In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). Approximate the height of the mountain. (Round your answer to one decimal place.)
To solve such problems we must know about Tangent (Tanθ).
What is Tangent (Tanθ) ?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain is 1.495 miles.
Given to us
AB = 15 miles∠CAD = 3.5°∠CBD = 9°In ΔCAD,[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]
[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]
[tex]CD=tan(3.5^o) \times(x+15)[/tex]
In ΔCBD,[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]
[tex]tan(9^o) = \dfrac{CD}{x}[/tex]
[tex]CD=tan(9^o) \times(x)[/tex]
Equating CD,
[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]
Substituting the value of x
[tex]CD=tan(9^o) \times(x)[/tex]
[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]
Hence, the height of the mountain is 1.495 miles.
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If Adela has 12.4 L of diesel and Madison has 840 cL of diesel, how much does the pair have altogether?
The total volume of diesel that the pair have altogether is equal to 20.8 L.
What is measurement?Measurement is a process through which the size, magnitude, volume or other physical quantities that are associated with an object or chemical substance are taken, especially for the purpose of a scientific research (experiment).
In order to determine the total volume of diesel that they have, we would convert the value in centiliter (cL) to liter (L) and then add them together as follows:
840 cL to L = 840/100 = 8.4 L.
Total = 8.4 + 12.4
Total = 20.8 L.
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In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. If you want to spend 1 year in the club, how much money did you spend?
To reduce laboratory costs, water samples from two public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.009 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from twotwo public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
The probability of a positive test result is _____.
Is the probability low enough so that further testing of the individual samples is rarely necessary?
A. The probability is quite low, indicating that further testing is necessary for all of the combined samples.
B. The probability is quite low, indicating that further testing is not necessary for any of the combined samples.
C. The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
D. The probability is quite low, indicating that further testing of the individual samples will not be a rarely necessary event.
Answer:
The probability of a positive test result is 0.017919
Option C is correct.
The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
Step-by-step explanation:
Probability of finding bacteria in one public swimming pool = 0.009
We now require the probability of finding bacteria in the combined test of two swimming pools. This probability is a sum of probabilities.
Let the two public swimming pools be A and B respectively.
- It is possible for public swimming pool A to have bacteria and public swimming pool B not to have bacteria. We would obtain a positive result from testing a mixed sample of both public swimming pools.
- It is also possible for public swimming pool A to not have bacteria and public swimming pool B to have bacteria. We would also obtain a positive result from testing a mixed sample of both public swimming pools.
- And lastly, it is possible that both swimming pools both have bacteria in them. We will definitely get a positive result from this too.
So, if P(A) is the probability of the event of bacteria existing in public swimming pool A
And P(B) is the probability of the event of bacteria existing in public swimming pool B
P(A') and P(B') represent the probabilities of bacteria being absent in public swimming pool A and public swimming pool B respectively.
P(A) = P(B) = 0.009
P(A') = P(B') = 1 - 0.009 = 0.991
Since the probabilities for each public swimming pool is independent of the other.
P(A or B) = P(A n B') + P(A' n B) + P(A n B)
= P(A)×P(B') + P(A')×P(B) + P(A)×P(B)
= (0.009×0.991) + (0.991×0.009) + (0.009×0.009)
= 0.008919 + 0.008919 + 0.000081
= 0.017919
Evidently, a probability of 0.017919 (1.7919%) indicates an event with a very low likelihood. A positive result is expected only 1.7919% of the time.
Hence, we can conclude that the probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
Hope this Helps!!!
A van travels 300 miles on 15 gallons of gas. Find how many gallons the van needs to travel 360 miles. 72 gallons of gas 18 gallons of gas 23 gallons of gas 67 gallons of gas
simple first we find the miles per gallon
so 300/15=20 therefor he would only need a extra 3 gallons to go 360 miles so your answer is
B.18
The bakers Healthy Bakery make 250 bagels in 10 hours. How many bagels can they bake in 12 hours? What was that rate per hour?
250/10 = 25 bagels per hour
25*12 = 300 bagels in 12 hours
Does anyone know this??
The range of the following relation R {(3, −2), (1, 2), (−1, −4), (−1, 2)} is
A {−1, 1, 3}
B {−1, −1, 1, 3}
C {−4, −2, 2, 2}
D {−4, −2, 2}
which number is halfway between 1/2 and 5/6
The fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
What is a fraction ?
A fraction is used to represent a portion or component of a whole. The numerator and denominator are its two parts.
The two fractions are given which are [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex].
We know that numerator is the top value of the fraction whereas the denominator is the bottom value of the fraction. We need to add the given fractions and then divide it by 2 to find the halfway between the two given functions.
To add the fractions we need to equal denominator firstly. The common denominator of 2 and 6 will be 6 because 6 is a multiple of both 2 and 6.
So ,
Halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is :
= ( [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{6}[/tex] ) / 2
= [tex]\frac{3 + 5}{6}[/tex] / 2
= [tex]\frac{8}{6}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{6}[/tex]
or
[tex]\frac{2}{3}[/tex]
Therefore , the fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
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Manny and Emma are both competing in a long jump competition at their school .mang can jump for fifths of the distance that Emma can jump . many can jump 40 inches how far can Emma jump
divide 40 by 4/5 =
40*5/4 = 200/4 =50
Emma can jump 50 inches
Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?
thank you!
Wyatt uses 3/4 gallon of paint to paint two identical doghouses. Wyatt has 11/2 gallons of paint. Assuming that the doghouses are identical, ow many doghouses can Wyatt paint with 11/2 gallons of paint?
Which ordered pairs are on the line with the equation y+3.5=0.75(x-2)? I will mark brainliest. Thanks!
come back and mark him brainliest
-lemons 2021
One more math question! Thanks!
The circle design a class which represents a circle in the (x,y) coordinate plane. a circle object is initialized with three input arguments. the center of the circle specified as the first two inputs (x,y) and the radius of the circle. by default the circle will be centered at (0, 0) with a radius of 1. c = circle(0, 0, 1) the circle class should provide proper getters/setters for the x and y coordinates of the center as well as the radius. the circle should also have a getarea() and getperimeter() method. finally, the circle should have a method called, ispointwithincircle(x, y) which takes as augments the x and y coordinate of a point and determines whether the point lies within the circle. it should return a boolean indicating whether the point is within the circle.
The circle design a class which represents a circle in the (x,y) coordinate plane.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
from math import dist # to calculate distance between two points
# defining class circle
class Circle:
# constructor of Circle
# with default parameters
def __init__(self, x_coord=0, y_coord=0, radius=1):
self.centre_x = x_coord
self.centre_y = y_coord
self.radius = radius
# getters
def getX(self):
return self.centre_x
def getY(self):
return self.centre_y
def getRadius(self):
return self.radius
# setters
def setX(self, x):
self.centre_x = x
def sety(self, y):
self.centre_y = y
def setRadius(self, r):
self.radius = r
# function to calculate and return area
def getArea(self):
return 3.141*(self.radius**2)
# function to calculate and return perimeter
def getPerimeter(self):
return 2*3.141*self.radius
# calculates the distance between circle centre and
# given coordinates
# returns true if distance is less than radius
def isPointWithinCircle(self, x, y):
return dist([self.centre_x, self.centre_y], [x, y]) < self.radius
c1 = Circle(3, 3, 7)
c2 = Circle()
print("First Circle perimeter: " + str(c1.getPerimeter()))
print("First Circle area: " + str(c1.getArea()))
c2.setX(3)
c2.sety(3)
c2.setRadius(2)
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
print("Moving second Circle")
c2.setX(3+c2.getX())
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
Thus, the circle design a class which represents a circle in the (x,y) coordinate plane.
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Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.
Answer: The length of the chord AB is √2 r units.
Step-by-step explanation: Given in the question that Circle P is tangent to the X-axis at the point A and tangent to the Y-axis at the point B.
Also, the co-ordinates of centre of the circle P are C(r, r). See the attached image below.
We are to find the length of the chord AB, with end-points A and B as the points of tangency.
From the figure, we note that
the co-ordinates of the points A and B are (0, r) and (r, 0) respectively.
As the X-axis and Y-axis are perpendicular to each other, so the lines parallel to them, OB and OA are also perpendicular to each other.
That is, ∠ACB = 90°.
This implies that the triangle ACB is a right-angled triangle.
Now, using Pythagoras theorem in ΔACB, we have
[tex]AB^2=CA^2+CB^2~~~~~~~~~~~~~~~~~~~~~(i).[/tex]
The lengths of the line segments CA and CB are calculated, using distance formula, as follows:
[tex]CA=\sqrt{(0-r)^2+(r-r)^2}=\sqrt{r^2}=r,\\\\CB=\sqrt{(r-r)^2+(0-r)^2}=\sqrt{r^2}=r.[/tex]
From equation (i), we get
[tex]AB^2=r^2+r^2\\\\\Rightrarrow AB^2=2r^2\\\\\Rightarrow AB=\sqrt2r~\textup{units}.[/tex]
Thus, the length of the chord AB is √2 r units.
A circle, tangent to the x-axis and y-axis, forms a square where its radius r is the side length. The chord, which is the diagonal, can be found using the Pythagorean theorem resulting to r√2.
Explanation:In the given problem, a circle P is tangent to the x-axis and y-axis at two points. This means that the radius of the circle is the distance from the center to either axis, which are both r, as the coordinates of the center are (r,r). We are asked to find the length of the chord whose endpoints are the points of tangency.
The chord is actually the diagonal of a square that has sides of length r. So, its length can be found using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the sides of the square and c is the diagonal. Hence the length of the chord can be found as √(r^2 + r^2) = √(2r^2) = r√2.
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A small train at an amusement park is carrying passengers. Half of the passengers are 4 years old, 1/10 are 5 years old, 3/10 are 6 years old, and 1/10 are 7 years old.
What is the expected age for one of the passengers on the train?
A. 5 years
B. 5.5 years
C. 6 years
D. 6.1 years
PLEASE HELP ME!
Diana made a recipe that yields 6 and 1 over 2 cups. If each serving is 1 over 4 cup, which expression will help Diana determine the number of servings her recipe will yield?
6 1/2 divided by 1/4
6.5 /0.25 =26 servings
After the z value is calculated, the ____________ is obtained from a table of z-scores.
After the z value is calculated, the probability is obtained by using the corresponding area under the normal curve from the z-table. The z-table shows the area to the left of the calculated z-score and can be used to determine probabilities and critical values for the standard normal distribution.
Explanation:After the z value is calculated, the probability is obtained from a table of z-scores. The z-table is used to find the area under the normal curve, which represents the probability associated with a z-score. When looking up a z-score in the z-table, you will see the area under the normal curve to the left of the z-score which corresponds to the probability of obtaining a score within that range. The z-table provides critical values for the standardized normal distribution which has a mean of 0 and a standard deviation of 1. To calculate the area between two z-scores, subtract the smaller area from the larger area.
For example, if we need to find the z-score that corresponds to an area of 0.9, we would look up this value in the z-table to discover that the z-score is approximately 1.28. This z-score then can be used with the mean and standard deviation of the distribution to find the original score using the formula μ + (z)(σ) = x. It's important to note that while most z-tables show the area to the left, some may provide the area from the mean to the z-score, so the method used will be indicated on the table itself.
I didn't get this one question right on a test. Could someone tell me what I did wrong? Plz and ty
I have a bag of trail mix. half of the bag contains peanuts, 1/4 of the bag is chocolate candies, and 1/4 of the bag is dried fruit. what is the probability that i will select a peanut?
recursive equation for 5,8,11,14,17
In the problem 17- 8= 9, the number 9 is the ____________
In the subtraction problem 17 - 8, the number 9 is the difference, which is the result obtained after subtracting 8 from 17.
In the problem 17 - 8 = 9, the number 9 is the difference. In subtraction, the difference is the result of subtracting one number from another. Here, when we subtract 8 from 17, we get the difference of 9. This is because 17 is the minuend (the number from which another number is subtracted), 8 is the subtrahend (the number that is to be subtracted), and 9 is the difference (the result of the subtraction).
Twice a number minus a second number is -1. twice the second number added to three times the first number is 9. find the two numbers
Marie worked 2 weeks during her college semester break. She earned $280 the first week and $245 the second week. If 1/2 oh her total earnings went to taxes and 1/4 went to college tuition,how much money dI'd she have left?
CAN someone please check this i will give out brainliest !
its proofs and theorems in geometry
check the ones in red
What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ? Enter your answer in the box. Do not round any side lengths.
A gasoline pump delivers 4 2/5 gallons of gas per minute. How many minutes will it take to fill a gas tank that holds 17 1/4 gallons?
Please show all steps and equation.
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
Please help it’s due tomorrow! I’m in a hurry!! Omg pls help! :( ahhhhhhhhhhh
There are 3 people who work full time and are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full time. if one of the people is budgeted for 1/2 of the time and the other person is budgeted for 1/3, what part od the third workers time should be budgeted to this project