Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?
Answers
Answer:
63.39 yards.
Step-by-step explanation:
Refer the attached figure
We are given that Caleb and Emily are standing 100 yards from each other i.e. BC = 100
Let BD = x
So, DC = 100-x
We are given that Caleb looks up at a 45° angle to see a hot air balloon i.e. ∠ABD = 45° and Emily looks up at a 60° angle to see the same hot air balloon i.e. ∠ACD = 60°
Let AD be the height of the balloon denoted by h.
In ΔABD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 45^{\circ} = \frac{AD}{BD}[/tex]
[tex]1= \frac{h}{x}[/tex]
[tex]x=h[/tex] ---1
In ΔACD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 60^{\circ} = \frac{AD}{DC}[/tex]
[tex]\sqrt{3}= \frac{h}{100-x}[/tex]
[tex]\sqrt{3}(100-x)=h[/tex] ---2
So, equating 1 and 2
[tex]\sqrt{3}(100-x)=x[/tex]
[tex]100\sqrt{3}-\sqrt{3}x=x[/tex]
[tex]100\sqrt{3}=x+\sqrt{3}x[/tex]
[tex]100\sqrt{3}=x(1+\sqrt{3})[/tex]
[tex]\frac{100\sqrt{3}}{1+\sqrt{3}}=x[/tex]
[tex]63.39=x[/tex]
Thus the height of the balloon is 63.39 yards.
Answer:
B
Step-by-step explanation:
Related Questions
Find the volume of a sphere with a great circle area of 201.06 square inches
Answers
so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².
keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=201.06 \end{cases}\implies 201.06=\pi r^2 \\\\\\ \cfrac{201.06}{\pi }=r^2\implies \sqrt{\cfrac{201.06}{\pi }}=r\\\\ -------------------------------[/tex]
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \sqrt{\frac{201.06}{\pi }} \right)^3}{3}\implies V=\cfrac{4\pi \left( \frac{\sqrt{201.06^3}}{\sqrt{\pi ^3}} \right)}{3} \\\\\\ V=\cfrac{4\pi \cdot \frac{\sqrt{201.06^3}}{\pi \sqrt{\pi }}}{3}\implies V=\cfrac{\frac{4\sqrt{201.06^3}}{\sqrt{\pi }}}{3}\implies V=\cfrac{4\sqrt{201.06^3}}{3\sqrt{\pi }}[/tex]
Final answer:
To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.
Explanation:
To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.
First, let's solve the equation 4πr² = 201.06 for r:
4πr² = 201.06
r² = 201.06 / (4π)
r² ≈ 16.06
r ≈ √16.06 ≈ 4.01
Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:
V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches
Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.
Answers
Your equation is:
(y₂ - y₁)/(x₂ - x₁) = Slope
Let:
(2,1) = (x₁,y₁)
(3,4) = (x₂,y₂)
Plug into corresponding numbers
(4 - 1)/(3 - 2) = 3/1
3/1 is your slope
hope this helps
Cancelling a dance class after several students hurt themselves is an example of which risk management strategy?
Answers
Avoid strategy as the threat/risk is directly related to identified threats and these sources of threats are cancelled
Explanation:
Risk management is defined as:
The identification , analysis, control and possibly elimination of any undesired hazards or risks arising from a certain situation or activity
There are four risk management strategies which are:
1- Avoid: To eliminate the risk by totally avoiding the situation/activity
2- Mitigate: To try to reduce the expected hazards of the situation/activity
3- Accept: To accept the hazards and take your chances
4- Transfer: To outsource the risk (as in case of insurance)
In case of cancelling the dance class, we can note that the risks are directly related to identified threats and the threats are totally cancelled in order to avoid those risks. Therefore, the best strategy describing this situation is "avoid strategy"
Hope this helps :)
The scenario of cancelling a dance class due to student injuries is an example of the 'risk avoidance' strategy in risk management, which aims to avoid potential harm.
Explanation:Canceling a dance class due to multiple students getting injured is a risk management strategy known as risk avoidance. This strategy eliminates the risk by not participating in the activity that could lead to the risk. In this context, the dance class risks injury to the students. In such a scenario, the dance instructor or school chooses to avoid the risk (moral hazard) by cancelling the activity (i.e., the dance class), thereby protecting the students from further harm. This is a common approach employed in situations where the potential adverse outcomes of risk outweigh any potential benefits of the activity.
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Subtract. (4x^2+8x−2)−(2x^2−4x+3) Enter answer, in standard form
Answers
You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
Answers
Given that the financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.
Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)
Thus,
[tex]2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44[/tex]
Therefore, his monthly payment is $119.44
An integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
Answers
eg 21 is composite and 23 is prime.
solve 4^x = 243 round to the nearest ten thousandth
Answers
your answer is 3.9624
Answer:
Value of x is 4.0
Step-by-step explanation:
Given:
[tex]4^x=243[/tex]
To find: Value of x.
We use the following rule,
[tex]log\,x^a=a.log\,x[/tex]
Consider,
[tex]4^x=243[/tex]
Take log on both sides.
[tex]log\,4^x=log\,243[/tex]
[tex]x\times log\,4=log\,243[/tex]
[tex]x=\frac{log\,243}{log\,4}[/tex]
[tex]x=\frac{2.386}{0.602}[/tex]
x = 3.962
x = 4.0 (nearest tenth)
Therefore, Value of x is 4.0
For each example below, determine whether a positive, negative, or no cause and effect relationship exists.
1) Smoking and cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day
3) The number of licks taken and the size of the Tootsie Pop
Answers
#2 - No relationship.
#3 - Negative
A positive relation between two things means that they are proportional to each other. One affects the other thing.
1) Smoking and cases of lung cancer. This is positive. As smoking affects lungs and can cause lung cancer. So, with increased smoking comes the increased risk of lung cancer thus increasing cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day - These two events are independent of each other. They are not based on each other. Hence, no relationship here.
A negative relation implies that if one thing increases, the other decreases.
3) The number of licks taken and the size of the Tootsie Pop. This is negative. As the number of licks increases, the size of the pop decreases.
Mr. and Mrs. Yeager want to buy a home valued at $320,000. If they have 15% of this amount saved for a down payment, how much have they saved? a. $480 b. $4,080 c. $4,800 d. $48,000
Answers
Answer:
The correct answer is D
Step-by-step explanation:
I got it right on Edge.2020. Have a great day!
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that Mr. and Mrs. Yeager want to buy a home valued at $320,000.
If they have 15% of this amount saved for a down payment, then
15% =15/100=0.15
Therefore, we get;
0.15 (320000)=48000
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
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Two trains leave towns 1250 km apart at the same time and travel toward each other. one train travels 10 km/hr slower than the other. if they meet in 5 hours, what is the rate of each train?
Answers
(n represents train A's speed)
A: n
B: n + 10
We know it is 5 hours, and total distance, so:
5(n) + 5(n + 10) = 1250
5n + 5n + 50 = 1250
10n = 1200
Divide:
n = 120
One train goes 120, the other goes 130
A distribution reasonably well described by the normal curve has a mean of 60.00 with a standard deviation of 10.00 points. basing your prediction on the normal (z) curve, approximately what percent of the population would you predict will score within 10.00 points of the mean (between 50.00 and 70.00)?
Answers
The empirical rule states that 68% of data will fall within 1 standard deviation of the mean. 10 is the standard deviation, so anything within 10 points of the mean is within 1 standard deviation.
Answer:
68%
Step-by-step explanation:
what are solutions to the equation sinx cosx = square root 3 over4
Answers
If a single die is rolled twice there are how many possible outcomes
Answers
AT a groyrey store salted peanuts in a shell cost 30 cents per ounce is 5$ enough money to buy 1 pound of peanuts if it is what amount of money will be leaft over
Answers
Money available = $5
Required purchase = 1 pound of slated peanuts = 16 ounces of peanuts
Given the cost per ounce,
16 ounces pf peanuts = 0.3*16 = $4.8
Balance = $5-$4.8 = $0.2 = 20 cents
There, $5 can buy 1 pound of peanuts will a balance of 20 cents.
The square root of the sum of a number and 7 is 8. find the number
Answers
Possibility 1: 8 = sqrt(x+7) in which the answer is 57.
Possibility 2: 8 = sqrt(x) + 7, in which the answer is 1.
Hope this helps! I'm sorry if I get it wrong.
When the temperature is 68 F, the speed of the sound in air is approximately 343 meters per second. Approximately how many kilometers dose sound travel in five seconds?
Show all your work
Answers
We want to find how many kilometers sound will travel when the air is at 68 degrees in five seconds.
Step 1: Multiply 343 by five. (1 sec. to 5 secs.)343 * 5 = 1715
Step 2: Divide 1715 by 1000. (1 m. to 0.001 km)1715/1000 = 1.715 km/5 secs.
At a temperature of 68°, sound will travel 1.715 km in 5 seconds.
A man has 28 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 520 cents, how many dimes and how many quarters does he have?
Answers
To solve the problem, we can set up a system of equations. The solution is 12 dimes and 16 quarters.
Explanation:To solve this problem, we can set up a system of equations. Let's say the number of dimes is x and the number of quarters is y. We know that the total number of coins is 28, so we can write the equation:
x + y = 28
We also know that the value of the dimes is 10 cents and the value of the quarters is 25 cents. The total value of the change is 520 cents, so we can write the equation:
10x + 25y = 520
We can solve this system of equations using substitution or elimination. Let's use substitution:
From the first equation, we can express x in terms of y:
x = 28 - y
Substitute this value of x into the second equation:
10(28 - y) + 25y = 520
Simplify and solve for y:
280 - 10y + 25y = 520
15y = 240
y = 16
Now substitute this value of y back into the first equation to find x:
x + 16 = 28
x = 12
Therefore, the man has 12 dimes and 16 quarters.
Please help i'm really confused.
0! = 0
True
False
Answers
0! is defined to be 1
please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.
Answers
[tex]1298ft*\frac{1mi}{5280ft}= \frac{59}{240} mi[/tex]
Next, we are going to set up a right triangle using the radius of the Earth and the distance above the planet.
The hypotenuse of our triangle will be the radius of the Earth + the distance above the planet. One of the legs of our triangle will be the radius of the Earth, and the other leg, [tex]d[/tex], will be the distance that a person will see on a clear day.
Using the Pythagorean theorem:
[tex]d^2= (\frac{984059}{240} )^2-4100^2[/tex]
[tex]d= \sqrt{(\frac{984059}{240} )^2-4100^2} [/tex]
[tex]d=44.9[/tex] miles
We can conclude that the distance, [tex]d[/tex], to the horizon that a person can see on a clear day from a height of 1298 feet above the planet is 44.9 miles.
Anyone know this geometry question?
Answers
∠JEK + ∠DFH = 90°
Find:
relationship, if any, of ∠JEK to angles CFL, HFG, LFE
Solution:
We note that ∠DFG = 90° = ∠DFH + ∠HFG, so ∠JEK ≅∠HFG.
We also note that ∠HFG and ∠CFL are vertical angles, so ∠JEK ≅∠CFL.
And ∠LFE and ∠DFH are vertical angles, so ∠JEK + ∠LFE = 90°.
Evaluating the choices, we find
A) false. The angles are not complementary, they are equal.
B) false. The angles are not equal, they are complementary.
C) false. The angles are not supplementary, they are equal.
D) TRUE. The angles are equal.
The appropriate choice is ...
D) ∠JEK ≅∠CFL
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
What is the measure of convex arc upper ZWX?
Answers
WZ + 41 = ZWX
From here, we must clear We must replace the value of WZ.
The value of WZ is given by
WZ=180
We have then:
ZWX = 180 + 41
ZWX = 221 degrees
Answer:
the measure of convex arc upper ZWX is:
ZWX = 221 degrees
The measure of convex arc upper ZWX is 180 degrees.
Explanation:The measure of convex arc upper ZWX can be found by considering the angles formed by the diameters WZ and XR. Since WZ and XR are diameters of the circle, they intersect at the center of the circle. The angle formed by the diameters at the center is a right angle, which means that arc upper ZWX is a semicircle. A semicircle has a measure of 180 degrees. Therefore, the measure of convex arc upper ZWX is 180 degrees.
Find the volume of the following solid figure. Use = 3.14. V = 4/3r3. A sphere has a radius of 5.7 inches. Volume (to the nearest tenth) = cubic inches.
Answers
Answer:
the answer is 775.3
Answer : The volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]
Step-by-step explanation :
To calculate the volume of sphere, we use the formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]
where,
r = radius of sphere
Given :
Radius of sphere = 5.7 inches
Now put all the given values in the above formula, we get:
[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{4}{3}\times 3.14\times (5.7inches)^3[/tex]
[tex]V=775.3\text{ inches}^3[/tex]
Thus, the volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]
BRAINLIEST please help?
A graph that displays bivariate data is called _________ ?
Positive Association
Strength of Association
Bivariate Data
Scatterplot
Two-Way Table
Two-Way Relative Frequency Table
No Association
Relative Frequency
Association
Negative Association
Answers
Answer:
Scatterplot
Step-by-step explanation:
Bivariate data means that the data is in two variables. For example, if the height of the students is plotted against their age, this data will be the bivariate data.
A bivariate data is represented using the graph known as Scatter Plot. One variable is plotted along x-axis and second variable is plotted against y-axis. After plotting the two variables we can observe the relation(association) between the two variable using the line of best-fit which models the relation between the two variables.
So, the answer to this question is Scatterplot.
A graph that displays bivariate data is called a Scatterplot. It represents two variables and can indicate Positive Association, Negative Association, or No Association, based on the scatter pattern.
Explanation:In the field of Statistics, a graph that displays bivariate data is referred to as a Scatterplot. Bivariate data represents two different variables, and a scatterplot is a graphical representation that uses dots to show the relationship, if any, between these two sets of data.
When looking at a scatterplot, the patterns of the dots can indicate associations. Positive Association is when as one variable increases, so does the other. Negative Association is when one variable decreases as the other increases. If the dots seem randomly scattered, it exhibits No Association.
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What is the height of the trapezoid?
Answers
40 *2 = (10+6)*h
80/16 = h
5 unit = h
able below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often? Male Female Total Blue Car 0.04 0.12 0.17 Black Car 0.08 0.06 0.13 White Car 0.11 0.20 0.31 Gray Car 0.02 0.09 0.11 Red Car 0.17 0.10 0.27 Total 0.43 0.57 1.00
Answers
Answer:
31%
Step-by-step explanation:
Answer:
31%
Step-by-step explanation:
What does y=mx+b mean
Answers
m = rise/run = Δy/Δx = (y2-y1)/(x2-x1)
with (x1,y1) and (x2,y2) as points on the line. b is the quantity defined as the y-intercept, that is, the y-value of where the line crosses the vertical y-axis.
consider the enlargement of the pentagram
Answers
Solving for x:
7(x/7)=7(7/15)
x=(7)(7)/15
x=49/15
Answer: x=49/15
I really need help with this!!
Answers
= wx/xy substitute
= 12/13 plug in wx
12 and xy= 13
A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?
18
27
33
45
Answers
to find the rate it burns:
20 ounce / 60 hours = 1/3 ounce per hour
divide 9 ounces by 1/3 ounce per hour to find total time:
9 / 1/3 = 27 hours
Answer:
B. 27.
Step-by-step explanation:
We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.
We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.
Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:
[tex]60=k*20[/tex]
[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]
[tex]3=k[/tex]
The equation [tex]y=3x[/tex] represents our given direct proportional relation.
Now, we will substitute [tex]x=9[/tex] to solve for y as:
[tex]y=3*9[/tex]
[tex]y=27[/tex]
Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.
How would you find the width of a golden rectangle if your givin the length?
Answers
Given the length, you would divide by 1.618 to find the width.
Edit: The exact value is [tex] \frac{ 1+\sqrt{5} }{2} [/tex], but 1.618 should suffice.