The hiking path to the top of a mountain makes, at the steepest place, an angle of 20° with the
horizontal, and it maintains this constant slope for 500 meters, as illustrated below. Which of the
following is the closest approximation to the change in elevation, in meters, over this 500-meter
section?
500 meters
20
A 20
B) 170
180
D 250

The Hiking Path To The Top Of A Mountain Makes, At The Steepest Place, An Angle Of 20 With Thehorizontal,

Answers

Answer 1

We are given:

a right angled triangle with the angle of elevation = 20 degrees

Hypotenuse of the Triangle = 500 m

Finding the change in Elevation:

We will use trigonometry in the given triangle to find the length of the perpendicular of the triangle

Using trigonometry, we found that the perpendicular = 500 * Sin 20 degrees

Perpendicular = 500 * 0.342           [sin(20 degrees) = 0.342]

Perpendicular = 171 m

The closest value to 171m in the given options is 170m

Therefore, 170m (option B) is correct


Related Questions

On average, 2.8 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?

Answers

Answer:

The probability is [tex]P(X = 0) =  0.6997[/tex]

Step-by-step explanation:

From the question we are told that

   The  mean is  [tex]\mu = 2.8[/tex]

Generally the Poisson distribution constant  [tex]\lambda[/tex] is mathematically represented as

        [tex]\lambda = \frac{1}{\mu }[/tex]

=>     [tex]\lambda = \frac{1}{2.8 }[/tex]

=>     [tex]\lambda = 0.3571[/tex]

Generally the probability distribution for Poisson distribution is mathematically represented as  

     [tex]P(X = x) =  \frac{(\lambda t)^x e^{-t \lambda}}{x!}[/tex]

Here  t =  1 day

Generally the probability  that no babies are born today is mathematically represented as

       [tex]P(X = 0) =  \frac{(0.3571 * 1 )^0 e^{-1 * 0.3571}}{0!}[/tex]

=>    [tex]P(X = 0) =  0.6997[/tex]

PLEASE
Solve for x and y by graphing the system of linear equations.
y=-7/2x+3
y=-3/2x-1

Answers

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Step-by-step explanation:

hope its right

y - 2/5 = 1 3/5 (plz show work)

Answers

Answer:

y=2

Step-by-step explanation:

that's the answer hope u understand it

Answer:

[tex]y = 2[/tex]

Step-by-step explanation:

Sure.

[tex]y - \frac{2}{5} = 1 \frac{3}{5} \\[/tex]

Convert to improper fraction

[tex]y - \frac{2}{5} = \frac{8}{5}[/tex]

Combine like terms

[tex]y - \frac{2}{5} = \frac{8}{5} \\[/tex]

[tex]+\frac{2}{5}[/tex] from both sides

[tex]y = \frac{8}{5} + \frac{2}{5} \\y = 2[/tex]

Love from Nepal :)

Help anyone 5th grade math

Answers

Answer:

Equal???

Step-by-step explanation:

con las medidas de los lados 8cm , 9cm ,2cm se existe un triángulo ?

Answers

Answer:

si

Step-by-step explanation:

la longitud mayor es menor que la suma de las otras 2 longitudes que es 10

What is the difference between an expression and an any quality

Answers

Answer:

A expression is a number, variable, or a combination of numbers and variables and operation symbols. A equality is a relationship between 2 quantities or more . Hope it helps:)))

Step-by-step explanation:

What is the remainder when 19x^2 + 15x + 12 is divided by x - 2?

Answers

Answer:

R = 118

Step-by-step explanation:

Given

Represent the polynomial with P and the divisor with D

[tex]P = 19x^2 + 15x + 12[/tex]

[tex]D = x -2[/tex]

Required

Determine the remainder

We start by equating the divisor to 0

i.e.

[tex]D = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

Substitute 2 for x in the polynomial.

This gives remainder (R)

[tex]R = 19*2^2 + 15*2 + 12[/tex]

[tex]R = 19*4 + 15*2 + 12[/tex]

[tex]R = 76 + 30 + 12[/tex]

[tex]R = 118[/tex]

Hence, the remainder is 118

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.
f(x) = −one twelfth(x − 5)2 + 2
f(x) = one twelfth(x − 5)2 + 2
f(x) = −one twelfth(x + 5)2 + 2
f(x) = one twelfth(x + 5)2 + 2

Answers

Answer:

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].

Step-by-step explanation:

From statement we understand that parabola has its axis of symmetry in an axis parallel to y-axis. According to Analytical Geometry, the minimum distance between focus and directrix equals to twice the distance between vertex and any of endpoints.

If endpoints are (-5, 5) and (-5, -1), respectively, then such distance ([tex]r[/tex]), dimensionless, is calculated by means of the Pythagorean Theorem:

[tex]r = \frac{1}{2}\cdot \sqrt{[-5-(-5)]^{2}+[5-(-1)]^{2}}[/tex]

[tex]r = 3[/tex]

And the location of the vertex ([tex]V(x,y)[/tex]), dimensionless, which is below the focus, is:

[tex]V(x,y) = F(x,y)-R(x,y)[/tex] (1)

Where:

[tex]F(x,y)[/tex] - Focus, dimensionless.

[tex]R(x,y)[/tex] - Vector distance, dimensionless.

If we know that [tex]F(x,y) = (-5,5)[/tex] and [tex]R(x,y) = (0,3)[/tex], then the location of the vertex is:

[tex]V(x,y) = (-5,5)-(0,3)[/tex]

[tex]V(x,y) =(-5,2)[/tex]

In addition, we define a parabola by the following expression:

[tex]y-k = \frac{(x-h)^{2}}{4\cdot r}[/tex] (2)

Where:

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.

[tex]r[/tex] - Distance of the focus with respect to vertex, dimensionless.

If we know that [tex]h = -5[/tex], [tex]k = 2[/tex] and [tex]r = 3[/tex], then the equation of the parabola is:

[tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex]

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].

Please help!!!
If h(x)= -3x-10, find h(-3)
Please give an explanation too. Thank you.

Answers

Answer:

h(-3)=-1

Step-by-step explanation:

Replace all x in h(x)= -3x-10 by -3:

h(-3)=-3(-3)-10

Now multiply -3 and -3:

h(-3)=9-10

Simplify 9 and -10 (aka add 9 and -10 together):

h(-3)=-1

Answer: h(-3)=-1

Hope this helps!

Answer:

-1

Step-by-step explanation:

If h(x)= -3x-10 and we want to solve for h(-3) then we have to plug in -3 for all x variables. h(-3)= -3(-3)-10, then solve using PEMDAS.

First multiple h(-3)= 9-10, multiple -3*-3 to get 9.

Then subtract, h(-3)=-1

PLZ HELP ASAP (This is not a text or an exam)

Answers

Answer:

x=4

Step-by-step explanation:

As the two angles are clearly congruent because of the bisector, we set them equal to each other:

7x=3x+16

4x=16

x=4

Therefore, the value of x is 4 and not 9

is x= 3 a solution to the equation 2(2x +1) + x = 8x +2-3x

Answers

I think u got right answer...

About 50% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.(a) Is the experiment a binomial experiment?⪠Yes⪠No(b) What is a success in this experiment?⪠This is not a binomial experiment.⪠Baby recovers⪠Baby doesn't recover(c) Specify the value of n.A. n = _____B. This is not a binomial experiment.(d) Specify the value of p.A. p = _____B. This is not a binomial experiment.

Answers

Answer:

a. yes it is a binomial experiment

b. success is that baby recovers

c. n = 6

d. p = 0.5

e. q = 0.5

f. X: 0,1,2,3,4,5,6

Step-by-step explanation:

a.

the answer is yes this is a binomial experiment. This is true because we have a finite number of babies and these babies are independent of each other. there are two possible outcomes. 1. baby recovers 2. baby does not recover.

b.

success: baby recovers

c.

n = number of babies born with ailment. n = 6

d.

p = 50% = 0.5

e.

q = 1-p = 1-0.5

q = 0.5

f.

possible values of X: 0,1,2,3,4,5,6

what is the slope and the y-intercept for the equation y = -3 + 6x?

Answers

Answer:

slope-6

y-intercept-(0,-3)

Step-by-step explanation:

What is the simplest form of 1.764?

0 21
0 42
0 3²(7²)
22(32)(74)

please explain why because I don’t want someone to guess this is kinda important, ty

Answers

Answer:

[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]

Step-by-step explanation:

Divide by the prime numbers in increasing order until you find all the prime factors.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17

1764/2 = 882

882/2 = 441

441/3 = 147

147/3 = 49

49/7 = 7

7/7 = 1

[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]

What is the factored form of the equation 4x^2-11+6=0

Answers

Answer:

(4x−3)(x−2)=0

Step-by-step explanation:

Step-by-step explanation:

4x²-11+6=0

4x²-5=0

x²=5

4

x=√5

4

hope it help u

I believe SAS is the correct answer but SSS is also possible so which one is it?

Answers

SSS because the middle line is equal on both triangles. They have three sides that are the exact same length.

the research director at NASA must choose five experiments for the next space shuttle. Twelve experiments are proposed. in how many ways can this decision be made if order does not matter.. how many ways can this be arranged?

Answers

Answer:

95040

Step-by-step explanation:

This is the combination of 5 experiments out of 12

Formula to find the combination:

P(n,r) = n!/(n-r)!P(12,5) = 12!/(12-5)! = 12!/7! = 12*11*10*9*8 = 95040

So this can be arranged in 95040 ways

Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69, 65. 87.
What is the mean height of Bella's corn stalks?
A 69 cm
B. 75 cm
C. 78 cm
D. 80 cm
E. 81 cm

Answers

Answer:

d

Step-by-step explanation:

.................have a great day

Sammy deposits $200 in an account at his bank.The simple interest rate is 8%.How much interest will he earn in three years

Answers

Answer:

$48

Step-by-step explanation:

Multiply 200 by 0.08 or 8%. That is how much interest he will earn in a year. Then multiply the product by 3.

How many metres and centimetres are in 3080mm​

Answers

Answer:

3080mm = 3.08 meters

3080mm = 308 centimeters

Step-by-step explanation:

1 meter = 1000 mm

3080mm = 3080/1000 = 3.08 meters

1 centimeter = 10 mm

3080mm = 3080/10 = 308 centimeters

Homer is 30 feet below sea level and Marge is 45 feet above sea level. Bart’s elevation is at the exact midpoint of those two values. What is the expression that model this problem, and which is Bart’s elevation?

Answers

Answer:

14.5 feet

Step-by-step explanation:

the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2

Answer:

7.5 m above sea level

__________________________________________________________

Step-by-step explanation:

We are given:

The elevation of Homer = -30 feet                         [30 feet below sea level]

The elevation of Marge = +45 feet                         [45 feet above sea level]

The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

The elevation of Bart:

We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

So, Half the distance between the elevation of Homer and Marge is the elevation of Bart

Elevation of Bart (with respect to the elevation of Homer) =

(elevation of Marge - Elevation of Homer) / 2

replacing the variables with the suitable values:

(+45 - (-30))/2

(45 + 30) / 2

75 / 2

Elevation of Bart (w.r.t. Homer) = 37.5 feet

Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer

So, we can say that:

Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer

replacing the values

37.5 = Elevation of Bart -(-30)

37.5 = Elevation of Bart + 30

Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]

A commuter train travels 45 miles in 34 minutes. What is its speed in miles per hour?

Answers

I think the answer is 79.41

If 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box?

Answers

Answer:

1400

Step-by-step explanation:

2/v+1/w+1/2 solve for v

Answers

Answer:

look go search Math - way its a calculator and type in your question ir really helps gives you the answer

Step-by-step explanation:

During a period of 112 minutes, a music station played 40 minutes of commercials. What
is the ratio of music they played to commercials they played?

Answers

Answer:

9:5

Step-by-step explanation:

112 - 40 = 72. 112 represents the total time, but you are comparing music to commercials, so you have to subtract the commercial time from the total time.Find the GCF of 72 and 40, which is 8. Divide 72 and 40. The simplified ratio is 9:5.

oredr -3/4, 3/8, -1 1/8, - 1/2 from least to greatest.​

Answers

Answer: -1 1/8 -3/4 -1/2 3/8

Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, and below the cone z = x^2 + y^2.

Answers

Answer:

The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]

[tex]2(x^2 + y^2) =81[/tex]

[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

[tex]z = \sqrt{x^2+y^2}[/tex]

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]

Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]

[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]

[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]

[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]

V = 243[tex]\sqrt{2} \ \pi[/tex]

In the graph above what is the average speed for the object?

a. 0.4m/s
b. 2.5m/s
c. 3m/s
d. 0.8m/s

Answers

Answer:

c

Explanation:

Just because

Erica makes $27 an hour how much does ahe make in 140 hours​

Answers

$27*140=

$3780 is your answer

Answer:

$3,780

Step-by-step explanation:

27*140=3780

What type of transformation has occurred?
A Translation
B Dilation
C Reflection
D Rotation

Answers

Answer:

B dilation

Step-by-step explanation:

the shape didnt move but it got bigger

Other Questions
Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69, 65. 87.What is the mean height of Bella's corn stalks?A 69 cmB. 75 cmC. 78 cmD. 80 cmE. 81 cm 1. At a temperature of 22oC, a liquid that has a volume of 5 mL. The liquid also has a mass of 3 grams. What is the density of this liquid?.6 g/mL1.67 g/mL15 g/mL In a proportional relationship when x=9 we know that y=15. Which of the following is the value of y when x=24? (1) 30 (3) 48 (2) 40 (4) 54 PLZ HELP ASAP (This is not a text or an exam) _______ teams do not generally have direct patient contact.CoreContingencyAncillarySupport What is the simplest form of 1.764?0 210 420 3(7)22(32)(74)please explain why because I dont want someone to guess this is kinda important, ty can somebody answer please. Jay's Treaty significance. PLEASE HELP!!!!!!! A commuter train travels 45 miles in 34 minutes. What is its speed in miles per hour? Create a multimedia presentation using a Web 2.0 tool (such as Google Docs, Google Slides, Animoto, or Prezi.) In this module, you have learned about multiple historical, cultural and literary influences in early 20th century America. You have also read several poems which are representative of early 20th century American literature. Use your timeline chart from lesson 5.04 to create this presentation. Choose two poems and create a presentation explaining the ways in which the literary works were influenced by the events of the early 20th Century.. Your presentation should: 1. Showcase 2 poems. 2. Contain at least one image for each poem 3. Text explaining the ways in which the literary works were influenced by the events of the 20th century Poems: (These are linked in the lesson under "Sneak Peek") "Rhapsody on a Windy Night" by T.S. Eliot "Mending Wall" by Robert Frost "Stopping by Woods on a Snowy Evening" by Robert Frost "The River Merchant's Wife: A Letter" by Ezra Pound "The Red Wheelbarrow" by William Carlos Williams "Languages" by Carl Sandburg "Fog" by Carl Sandburg What type of transformation has occurred?A TranslationB DilationC ReflectionD Rotation For an object to remain at rest which of the following statements must be true A nonviolent, public refusal to obey allegedly unjust laws is called Pleassssseeee help. I neeed help About 50% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.(a) Is the experiment a binomial experiment? Yes No(b) What is a success in this experiment? This is not a binomial experiment. Baby recovers Baby doesn't recover(c) Specify the value of n.A. n = _____B. This is not a binomial experiment.(d) Specify the value of p.A. p = _____B. This is not a binomial experiment. Please help this is due in 30 mins The equation y = 13x represents the rate, in gallons per minute, that Tank A at an aquarium fills with water. The table represents the rate that Tank B fills with water. Determine which tank fills faster. PT2 To my last question!!!! please answer quickly What is the remainder when 19x^2 + 15x + 12 is divided by x - 2? PLSS HELPPPPPPPP HELPP ASP