17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angleof depression of 15°. A short while later, the same boat is at an angle ofdepression of 22° along the same line of sight. To the nearest meter, how fardid the boat travel?A 6 mB 7 mC 20 mD 63 m
Answers
Explanation
Lets first graph the situation:
Using the sine law for x, we have:
\(\frac{x}{sin(15°)}=\frac{50}{sin(75°)}\)\(x=\frac{50sin(15°)}{sin(75°)}\)\(x\approx13.39746\)And for y:
\(\frac{y}{sin(22°)}=\frac{50}{sin(68°)}\)\(y=\frac{50sin(22°)}{sin(68°)}\)\(undefined\)
Related Questions
Which pattern will have 32 squares?
Answers
Square of 32: 32² = 1024. surface, a group of points arranged in two dimensions (flat surface), a group of points arranged in three dimensions (curved surface), or the perimeter of any three-dimensional object.
What is dimensions?The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line. A topological measurement of an object's dimension is the extent of its covering qualities. It is, essentially, the quantity of coordinates required to specify a location on the object. A cube is three dimensional, whereas a rectangle is two dimensional.Dimensions include length, breadth, and height. One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube (3D).
To learn more about dimensions refer to:
https://brainly.com/question/19819849
#SPJ1
Can you guys help me on question eight?!
Answers
Answer: Car Rental Company A and B
Step-by-step explanation: Everyone else charges higher prices! Good luck! :D
brainist to correct people
Answers
Akili has two tests next week. The probability that he will pass the first test, science, is 3 4 . How he does on that test affects how he will do on his math test. If he passes science, then the probability that he will also pass the math test is 4 5 ; otherwise, the probability is only 1 3 that he will pass the math test. What is the probability he passes exactly one test
Answers
Answer:
0.2333 = 23.33% probability he passes exactly one test
Step-by-step explanation:
We have these following probabilities:
3/4 probability that he passes the first test.
If he passes the first test, 4/5 probability that he passes the math test.
If he does not pass the first test, 1/3 probability that he passes the math test.
What is the probability he passes exactly one test
Two scenarios:
Pass first(3/4 probability) and fails second(1/5 probability).
Fails first(1/4 probability) and passes second(1/3 probability). So
\(p = \frac{3}{4}*\frac{1}{5} + \frac{1}{4}*\frac{1}{3} = \frac{3}{20} + \frac{1}{12} = \frac{9 + 5}{60} = \frac{14}{60} = 0.2333\)
0.2333 = 23.33% probability he passes exactly one test
Dan has ¾ of a cake left over from his birthday party. His best friend Amy ate 1/7 of the leftover cake. How much of the cake does Dan have left?
Answers
Answer:
9/14 of cake leftStep-by-step explanation:
3/4 left and 1/7 of that eaten:
3/4 - 3/4(1/7) = (3/4) (1 - 1/7) = (3/4)(6/7) =18/28 = 9/14Answer:
9/14
Step-by-step explanation:
tell me in I'm wrong
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
For more such questions on expression
https://brainly.com/question/1859113
#SPJ8
In the year 2003, a person bought a new car for $25000. For each consecutive year
after that, the value of the car depreciated by 12%. How much would the car be worth
in the year 2006, to the nearest hundred dollars?
Answers
Step-by-step explanation:
multiply 25000×12/10
and 2003-2006 is 3 years
next steps are in the attached pic
Answer:
$17000Step-by-step explanation:
Given
Initial value PV = $25000Depreciation rate r = 12% per yearTime t = 2006 - 2003 = 3 yearsFV = ?Required formula and solution
FV = PV*(1 - r)^tFV = 25000*(1 - 0.12)^3 = $17036.80 ≈ $17000 (rounded)You have 137.26 in a bank account. The bank requires you to have at least 50$ in your account or else you are charged a fee. Write and solve an inequality that represents the amount you can write for your next check for without being charged
Answers
Answer: x ≤ 87.26
Step-by-step explanation:
137.26-x=50
x=87.26
you can withdraw 87.26 or less, so the inequality is: x ≤ 87.26
The inequality represents the amount you can check for without being charged is x + 50 ≤ 137.26 and its solution is x ≤ $87.26.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
You have 137.26 dollars in your bank account. If you do not have at least $50 in your account, you will be charged a fee.
Let x be the amount of can be taken from the account without being charged.
x + 50 ≤ 137.26
Simplify the inequality, then the value of 'x' will be
x + 50 ≤ 137.26
x ≤ 137.26 - 50
x ≤ $87.26
The inequality represents the amount you can check for without being charged is x + 50 ≤ 137.26 and its solution is x ≤ $87.26.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
My checking account balance was $443 on February 1st and $872 on February 7th. Show the rate of change
Answers
Answer:
$61.29 per day.
Step-by-step explanation:
Checking account balance on February 1st: $443
Checking account balance on February 7th: $872
Difference in balances: $872 - $443 = $429
Number of days between February 1st and February 7th: 7 days
Rate of change = Difference in balances / Number of days
Rate of change = $429 / 7 days
To find the rate of change per day, divide the difference in balances by the number of days:
Rate of change = $429 / 7 days ≈ $61.29 per day
Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.
I need 2 expressions that are equal to 30m+15 when you solve them! Please be quick!
Answers
Answer:
\(30m + 15 = 3(10m + 5)\\\)
\(30m + 15 = 5(6m+3)\)
Step-by-step explanation:
Given
\(30m + 15\)
Required
Equivalent expressions
We have:
\(30m + 15\)
Factor out 3
\(30m + 15 = 3(10m + 5)\)
Also:
\(30m + 15\)
Factor out 3
\(30m + 15 = 5(6m+3)\)
Name the two congruent triangles
Answers
\( \boxed{ \blue{Answers + Explain}} \)
the two triangles are congruent. Because it has sides that match and are the same length.
.
the corresponding side is:
\( \rm AC \cong CE \)\( \rm CD \cong BC \)\( \rm AD \cong BE \).
the corresponding angle is:
\( \rm \angel{CAD} = \angel{BEC} \)\( \rm \angel{ADC} = \angel{EBC} \)\( \rm \angel{ACD} = \angel{BCE} \)Write the expression using exponents.
−(4b)(4b)(4b)
Answers
The expression −(4b)(4b)(4b) using positive exponents is -(4b)³
How to rewrite the expression using exponentsFrom the question, we have the following parameters that can be used in our computation:
−(4b)(4b)(4b)
Express properly
So, we have
−(4b) * (4b) * (4b)
5⁻¹² * 32⁻³ * 9⁻¹⁵
By using the definition of positive exponents, we have
−(4b) * (4b) * (4b) = -(4b)³
So, the solution is -(4b)³
Read more about expressions at
brainly.com/question/15775046
#SPJ1
Josiah owes $3,500 on his credit card with a minimum percentage of 3% or $100 (whichever is higher). How much is the minimum payment due?
Answers
$105 is higher than $100, the minimum Payment due on Josiah's credit card is $105.
The minimum payment due on Josiah's credit card 3% of his outstanding balance and compare it to the minimum payment of $100. The higher amount between the two will be the minimum payment.
1. Calculate 3% of $3,500:
3% * $3,500 = 0.03 * $3,500 = $105
2. Compare the calculated amount with the minimum payment of $100:
Minimum payment = max($105, $100)
Since $105 is higher than $100, the minimum payment due on Josiah's credit card is $105.
The credit card company sets a minimum payment to ensure that the cardholder makes regular payments towards their outstanding balance. The minimum payment is usually a percentage of the balance or a fixed amount, whichever is higher. In this case, the minimum payment is calculated as 3% of the outstanding balance or $100, whichever amount is greater.
To know more about Payment due.
https://brainly.com/question/3656193
#SPJ11
please answer! giving brainliest
Answers
Answer:
d .
x=11
Step-by-step explanation:
ML and JK are chords of the circle
MN*LN=JN*KN
(x-7)*(x+21)=(x+5)*(x-3)
x^2+21x-7x-7*21=x^2-3x+5x-5*3
x^2+14x-147=x^2+2x-15
x^2-x^2+14x-2x=147-15
12x=132
x=132/12=11
(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
Answers
(ii) Substituting the coordinates of point A (b, 4) into the equation of the line l₁, 4 = -2b + 3. Solving for b, we have b = -1/2.
(iii) Since the line 12 is perpendicular to l₁, its gradient is the negative reciprocal of the gradient of l₁. Thus, the gradient of the line 12 is 1/2. Using the point-slope form of the equation of a straight line, the equation of the line 12 is y + 5 = 1/2(x - 0) or y = 1/2x - 5.
answer rn and you get so many points it will melt your teeth
if its right u get brain list
What is the value of x if x * x + 2x - 35 = 0?
Answers
Answer: 5 and -7
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
5
Step-by-step explanation:
x * x + 2x - 35 = 0
5× 5+ 10 - 35= 0
What is the least common multiple of 12 and 16?
1cm(12, 16) =
Answers
Multiples of 12: 12,24,48,60
Multiples of 16: 16,32,48,64,
Select the correct answer. Which is the correct solution to the expression 3 + 5^2? You can use a calculator to find the answer. A. 10 B. 13 C. 28 D. 64
Answers
The correct solution to the expression 3 + 5^2 is C. 28.
What is an expression?Mathematically, an expression is a combination of variables with numbers, values, or constants.
Mathematical or algebraic expressions use the mathematical operands like addition (+), subtraction (-), division (÷), multiplication (×), exponents (^), etc.
An algebraic expression does not go with the equal symbol (=), unlike an equation.
3 + 5^2
= 3 + 5 x 5
= 3 + 25
= 28
Thus, an evaluation of the algebraic expression 3 + 5^2 gives the solution as Option C.
Learn more about algebraic expressions at https://brainly.com/question/2164351.
#SPJ1
What is the equation for proportions? What does each letter represent?
Answers
Answer:
Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."
Step-by-step explanation:
look at the attachment.
Ciara budgeted $30 per month for entertainment. Movies cost $7 and sports games cost $5.
Let x represent the number of movies she attended in a given month and let y represent the number of sports games she attended in the same month.
What inequality models this problem?
_____x + y ≥ ________
Answers
The inequality that models the given problem is:
7x + 5y ≥ 30
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The budgeted amount for the month = $30
Cost of the movie = $7
Cost of sports games = $5
x = represent the number of movies she attended.
y = represents the number of sports games she attended.
The inequality that models the situation above is:
7x + 5y ≥ 30
Thus,
The inequality that models the situation above is:
7x + 5y ≥ 30
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
How do you factor and simplify 4x^2+ 25
Answers
Answer:
(4x + 5)(4x + 5)
Step-by-step explanation:
4x * 4x = 4x^2, and 5 * 5 = 25. Thus being 4x^2 + 25
Why is 3/7, and 12/21 non-proportional
Answers
If two fractions are proportional, what you do to the denominator, you must do also to the numerator.
In this case, 3/7 and 12/21 is non-proportional, because the numerator was multiplied by 4 (3 x 4 = 12) , while the denominator was multiplied by 3 (7 x 3 = 21). If it was proportional, both the numerator and denominator must be multiplied by either 3 or 4.
~
Jenelle bought a home for $470,000, paying 18% as a down payment, and financing the rest at 5.4% interest
for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she
will spend on this home. Include the down payment in your answer. $
Video
Answers
Using percentage, we can find:
1- 84600
2- 385400
3- 20811.6
4- 7576776
What do you mean by percentage?A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".
Now in the question,
Downpayment = 18% of 470000
= 84600
original amount financed =
470000-84600
= 385400
Monthly payment = 5.4% of 385400
= 20811.6
Total payment in 30 years = 7576776
To know more about percentage, visit:
https://brainly.com/question/29306119
#SPJ1
Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
Answers
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
for such more question on percentile
https://brainly.com/question/24877689
#SPJ8
Write a word description of the set.
{−9, −8, −7, −6, −5, −4, −3, −2, −1}
the set of which one whole numbers,natural numbers, negative integers or integers
greater than__________________.
Answers
Answer: negative integers greater than -10
This is because stuff on the number line to the right is larger than stuff on the left. We can say 2 < 7 since 7 is to the right of 2.
Also, -7 < -2 for similar reasoning.
Saying integers greater than -10 excludes this endpoint. We stop once we reach -1 because 0 and anything larger aren't negative integers.
What is the remainder when f(x) = x^2 + 14x − 8 is divided by (x − 5)? 103 88 87 72
Answers
Answer:
The answer is 87Step-by-step explanation:
f(x) = x² + 14x - 5
To find the reminder when f(x) is divided by x - 5 , substitute the value of x into the above formula
That's
x - 5 = 0
x = 5
So we have
f(5) = 5² + 14(5) - 8
f(5) = 25 + 70 - 8
f(5) = 95 - 8
We have the final answer as
87Hope this helps you
Answer: 87
Step-by-step explanation: took the test hope this helps :)
Find the population statistics for Florida from 1950-2010. Find a linear regression model, quadratic regression model and an exponential regression model for the current population of your state.
Answers
1950 2,771,305
1960 4,951,560
1970 6,789,443
1980 9,746,324
1990 12,937,926
2000 15,982,378
2010 18,801,310
Sorry I couldn't find models.
Evaluate the circulation of G =xyi +zj +4yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis.
Answers
Answer:
I didn't know the answer and sorry I am here taking freepoint because I needed them in a hurry so that I can ask my questions from someone else that's why I really sorry and thank you for free points
Select all of the expressions that are less than 10 2/3.A.10 2/3×9/10B.1×10 2/3C.10 2/3×2 1/3D.1/8×10 2/3E.10 2/3×3/5
Answers
Given:
\(10\frac{2}{3}\)To Determine: All expressions that are less than 10 2/3
Verify for each of the options
OPTION A
\(\begin{gathered} 10\frac{2}{3}\times\frac{9}{10} \\ =\frac{32}{3}\times\frac{9}{10} \\ =\frac{96}{10}=9\frac{6}{10} \end{gathered}\)OPTION B
\(1\times10\frac{2}{3}=10\frac{2}{3}\)OPTION C
\(undefined\)8 Select the correct answer from each drop-down menu. Some of the images in the diagram are images of polygon 1 from similarity transformations. Graph shows 5 polygons plotted on coordinate plane. Polygon 1 is at A(4, 14), B(6, 22), C(18, 22), D(22, 14). Polygon 2 is at E(3, 10), F(5, 8), G(7, 8), H(9, 10). Polygon 4 is at M(15, 8), N(16, 12), O(22, 12), P(24, 8). Below are polygons 3 and 5. Polygon and polygon are similar to polygon 1. Reset Next
Answers
It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.
What exactly is polygon?In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.
In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.
In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.
Learn more about polygon on:
https://brainly.com/question/24966296
#SPJ1
