 36π square inches

Part B: Area of the Circular Mirror and Frame

The frame adds 3 inches to the radius on all sides, making the overall radius of the mirror and frame 9 inches (6 inches + 3 inches). Using the area formula again, A = π(9 inches)² = 81π square inches.

To find the combined area of the mirror and frame, we subtract the area of the mirror from the total area. Hence, combined area = 81π square inches - 36π square inches = 45π square inches.

what is the length of the diagonal AC in the rectangle below?

Answers

Find lengths of BC and DC.

Then use Pythagorean Theorem to find BD (the hypotenuse of right triangle DCB). So Pythag here would be:

[tex]BC^2+DC^2=BD^2[/tex]

See attached picture for full work.
I used the distance formula to find the length of diagonal AC.

What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?

i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.

Answers

For rotation by an angle, θ, in the counter-clockwise direction about the origin, the transformation matrix is given by 
     [tex]\begin{pmatrix}cos\:\theta &-sin\:\theta \\ sin\:\theta &cos\:\theta \end{pmatrix}[/tex]

The given angle is θ=300°. 

The values we need are
     [tex]cos\left(300^{\circ} \right)=\frac{1}{2}[/tex]
     [tex]sin\left(300^{\circ} \right)=-\frac{\sqrt{3}}{2}[/tex]

Substituting these into the given transformation matrix, we have
     [tex]\begin{pmatrix}\frac{1}{2}&\frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2}&\frac{1}{2}\end{pmatrix}[/tex]

the answer is B

hope this helps :)

Justin is a musician. For eight months a year, he teaches school and is paid $34,780 annually. During the summer months, he teaches private students and plays in clubs, earning another $5,700. What is his average monthly salary, based on his yearly earnings?

Answers

Hi there!

First, we'll need to add the two values together. This gives us $40,480. Then, since we know that there are 12 months in a year, we need to divide the total amount by 12. This gives us, on average, $3373.33 each month.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

What is the radius of the circle given the equation x2 - 6x + y2 + 10y - 2 = 0?

Answers

[tex]\text{Equation of the circle in standard form:}\\\\(x-h)^2+(y-k)^2=r^2\ \text{where}\\\\\text{(h; k) - coordinates of the center of the circle}\\\\\text{r-the radius}[/tex]

[tex]\text{We have:}\\\\x^2-6x+y^2+10y-2=0[/tex]

[tex]\text{Use:}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]\underbrace{x^2-2\cdot x\cdot3+3^2}_{(x-3)^2}-3^2+\underbrace{y^2+2\cdot y\cdot5+5^2}_{(y+5)^2}-5^2-2=0\\\\(x-3)^2+(y+5)^2-9-25-2=0\\\\(x-3)^2+(y+5)^2-36=0\ \ \ \ |+36\\\\(x-3)^2+(y+5)^2=36[/tex]

[tex]\text{coordinates of the center of the circle (3; -5)}\\\\\text{a radius}\ r=\sqrt{36}=6[/tex]

A quality control expert randomly samples 60 pairs of sunglasses and finds 5 defective pairs. predict how many defective pairs will be in a shipment of 420 sunglasses.

Answers

420/60=7
7*5=35 sunglasses

For this case the first thing you should do is find the percentage of sunglasses that are defective.

For this, we make the following rule of three:

60 pairs -------------------> 100%

5 pairs ---------------------> x

From here, we clear the value of x.

We have then:

[tex] x = (\frac{5}{60}) * (100)

x = 8.3%
[/tex]

We now look for the amount of sunglasses that may come with defects.

We have then:

[tex] N = (0.083) * (420)

N = 34.86
[/tex]

Rounding to the nearest whole number:

[tex] N = 35
[/tex]

Answer:

About 35 defective pairs will be in a shipment of 420 sunglasses

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