A trigonometric identities calculator is an online tool that helps you simplify or prove trigonometric identities using various trigonometric formulas and rules.
Describe Equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.
The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.
Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.
Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. These identities are used to simplify expressions involving trigonometric functions, and can be helpful in solving trigonometric equations and evaluating trigonometric functions.
Trigonometric identities calculators can be helpful for students studying trigonometry, as well as for professionals who use trigonometric functions in their work. These calculators typically allow you to enter the trigonometric expression or equation you want to simplify or prove, and then apply various trigonometric identities and rules to arrive at the final result.
There are many online trigonometric identities calculators available that can be accessed for free, including some that provide step-by-step solutions to help you understand how the identities are being applied.
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Que volumen en metros cúbicos ocupan 1000kg de alcohol con una densidad de 790kg/m3
The Volume of Alcohol when Mass is 1000 Kg and Density is 790kg/m³
is 1.265 m³
What is Density?The relationship between a substance's mass and the amount of space it occupies is known as its density (volume). The density of a substance is determined by the mass, size, and arrangement of its atoms. Density (D) is defined as the product of a substance's mass and volume.
Given:
Mass of Alcohol = 1000 Kg
Density of alcohol = 790kg/m³
Using The formula
Density= Mass / Volume
790 = 1000/ Volume
Volume = 1000/ 790
Volume = 1.265 m³
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The Translation of given Question:
What volume in cubic meters does 1000kg of alcohol occupy with a density of 790kg/m3
[tex]1/p^2q^-4r^9[/tex]
a rare coin is currently worth $450. the value of the coin increases 4% each year. determine the value of the coin after 7 years.
Answer:310.45
Step-by-step explanation:
if the matrix M is a linear combination of the matrices Mi, M2 and M3:M = [2 3 ] [1 2 ]M1 = [ 2 2 ][ 1 1 ] M2 = [ -1 1 ][ 2 1 ]M3 = [ 1 2 ] [ 3 1 ]if so, determine scalars c1, c2, c3 such that c1M1 + c2M2 +C2M3 = M.
The scalars c1 = 2/5, c2 = -3/5, and c3 = -8/5 satisfy the equation:
c1M1 + c2M2 + c3M3 = [ 2 3 ][ 1 2 ]
We want to find the scalars c1, c2, and c3 such that:
c1M1 + c2M2 + c3M3 = M
Substituting the given matrices:
c1[ 2 2 ] c2[ -1 1 ] c3[ 1 2 ] [ 2 3 ]
[ 1 1 ] [ 2 1 ] [ 3 1 ] [ 1 2 ]
Multiplying each scalar by its corresponding matrix:
[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ]
[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ]
Setting the result equal to M:
[ 2c1 - c2 + c3 2c1 + 2c2 + 3c3 ] = [ 2 3 ]
[ c1 + 2c2 + 3c3 c1 + c2 + 2c3 ] [ 1 2 ]
This gives us two equations:
2c1 - c2 + c3 = 2
2c1 + 2c2 + 3c3 = 3
c1 + 2c2 + 3c3 = 1
c1 + c2 + 2c3 = 2
We can solve this system of equations using any method we prefer, such as elimination or substitution. Here, we will use elimination.
Subtracting the first equation from the second, we get:
3c2 + 4c3 = 1
Subtracting the third equation from fourth, we get:
c2 - c3 = 1
Multiplying second equation by 2, we get:
4c1 + 4c2 + 6c3 = 6
Subtracting first equation from this, we get:
5c2 + 5c3 = 4
Now we have three equations for c2 and c3:
3c2 + 4c3 = 1
c2 - c3 = 1
5c2 + 5c3 = 4
Solving for c2 and c3 using elimination, we get:
c2 = -3/5
c3 = -8/5
Substituting these values into the third equation, we get:
c1 = 2/5
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(3x-1)(x^2+5x-4)
Find the perimeter of the rectangle.
Answer:
2(8x−5+x^2 )
Step-by-step explanation:
2(3x−1+x^2+5x−4)
2((3x+5x)+(−1−4)+x^ )
2(8x−5+x^2 )
Answer: look at the image for the answer and explanation
Step-by-step explanation:
When filling out a W-4 form, in what situation would a teen want to claim exemption from federal income taxes being withheld from their paycheck? What is the benefit of doing so?
The benefit of doing so is: If the teenager has earned less than $12,000 then they don't get the federal taxes withheld. It would be beneficial to the teen because they would get more money.
A teen might want to claim exemption from federal income taxes being withheld from their paycheck if they expect to earn less than the standard deduction amount for the tax year and they will not owe any federal income tax.
For the tax year 2022, the standard deduction amount for a single taxpayer who is not claimed as a dependent on another taxpayer's return is $12,950.
By claiming exemption from federal income taxes, the teen would have more money in their paycheck and would not have to wait to receive a tax refund when they file their tax return at the end of the year.
However, if the teen ends up earning more than the standard deduction amount or if they have other sources of taxable income, they may owe federal income tax and may have to pay a penalty for not having enough taxes withheld during the year.
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what does a rhombus look like
A rhombus with opposite sides are parallel and equal, and opposite angles are equal looks like Diamond.
A closed two-dimensional plane figure is a rhombus. It is regarded as a peculiar parallelogram, and due to its distinctive characteristics, it acquires a distinct identity as a quadrilateral. Due to its equal length sides, a rhombus is also known as an equilateral quadrilateral. The name "rhombus" is derived from the Greek word "rhombos," which really refers to a spinning object.
Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram. A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square. To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.
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what is steps per mile?
Steps per mile is a measure of how many steps a person takes to walk one mile, Which is 2000 steps.
It takes over 2,000 steps to walk one mile and 10,000 steps would be almost 5 miles, as the average person has a stride length of approximately 2.1 to 2.5 feet.
The number of steps required to walk a mile can vary from person to person depending on their height, weight and stride length. And Generally, taller people with longer strides take fewer steps per mile, while shorter people with shorter strides take more steps per mile.
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 32ft long and 26ft wide.
Find the area of the garden. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
Using 3.14 for π, we have:
[tex]32(26) + \frac{1}{2} (3.14)( {13}^{2} ) = 1097.33[/tex]
about 1,097.33 square feet
karen bought some clothes that were on sale. she paid $85 after the 15% off what was the original cost of the clothing
Karen received a 15% discount of $15, which brought the price down to $85.
How to determine the original priceLet's assume the original cost of the clothes was x dollars.
If Karen got a 15% discount, then she paid 85% of the original price.
This can be expressed in an equation as:
0.85x = 85
To find x, we need to isolate it on one side of the equation.
We can do this by dividing both sides by 0.85:
x = 85 / 0.85
x = 100
Hence, the original cost of the clothes was $100.
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Which input in this table is incorrect?
nakunan amma...ne
Cost of
Tax on
Item
Item
1.00
.08
2.00
.16
3.00
.24
9.00
.64
10.00
.80
Note: all entries are in dollars
OA. 10.00
OB. 2.00
OC. 3.00
D. 9.00
Total Cost
of Item
1.08
2.16
3.24
8.64
10.80
Answer:ob
Step-by-step explanation:
Add.
8/9 + 2/3 + 1/6
Answer: 31/18.
Step-by-step explanation:
To add these fractions, we need to find a common denominator. In this case, the least common multiple of 3, 6, and 9 is 18. We can convert each fraction to an equivalent fraction with a denominator of 18, and then add the numerators:
8/9 + 2/3 + 1/6
= (8/9) * (2/2) + (2/3) * (6/6) + (1/6) * (3/3) (Multiplying each fraction by a form of 1 to obtain a common denominator of 18)
= 16/18 + 12/18 + 3/18 (Simplifying each fraction by multiplying the numerators)
= 31/18 (Adding the simplified numerators)
Therefore, the sum of 8/9, 2/3, and 1/6 is 31/18.
60 cars embedded in 40,000 poundf of conrtet. How many ton of pounds are in 40,000 pounds
Answer:
20 tons
Step-by-step explanation:
To convert pounds to tons, we need to divide the number of pounds by the number of pounds in a ton.
There are 2,000 pounds in one ton.
To convert 40,000 pounds to tons, we divide 40,000 by 2,000:
40,000 pounds / 2,000 pounds/ton = 20 tons
Therefore, 40,000 pounds is equivalent to 20 tons.
if the given triangles form 90 degree angle
then it is right angle if not form 90 degree
angle then it is not
It is possible to determine if a triangle contains
a right angle using Pythagoras' theorem . If the
squares of the two shorter sides add up to the
Answer:
hypotenuse squared
Step-by-step explanation:
for example
if we have a triangle with sides 6,8, and 10
then
36+64=100
the complete equation is
[tex]\sqrt{a^{2} +b^2[/tex]=c
what is sum of odd integers from 1 to 99
The sum of all the odd integers numbering from 1 to 99 is given by th e term 2500.
S = n(a + l)/2, where S is the sum of the successive numbers, n is the number of integers, an is the first term, and l is the last term, is the formula for computing the sum of integers.
Finding the sum of odd numbers from 1 to 99
so the series become
1 + 3 + 5 + 7 + ......+ 99
So this is arithmetic series with common difference of d = 2 and first term be a = 1 and last term be 99
l = a + (n-1)d
99 = 1 + (n-1) 2
n-1 = 98/2
n-1 = 49
n = 50
We know that sum of nth term of AP
s = n/2(a + l)
s = 50/2 (1 + 99)
s = 25(100)
s = 2500
Therefore, the sum of all odd number from 1 to 99 is 2500.
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what is substitution method calculator online
The substitution method calculator online shows the substitution method's result for the pair of linear equations.
One way to solve a system of linear equations with one or more unknown variables in mathematics is the substitution method. For the purpose of solving simultaneous equations, the substitution method is regarded as an algebraic technique. By resolving the equations, this method allows one variable's value to be determined. Any of the preceding equations can be solved by replacing the first variable's value for another variable.
The substitution technique calculator should be used as follows:
Step 1: Type the linear equations' coefficients into the input field.
Step 2: Then, select "Solve" to see the outcome.
Step 3: Lastly, the output field will show the value of the variables x and y in the linear equations solved using the substitution approach.
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Study the right square pyramid and its net shown here.
Then complete the statements below to find the surface area of the pyramid.
The surface area of the square base pyramid is 736 cm².
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape. The surface area of a solid object is a measure of the total area that the surface of the object occupies.
here, we have,
Surface area = A + 1 / 2 ps
where
A = base area
p = perimeter of the base
s = slant height
Therefore,
A = 16² = 256 cm²
p = 4(16) = 64 cm
s = 15 cm
surface area = 256 + 1 / 2 × 64 × 15
surface area = 256 + 480
surface area = 736 cm²
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To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted
the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
O
Relative Frequency
Relative Frequency
7
9
2
11
9
7
X+S
9
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
8
x + 2s
9
x + 3s
H
Need Help?
7 4 8 10
1
6
5
10
8
748
10 8
USE SALT
5. 526
8
4
9
8
7
(a) Construct a relative frequency histogram to describe the data.
Frequency of lumber
5
Interval
Read It
3. 382 to 11. 961
6
06 9
11 10 11 8 8 10 8 8 12
1. 237 to 14. 106
7
7
11
8 8 10
9
9560
Frequency of lumber
L
77
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 8
to 9. 816
7 7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 7
10 10 7 4 8 7
(c) Calculates for the data. (Round your answer to three decimal places. )
S = 2. 145
✔timber trees
(b) Calculate the sample mean x as an estimate of μ, the mean number of trees for all 50-by-50-foot squares in the tract.
(Round your answer to three decimal places. )
X = 7. 671
timber trees
Construct the intervals x ±s, x ± 2s, and X + 3s. Calculate the percentage of squares falling into each of the three intervals,
and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem. (Round your
interval values to three decimal places. Round actual percentages to two decimal places. )
Actual Percentage
Relative Frequency
X %
Relative Frequency
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
Frequency of lumber
7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Frequency of lumber
at least 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Tchebysheff
at least 75%
at least 89%
%
95
Empirical
≈ 68%
≈ 99. 7%
%
The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67
In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.
By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.
In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:
=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).
If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.
If the owner counted 7 trees in the first square, the formula would be
=> (7 / 70) x (2500 / 12) = 16.67.
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Complete Question:
To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5
Please help me I am very confused
The solutions are x=3.69 and x=-4.2
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
2x²+x-31=0
Solve this with the quadratic formula
x=-b±√b²-4ac/2a
a=2,b=1,c=-31
x=-1±√1+248/4
x=-1±√249/4
x=-1+√249/4
x=-1 + 15.77/4 =14.77/4
x=3.6925
and x=-1-√249/4
x=-1 -15.77/4 =-4.1925
Hence, the solutions are x=3.69 and x=-4.2
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A square lawn with a side length of 15 yards has a square shed built near the back, which has a side length of x yards. What are the factors that represent the
area of the yard that can be mowed?
xn
The factor that represents the area of the yard that can be mowed is (225 - x²).
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The total area of the lawn is given by the formula -
Area of square lawn = (side length of square lawn)²
= (15 yards)²
= 225 square yards
The shed is also a square, with side length x yards.
So, the area of the shed is -
Area of square shed = (side length of square shed)²
= x²
To find the area of the yard that can be mowed, we need to subtract the area of the shed from the total area of the lawn -
Area of yard that can be mowed = Area of square lawn - Area of square shed
= 225 - x²
Therefore, the value is obtained as (225 - x²).
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1. Sketch the solid of rotation formed by rotating the given two-dimensional figure
using the horizontal line shown as an axis of rotation.
The image of the transformation is added as an attachment
How to determine the image of the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we can see that
The horizontal line is the axis of rotation
Using the above as a guide, we have the following:
The image of the transformation would be a reflection of the original figure on the other axis
See attachment for the image of the transformation
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Solve the following word problem.
1. Mikey worked on her mathematics homework for 3/4 hour and her science
homework for 7/8 hour. How long did she spend in all doing homework?
2. There are 60 students in a class. Three-fourths of them are girls. How many
boys are there?
3. One day in Baguio, the temperature went from - 2 °C to 8°C. What is the
change in temperature?
4. The elevation of Mt. Everest is 29 028 ft. The elevation of the Dead Sea is -485
ft. Find the difference in the elevation between Mt. Everest and the Dead Sea.
1
5. Angie cleans 3 of the yard. Alex cleans 4 of the remaining. What fraction of
the yard is left unclean?
Answer:
Listed below
Step-by-step explanation:
1. To solve number 1 we need to find a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator.
[tex]\frac{3}{4} =\frac{6}{8}[/tex]
How can we convert this? Well, to go from 4 to 8, we multiply by 2. Doing the same to the top number (Numerator) will get us a fraction of [tex]\frac{6}{8}[/tex].
Adding the two fractions together:
[tex]\frac{7}{8} +\frac{6}{8}= \frac{13}{8} or1 \frac{5}{8}[/tex]
Therefore, the answer to question 1 is [tex]1\frac{5}{8}[/tex].
2. If there are 60 students in a class, and [tex]\frac{3}{4}[/tex] of them are girls, we can use this equation to solve for the number of girls in the class:
60 × 0.75 = 45Why do we multiply by 0.75?We multiply by 0.75 because 0.75 is equivalent to [tex]\frac{3}{4}[/tex].
So, there are 45 girls in the class.
To solve for the rest of the class that are boys, we can use this equation:
60 - 45 = 15The answer to question 2 is 15 boys.
3. If the temperature was -2°C, and it is now 8°C, we can use this equation to solve for the temperature difference:
-2 + 10 = 8So, the temperature difference is 10°C.
4. If Mt. Everest's elevation is at 29,028 feet, and the dead sea is -458, we can use this equation to solve for the difference in elevation:
29,028 + 458 = 29,486Therefore, the difference in elevation is 29,486 feet.
suppose you have 100 dollars in your bank account and you earn 2.25% interest per year. let mn be the amount of money in your account after n years. determine the amount of money you have in your account after years 1, 2, 3, and 4 to 2 decimal places:
The amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan.
Given that, you have 100 dollars in your bank account, and you earn 2.25% interest per year.
We need to find the amount of money you have in your account after years 1, 2, 3, and 4 years
Find for Simple interset :-
Simple interset = PRT / 100
P = Principal amount, r = rate and t = year
For 1 year, put t = 1
A = 100×1×2.25 / 100 + 100
= $102.25
To find the amount for 2nd, 3rd and 4th year, just multiply these numbers to the interset earned in 1st year,
For 2 year,
A = $102.25×2
A = $204.5
For 3 year,
A = $102.25×3
A = $306.75
For 4 year,
A = $102.25×4
A = $409
Hence, the amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.
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Is ABC~DEC? Explain.
(A) No;they are both right triangles but all of their sides are different, so they are not similar
(B) yes; they share two sides, so they are similar.
(C) Yes; they are both right triangle and they share a common vertex, so they are similar
(D) There is not enough information to tell whether they are similar
pls helpp!! need answer asap!! thanks <3
Answer:
b = 70 degrees
Step-by-step explanation:
A triangle has a total of 180 degrees.
We know 2 angles, one is 80 degrees, and one is 30 degrees.
80 + 30 = 110 degrees.
180 - 110 = 70 degrees
So, b = 70 degrees.
Find step-by-step Discrete math solutions a. Is {{a, d, e}, {b, c}, {d, f}} a partition of {a, b, c, d, e, f}?
b. Is {{w, x, v}, {u, y, q}, {p, z}} a partition of {p, q, u,v, w, x, y, z}?
c. Is {{5, 4}, {7, 2}, {1, 3, 4}, {6, 8}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}?
d. Is {{3, 7, 8}, {2, 9}, {1, 4, 5}} a partition of {1, 2, 3, 4, 5, 6, 7, 8, 9}?
e. Is {{1, 5}, {4, 7}, {2, 8, 6, 3}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}?
The solution for these discrete mathematics questions will be: a) No. The element d is in two of the sets. B) Yes C) No. The element 4 is in two of the sets. D) No. None of the sets contains 6. E) a) no b) yes
The study of mathematical structures that are discrete rather than continuous (it's similar to discrete variables and having a bijection with the set of natural numbers) is known as discrete mathematics. Graphs, integers, and logical statements are among the objects studied in discrete mathematics.
Both finite and infinite sets of objects can be studied in discrete mathematics. Some areas of discrete mathematics that deal with finite sets, especially those that have a bearing on business, are referred to as "finite mathematics" at times.
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Note that the full question is:
a) Is {{a, d, e}, {b, c}, {d, f}} a partition of {a, b, c, d, e, f }?
Yes or No
(b) Is {{w, x, v}, {u, y, q}, {p, z}} a partition of {p, q, u, v, w, x, y, z}?
Yes or No
(c) Is {{5, 4}, {7, 2}, {1, 3, 4}, {6, 8}} a partition of (1, 2, 3, 4, 5, 6, 7, 8}?
Yes or No
(d) Is {{3, 7, 8}, {2, 9}, {1, 4, 5}} a partition of {1, 2, 3, 4, 5, 6, 7, 8, 9}?
Yes or No
(e) Is {{1, 5}, {4, 7}, {2, 8, 6, 3}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}?
Yes or No
An Airplane flies in the path shown by the vector PQ on the graph below. What is the magnitude and direction of PQ (1 unit represents 1 mile)
a. 80.5 east of south for 6 miles
b. 80.5 west of north for 7 miles
c. 9.5 south of west for 6.1 miles
d. 9.5 north of east for 6.1 miles
Based on the data, it can be inferred that the magnitude and direction of PQ is 9.5 north of east for 6.1 miles (option D).
How to identify the magnitude and direction of the plane?To identify the magnitude and direction of the plane, we must carefully look at the information in the graph and identify the option that corresponds to the information.
So, we can say that this is moving from the south to the north and from the west to the east, so options A and C would be ruled out. Now we must identify the magnitude and degrees. Taking a completely horizontal line as a reference, we could say that the plane has 9.5 degrees in its trajectory. So the correct option would be D.
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The ages of 12 runners in a recent marathon are listed. 24, 16, 30, 14, 19, 31, 23, 33, 15, 31, 19, 27 Find the median and interpret its meaning as it relates to the runners. The median is 19.5, and it represents the typical age of the runners. The median is 23.5, and it represents the typical age of the runners. The median is 25.5, and it represents the difference in the lowest and highest ages of runners. The median is 28.5, and it represents the difference in the lowest and highest ages of runners.
The median age of the runners is 23.5.
What does "median" mean?By adding up all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined. The median is the middle when a data set is sorted from least to greatest.
We must first arrange the ages from youngest to oldest in order to determine the median:
14, 15, 16, 19, 19, 23, 24, 27, 30, 31, 31, 33
The median will be the average of the sixth and seventh values in this sorted list because there are 12 runners:
(23 + 24) / 2 = 23.5 is the median.
Hence, 23.5 is the runners' median age.
The median, in terms of meaning, is the data set's middle value. In this instance, the age is the exact midpoint between the ages of the 12 racers. It is a central tendency index that shows how typical or representative the data are.
In this situation, the median age of 23.5 can be interpreted as the typical age of the marathon runners. Half of the runners were over 23.5 years old, and half were under that age. Although the middle figure is closer to the lower end of the age spectrum than the higher end, it can also help us estimate the runners' age range. The disparity between the runners' lowest and highest ages is not, however, directly shown.
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-A 10 kg iron plate contains 2000 I potential energy at a height. find out its heigt
Assuming that the iron plate is lifted to a height against the gravitational force, we can use the formula for potential energy:
Potential Energy = mass x gravity x height
where mass is in kg, gravity is 9.81 m/s^2, and height is in meters.
Rearranging the formula to solve for height, we have:
height = Potential Energy / (mass x gravity)
Plugging in the given values, we have:
height = 2000 J / (10 kg x 9.81 m/s^2)
height = 20.34 meters (rounded to two decimal places)
Therefore, the height of the iron plate is approximately 20.34 meters.
Scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. Let X be the random variable for the scores in an exam. On comparing, we get z=1.751 . Hence the minimum score you would need to be in the top 4 % is ____________
To find the minimum score you would need to be in the top 4%, we need to use the standard normal distribution and the given z-score.
First, we find the z-score corresponding to the top 4% using a standard normal distribution table or a calculator:
z = invNorm(1 - 0.04) = invNorm(0.96) = 1.7507 (rounded to four decimal places)
The minimum score needed to be in the top 4% is the score that corresponds to this z-score in the distribution of exam scores. We can use the formula for standardizing a normal random variable to find this score:
z = (X - μ) / σ
where X is the exam score, μ is the mean of the exam scores, and σ is the standard deviation of the exam scores.
Solving for X, we get:
X = zσ + μ = 1.75076.1 + 76.4 = 87.46
Therefore, the minimum score you would need to be in the top 4% is approximately 87.46 points.
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