An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?
Answers
The two ships are 1933.32 ft apart
Explanation:Given:
The height of the lighthouse = 350 ft
The angles of depression to the ships are 4 degree and 6.5 degree
To find:
the distance between the two ships
To determine the distance, we will use an illustration of the situation
First we will find the value of y as we need to know this value to get x
To get y, we will apply tan ratio (TOA)
[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]Next is to find x using tan ratio (TOA):
[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]
Related Questions
Which inequalities are shown on the graph?Find your inequalities in the grid below. Check the ONE box that pairs the two correct inequalitiesY-3-1 y>-**-172-**-1 y<-**-1<3+3y>+3y< <+3y2 ++3D D D DOOOO"OOOOPreviousPauseO Search for anything0-
Answers
From the graph we could see that y = x + 3 for the first line . The shaded line is where y is less than or equals to x + 3.
For the second line we can see that y = x - 1 . The shaded line is where y is greater than or equals to x - 1 . Therefore, the inequalities are as follows
[tex]\begin{gathered} y\leq x+3 \\ y\ge x-1 \end{gathered}[/tex]Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month
Answers
Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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Write an equation for the line through the point (x0,y0) with a slope of M in point slope form. Enter X0 and Y0 as y0. Use X and Y for variables names. Your equation should be of the form y=….
Answers
The equation of the line in point slope form is y = M(x - x₀) + y₀ .
The Point slope form of the line passing through the point (x₁,y₁) with slope m is given by the formula
(y - y₁) = m(x - x₁)
In the question ,
it is given that
the required line passes through the points (x₀ , y₀)
and the slope is M .
So, the point slope form equation of the line will be
( y - y₀) = M(x - x₀)
y - y₀ = M(x - x₀)
y = M(x - x₀) + y₀
Therefore , the equation of the line in point slope form is y = M(x - x₀) + y₀ .
The given question is incomplete , the complete question is
Write an equation for the line through the point (x₀,y₀) with a slope of M in point slope form. Your equation should be in the form of y = ... ?
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How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answers
Answer:
Step-by-step explanation:
64.528 is the decimal
Solve the following expression when p = 15 p/3 + 4
Answers
So, our answer is 9!
Which of the following sampling methods would most likely have the smallest margin of erro?A. Roll a die 1000 times and estimate the proportion of 5's that result.OB. Sample 250 registered voters in a large city and ask them their political preference and use the results to estOC. Flip a coin 100 times and estimate the proportion of "heads" that resul.OD. Sample 10 adults and ask them if they support the current President's foreign policy and use this data to reReset SelectionMext
Answers
The sample methodology whose accuracy is better than another is the one with more approximation, this comes from the number of repetitions.
Therefore, option A is the one with more approximation, which mean the least error margin.
Find the x-intercept and y-intercept of the line.
5x-9y=-12
Answers
The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
What is termed as the x and y intercepts?An intercept is a y-axis point that the slope of a line passes. It is the y-coordinate of the a point on the y-axis where a straight line or even a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c seems to be the y-intercept. There are two types of intercepts: x-intercept and y-intercept.For the given question,
The equation of the line is 5x-9y=-12.
For the x intercept, Put y = 0.
5x-9×0=-12.
x = 12/5
x intercept = (12/5, 0)
For y intercept, put x = 0.
5×0-9y=-12
y = -12/9
y = -4/3
y intercept = (0, -4/3)
Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
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This is a graph of the motion of a small boat traveling at a constant speed. Total Distance Traveled 12 10 8 Distance (Kilometers) 6 0 2 4 6 8 1012 Time (Hours) How far will the boat travel in 15 hours? O A. 25 km O B. 30 km O C. 15 km O D. 10 km
Answers
The speed of the boat is given by the gradient of the line.
Given two points (x1,y1) and (x2,y2) on a graph, the gradient of the line that passes through the two points is given by
[tex]\text{ gradient = }\frac{y_2-y_1}{x_2-x_1}[/tex]In this case,
the line passes through the points (0,0) and (2,2).
We can set (x1,x2) = (0,0) and (y1,y2) = (2,2)
Therefore,
[tex]\begin{gathered} \text{ gradient = }\frac{2-0}{2-0}=\frac{2}{2}=1 \\ \text{therefore} \\ \text{the speed = 1km/h} \end{gathered}[/tex]Given that a body travels with speed, s, and in time, t, the distance travelled, d, is given by
[tex]d=st[/tex]In this case,
s = 1km/h, and t = 15hours
Therefore,
[tex]d=1\times15=15\operatorname{km}[/tex]Therefore, the boat travelled a distance of 15km
find the value of XA. 11√ 41inB. 11 inC. 33 inD. 35 in
Answers
From the diagram provided, we have a right angled triangle with the hypotenuse (side facing the right angle) given as 55, while one of the other two sides is given as 44.
We shall apply the pythagoras' theorem as follows;
[tex]c^2=a^2+b^2[/tex]Where,
c = hypotenuse,
a and b = the other sides.
Therefore, we'll now have;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 55^2=44^2+c^2 \\ 3025=1936+c^2 \end{gathered}[/tex]Next step, we'll subtract 1936 from both sides of the equation;
[tex]\begin{gathered} 3025-1936=1936-1936+c^2 \\ 1089=c^2 \end{gathered}[/tex]Add the square root sign to both sides of the equation;
[tex]\begin{gathered} \sqrt[]{1089}=\sqrt[]{c^2} \\ 33=c \end{gathered}[/tex]ANSWER
Therefore, the correct answer is option C, that is 33 inches.
LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Answers
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
The mean of a population is 100, with a standard deviation of 15. The mean of
a sample of size 100 was 95. Using an alpha of .01 and a two-tailed test, what do
you conclude?
O Accept the null hypothesis. The difference is not statistically significant.
Reject the null hypothesis. The difference is statistically significant.
Accept the null hypothesis. The difference is statistically significant.
Reject the null hypothesis. The difference is not statistically significant.
Answers
We conclude that Reject the null hypothesis. The difference is statistically significant.
Define integers.The symbol used to represent integers is the letter (Z). A positive integer can be 0 or a positive or negative number up to negative infinity. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Given,
The mean of a population is 100, with a standard deviation of 15. The mean of a sample of size 100 was 95.
z = [tex]\frac{95-100}{15/10}[/tex]
z = 3.333
Using the p value technique, the value of p is 0.0009, and since p = 0.0009 0.01 the null hypothesis is rejected, the conclusion is made.
Reject the null hypothesis. The difference is statistically significant.
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I need help with this kind of math please. I have tried doing it but I’m so lost and confused
Answers
GF < GE < EF
Explanation:The given angles:
∠G = 74°
∠F = 65°
∠G + ∠F + ∠E = 180° (sum of angles in a triangle)
74 + 65 + ∠E = 180
139 + ∠E = 180
∠E = 180 - 139
∠E = 41°
The size of the side length of the triangles corresponds the size of the angles.
The higher the angle, the higher the side length and viceversa
∠E corresponds to side GF
∠F corresponds to side GE
∠G corresponds to side EF
∠E = 41 is the lowest, followed by ∠F = 65, highest is ∠G = 74
From least to greatest:
GF < GE < EF
......................
Answers
Answer: x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Given that the values of x =
Television 0 1 2 3
Household 30 443 727 1401
Let television be = x
Household = frequency = distribution
Firstly, we need to find the interval of x
The interval of x = Range between two numbers
1 - 0 = 1
2 -1 = 1
3 - 2 = 1
Hence, the interval is 1
[tex]p(x)\text{ = }\frac{frequency\text{ for x interval}}{N\text{ x w}}[/tex]Where N = total frequency
w = interval
Total frequency = 30 + 443 + 727 + 1401
Total frequency = 2601
[tex]\begin{gathered} \text{when x = 0} \\ p(x)\text{ = }\frac{30}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{30}{2601} \\ p(x)\text{ = }0.011 \end{gathered}[/tex]when x = 1
[tex]\begin{gathered} p(x)\text{ = }\frac{443}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{443}{2601} \\ p(x)\text{ = 0}.170 \end{gathered}[/tex]When x = 2
[tex]\begin{gathered} p(x)\text{ = }\frac{727}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{727}{2601} \\ p(x)\text{ = 0.279} \end{gathered}[/tex]when x = 3
[tex]\begin{gathered} p(x)\text{ = }\frac{1401}{1\text{ x 2601}} \\ p(x)\text{ = }\frac{1401}{2601} \\ p(x)\text{ = 0.539} \end{gathered}[/tex]Therefore,
x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Find the lateral surface area and volume of the object in picture below
Answers
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
could you please help me answer this please and thank you it's about the rectangular prism....
Answers
ANSWER:
[tex]A_T=8+8+20+20+40+40[/tex]STEP-BY-STEP EXPLANATION:
In this case, what we must do is calculate the face area and then add each face, like this:
The area of each area is the product between its length and its width, therefore
[tex]\begin{gathered} A_1=2\cdot4=8 \\ A_2=10\cdot4=40 \\ A_3=10\cdot2=20_{} \\ A_4=10\cdot4=40 \\ A_5=10\cdot2=20_{} \\ A_6=2\cdot4=8 \end{gathered}[/tex]The total area would be the sum of all the areas, if we organize it would be like this:
[tex]A_T=8+8+20+20+40+40[/tex]Lesson 4-2: Relations VA Name the ordered pair for each point. C С 1.A 2.B DI 3.C 4.D e е )
Answers
Assign the pair of coordinates for each point (use the graph)
A. (1,4)
B. (-2,-4)
C. (-2,2)
D. (4,-2)
Find an equation of line L. Write your answer using fractions or integers.The equation of line L is y =
Answers
Find slope m, in equation y= mx + b
m = Y/X =( y - y')/ (x - x')
m= (5 - -5 )/ (-3 -3) = 10/-6 = -5/3
Now find b
b = y - mx
= 5 - (-5/3)•-3
. = 5 - 5 = 0
b = 0
Then answer is, equation is
y = (-5/3)x
a.a + 0 = 0Additive Identityb. Multiplicative IdentityCommutative Property of Additiond. Associative Property of AdditionC.
Answers
Answer:
a. Additive Identity
Explanation:
Given the equation:
[tex]a+0=a[/tex]When zero(0) is added to 'a', the result is still 'a'.
The number 0 is the additive identity of 'a'.
Coronado co. sells product p-14 at a price of $52 a unit. the per unit cost data are direct materials $16, direct labour $12, and overhead $12 (75% variable) Coronado has no excess capacity to accept a special order for 38,700 units at a discount of 25% from the regular price. Selling costs associated with this order would be $3 per unit. Indicate the net income/loss
Answers
The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.
How is the net loss determined?Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.
Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.
This results in a loss of $1 per unit.
Selling price per unit = $52
Unit Costs:
Direct Materials = $16
Direct Labor = $12
Variable Overhead = $9 (75% of $12)
Total variable cost per unit = $37
Fixed Overhead = $3 (25% of $12)
Special order price per unit = $39 ($52 x 1 - 75%)
Contribution margin per unit = $2 ($39 - $37)
Total contribution margin = $77,400 ($2 x 38,700)
Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)
Net loss = $38,700 ($77,400 - $116,100)
Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.
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write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas
Answers
Here, we want to write ratios in part to part and in part to whole ratio
For the part to part
Writing carrot to peas, we have;
[tex]142\colon97[/tex]For the parts to whole ratio, we have;
[tex]\begin{gathered} \text{Carrot} \\ \frac{142}{250}\text{ = 142:250} \\ \text{Peas} \\ \frac{97}{250}\text{ = 97:250} \end{gathered}[/tex]Given f(x)=6(1-x), what is the value of:a) f(-8)_____b) f(x) = -30 _____c) f(x) = 30____d) f(30)_____
Answers
Answer:
a) f(-8) = 54
b) f(x) = -30, x = 6
c) f(x) = 30, x = -4
d) f(30) = -174
Explanation:
Given the function:
f(x) = 6(1 - x)
To find f(-8), we replace x by -8 in the equation and then solve
f(-8) = 6[1 - (-8)8]
= 6(1 + 8)
= 6(9)
= 54
For f(x) = -30, we replace f(x) by -30 and solve for x
-30 = 6(1 - x)
Divide both sides by 6
1 - x = -30/6 = -5
Subtract 1 from both sides
-x = -6
Multiply both sides by -1
x = 6
For f(x) = 30, we replace f(x) by 30 and solve for x
30 = 6(1 - x)
Divide both sides by 6
1 - x = 30/6 = 5
Subtract 1 from both sides
-x = 4
Multiply both sides by -1
x = -4
f(30) = 6(1 - 30)
= 6(-29)
= -174
Find the solutions to the following quadratic equation negative 3X squared plus 4X plus one equals zero (-3x^2 + 4x + 1 = 0)
Answers
Answer:
Explanation:
Given:
[tex]-3x^2+4x+1=0[/tex]To find:
the value of x using the quadratic formula
The quadratic formula is given as:
[tex]$$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$[/tex]where a = -3, b = 4, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-4\pm\sqrt{(4)^2-4(-3)(1)}}{2(-3)} \\ \\ x\text{ = }\frac{-4\pm\sqrt{16+12}}{-6} \\ \\ x\text{ = }\frac{-4\pm\sqrt{28}}{-6} \end{gathered}[/tex][tex]undefined[/tex]Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
Answers
Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
1)
we have
100%-22%=78%=78/100=0.78
so
If is discounted 22%
the new price is 100,000*0.78=$78,000
2) If it is then marked up 22%
the new price is
100%+22%=122%=122/100=1.22
78,000*1.22=$95,160
therefore
The new price is not $100,000
the new price is $95,160
Which expression is equivalent to -(-r - 16)?
Answers
Answer: Hi that would be (r+16) since they are generally the same thing, hope this is what you are asking for!
Step-by-step explanation:
What is the probability that a randomly selected oar was purchased in the 2010s given that the oar was made from ash wood?Simplify any fractions
Answers
P (A) = probability of a car purchased in 2010's
P (B) = probability of the car being made from ash wood
P (A and B) = 4
P (B) = 4 +3 = 7
Conditional probability:
P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714
May I please get help with this. For I have tried multiple times but still can’t get the right answer or the triangle after dilation?
Answers
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
[tex]\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}[/tex]step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
[tex]\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}[/tex]step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
does (51, 58) make the equation y =x -7 true?
Answers
The objective is to verify whether the point (51,58) maes the equation y=x-7.
Substitute the values of x and y coordinate in the given equation.
[tex]\begin{gathered} y=x-7 \\ y-x=-7 \\ 58-51=-7 \\ 7=-7 \end{gathered}[/tex]Since, LHS is not equal to RHS.
Thus, the coordinate (51,58) does not make the equation y=x-7.
Hence the answer is NO.
The population of a town is decreasing at a rate of 1% per year. In 2000there were 1300 people. Create a function to find the populationin 2008.
Answers
Given that;
The population of a town is decreasing at a rate of 1% per year.
[tex]\text{Rate r = 1\% = 0.01}[/tex]In 2000 there were 1300 people.
[tex]P_o=1300[/tex]To find the population in 2008;
[tex]P_8[/tex]The time taken is;
[tex]\begin{gathered} t=2008-2000 \\ t=8\text{ years} \end{gathered}[/tex]We can calculate the population of the town in 2008 by applying the formula;
[tex]P_8=P_o(1-r)^t[/tex]Substituting, the given values;
[tex]\begin{gathered} P_t=1300(1-0.01)^t \\ P_t=1300(0.99)^t \end{gathered}[/tex]Above is a functon for calculating the population of the town at time t years after 2000.
The population of the town in the year 2008 is;
[tex]\begin{gathered} P_8=1300(0.99)^8 \\ P_8=1,199.568 \\ P_8\approx1,200 \end{gathered}[/tex]Therefore, the population of the town in 2008 is approximately 1,200 people.
We can also write the equation as;
[tex]y=1300(0.99)^8[/tex]Where y is the population of the town in year 2008.
X + 2y = 3x = 5Enter your answer as a point using parenthesis and a comma. Do not use any spaces in youranswer.If there are no solutions, type "no solutions." If there are infinitely many solutions, type"infinitely many."Answer:
Answers
thats the explanation
answer is : (5, -1)
Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
Answers
We would section the figure into two shapes as shown below
We can see a trapezium and a rectangle. We would find the area of each figure and add them.
For the trapezium,
Area = 1/2 * (a + b)h
a nd b are the opposite sides of the trapezium while h represents the height.
Thus,
a = 20, b = 24 and h = 9es of the trapezium while h represents the height.
Thu sid
