A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
The boat's travel from when it was first noticed until it stopped is 554.89 ft.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
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Describe the correlation in terms of strength (weak or strong) and direction positive or negative).
The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.
How to Interpret Correlation Problems?
A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.
Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.
Now, in terms of direction;
A correlation of +1 indicates a perfect positive correlation which tells us that both variables move in the same direction together. A correlation of –1 indicates a perfect negative correlation, which tells us that as one variable goes up, the other goes down.A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables.Read more about Correlation at; https://brainly.com/question/4219149
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A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
Answer:
7m tall convert this into imperial measurement
Giving brainliest
Determine the current temperature in degrees Fahrenheit if the current temperature is 32 degrees Celsius in Lima, Peru. Round the final answer to the nearest whole number.
32
56
90
103
Answer:
The answer is 90.
Thank you
Answer:
89.6
Step-by-step explanation:
The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32
F = [ C × (9/5) + 32 ]
Given that, C = 32
F = 32 × (9/5) + 32
F = 32 [ 1 + (9/5) ]
F = 32 [ 1 + 1.8 ]
F = 32 × 2.8
F = 89.6
Finding the LCM of algebraic term and algebraic expressions.
Answer:
The LCM is made by multiplying all factors included in the factoring of the given expressions. Common factors are used once only and the one with the highest power is used. x + 3 is a factor in the first expressions is therefore used.
Step-by-step explanation:
What is the factored form of 50x^2-8
Answer:
2(5x-2)(5x+2)
Step-by-step explanation:
An amusement park prices tickets at $55 and sells an average if 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
P(x) = -40x^2- 100x + 27,500
Use the given Information to complete the sentences.
The constant of the polynomial expression represents the
___ in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the ___ in the price of a ticket.
The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
[tex]P(x) = -40x^2- 100x + 27,500[/tex].
What is the combined function?In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
We need to use the given information to complete the sentences.
The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
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The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
An amusement park prices tickets at $55 and sells an average if 500 tickets daily.
The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
Plug x = 0
P(0) = 27500
The above value is the constant of the polynomial function.
The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.
As the x is the number of $2 increases in the price of a ticket.
Then,
= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2
Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
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Which congruence theorem can be used to prove ?
Answer:
ASA
Step-by-step explanation:
by ASA congruence theorem
how can i soolve it?
Answer:
x = 4 y = 1
Step-by-step explanation:
Opposite sides are equal , so
2x-3y = 5
x+5y =9 <====== multiply this by -2 and add to first equation
-13y = -13
then y = 1 and x + 5y = 9 so x = 4
Triangle ABC has vertices at A(1,2), B(4,0) and C(1,-4) Find the area of triangle ABC.
PLEASE EXPLAIN HOW YOU DID IT
The area of triangle ABC from the given vertices is gotten as; 7.5
How to find the area of a triangle?We are given the vertices of the triangle as;
A(1, 2)
B(4, 0)
C(1,-4)
The formula for area of a triangle with 3 vertices is;
Area = ¹/₂[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
Thus;
Area = ¹/₂[1(0 + 4) + 4(-4 - 1) + 1(1 - 0)]
Area = ¹/₂(4 - 20 + 1)
Area = -7.5
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It’s math can you guys help me out 10 points:)
Answer:
90 liters
Step-by-step explanation:
According to the graph in order to gain $36 you must sell 90 liters. Hope this helps :)
Solve using a proportion.
Jasmine uses 4 inches of tape to wrap 5 presents. How many inches of tape will Jasmine use to wrap 15 presents?
A. 12 inches
B. 10 inches
C. 15 inches
D. 14 inches
helppppppppp markingbrainliest
a)
x×3+4=22
b)
x×3+4=22
x×3=22-4
x×3=18
x=18÷3
x=6
Hope it helps
Answer:
x=6
Step-by-step explanation:
your equation would be X * 3 + 4 = 22
to solve you subtract four from both sides then divide three by both sides because you do the opposite of the sign thats there and you get x= 6! i hope this helped
(49p2–490p) ÷(p–10)
please help!!
Answer:
(49p2–490p) ÷(p–10)
Step-by-step explanation:
On a farm, there is a grain silo.The silo is cylindrical with a tile roof. The silo has a diameter of 8 metres and is 6 metres tall. The farmer wants to paint the curved surface of the silo.Each can of paint will cover 20m². The paint costs $11.75 per can. How much will it cost the farmer to paint the silo?
The paint that the farmer needs to paint his Silo will cost $152.75.
How to calculate the price of the paint that the farmer will require?To calculate the value of the total paint that the farmer will require, we must carry out the following procedure:
1. Identify the area you need to paint
2πrh + 2πr²2 * 3.14 * 4m * 6m + 2 * 3.14 *4m² = 251.32m²2. Find how many cans of paint he needs.
251.32m² ÷ 20m² = 12.56That is, he will need 13 cans of paint.
3. Find the price of 13 cans of paint.
$11.75 × 13 = $152.75Learn more about area in: https://brainly.com/question/27683633
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What is the formula for the margin of error?
Answer:
[tex]ME =\frac{z*s}{\sqrt{n}}[/tex]
Step-by-step explanation:
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings
To find margin of error, you need
Get the population standard deviation (σ) and sample size (n)n = sample size
Take the square root of your sample size and divide it into your population standard deviationσ = population standard deviation Multiply the result by the z-score consistent with your desired confidence interval according to the following table:z = z-score
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answer must be in simplest form
The trigonometric ratios shows that the cos M is 4/5.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypothenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin [tex]\alpha[/tex], cos [tex]\alpha[/tex] and tan [tex]\alpha[/tex], where:
[tex]sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}[/tex]
For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.
[tex]hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24[/tex]
If MN=24, the cos M will be
[tex]cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}[/tex]
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When you multiply a number by 12 and subtract the product from 360, the difference is 216. Find the number.
The equation will be 12a – 360 = 216. Then the value of the variable a will be 48.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
When you multiply a number by 12 and subtract the product from 360, the difference is 216.
Let the number be a.
Then we have the equation
12a – 360 = 216
By solving the equation, we have
12a = 216 + 360
12a = 576
a = 576/12
a = 48
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.A bacteria culture grows at a rate of 20%
per minute. If the culture initially has 3,200
bacteria specimens, how many specimens
would be in the culture after 5 minutes?
The number of the specimens would be in the culture after 5 minutes will be 7,962.62.
What is an exponent?Consider the function:
y = a (1 + r) ˣ
Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.
A bacteria culture grows at a rate of 20% per minute.
If the culture initially has 3,200 bacteria specimens.
Then the equation will be
y = 3200 (1 + 0.2) ˣ
y = 3200 (1.20) ˣ
Then the number of the specimens would be in the culture after 5 minutes will be
y = 3200 (1.20)⁵
y = 7962.62
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Probability of Next Candy
Fill in the chart below with the probability of choosing the next candy.
Answer:
8 is correct.
Mark as brainlist, thanks me, and rate. Hope it helps you!!!
3(2x − 8) – 11x ......
Answer:
-5x-24
Step-by-step explanation:
3(2x-8)-11x
Use distributive property.
6x-24-11x.
Combine like terms.
6x-11x-24=-5x-24
-5x-24
Hope this helps!
If not, I am sorry.
Answer:
-5x - 24
Step-by-step explanation:
3(2x − 8) – 11x =
Distribute the 3, then combine like terms.
= 6x - 24 - 11x
= -5x - 24
W+15x-9y+2z
Terms:
Coefficients:
In the problem given:
W + 15x - 9y + 2z
The term are single mathematical expressions that separate values.
In the expression, there is a + and -; these concludes 2 terms.
There are 3 coefficients next to each variable.
The coefficients are 15x, -9y, and 2z.
That means there are 3 coefficients.
Cheers
- ROR
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \sf{W \rightarrow coefficient = 1} [/tex][tex] \sf{15x \rightarrow coefficient = 15} [/tex][tex] \sf{-9y\rightarrow coefficient = -9} [/tex][tex] \sf{2z\rightarrow coefficient = 2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]
[tex] \large\textsf{Terms :} [/tex]
[tex] \texttt{W } [/tex][tex] \texttt{coefficient = 1} [/tex]
[tex] \texttt{15x} [/tex][tex] \texttt{coefficient = 15} [/tex]
[tex] \texttt{-9y} [/tex][tex] \texttt{coefficient = -9} [/tex]
[tex] \texttt{ 2z} [/tex][tex] \texttt{coefficient= 2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The mass of Jupiter is 1.898x10^27 kg, while the mass of Earth is 5.972x10^24 kg. How many times greater is the mass of Jupiter compared to the mass of the Earth? Round the answer in standard form to the nearest whole number.
Answer:
318
Step-by-step explanation:
(1.898×10^27)÷(5.972×10^24)=317.82=318
Can I take a picture of the problem and upload for you to see?
A similarity transformation maps AABC to AJKL The measure of ZA of prelmage AABC Is 105°. The scale factor of the dilation in the similarity
transformation is 1.5. If ZA In the prelmage corresponds to ZJ in the image, what is m
a 70°
b 140°
c 105°
d 35°
its reserved.
Answer:
The answer is 105.
Step-by-step explanation:
17/21 - (2/7 + 1/7)
Please solve!!
Answer:
8/21
Step-by-step explanation:
17/21 - (2/7 + 1/7)
= 17/21 - ( 3/7)
= 17/21 - (3×3/7×3)
= 17/21 - 9/21
= 8/21
What is the GCF of the numbers in the expression (32 + 16)?
Answer:
the GCF of the number in the given expression (32+16) is 16.
Step-by-step explanation:
This is your answer
There are 7 pieces of pie left over in the cafeteria. If 4 pieces are apple and 3
are cherry, what fraction of the remaining pieces are apple?
blem Sets Questions
e the questions below. Show your work.
1. Mike and Juan are going on a road trip for graduation. Together they have $300 dollars to spend on a
rental car. If the company charges a flat fee of $50 plus $0.75 a mile, how many miles can they travel
and still be within their budget?
Answer:
333.33 miles
Step-by-step explanation:
Let x be the number of miles Mike and Juan drive.
They only have $300, however, so let's set an equation that will tell us how many miles, x, does it take to result in a total bill of $300. The mileage fee will be ($0.75/mile)*(x miles driven). Start with the $300 and subtract both the fixed fee of $50 and the mileage fee of 0.75x and set the result to zero, the point at which they spend $300.
$300 - $50 - ($0.75)x = 0
$250 - ($0.75)x = 0
- ($0.75)x = -$250
x = -($250)/(-$0.75)
x = 333.33 miles
CHECK:
Would Mike and Juan spend $300 on the rental car if they drove 333.33 miles?
Rental Fee: $50
Mileage: ($0.75/mile)*(333.333 miles) = $250
Total Cost: $300 YES
Nothing left for burgers,
Find the value of x. Round to the
nearest tenth.
12
x=[?]
Answer:
17.1
Step-by-step explanation:
Given we have one side and one degree, we can use the trigonometric function "tangent" to solve this right triangle.
Remember that tangent is opposite side over adjacent side, so lets set up the equation:
[tex]tan(35)=\frac{12}{x}[/tex]
Now solve:
[tex]x(tan(35))=12\\x=\frac{12}{tan(35)}[/tex]
As a result, x is equal to approximately 17.1
Any questions feel free to ask :)
