The height of the tree is given as follows:
44.4 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For the height, we have that:
The opposite angle is of 32º.The side adjacent to the angle of 32º is of 71 feet.Hence the height is obtained as follows:
tan(32º) = h/71.
h = 71 x tangent of 32 degrees
h = 44.4 feet.
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Jamal spent $27.00 on 3 tickets to a concert. Debra bought 5 of the same tickets. How much did she spend
A man standing on a window of the first floor of a building observes (4)
that the angle of depression of a dustbin which is 1 Om from the foot of
the building is 45°. He climbs to the window of the second floor,
directly above the first floor and observes the angle of depression of
the dustbin to be 60°. Calculate the difference in height between the
first floor and the second floor
10m for the 1st floor. 7.32m for the 2nd floor.
What is the Trigonometry?
Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
Let the point where the man is standing on window be A.
Let the point where the dustbin is there be B.
Let the foot of the building be C.
So, according to the given details,
CB = 10m.
angle (ABC)= 45 degrees.
Let the point of the 2nd floor be P.
We must understand what the angle of depression is: It is the angle measured below the horizontal level.
In triangles ABC and PBC, we use trigonometric ratios as follows:
[tex]tan(45) = AC/BC\\\\AC = BC = 10cm.\\tan(60) = CP/BC\\\\CP = BC\sqrt[2]{3}\\CP = 10\sqrt[2]{3}\\ CP = 17.32m. \\\\2ndfloorheight = CP - AC = 7.32m[/tex]
Hence, 10m for the 1st floor. 7.32m for the 2nd floor.
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Hello everyone, Please can someone help me with these questions?
The quadratic equation that would not cross the x-axis is given as follows:
y = 4x² - 4x + 5.
The quadratic equation with imaginary roots is given as follows:
y = x² + 6x + 10.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.When a function has a negative discriminant, it does not cross the x-axis, meaning that it has imaginary roots.
Hence the functions are given as follows:
Item 1: y = 4x² - 4x + 5 -> Δ = (-4)² - 4(4)(5) = -64.Item 2: y = x² + 6x + 10 -> Δ = (6)² - 4(1)(10) = -4.More can be learned about quadratic functions at https://brainly.com/question/1214333
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what is the solution of 3+ x-2/x-3 ≤ 4
im positive the answer is x<3
how to convert 30 cm to in?
According to the concept of measurement, 30 cm is equal to 11.811 in.
Measurement conversion is an important skill to have in many areas of life, including science, construction, and cooking. Knowing how to convert measurements from one unit to another can be especially helpful when dealing with international standards, as different countries often use different units of measurement.
In this question, we will explain how to convert 30 cm to in, using simple mathematical formulas.
Firstly, it is important to understand the basic units of measurement that we will be dealing with. The unit of measurement for length in the metric system is the centimeter (cm), while the unit of measurement for length in the imperial system is the inch (in).
To convert 30 cm to in, we need to use a conversion factor, which is a ratio of equivalent values expressed in different units. The conversion factor for cm to in is 1 inch equals 2.54 cm. This means that one inch is equal to 2.54 cm, or conversely, one cm is equal to 0.3937 inches.
To convert 30 cm to in, we can use the formula:
30 cm x 0.3937 in/cm = 11.811 in
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361 divided by 2,510
0.14382470119, rounded to 0.14, is the answer.
Answer: 0.1438 (to 4 decimal places)
the sweet shoppe uses a snack mix recipe that calls for one pound of chocolate chips and three pounds of raisins. the owner pays $3.40 for two pounds of chocolate chips and $1.80 for four pounds of raisins. how much will the ingredients for the snack mix recipe cost? responses
The ingredients for the snack mix recipe will cost $3.05
How to determine how much the ingredients for the snack mix recipe will cost?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
To find the cost of the ingredients for the snack mix recipe, we need to first calculate the cost per pound of each ingredient, and then multiply that by the amount required in the recipe.
The owner pays $3.40 for 2 pounds of chocolate chips:
cost per pound = $3.40 ÷ 2 = $1.70
The owner pays $1.80 for 4 pounds of raisins:
cost per pound = $1.80 ÷ 4 = $0.45
Now we can use these costs to find the total cost of the ingredients for the recipe:
1 pound of chocolate chips = $1.70
3 pounds of raisins = 3 × $0.45 = $1.35
Total cost of the ingredients = $1.70 + $1.35 = $3.05
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A camera has a listed price of $637.95 before tax. If the sales tax rate is,6.5% find the total cost of the camera with sales tax included.
Round your answer to the nearest cent
1:
Sam arrives at an amusement park with $61 that he
can spend at the amusement park. The entrance fee at
the amusement park is $20. It costs $3 to play a game
and $4 for each ride. He plays 6 games and goes on x.
rides. The inequality shown below represents this
situation.
38+4x≤61
The solution of the inequality is x ≤ 5.75. Based on the
solution, which statement must be true?
A.Sam went on at most 5 rides
B.Sam went on at most 6 rides
C.Sam went on more than 6 rides
D.Sam went on fewer than 5 rides
Using the inequality 38+4x≤61 shown to represent the situation, based on the solution that x ≤ 5.75, the true statement is A. Sam went on at most 5 rides.
What is inequality?Inequality is an algebraic statement showing that two or more mathematical expressions are unequal.
Inequalities are represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount Sam has to spend at the amusement park = $61
The entrance fee = $20
The unit cost of a game = $3
The unit cost of a ride = $4
The total number of games Sam plays = 6
The amount spent on games = $18 ($3 x 6)
The total known cost = $38 ($20 + $18)
Let the number of rides Sam goes on = x
Inequality:38 + 4x ≤ 61
Thus, the correct statement about the inequality is Option A.
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You eat at a restaurant for $22. You calculate the tip by multiplying $22 by 0.20. You calculate the tax by multiplying $22 by 0.05. How much did you pay for the meal, including the tip and the tax?
Answer: $27.50
(correct me if i'm wrong, please)
Step-by-step explanation:
(22) + (22 * 0.20) + (20 * 0.05)
22 + 4.40 + 1.10
22 + 5.50
= $27.50
What is 22 1/4 in fraction and divided by 890
The fraction 22 1/4 divided by 890 gives 1/40 or 0.025.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
Given is a mixed fraction 22 1/4.
This has to be first converted to improper fraction.
22 1/4 = (22 × 4 + 1) / 4 = 89/4
Now we have to divide the fraction 89/4 by 890.
89/4 ÷ 890 = 89/4 × 1/890
(since in the division of fractions, the second term becomes the reciprocal and the operation changes to multiplication).
89/4 ÷ 890 = 89/4 × 1/890
= 1/40
= 0.025
Hence the quotient when 22 1/4 divided by 890 is 0.025.
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Does anyone know what is 21% of 200?
21% of 200 is going to be 42.
If you want this the simple way, multiply 21% to 200 and it will actually tell you the answer. :)
Answer:
42
Step-by-step explanation:
To find the percentage of a number, take the percent and change it to decimal form.
21% = .21
Multiply this by the number
.21 * 200
42
21% of 200 = 42
what is km to miles per hour?
Kilometers per hour (km/h) and miles per hour (mph) are both units of speed used to measure how fast something is moving.
Kilometers per hour are the standard unit of speed used in most countries that use the metric system, while miles per hour is more commonly used in the United States and other countries that use the imperial system.
To convert km/h to mph, you can multiply the speed in kilometers per hour by 0.621371. This conversion factor is based on the fact that one mile is equivalent to 1.60934 kilometers. Converting between these two units is a common task when traveling, driving, or using fitness trackers or GPS devices.
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how to convert 20 celsius to fahrenheit
Answer:
convert the units
Step-by-step explanation:
68
What is the conversion of 2/5 in decimal ?
The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.
A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.
2/5 = (2 × 2) / (5 × 2) = 4/10
Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.
The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.
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In observational studies, the variable of interest a. is not controlled b. is controlled c. cannot be numerical d. must be numerical
In observational studies, the variable of interest The correct answer is (a) is not controlled.
The variables are measured as they occur naturally, without any manipulation or intervention by the researcher. Therefore, the variable of interest is not controlled in observational studies.
Observational studies are used in situations where it is not feasible or ethical to conduct controlled experiments, such as in studies of the effects of environmental exposures or lifestyle factors on health outcomes. In these studies, the researcher cannot control the exposure or intervention and must rely on observational data to draw conclusions about the relationship between the exposure and the outcome.
The other options are not correct because:
b. If the variable of interest is controlled, then the study is a controlled experiment, not an observational study.
c. The variable of interest can be numerical or categorical in observational studies.
d. The variable of interest does not have to be numerical in observational studies, as it can also be a categorical variable
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solve the equation explicitly for y and differentiate to get y ′ in terms of x.1/x+1/y=1
Solving the equation explicitly for y and differentiating we get y' = -1/(x - 1)²
What is differentiation?Differerentiation is the process of finding the derivative of a function.
How to solve the equation explicitly for y and differentiate to get y ′?Since we have the equation 1/x + 1/y = 1, to solve explicitly for y, we make y subject of the formula.
So, 1/x + 1/y = 1
1/y = 1 - 1/x
y = 1/(1 - 1/x)
To find y', we differentiate y with respect to x.
So, y' = dy/dx
= d[1/(1 - 1/x)]/dx
Let u = 1 - 1/x
So,y' = d(1/u)/dx
= d(1/u)/du × du/dx
Now,
d(1/u)/du = -1/u² and du/dx = d(1 - 1/x)/dx = d1/dx - d(1/x)/dx = 0 - (-1/x²) = 1/x²So, substituting these into dy/dx, we have that
y' = = d(1/u)/du × du/dx
= -1/u² × 1/x²
= -1/(ux)²
= -1/[(1 - 1/x)x]²
= -1/(x - 1)²
So, y' = -1/(x - 1)²
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Printer A prints 100 pages for $26.99. Printer B prints 275 sheets for $67.99. Which printer has the better rate of cost per page?
Printer A, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer A, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page
Printer B, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page
Answer:
Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Step-by-step explanation:
Rate of cost for printer A = $26.99/100 pages
= $ 0.2699 ≈ $0.27 per page
Rate of cost for printer B = $67.99/275 pages
=$ 0.2472 ≈ $0.25 per page
0.25 < 0.27
So Printer B has the better rate of cost
Answer:Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Step-by-step explanation:
which rational number is equivalent to the expression 69 2/9 - (-12 4/9)?
Answer:
81 2/3
Step-by-step explanation:
69 2/9 - ( - 12 4/9)
= 69 2/9 + 12 4/9
Add the whole parts to get 69 + 12 = 81
Add the fractional parts: 2/9 + 4/9 = 6/9 = 2/3
So
69 2/9 - (-12 4/9) = 81 2/3
Suppose we want to choose 6 colors, without replacement, from 10 distinct colors.
(a) How many ways can this be done, if the order of the choices is not taken into consideration?
(b) How many ways can this be done, if the order of the choices is taken into consideration?
Answer: (a) If the order of the choices is not taken into consideration, we want to count the number of combinations of 6 colors chosen from 10 distinct colors. The formula for the number of combinations of k objects chosen from a set of n distinct objects is:
n choose k = n! / (k! * (n-k)!)
So, the number of ways to choose 6 colors from 10 distinct colors, without replacement and without considering the order, is:
10 choose 6 = 10! / (6! * (10-6)!) = 210
Therefore, there are 210 ways to choose 6 colors from 10 distinct colors without considering the order.
(b) If the order of the choices is taken into consideration, then each choice can be made in 10 ways, and there are 6 choices to be made. Thus, the total number of ways to choose 6 colors from 10 distinct colors, with replacement and considering the order, is:
10 * 10 * 10 * 10 * 10 * 10 = 10^6 = 1,000,000
Therefore, there are 1,000,000 ways to choose 6 colors from 10 distinct colors, considering the order.
Step-by-step explanation:
Drag and drop the labels to classify the pairs of angles formed by a transversal intersecting two parallel lines. Each label may be used once, more than once, or not at all.
Alternate interior angles - Congruent
Corresponding angles - Neither
Same side interior angles - Supplementary
What are alternate angles?Alternate angles are a type of angle formed when a straight line intersects two parallel lines. When this happens, alternate angles are formed on opposite sides of the transversal (the line that intersects the parallel lines).
Alternate angles are also known as "alternate interior angles" because they are located inside the parallel lines, but on opposite sides of the transversal. They are called "alternate" because they are located on opposite sides of the transversal and they are congruent, meaning they have the same angle measure.
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Stan bought a car that was valued at $24000 at the time of purchase. Stan calculates that the car will depreciate, lose value, at a rate of $1100 per year before it has no value. Write a function that will represent the value of the car, V, with respect to the number of years, t.
Answer:
in which year does a car lose the most of its value
Step-by-step explanation:
Santos invested $1200 into an account with an interest rate of 8% compounded monthly. Use a calculator to approximate how long it will take for Santos’s investment to reach $2500. Round to the nearest tenth
The number of years it will take to reach $2500 is 9.21 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
Principal = $1200
Rate = 8%
Compounded monthly.
So,
n = 12
A = $2500
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
Substituting all the values above.
2500 = 1200 x [tex](1 + 0.08/12)^{12t}[/tex]
25 = 12 x [tex](1.0067)^{12t}[/tex]
25/12 = [tex](1.0067)^{12t}[/tex]
2.0833 = [tex](1.0067)^{12t}[/tex]
Taking logs on both sides.
log (2.0833) = 12t log (1.0067)
12t = log (2.0833) / log (1.0067)
t = 9.205 years
Thus,
It will take 9.21 years to reach $2500.
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Mrs. Milton travels 60 miles round-trip to work. She works five days a week. Her car gets about 25
miles per gallon of gasoline. About how many gallons of gasoline does Mrs. Milton's car use during her
weekly commute?
Answer:
Mrs. Milton's car uses about 12 gallons of gasoline each week for her commute.
A hemispherical bowl of radius R is placed in a uniform magnetic field that has magnitude B0 and is in the positive z direction. The open top of the bowl is in the xy plane.
Part A
Obtain an expression for the magnetic flux through the hemispherical surface of the bowl.
Express your answer in terms of some or all of the variables B0, R, and the constant ?.
The expression for the magnetic flux through the hemispherical surface of the bowl is EπR².
Hemisphere:
The word hemisphere can be divided into hemisphere and sphere. Hemisphere means half, and sphere means three-dimensional shape in mathematics. Thus, a hemisphere is a three-dimensional geometric shape that is a hemisphere that is flat on one side and a round bowl on the other. It is formed when a sphere is cut exactly down the center along its diameter, leaving two identical hemispheres.
The volume of a hemisphere is the number of unit cubes that can fit inside it. The units of volume are cubic units, such as m³, cm³, ft³ and so on.
The volume of a hemisphere = 2/3πr³
where
r is the radius of the hemisphere.
According to the Question:
Flux passing through the curved surface is equal to the flux passing through the flat surface.
Since flux through the flat surface
ϕ flat = E× Area
= E× πR²
The electric flux through a closed surface is 1/E₀ times the total charge unclosed.
By Gauss's law, flux ,
Since number of field lines entering from circular side is equal to number of field lines leaving the hemispherical surface, net flux is 0.
Therefore,
(Flux)h + (flux)c = 0 -------------------------(1)
[* (flux)h means flux from hemispherical surface and (flux)c means flux from circular surface]
Therefore,
(flux)h = - (flux)c ---------------------------- (2)
Flux = E.A [ Where E and A are vectors ]
Flux = E A cos θ
(Flux)c = EA cos π [ Because field and surface area vector are anti parallel]
(flux)c = E πR² (-1) ------------------------------ (3)
From equation (2) and (3)
(flux)h = - (- EπR²)
⇒ (Flux)h = EπR²
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on a unit circle θ=pi/2 radians. identity the terminal point and sin θ
Answer:
A.
Step-by-step explanation:
Answer A. sin(pi/2)=1, and because it is orthogonal to the x-axis, the x value is 0.
the probability that a discrete random variable equals any of its values is
The probability that a discrete random variable equals any of its values is 1. This is because each discrete random variable can take any value within its range with equal probability.
X is a discrete random variable, then for any value x that X can take on, the probability P(X=x) is a number between 0 and 1. This means that there is a non-zero probability for each possible value of X. The sum of the probabilities of all possible values of X must equal 1. This is known as the probability distribution of X.
Mathematically, we can express this as:
0 ≤ P(X=x) ≤ 1 for all x
∑ P(X=x) = 1 over all possible values of x
For example, if X represents the outcome of a fair six-sided die roll, then the probability of X equaling any of its values (1, 2, 3, 4, 5, or 6) is 1/6, since each outcome has an equal probability of occurring and there are six possible outcomes. Therefore, P(X=1) = P(X=2) = P(X=3) = P(X=4) = P(X=5) = P(X=6) = 1/6 and the sum of these probabilities is 1.
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What is the conversion of 6,25% as a fraction?
After converting 6.25% into fraction we get 16/256 or 1/16.
The percentage means divied by hundred.
A fraction consists of two parts one is the numerator and other is denominator.
Where the number which is written in upper most part of the line is called numerator, and the number bottom most part of the line is called denominator.
To convert a percentage into a fraction divide the percentage by 100,
And simplify the resulting fraction.
So,
To convert 6.25% to a fraction,
We divide 6.25 by 100:
6.25% ÷ 100 = 0.0625
Divide by 0.0625
0.0625 ÷ 0.0625 = 1
1 ÷ 0.0625 = 16
Therefore, After simplification 6.25% is equal to 16/256 or 1/16.
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how to convert 166 lbs to kg?
On converting the weight of 166 lbs to Kg , we get that 166 lbs is equivalent to 75.29 Kg .
One Kilogram (Kg) is defined as the base unit of mass in the International System of Units (SI). and
One Pound (lb) is defined as a unit of mass which is commonly used in the United States to measure the weight .
We know that ; 1 pound is approximately equal to 0.4535 Kilograms ;
To convert 166 lbs to Kg ; we multiply the given weight with 0.4535 ;
We get ;
⇒ 166 lbs = 166 × 0.4535 Kg ;
⇒ 166 lbs = 75.281 Kg ≈ 75.29 Kg .
Therefore , 166 pounds is approximately equal to 75.29 Kilograms .
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show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation. what are the equivalence classes of f and of t?
we have seen that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection.
What's more, the equivalence classes of F,T are :
[tex][F]_{R}[/tex] = Set, all things considered,
[tex][T]_{R}[/tex] = Set of all redundancies .
We have been given :
A= Set of every single compound suggestion
R= Logical equivalence of compound propositions .
We need to show that the connection of logical equivalence on the arrangement of all compound propositions is an equivalence connection i.e.R is an equivalence connection .
Then, at that point, we have find the equivalence classes of F and T .
To show that R is an equivalence connection, we need to demonstrate that the connection R is reflexive, transitive and symmetric .
Reflexive
We will let a ∈ A.
As, a compound suggestion is in every case logically comparable to itself .
In this manner, a ≡ a, which suggests that (a,a) ∈ R.
Thus,R is reflexive .
Symmetric
We will let(a,b) ∈ R.
This implies that a ≡ b.
On the off chance that an and b have a similar truth table, b and a have a similar truth table .
Thus, by the evenness of logical equivalences, we get : b ≡ a
which suggests (b, a) ∈ R.
In this way, R is symmetric.
Transitive
We will let (a,b) ∈ R and (b,c) ∈ R.
This infers that :
a ≡ b
b ≡ c .
If an and b have a similar truth table and in the event that b and c have a similar truth table then,a and c
have a similar truth table.
Thus, by transitivity of logical equivalences, we get: a ≡ c
which suggests that (a,c) ∈ R.
Along these lines, R is transitive.
Presently, we can infer that R is an equivalence connection.
Presently, we need to find the equivalence classes of Fand T.
The equivalence class of F has every one of the logical equivalences that are misleading. Also, such logical equivalences are contradictions.
Accordingly,
[tex][F]_{R}[/tex] = Set, everything being equal.
The equivalence class of T have every one of the logical equivalences that are valid. Furthermore, such logical equivalences are redundancies .
Hence,
[tex][T]_{R}[/tex] = Set, all things considered.
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