A kite is currently flying at an altitude of 9 meters above the ground. If the angle of elevation from the ground to the kite is 32 degrees, find the length of the kite string to the nearest meter. hurry!!
Answers
The length of the kite string is 16. 984m
A kite is currently flying at an altitude of 9 meters above the ground.
and, the angle of elevation from the ground to the kite is 32 degrees.
To find the length of the kite string to the nearest meter.
Now, According to the question:
Let the length of the kite string be x m.
From the diagram, the length of the kite string x m is hypothesis
The altitude is 9 m is opposite
and, horizontal line is adjacent.
Formula is:
Sin θ = opposite / hypotenuse
where Sinθ = 32 degree
opposite = 9 m
Hypotenuse = x m
Hence, Sin 32 = 9/x
x = 9/ sin 32 , and Sin 32 degree = 0.5299(approx.)
x = 9/ 0.5299
x = 16. 984 (approx.)
Hence, The length of the kite string is 16. 984m
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Related Questions
A 17 foot ladder is leaning on a wall. the bottom of the ladder on the ground is at a distance of 3 feet from the base of the wall.
What is the distance, in feet, between the griund and the top of the ladder? round your answer to the nearest tenth
Answers
The distance in feet between the ground and the top of the ladder is 16.7 feet.
Let the distance in feet between the ground and the top of the ladder be x.
According to the given question.
Length of the ladder = 17 foot
The distance of the ladder from the base of the wall is 3 feet.
From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.
Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
Therefore,
17^2 = 3^2 + x^2
⇒ 289 = 9 + x^2
⇒ 280 = x^2
⇒ x = 16.7 feet
Hence, the distance in feet between the ground and the top of the ladder is 16.7 feet.
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An average middle-income family will spend $242,020 to raise a child born in 2004
from birth to age 17. The graph shows the percents spent for various categories. To
the nearest dollar, how much will be spent to provide housing for the child? Use the
graph to answer.
graph numbers-- housing 34%, food 17%, miscellaneous 11%, child care 11%, health care 7%, clothing 6%, transportation 14%
Answers
Work Shown:
34% of $242,020 = 0.34*242020 = 82,286.80
This rounds to 82,287 when rounding to the nearest whole number.
Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument? Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons.
Answers
"Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons." This is a Valid Argument
This is further explained below.
What is a Valid Argument?Generally, In the context of deductive reasoning, an argument is considered to be sound if and only if it can be expressed in a way that makes it logically impossible for all of the premises to be true while still leading to an incorrect conclusion.
In conclusion, This is a Valid Argument
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What is the equation of a line through the points (0, 9) and (3, 0)?
0-9
3-0 y=-3x + 9
Obecause m=
Obecause m=
Obecause m=
O because m=
0-9
3-0 y=-3x + 3
3-0
0-9;y=-
y=-x+9
3-0
1
0-9; X=-3x+3
Answers
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ -9 }{ 3 }\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-9=-3x\implies y=-3x+9[/tex]
The probability of passing the math class of Professor Goodrum is 59%, the probability of passing Professor Cruise's physics
class is 26%, and the probability of passing both is 17%. What is the probability of passing one or the other?
(Give your answer as a whole percent number.)
probability of passing one or the other:
Answers
Answer:
51%
Step-by-step explanation:
Given P(passing math) = 59%, P(passing physics) = 26%, and P(passing both) = 17%, you want to find the probability of passing only one of the courses.
Probability relationsWe can record the given probabilities in a 2-way table (values shown in blue). The table is completed by making sure the totals add up (values shown in black).
The probability of passing one course and failing the other is the sum of the probabilities with a yellow background:
42% +9% = 51%
The probability of passing one or the other is 51%.
__
Additional comment
We can also get there using the relation ...
P(A+B) = P(A) +P(B) -P(AB)
The union of A and B also includes their overlap:
P(A+B) = P(AB') +P(A'B) +P(AB)
In other words, the probability of interest is ...
P(AB') +P(A'B) = P(A) +P(B) -2×P(AB) = 59% +26% -2(17%)
P(AB') +P(A'B) = 51%
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
Answers
The height of the density curve is 1/5
How to determine the height of the density curve?From the graph, we have the following parameter
Base = 5 units
As a general rule, the area under the density curve must have a value of 1
This means that
Area = 1
So, we have
Area = Base * Height
So, we have
1 = 5 * Height
Evaluate
Height = 1/5
Hence, the height of the density curve is 1/5
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Vincent earns $892 on Monday and he earns $711 on Tuesday. How much total money does Vincent
earn?
Answers
Westside Energy charges its electric customers a base rate of $8.00 per month, plus 12¢ per kilowatt-hour (kWh) for the first 300 kWh used and 4¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month. Express the monthly cost E as a piecewise defined function of x. (Assume E is measured in dollars.)
Answers
The linear function that gives the monthly cost E for x > 300 is given by:
E(x) = 44 + 0.04x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When x > 300, we have that:
The base rate of $8.00 was paid.The 12 cents for each kWh up to 300 was paid.Hence the intercept is given by:
b = 8 + 0.12 x 300 = 44.
The slope is the cost per kWh of 4 cents, hence the function is:
E(x) = 44 + 0.04x.
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how can you make the equation true?
111+222=
Answers
Answer: 111 + 222 = 333
Please help
(100 Points)
Answers
Answer:
Equation: (14.71-4.48) [divided by] 3 =x
"Answer x": 3.41
Explanation:
14.71-4.48=10.23
10.23/3 = 3.41
3.41
"The unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November." What is the relative change in the unemployment rate expressed as a percentage?
Answers
If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
Given,
The unemployment rate in February = 8.9%
The unemployment rate in November = 7.1%
The relative change in unemployment rate = [(unemployment rate in February - unemployment rate in November )÷ unemployment rate in November ] ×100
The relative change in unemployment rate= [tex](\frac{8.9-7.1}{7.1} )100[/tex]
=25.35%
Hence, If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
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A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 171 yd^2, determine the radius of the region (the radius is the length of the stream of water). Round the answer to the nearest yard.
The radius is approximately ___ yd.
Answers
The radius of the sprinkler is approximately 7 yards.
How long is the arm of the sprinkler?
In this situation we find the case of a sprinkler that rotates until a complete revolution is done, that is, the area of complete circle is covered due to the rotation. That area can be found by using this formula:
A = (θ / 360) · π · r²
Where:
A - Area of rotation, in square yards.θ - Angle of rotation, in degrees.r - Radius of the sprinkler, in yards.If we know that A = 171 yd² and θ = 360°, then the radius is approximately:
171 = π · r²
r = √(171 / π)
r ≈ 7.378 yd (approx. 7 yd)
The radius of the sprinkler is approximately 7 yards.
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At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
Child
Ava
Grayson
Mason
Tyler
Amount of
Trail Mix (oz)
15
14
10
17
The trail mix costs $4.50 per pound. How much will Mr.
Arnett pay for all the trail mix?
Answers
During a science experiment Mary found the mass of two rocks to be 36.81 grams and 52.4 grams what is the total mass of these two rocks
Answers
Answer: 89.21g
Step-by-step explanation:
36.81g + 52.40g = 89.21g
In the diagram m∠ACB=25° and CE bisects ∠DCF. explain how to find m∠DCE
Answers
The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
We are given a ray diagram.
In the diagram, the measure of angles are given as:
∠ ACB = 25°
∠ ACG = 90°
We need to find the measure of angle ∠ DCE when CE bisects ∠ DCEF.
Now, we know that:
∠ BCG = ∠ DCF ( Vertically opposite angles.) … (1)
Now,
∠ BCG = ∠ ACB + ∠ ACG
∠ BCG = 25° + 90°
∠ BCG = 115° … (2)
∠ DCF = ∠ DCE + ∠ CEF
∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)
∠ DCF = 2 ∠ DCE … (3)
Now, put (2) and (3) in (1), we get that:
115° = 2 ∠ DCE
∠ DCE = 115 / 2°
∠ DCE = 57.5°
Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
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30 points!!! But I need a 2 step problem with variables on both side and a fraction that equal 23
Answers
The equation of the two-step problem is 2x = x + 2/3
How to determine the two-step problem?The conditions are given as
Fraction = 2/3Variable on both sidesLet the variable in the equation be x
So, a possible equation is as follows
2x = x + 2/3
The solution to the equation is as follows
2x = x + 2/3
Subtract x from both sides
x = 2/3
Hence, the equation of the two-step problem is 2x = x + 2/3
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Hello! I'd really appreciate it if someone helped me solve this logarithm! It was my first class but the professor only showed the more simple versions :)
Answers
Answer:
(1/3)log(5) +(4/3)log(x) +log(y)
Step-by-step explanation:
You want the expanded form of the expression log(∛5·x^4·y^3).
Rules of logarithmsThe applicable rules of logarithms are ...
log(ab) = log(a) + log(b)
log(a^b) = b·log(a)
In addition to these, you need to know that a root is a fractional power: the cube root is the 1/3 power. Of course, the rules of powers tell you ...
(a^b)^c = a^(bc)
ApplicationYou can express the root as a fractional power before or after taking logs. Either way, you get the same result.
Before
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\log\left(5^{\frac{1}{3}}\cdot x^{\frac{4}{3}}y^{\frac{3}{3}}\right)=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
After
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\dfrac{1}{3}\log\left(5}\cdot x^{4}y^{3}}\right)=\dfrac{1}{3}\left(\log(5)+4\log(x)+3\log(y)\right)\\\\=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
__
Additional comment
Working a more complex problem is like working a simple problem, except it has more parts and may require the use of the rules more times. It may be tedious to keep track of all the parts, but it is not difficult.
Find rules for the tables below. State your rules in two different ways: (1) as a sentence; and (2) as a rule, using x for the input and y for the output. a. X 6 0 2 -3 1 Process y -3 9 -21 3 33 Rule: (1) X and Topic 3: Foundations of Y are Linear (2) relationship Y = 6x=3
Answers
Answer:6x+3
Step-by-step explanation:
what is the value of x?!?
please help!
Answers
Answer:
x = 25
Step-by-step explanation:
The given angles, x° and (6x+5)° form a linear pair. You want the value of x.
Linear pairTwo angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.
x° +(6x +5)° = 180°
7x +5 = 180 . . . . . . . . . divide by °, collect terms
7x = 175 . . . . . . . . . . subtract 5
x = 25 . . . . . . . . . . divide by 7
The value of x is 25.
The temperature is-2°C. if the temperature reses by 15°C, what is the new temperature?
Answers
Explanation:
Draw a vertical number line (see below). Mark -2 on it. Then move up 2 units to arrive at 0. Move up the remaining 13 units to arrive at 13
This shows that -2+15 = 13
It takes 3 people 4 hours to paint a wall. Assume that all people paint at the same rate. How long would it take 5 people to paint the same wall?
Answers
Answer:
2 [tex]\frac{2}{5}[/tex] hours or 2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
HELP QUICK I WILL GIVE BRAINLIEST ANSWER! In the diagram, line m intersects line n. A two-column proof shows that vertical angles 21 and 23 are
congruent. What should be the statement and justification for step 3?
Answers
Answer:
Option A=============================
The missing statement is:
∠1 + ∠2 = 180°∠2 + ∠3 = 180°Justification is:
Angles that form a linear pair have measures that sum to 180°.All the other options have mismatching or wrong statements or justifications:
B) Wrong statement, the angles are not congruent.C) Wrong justification, angles are not vertical.D) Wrong justification, not matching the statement.1.
destions. Show your wor
For a recent Broadway musical, orchestra main floor seats cost $148 each, and
balcony seats cost $65 each. A theatre group purchased 30 tickets for an upcoming
show in June. If the total cost of the 30 tickets was $2,614, how many of each type
of ticket did the theatre group buy?
Number of orchestra tickets
Number of balcony tickets
Answers
Answer:
Number of orchestra tickets = 8
Number of balcony tickets = 22
Step-by-step explanation:
Let the number of orchestra tickets be x and number of balcony tickets be y.
So, cost of x orchestra tickets = $148 × x = $148x
Cost of y balcony tickets = $65 × x = $65y
Also given, total number of tickets = 30
Cost of 30 tickets = $2,614
So, the system of equations that can ne formed is :
x + y = 30 ....eq 1
148x + 65y = 2614 ....eq 2
Multiplying eq 1 by 148 and subtracting eq 2 by it,
148x + 148y - 148x - 65y = 4440 - 2614
83y = 1826
y = 1826/83 = 22
Substituting y = 22 in eq 1,
x + 22 = 30
So, x = 30 - 22 = 8
Thus,
Number of orchestra tickets = 8
Number of balcony tickets = 22
I am stuglling please someone help me
Answers
76 degrees n 83 degrees it's div
Use the map shown below to find the distance between cities A and B to the nearest tenth.
Answers
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{(~~0 - (-3)~~)^2 + (~~0 - 6~~)^2} \implies BA=\sqrt{(0 +3)^2 + (0 -6)^2} \\\\\\ BA=\sqrt{( 3 )^2 + ( -6 )^2} \implies BA=\sqrt{ 9 + 36 } \implies BA=\sqrt{ 45 }\implies BA\approx 6.7[/tex]
A cookie recipe requires 4 2/3 cups of flour. If a person only wanted to make 3/4 of a batch, how many cups of flour would they need? (Do not add the label)
Answers
[tex]\begin{array}{ccll} \stackrel{recipe}{batch}&\stackrel{recipe}{flour}\\ \cline{1-2} 1&4\frac{2}{3}\\[1em] \frac{3}{4}&f \end{array}\implies \cfrac{1}{ ~~ \frac{3}{4}~~ }~~ = ~~\cfrac{ ~~ 4\frac{2}{3} ~~ }{f}\implies \cfrac{4}{3}~~ = ~~\cfrac{ ~~ \frac{4\cdot 3+2}{3}~~ }{f}\implies \cfrac{4}{3}=\cfrac{ ~~ \frac{14}{3} ~~ }{f} \\\\\\ \cfrac{4}{3}=\cfrac{14}{3f}\implies 12f=42\implies f=\cfrac{42}{12}\implies f=\cfrac{7}{2}\implies f=3\frac{1}{2}[/tex]
pls help 50 if corrret
Answers
Answer:
-4.2
Step-by-step explanation:
Check the attached photo for work.
Use the number line to answer the following 2 questions
Answers
Answer:
for first question the answer will be .. 5
Step-by-step explanation:
easily,
[tex] \frac{1}{5} \times 5 = 1 [/tex]
There are [tex]6\frac{1}{4}[/tex] groups of 1/5 in 5.
The simplified value of 5 ÷ 4/5 is also [tex]6\frac{1}{4}[/tex].
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
From the bar given above the number line, each group has subgroups of 4.
Therefore, The number of groups of (1/5) in 5 is [tex]6\frac{1}{4}[/tex] groups.
We know when a fraction is in the division we can reciprocate the fraction and the division changes to multiplication,
Therefore, 5 ÷ 4/5 = 5×5/4 = 25/4 = [tex]6\frac{1}{4}[/tex]
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Robert buys last year's best-selling novel, in hardcover, for $22.40. This is with a 20% discount from the original price. What was the original price of the novel?
Answers
Answer:
$28.00
Step-by-step explanation:
Set up an equation:
$22.40 = y(1 - 0.20)
Solve the contents of the parentheses first:
$22.40 = y(0.80)
Divide by 0.80 on both sides to isolate y:
($22.40)/0.80 = y
Solve:
$22.40 / 0.80 = $28.00
HURRY IM TIMED Which benchmark fraction is closest to 9/10-3/10 A. 3/4 B. 1/2 C. 1/4 D. 4/4
Answers
Answer:
I am pretty sure it is a i think.
Step-by-step explanation:
just subtract the fractions and you will get 6\10 and the you will simplify and get 3\5. so 3\4 is closest to 3\5.