You are holding a kite string in your hand and your hand is 3 feet above the ground. The kite is 225 feet above the ground and the angle of elevation from your hand to the kite is 42°. How long is the kite string?
The kite string is 331.77 feet long.
How to find how long the kite string is?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for labeling. Where l represents the length of kite string.
h = 225 - 3 = 222 ft
Using trig. ratio:
sin 42° = 222/l
l = 222 / sin 42°
l = 331.77 feet
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geometry need help please
HELP PLEASE ASAP PHOTO INCLUDED
The volume of water that the pool can hold is 150.72 cubic centimeters.
How to find the volume of the pool?Remember that the volume of a cylinder of radius R and height H is:
V = pi*R²*H
Where pi = 3.14
For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft
Replacing that in the volume formula we will get:
V = 3.14*(4cm)²*3cm
V = 150.72 cubic centimeters.
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Suppose you pick 4 cards randomly from a well shuffled standard deck of 52 playing cards. The probability that you draw the 2,4,6, and 8 of spades in that order is
The probability of drawing the 2, 4, 6, and 8 of spades in that specific order is 0.0002.
What is the probability?The probability of drawing a specific card without replacement from a well-shuffled deck is 1/52 for the first card, 1/51 for the second card, 1/50 for the third card, and 1/49 for the fourth card.
We wish to draw the specific cards (2, 4, 6, and 8 of spades) in that specific order.
The probability will be:
Probability = (1/52) * (1/51) * (1/50) * (1/49)
probability = 0.0002.
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Given: KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
Prove:
An incomplete flowchart proof is shown.
By ASA congruency triangle KBH is congruent to triangle NWH.
Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
From the given figure,
Consider ΔKBH and ΔNWH,
∠KHB=∠NHW (Vertically opposite angles)
∠HKB=∠HWN (Interior alternate angles parallelogram)
KH=HW (Diagonals bisect each other)
By ASA congruency ΔKBH ≅ ΔNWH
Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.
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There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
The ratio is 3:7
Step-by-step explanation:
You add 104+78
The un-simplified ratio is 78:182
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Find the greatest common factor of 21x^4 and 49x^3
The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to 7x³.
To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.
To find the factors, we can break each term down into its prime factors:
21x⁴ = 3 * 7 * x * x * x * x
49x³ = 7 * 7 * x * x * x
The common factors are 7 and x³. To find the GCF, we multiply these common factors together:
GCF = 7 * x³
GCF = 7x³
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The proof of ΔRUV ≅ ΔSUT is shown below.
Given that:
RSTV is a rectangle and U is the midpoint of VT.
Here, We have to Prove:
⇒ ΔRUV ≅ ΔSUT
Now, We can prove as;
Statement Reason
1) RSTV is a rectangle Given
2) Angle V and T are Because every angle in a rectangle is 90
right triangle.
3) ∠V ≅ ∠T Because both are right angle.
4) U is the midpoint of VT. Given
5) VU = UT By midpoint theorem.
6) VR ≅ TS Opposite sides of rectangle.
7) ΔRUV ≅ ΔSUT By SAS congruency theorem.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
The probability that it is raining if the flight has been delayed is 0.07, or 7%.
How to calculate the probabilityWe can use the following formula to calculate the probability that it is raining if the flight has been delayed:
P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)
We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):
= 0.07 * 0.18
= 0.0126.
Substituting these values into the formula, we get:
P(Rain|Delayed) = 0.0126 / 0.18 = 0.07
Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.
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What is the ratio for 3 rectangles and 4 ovals in its simplest form?
The ratios for the rectangles and the ovals is 4 : 3
Calculating the ratios for the rectangles and the ovalsFrom the question, we have the following parameters that can be used in our computation:
Rectangle = 4
Oval = 3
The ratio can be represented as
Ratio = Rectangle : Oval
When the given values are substituted in the above equation, we have the following equation
Rectangle : Oval = 4 : 3
The above ratio cannot be further simplified
This means that the ratio expression would remain as 4 : 3
Hence, the solution is 4 : 3
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What’s the constant term of the polynomial 2x^3-5x^2+8*x+3
The constant term of the polynomial 2x³-5x²+8x+3 is 3.
A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.
The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.
The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.
Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.
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make a table for each equation using the following numbers as : x -2,-1,0,1
y=3x-2
The equation y = 3x - 2. can be placed in table as shown below. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
In this table, each row represents a pair of values (x, y) that satisfy the equation y = 3x - 2. For example, when x is -2, y is calculated as 3(-2) - 2 = -8. Similarly, for the other values of x, the corresponding values of y are calculated accordingly.
Here's a table showing the values of x and the corresponding values of y for the equation y = 3x - 2:
x y
-2 -8
-1 -5
0 -2
1 1
To fill in the table, substitute each value of x into the equation and calculate the corresponding value of y. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.
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increase a gross by 10%
The results of increasing a gross by 10% is 158.4.
What is percentage?Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.
In mathematics, gross is written in figures as 144
increase a gross by 10%
= 144 + (10% × 144)
= 144 + (0.1 × 144)
= 144 + 14.4
= 158.4
Hence, 158.4 is the 10% increase in gross.
Complete question:
Calculate the increase in a gross by 10%.
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Find the distance between (2, 5) and (-5, 8).
58
√58
2√43
2
Answer:
d = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )
d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]
= [tex]\sqrt{(-7)^2+3^2}[/tex]
= [tex]\sqrt{49+9}[/tex]
= [tex]\sqrt{58}[/tex]
Extract the common factor from
(1) 2.x-2.y
(2) 5.x.x.x+5.3.x.y
Answer:
(1) 2x - 2y = 2(x - y)
(2) 5x^3 + 15xy = 5x(x^2 - 3y)
Find your answer on above picture ihope it will help you thank you.
At the beginning of the week, James has 8 quarts of milk. At the end of the week there are 412 cups of milk left.
How many cups of milk did James drink during the week?
James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week
To determine how many cups of milk James drank during the week, we need to find the difference between the initial amount of milk and the amount of milk left at the end of the week. The initial amount of milk: 8 quarts = [tex]$8 \times 4 = 32$[/tex] cupsThe remaining amount of milk: [tex]$4 \frac{1}{2}$[/tex] cupsTo find the amount of milk James drank, we subtract the remaining amount from the initial amount: [tex]$32 \text{ cups} - 4 \frac{1}{2} \text{ cups} = 27 \frac{1}{2}$[/tex] cupsThe concept used in this problem is subtraction. By subtracting the amount of milk left at the end of the week from the initial amount of milk, we can determine how much milk James consumed during the week. The difference between these two values represents the amount of milk that James drank.Therefore, James drank [tex]$27 \frac{1}{2}$[/tex] cups of milk during the week.
NOTE: The given question has wrong information. The correct question is:
"At the beginning of the week, James has 8 quarts of milk. At the end of the week, there are [tex]$4 \frac{1}{2}$[/tex] cups of milk left. How many cups of milk did James drink during the week?"
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A thermometer reading 10°C is brought into a room with a constant temperature of 36°C. if the thermometer reads 14°C after 2 minutes, what will it read after beint left in the room for 4 minutes? and for 9 minutes?
Answer:
4 minutes: 17.4 °C9 minutes: 23.7 °CStep-by-step explanation:
You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.
Newton's law of coolingNewton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...
T = 36 -26·(22/26)^(t/2)
At times of t=4 and t=9, the temperature readings will be ...
4 minutes: 36 -26(11/13)^(4/2) ≈ 17.4 °C9 minutes: 36 -26(11/13)^(9/2) ≈ 23.7 °C__
Additional comment
The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.
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I just need the answer for letter b
If f(x) = 1/343, then x = -3. The point on the graph of f when f(x) = 1/343 is (-3, 1/343).
How to explain the valueA point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate.
If f(x) = 1/343, then x = -3. This is because 343 = 7³, therefore the inverses is 1/343. The point on the graph of f when f(x) = 1/343 is (-3, 1/343
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the box plot below represents some data set. what percentage of the data values are greater than 130
The percentage of the data values that are greater than 130 is 25%
What percentage of data values are greater than 130From the question, we have the following parameters that can be used in our computation:
The box plot
From the box plot, the five-number summary are
40, 70, 110, 130, and 150
In the above five-number summary, we have
Third quartile = 130
This means that the percentage of the data values that are greater than 130 is 25%
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find the surface area of a regular hexagonal pyramid with the base edges of 10 and a slant height of 9 inches.
The surface area of the regular hexagonal pyramid is equal to 529.8 in² to the nearest tenth.
How to calculate for the surface area of the regular hexagonal pyramidArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of nonagon × (n)number of side
apothem = s/[2tan(180/n)]
apothem = 10in[2tan(180/6)]
apothem = 5√3in
perimeter = 6 sides × 10in = 60 in²
Area of the bottom hexagon = 1/2 × 5√3 × 60 in²
Area of the bottom hexagon = 259.8075 in²
Area of one triangle side face = 1/2 × 10in × 9in = 45 in²
Area of 6 triangle side faces = 6 × 45 in² = 270 in²
Surface area of the regular pyramid = 259.8075 in² + 270 in²
Surface area of the regular pyramid = 529.8 in²
Therefore, the surface area of the regular hexagonal pyramid is equal to 529.8 in²
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The side of a square is measured to be 16 ft with a possible error of ±0.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your answer.
The estimated error in the calculated area is approximately 3.2ft²
How did we estimate the error?To estimate the error in the calculated area of a square, use linear approximation or differentials.
The area of a square is given by the formula A = s², where s represents the length of a side.
Calculate the area of the square using the given side length of 16 ft:
A = (16 ft)²
A = 256 ft²
Now, let's consider the possible error in the side length, which is ±0.1 ft. Treat this error as a change in the side length (Δs) and use linear approximation or differentials to estimate the corresponding change in the area (ΔA).
Using linear approximation, express the change in the area as:
ΔA ≈ 2s Δs
Substituting the values:
ΔA ≈ 2(16 ft)(0.1 ft)
ΔA ≈ 3.2 ft²
Therefore, the estimated error in the calculated area is approximately 3.2ft².
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Please urgent help I can’t figure this out thank you guys for always helping
Answer:
Domain: {-24, -12, -8, 9, 14, 50}
Range: {23, 69, 83, 92, 97, 32}
Step-by-step explanation:
The domain of a function is the set of all possible input values (usually x) for which the function is defined. The range of a function is the set of all possible output values (usually y, which is synonymous with f(x)) that the function can produce.For a function like f(x), each coordinate is in the form (x, f(x)) aka (x, y)
Since our x-coordinates are -24, -12, -8, 9, 14, and 50, the domain of f(x) is {-24, -12, -8, 9, 14, 50}
Since our f(x) or y-coordinates are 23, 69, 83, 92, 97, and 32, the range is {23, 69, 83, 92, 97, 32}
Find the quotient and express the answer in scientific notation. 302 ÷ (9.1 x 10^4 )
The quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]
How to find the quotientDividing 302 by 9.1 gives:
302 ÷ 9.1 ≈ 33.1868131868
Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:
33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]
Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]
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Does the data follow a normal distribution? Why or why not?
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answer: where is the answer choices
Step-by-step explanation:
You deposit $5000 in an account earning 3% interest compounded continuously. How much will you have in the
account in 15 years?
Answer:
$7841.56----------------------
Use the compound interest formula:
[tex]A = Pe^{rt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 3% = 0.03;t = time period in years = 15.Plugging in the values, we get:
[tex]A = 5000*e^{0.03*15}[/tex][tex]A = 7841.56[/tex]please help me important question in image
Segment BF is 36 will be the accurate statement.
Similarity theorem of triangleA triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.
From the given triangle, the following expression is true:
EC/FC = AC/BF+FC
Substitute the given parameters into the formula to have:
20/30 = 24+20/BF+30
20/30 = 44/BF+30
2/3 = 44/BF + 30
2(BF+30) = 132
2BF + 60 = 132
2BF = 132 - 60
2BF = 72
BF = 36
Hence the correct statement will be that segment BF is 36
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Identify the part, percent and base.
$37.60 interest earned on a $460 investment at 8%.
Part:
Percent:
Base:
The given information is,$37.60 interest earned on a $460 investment at 8%.
Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.
Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.
Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.
Thus,
Part: $37.60
Percent: 8%
Base: $460.
Part: The part is the interest earned, which is $37.60.
Percent: The percent is 8%, which represents the annual interest rate.
Base: The base is the amount of the investment, which is $460.
Esther ran round the playground and 12 times. The playground is 240 m by 160 m. what distance did she cover?
The total distance she cover after running is 9600 meters
How to calculate the total distance she cover?From the question, we have the following parameters that can be used in our computation:
Number of times = 12 times
Dimensions of the playground = 240 m by 160 m
The perimeter of the playground is calculated as
Perimeter = 2 * sum of dimensions
substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (240 + 160)
The total distance she cover is calculated as
total distance = 12 * 2 * (240 + 160)
Evaluate
total distance = 9600 meters
Hence, the total distance she cover is 9600 meters
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A school class went on a field trip to see a magician perform there were 17 females 20 males in the class the magicians randomly selected a volunteer from the audience in which had 52 females and 68 males given that the randomly selected audience member is a student from the class which equation can be used to find the probability p that the perdimos also a female?please help does anyone know the answer
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The probability p that the perdimos is also a female is 17/120
What is Conditional Probability?Conditional Probability is the possibility or likelihood of an event or outcome happening, based on the existence of a previous event or outcome.
How to determine this
When there were 17 females in class
And 20 male in class
When randomly selected, the female are 52
And males are 68
To calculate the selected volunteer is a student of the class.
= 20 + 17/52 + 68
= 37/120
To calculate the probability that the selected student is female.
= 17/52 + 68
= 17/120
= 0.14
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