Answer: 8
Hope this helps
From the observation deck of a skyscraper,
Taylor measures a 67° angle of depression
to a ship in the harbor below. If the
observation deck is 1014 feet high, what is
the horizontal distance from the base of the
skyscraper out to the ship? Round your
answer to the nearest tenth of a foot if
necessary.
Given:
Angle of depression from observation deck to a ship = 67°
Height of observation deck = 1014 feet.
To find:
The horizontal distance from the base of the skyscraper out to the ship.
Solution:
Let x be the horizontal distance from the base of the skyscraper out to the ship.
Using the given information draw a diagram as shown below.
In a right angle triangle,
[tex]\tan\theta=\dfrac{Perpendicular}{Base}[/tex]
For triangle ABC,
[tex]\tan A=\dfrac{BC}{AB}[/tex]
[tex]\tan (67^\circ)=\dfrac{1014}{x}[/tex]
[tex]x=\dfrac{1014}{\tan (67^\circ)}[/tex]
On further simplification, we get
[tex]x=\dfrac{1014}{2.35585}[/tex]
[tex]x=430.41789[/tex]
[tex]x\approx 430.4[/tex]
Therefore, the horizontal distance from the base of the skyscraper out to the ship is 430.4 feet.
Applying the Trigonometry ratio, TOA, the horizontal distance from the base of the skyscraper out to the ship is: 430.4 ft.
Recall:
To solve a right triangle, apply any of the Trigonometry ratios, SOH CAH TOA, where necessary.The situation described is shown in an image attached below, where:
BA = horizontal distance from the base of the skyscraper out to the ship (adjacent side length)BC = 1014 ft (Opposite side length)∠A = 67° = reference angle (∅)To find BA, apply TOA, which is:
tan ∅ = Opp/Adjacent
Substitutetan 67 = 1014/BA
[tex]BA = \frac{1014}{tan(67)} \\\\\mathbf{BA = 430.4 $ ft}[/tex]
Therefore, applying the Trigonometry ratio, TOA, the horizontal distance from the base of the skyscraper out to the ship is: 430.4 ft.
Learn more about Trigonometry ratio on:
https://brainly.com/question/10417664
NEED HELP ASAP PLEASE
Assume that a three-month CD purchased for $3000 pays simple interest at an annual rate of 10%. How much total interest does it earn?
$ ____
What is the balance at maturity? ______
Answers:
interest = $75balance at maturity = $3075=============================================================
Explanation:
The simple interest formula is
i = p*r*t
where in this case,
p = 3000 = principal (amount deposited)r = 0.10 = annual interest rate in decimal formt = 3/12 = 0.25 = number of yearsSo,
i = p*r*t
i = 3000*0.10*0.25
i = 75 is the amount of interest earned
This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)
The balance at maturity is p+i = 3000+75 = 3075 dollars
---------------
In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.
Solve the equation and check the result
3(2y-8)-y=9
Answer:
y = 33/5
Step-by-step explanation:
Distribute
3(2y-8)-y = 9
6y - 24 - y
5y - 24 = 9
Add 24 to both sides
5y = 9 + 24
5y = 33
y = 33/5
QUESTION 6 The scale on a map is given as 1 : 320,000. If the distance between the top of the two mountains on the map is 6.8cm, what is the actual distance in kilometres between the two tops of the mountain. ? show working out to prove answer.
Answer:
The actual distance is of 21.76 kilometers.
Step-by-step explanation:
Scale problems are solved by proportions, using a rule of three.
The scale on a map is given as 1 : 320,000
This means that each unit on the map represents 320,000 units of distance.
Distance between the top of the two mountains on the map is 6.8cm
Then
1 cm - 320,000 cm
6.8 cm - x
Applying cross multiplication:
[tex]x = 6.8*320000 = 2176000[/tex]
Distance in kilometers
To convert from centimeters to kilometers, we divide by 100000. So
2176000/100000 = 21.76
The actual distance is of 21.76 kilometers.
Triangle ABC has vertices A (-2, 2), B (2, 4) and C (3, -1). What are the coordinates of A' after a dilation by a scale factor of 2.5?
Answer:
A’(-5,5)
Step-by-step explanation:
x’ = 2.5 * -2 = -5
y‘ = 2.5 * 2 = 5
A ordinary fair dice is thrown once. What is the probability the dice lands on a even number
Please I need help in finding the diameter
Answer:
20
Step-by-step explanation:
diameter=√(12²+16²)=√[4²(3²+4²)]=4√(9+16)=4√25=4×5=20
fill in the blanks
864+2006=--------+864
5351 +(574+799)= 574+(5351+_____)
Answer:
2006
799
Step-by-step explanation:
Given the expression:
The right hand side of the sun must be equal to the left hand side ;
Therefore ;
864+2006=--------+864
The sum of 864 and 2006 must be equal to the right hand side sum ; hence
864+2006= 2006 +864
Similarly, the left hand side and right havd side must also be equal here ;
5351 + 574 + 799 = 574 + 5351 + 799
Hence, the missing value is 799
i need help finding the answer with step by step
Answer:
x= -1
Step-by-step explanation:
if
f(x) = -x-3
and
f(x) = -2
than
-x-3 = -2; add 3 to both sides
-x-3+3 = -2+3
-x = 1 ; multiply both sides by -1
x= -1
etermine whether the given description corresponds to an observational study or an experiment. In a study of 444 women with a particular disease, the subjects were photographed daily. Does the given description correspond to an observational study or an experiment?
Answer:
observational study
Explanation:
The above is an example of observational study. An observational study merely observes and takes note, it does not try to interfere or intervene with the sample by deciding who would be exposed or not exposed to a certain explanatory variable(such as a disease). On the other hand, the experimental study divide up samples into groups, having the experimental group and the control group. This way the researcher interfers with the sample: The experimental group being the group exposed to the independent/explanatory variable while the other/control group is not.
Determine the list of numbers 14, 18 and 33 can be measured of the sides of a triangle if so clarify the triangle as a cute right or obtuse
9514 1404 393
Answer:
no
Step-by-step explanation:
The measures 14, 18, 33 cannot correspond to the sides of a triangle. The two short sides total 32 in length, so cannot meet up with the ends of the side whose length is 33. A triangle cannot be formed.
can someone please tell me the answer .
Answer:
Step-by-step explanation:
Answer:
the last one
Step-by-step explanation:
congruent means they are the same and all sides of a square are the same size.
simplify -5-√-44
i have no idea
Answer:
Undefined
Step-by-step explanation:
The square root of a negative number does not exist in the set of real numbers so it would be Undefined
0.0543 nearest whole number
Answer:
0
Step-by-step explanation:
Ignore the next 2 numbers after 0.05. To the nearest whole number, round 0.05 to the nearest tenth, 0.1. Then round that to the nearest whole number, 0, which is your answer.
Determine the solution set of (x-4)^2 = 12
someone pls help its due soon
9514 1404 393
Answer:
II only
Step-by-step explanation:
You can simplify the inequality like this:
3 -8 > 8 -8 + 5x . . . . . . . . subtract 8 from both sides
-5 > 5x . . . . . . . . . . . . . simplify
-5/5 > (5x)/5 . . . . . . . divide both sides by 5
-1 > x . . . . . . . . . . . . simplify
I find this easier to compare to a numbers on a number line if the inequality symbol points to the left. (This is a personal preference. YMMV)
x < -1
Now, we can see that only numbers to the left of -1 on the number line will be suitable values for x. Of those listed, only -9 is a solution.
II only
Explain or show that the point (5,−4) is a solution to this system of equations:
3x−2y=23
2x+y=6
Answer:
The x and y values of the coordinates satisfy the system of equations.
Step-by-step explanation:
[tex]when \: x = 5 \: and \: y = - 4 \\ 3x - 2y = 3(5) - 2( - 4) \\ = 15 + 8 \\ = 23 \\ \\ 2x + y = 2(5) + ( - 4) \\ = 10 - 4 \\ = 6[/tex]
A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground? 5.78 inches 11.56 inches 2.88 inches
Answer:
104/4 pi
Step-by-step explanation:
Answer: The circumference of a circle is:
Radius = r, Diameter = d, C = Circumference
C=2πr (as 2r=d)
C=πd
-------------
If the radius of the circle is 26" then its diameter must be 52".
This means that the bicycle wheel has a circumference of 52π".
I'm going to divide 52π" into 360 parts (because a circle is made up of 360 degrees). I'll then multiply this value by 80 to give you an answer.
Given: DA≈ WG and WA≈DG. Prove that DAW≈ WGD.
Answer:
Step-by-step explanation:
Statements Reasons
DA ≅ WG Given
WA ≅ DG Given
DW ≅ WD Reflexive property
ΔDAW ≅ ΔWGD SSS
Which statement regarding the diagram is true?
mMKL+mMLK=mJKM mKML+mMLK=mJKM mMKL+mMLK=180 mJKM+mMLK=180
Answer:
mKML+mMLK=mJKM
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, equilateral, isosceles, and right triangle.
As shown in the diagram, polygon MLK is a triangle. The sum of angles in a triangle is equal to 180°, hence:
m∠MLK + m∠KML + m∠MKL = 180° (sum of angles in a triangle).
m∠MKL = 180 - (m∠MLK + m∠KML) (1)
Also along line JL, the sum of angles on one side of a straight line is 180°, therefore:
m∠JKM + m∠MKL = 180° (sum of angles in a straight line)
m∠JKM + m∠MKL = 180° (2)
From equations 1 and 2, equating give:
m∠JKM + [180 - (m∠MLK + m∠KML)) = 180
m∠JKM + 180 - m∠MLK - m∠KML = 180
m∠JKM = m∠MLK + m∠KML
At what values of x, does f(x) = 0?
(-1,0) (2,0) (4,0)
Answer:
-1, 2, 4
Step-by-step explanation:
As one can see in the given values,
(-1, 0), (2, 0), (4, 0)
When one substitutes these values for (x), the outputs, also known as the results or what (f(x)) equals or the (y) values are equal to (0). Therefore, (f(x)) equals zero at these given values.
The diameter of a circle is equal to twice it's radius
TRUE OR FALSE
Answer:
true
Step-by-step explanation:
The diameter of a circle is a single line segment that stretches the entire width of the circle, intersecting with the center point and two points around the circumference. The diameter measures how wide the circle is, and is always equal to twice the radius (2r).
Make x the subject of the formula p = x + a b
Answer:
Step-by-step explanation:
x + ab = p
x = p - ab
3.
- 4x + y = 6
- 5x - y = 21
Answer:
(-3,-6)
Step-by-step explanation:
You need to solve for the system of equations.
Step-by-step explanation:
-4x+y=6
-5x-y=21
y=6+4x
-5x-(6+4x)=21
-5x-6-4x=21
-5x-4x=21+6
-9x=27
-9x÷9=27÷9
x=3
y=6+4x
=6+4(3)
=18
Let X denote the number of bars of service on your cell phone whenever you are at an intersection with the following probabilities.
x 0 1 2 3 4 5
P(X=x) 0.1 0.15 0.25 0.25 0.15 0.1
Determine the following probabilities
a. Two or three bars
b. At least one bar
c. Fewer than two bars
d. More than three bars
Answer:
a. [tex]P(2 \leq X \leq 3) = 0.5[/tex]
b. [tex]P(X \geq 1) = 0.9[/tex]
c. [tex]P(X < 2) = 0.25[/tex]
d. [tex]P(X > 3) = 0.25[/tex]
Step-by-step explanation:
We are given the following distribution:
[tex]P(X = 0) = 0.1[/tex]
[tex]P(X = 1) = 0.15[/tex]
[tex]P(X = 2) = 0.25[/tex]
[tex]P(X = 3) = 0.25[/tex]
[tex]P(X = 4) = 0.15[/tex]
[tex]P(X = 5) = 0.1[/tex]
a. Two or three bars
[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3) = 0.25 + 0.25 = 0.5[/tex]
Thus:
[tex]P(2 \leq X \leq 3) = 0.5[/tex]
b. At least one bar
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1 = 0.9[/tex]
Thus:
[tex]P(X \geq 1) = 0.9[/tex]
c. Fewer than two bars
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1 + 0.15 = 0.25[/tex]
Thus:
[tex]P(X < 2) = 0.25[/tex]
d. More than three bars
[tex]P(X > 3) = P(X = 4) + P(X = 5) = 0.15 + 0.1 = 0.25[/tex]
Thus:
[tex]P(X > 3) = 0.25[/tex]
4( x + 2) + 6x in the simplest form
Answer:
10x+8
Step-by-step explanation:
4( x + 2) + 6x
Distribute
4x+8 +6x
Combine like terms
10x+8
Answer:
10x+8
Step-by-step explanation:
4x+8+6x
(4x+6x)+8
10x+8
A box has dimensions of 4.0 cm by 8.5 cm by 2.0 cm. The volume of the box in mL is:
y=x^2-2x-8
please help ♀️
Answer: (1, -9)
Hope this helped!
Step-by-step explanation:
Two sides and an angle are given:
a = 5, b = 4, angle B = 15°
Determine whether the given information results in one triangle, two
triangles, or no triangle at all.
Solve any triangle(s) that result(s).
Answer:
It results to two triangles
Step-by-step explanation:
There are two angle b
Without graphing, determine the vertex, domain, and range for each of the functions. Does the vertex of each function represent a maximum point or a minimum point? Show all algebraic work to calculate the vertices.
f(x)=(x+4)2+3
Answer:
f(x)=(x+4)+3
f(x)=4x+3