The given trigonometric equations have the value tan x, -cot x.
Since the given trigonometric equations are: cos2x-cos4x/sin2x+sin4x and cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)
since we know the formulas :
cos A + cos B = - sin (A+B)/2 sin(A-B)/2
sin A - sin B = sin( A+B)/2 cos (A-B)/2
so for the equation, we can
= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)
= sin 3x sin x/ (sin 3x) cos x
= tan x
for the second equation cos2x+cos4x/sin2x-sin4x
= cos 3x cosx/ cos3x sin(- x)
= - cot x
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which volume is greater? 7cm or 7cmX4cmX8cm
Please Write How
On solving the provide question, we got to know that volume of cube is [tex]343 cm^3[/tex] and volume of cuboid is [tex]224 cm^3[/tex], so volume cube is greater.
What is cuboid?We are aware that a rectangle has four corners and is a two-dimensional form. Think of the form as a collection of parallel rectangles. The resultant form is known as a cube. Take a look at the following three-dimensional cube. Height, Width, and Length
The volume of the cube = [tex]a^3[/tex]
Where a is the length of the side = 7cm
volume of cube = [tex]7 X 7 X 7= 343 cm^3[/tex]
volume of the cuboid = l*b*h
[tex]7 X 8 x 4 = 224 cm^3[/tex]
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TIME REMAINING
21:54
The ratios of punch mix to water for several fruit drinks are given.
Punch Mix
Mix
Water
Grape
1 cup
3 cups
Cherry
5 cups
12 cups
Lemon
7 cups
12 cups
Orange
2 cups
3 cups
Which flavor has the smallest ratio of mix to water?
grape
cherry
lemon
orange
Grape flavor has the smallest ratio of mix to water.
What is ratio proportion?
A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.
Here, we have
The ratios of punch mix to water for several fruit drinks as Grape mix (1 Grape flavor has the smallest ratio of mix to water.
cup to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups), and Orange mix (2 cups to 3 cups).
We have to find which flavor has the smallest ratio of mix to water.
So, we compare all the given proportions by having a common base.
Proportions of grape, cherry, lemon, and orange mixed in water = 1/3, 5/12, 7/12, 2/3
Now let us have a common denominator 12 as LCM of 3 and 12 is 12.
Proportions of grape, cherry, lemon, and orange mixed with water = 1×4/3×4, 5/12, 7/12, 2×4/3×4
Proportions of grape, cherry, lemon, and orange mixed with water = 4/12, 5/12, 7/12, 8/12
Hence, the Grape flavor has the smallest ratio of mix to water.
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in the expression 7a + b-12 which is a constant
Answer: Its -12
Step-by-step explanation:
In Algebra, a constant is a number on its own.
Which of the following statement is true ?
a) All the rhombuses are squares
b) each square is a parallelogram
c) each parallelogram is a square
d) each trapezium is a parallelogram
The following statement is true is a) All the rhombuses are squares .
Given :
In contrast to a square, the lengths of all four sides of a rhombus are equal, the diagonals of a rhombus bisect each other, and all four angles of a rhombus are not equal to 90 degrees.
Parallelograms are not all squares. Parallelograms have equal length opposite sides, hence squares with all sides equal are parallelograms. Rhombuses are the only kites that fly.
Because a parallelogram contains two pairs of parallel sides, a trapezium is not a parallelogram. A trapezium, on the other hand, has only one pair of parallel sides.
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Suppose a bag of colored marbles contains 33 marbles numbered 1 to 33. If you draw one marble at a time from the bag, without replacement, how many different ways can you draw all of the marbles from the bag? Remember that "without replacement" means that the marbles are not returned to the bag after they are chosen. Write your answer in factorial notation.
The ways you can draw all of the marbles from the bag is 33! ways
How to determine the ways you can draw all of the marbles from the bag?From the question, we have the following parameters that can be used in our computation:
Total number of marbles, n = 33
Total numbers of marbles picked at a time, r = 1
From the question, the marbles are selected without replacement
This means that the number of ways the marbles can be drawn from the bag is calculated using the following factorial formula
Total = n!
Where
n = 33
Substitute the known values in the above equation
Total = 33!
Apply the factorial formula
n! = n * (n - 1) * (n - 2) * .... * 1
So, we have
Total = 33 * 32 * 31 * 30 * .... * 1
Evaluate
Total = 8.6833176e+36
Hence, the number of ways is 33!
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demand for soccer balls at a new sporting goods store is forecasted using the following regression equation: y
The forecast of soccer ball demand for the month of April is 123.
What is regression?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable and one or more independent variables.
The main focus of regression to the mean is how data balances. In essence, it says that if a variable is extreme when measured for the first time, it will be more typical the next time.
The regression equation is Y = 98 + 2.2x, where x = 4 for April.
So the unadjusted forecast for April,
= 98 + 2.2x = 98 + (2.2 × 4) = 98 + 8.8 = 106.8
Seasonal index for April = 1.15
Adjusted forecast for April = Unadjusted forecast × seasonal index = 106.8 × 1.15 = 122.82 or rounded to 123
So the answer is 123.
Hence, the forecast of soccer ball demand for the month of April is 123.
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Complete question:
Complete question is attached below.
Tremaine's family owns a manufacturing plant that makes fake vomit. At high speed, the manufacturing line can produce 4 piles of fake vomit per hour. At medium speed, the manufacturing line can produce 50% fewer piles per hour of fake vomit than at high speed. How many piles of fake vomit can the manufacturing line produce at medium speed?
The amount of piles of fake vomit that the manufacturing line can produce at medium speed is of:
2 piles.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the equivalent measures in the context of a problem.
The amount that can be produced at high speed is of:
4 piles of vomit.
(as stated in the text).
At medium speed, the amount is 50% of the amount of 4 piles of vomit produced at high speed, hence 4 is multiplied by 0.5 to give the amount, as follows:
0.5 x 4 = 2 piles of vomit.
(as the decimal equivalent of the percentage of 50% is of 0.5).
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pls help help help i need help !!!!!!!!
The length of the unknown side is 6 units
How to determine the length of the unknown sides?From the question, we have the following parameters that can be used in our computation:
Triangles ABC and QRS
This triangles are similar triangles
This means that
AB : AC= QR : QS
Substitute the known values in the above equation, so, we have the following representation
5 : 3 = 10 : QS
Multiply the first ratio by 2
So, we have
10 : 6 = 10 : QS
By comparison, we have
QS = 6
Hence, the length is 6 units
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Valeria has been training for the Charlestown Cruisers bike race. The first week she trained, she rode 5 days and took the same two routes each day. She rode an 8-mile route each morning and a longer route each evening. By the end of the week, she had ridden a total of 115 miles. How many miles did Valeria ride each evening?
Valeria rode for 15 miles in the evening each day.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Valeria has been training for the Charlestown Cruisers bike race. The first week she trained, she rode 5 days and took the same two routes each day. She rode an 8-mile route each morning and a longer route each evening. By the end of the week, she had ridden a total of 115 miles.
Let the distance she covered in evening be x,
Establishing the equation,
(8+x)5 = 115
8+x = 23
x = 15
Hence, Valeria rode for 15 miles in the evening each day.
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I need help with this please
all because all of the equianlangular triangles are equal
Edmund is designing his garden. For every yellow tulip, he plans to plant two whites lilies. Using only these two types of flower, he plans to plant 12 flowers in his garden. How many of each type of flower will Edmund plant in his garden? Edmund will plant _______ tulips and _______ lilies.
Answer:
4 yellow tulips and 8 white lilies.
Step-by-step explanation:
Ratio is 1:2:3 for yellow tulips, white lilies and the total.
Set up a proportion
[tex]\frac{yellow}{total}[/tex] = [tex]\frac{yellow}{total}[/tex] Three of these numbers you know, Solve for the unknown
[tex]\frac{1}{3}[/tex] = [tex]\frac{x}{12}[/tex] Cross multiply and solve for x
3x = 12 Divide both sides by 3
x = 4 This is the number of yellow tulips
Set up another proportion:
[tex]\frac{white lilies}{total}[/tex] = [tex]\frac{white lilies}{todal}[/tex]
[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{12}[/tex] I can see that 3 x 4 = 12 so I will multiply the top number to 2 by 4 to get 8.
1. Mark says the two expressions (9a-27)-4
and -3 (-4-3) are equivalent is he correct
Explain how you know.
They (circle one) are/arenot
equivalent because
Show your work
Equations are not equivalent because the values are found to be different.
What is an expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Expressions are:
(9a - 27) - 4 = 9a - 31 -------(I)
and -3(- 4 - 3) = -3(-7) = 21 -----(II)
From (I) and (II), expressions are not equivalent.
Hence, equations are not equivalent because the values are found to be different.
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Is X 8 is a factor of f/x Which of the following must be true?
If (x + 8) is a factor of f(x), then the true statement is f(-8) = 0 .
In the question ,
it is given that , x [tex]+[/tex] 8 is factor of f(x) ,
we have to select the correct option about f(x) from the given options .
When solving the polynomials, a factor of the polynomial gives the solution of the polynomial.
that means , x + 8 = 0
So , x = -8 ,
So , it means that when x = -8 , then the value of the function f(-8) will be zero ,
which means that x = -8 will be a root of the given function f(x) .
Therefore , the true statement is f(-8) = 0 .
The given question is incomplete , the complete question is
If (x + 8) is a factor of f(x), which of the following must be true ?
(a) Both x = –8 and x = 8 are roots of f(x).
(b) Neither x = –8 nor x = 8 is a root of f(x).
(c) f(–8) = 0
(d) f(8) = 0
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Showwwwwwwwww workkkkkkkkkkkkk
In image.
In the Image is the anser and explanation.
Roy is skiing on a circular ski trail that has a radius of 0.7 km. Roy starts at the 3-o'clock position and travels 2.15 km in the counter-clockwise direction. a. How many radians does Roy sweep out? _____ radians Preview b. When Roy stops skiing, how many km is Roy to the right of the center of the ski trail? _____ v km Preview c. When Roy stops skiing, how many km is Roy above of the center of the ski trail? _____ * km
Part a: Roy sweeps out 2.15/0.7 radians.
Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial
Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail
The radius of the ski trail= 0.7 km
Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.
Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.
Now, using the formula for arc length.
Arc length=(Radius)(angle at center)
2.15=(0.7)θ
θ=2.15/0.7
Roy sweep out 2.15/0.7 radians.
Part b:
When Roy stops skiing how many km is Roy to the right of the ski trial
In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle
Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,
As in part, a central angle is 2.15/0.7=3.071.
Therefore,
cos(3.071)=OP/0.7
OP=cos(3.071)(0.7)
cos(3.071)(0.7) km.
Part c:
When Roy stops skiing how many km is Roy above the centre of the ski trial
From figure part of part b, we have to calculate side BP.
In right angle triangle sin(θ)=Opposite side/hypotenuse
Therefore,
sin(3.071)=BP/0.7
BP=sin(3.071)/(0.7)
sin(3.071)(0.7) km.
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division- answer in gallons and quarts. no fraction or decimals.
3/10gallons 11 quarts
1 gal =4 quarts
Answer:
Step-by-step explanation:
To solve this problem, we need to divide 3/10 gallons by 1 gallon, which is equal to 4 quarts.
First, let's convert the fraction 3/10 to a decimal by dividing the numerator by the denominator: 3 / 10 = 0.3
Then, we can divide 0.3 gallons by 1 gallon to get the equivalent number of gallons in quarts: 0.3 gallons / 1 gallon = 0.75 quarts
Since 1 quart is equal to 0.25 gallons, 0.75 quarts is equivalent to 3/4 of a gallon.
Finally, we can add the number of quarts given in the problem (11 quarts) to the number of quarts equivalent to the number of gallons (3/4 of a gallon, or 3 quarts). This gives us a total of 14 quarts, which is equivalent to 3 and 1/2 gallons.
Therefore, the final answer is 3 gallons and 11 quarts.
qualitative research methods are particularly strong in studying the meanings that participants attach to events.
Yes, it's true that the interpretations that participants make of events can be best studied through qualitative research techniques like participant observation or in-depth interviews.
Going into the field without telling every subject of the field research who you are is always unethical. The following are a number of the methodologies normally utilized in qualitative research: Ethnography commonly entails researchers immediately gazing members of their herbal environments over time. A key characteristic of ethnography is the truth that herbal settings, unadapted for the researchers' interests, are used.
A famous and useful categorization separate qualitative strategies into 5 groups: ethnography, narrative, phenomenological, grounded theory, and case study. John Creswell outlines those 5 strategies in Qualitative Inquiry and Research Design. As maximum qualitative information is amassed via interactions with members via the usage of interviews, surveys, questionnaires, or awareness groups, a researcher have to discover members who're inclined to talk approximately their experiences.
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Correct Question:
Qualitative research methods, such as participant observation or intensive interviews, are particularly strong in studying the meanings that participants attach to events. state true or false.
HELPPPP!!! 30 POINTS!!!!
Which of the following correlation coefficients would represent the strongest correlation?
A. -0.9
B. 0.04
C. -0.16
D. .78
Answer:
D
Step-by-step explanation:
i did this before trust me
Solomon has taken two tests each out of ten. his average score is 18. if the product of his scores is 56. what did he score in each test ?
The scores of both test Solomon took are 14 for the first test and 4 for the second test.
How to calculate the score of bother test?let a represent the first score and b represent the second score.
since the average score is 18, you get (a + b) / 2 = 18
multiply both sides of this equation by 2 to get a + b = 36
the product of her scores is 56 means that a × b = 56.
you have 2 equations that need to be solved simultaneously.
they are a + b = 36 and a × b = 56
solve for a in the second equation to get a = 56 / b.
replace a with 56/ b in the first equation to get 56/ b + b = 18
multiply both sides of this equation by b to get 56 + b^2 = 18b
subtract 14b from both sides of this equation and arrange the terms in descending order of degree to get b^2 - 18b + 56 = 0
Factorise the quadratic equation to get the following:
(b-4 ) ( b - 14) = 0
Solve for b to get b = 4 and b = 14
Therefore, the product of the of the two scores:
= 14×4 = 56. This means that he scored 14 in first test and 4 in the second test.
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Select the graph of the solution. Click until the correct graph appears. 2x - 1 > 5
open circle on 3
open circle on 3 pointing > right >
open circle on 3 pointing < left
Answer:
lick on 3 pointing left under the wear
The cost of rent in a instrument is 65$ for the first month, it cost $30 for each additional month x that the instrument is rented which expression
Represents the total cost of renting an instrument
Answer:
Step-by-step explanation:
it is C because 65 is a one Time thing and 30x means every month u rent it times the money.
I dont understand this ones. Please help
The distance between the line segment from P to RQ is 2.83 units
Distance Between Two PointsDistance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x₂ – x₁)² + (y₂ – y₁)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
In this case, we need to find the coordinate of P and RQ
From P to the line RQ, we will meet the midpoint of the line RQ which has a coordinate of (3, 3)
Let's use the formula of distance of a line segment and solve this
d = √((x₂ - x₁)² + (y₂ + y₁)²)
P = (1, 1)RQ = (3, 3)d = √(3 - 1)² + (3 - 1)²
d = √(2)² + (2)²
d = √8
d = 2√2
d = 2.83 units
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Milo worked for 5 hours on Monday and 4 hours on Tuesday. he earned $14 per hour. How much money did milo earn on both days combined? show
your work
Answer:
$126
Step-by-step explanation:
Monday: 5HR X $14 = $70
Tuesday: 4HR X $14 = $56
$70+$56=$126
Which of the following is an example of A.S.A. criterion of congruency for two triangles ∠ACB and ∠DEF? a)AB = EF, ∠B = ∠E and ∠C = ∠F b)BC = EF, ∠B = ∠F and ∠C = ∠E c)AC = EF, ∠B = ∠D and ∠C = ∠F d)AC = DE, ∠B = ∠D and ∠C = ∠F
Under ASA criterion, Δ ACB ≅ ΔDEF, as ∠C = ∠E, ∠B = ∠F, and the side CB = EF.
What is ASA Congruence Rule?
ASA Congruence rule stands for Angle-Side-Angle. Under this rule, two triangles are said to be congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. Look at the image given below to determine if the two given triangles, Δ ABC and ΔXYZ are congruent by the ASA rule.
Hence , Under ASA criterion, Δ ACB ≅ ΔDEF, as ∠C = ∠E, ∠B = ∠F, and the side CB = EF. Since Δ ACB ≅ ΔDEF, then the third angle ∠A and the other two sides of Δ ACB are bound to be equal to the corresponding angle ∠D and the sides of ΔDEF.
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What is 80% of a 25 question test?; How many questions do you have to get right out of 20 to get 80 %?
To get 80% percentage you need to attempt 20 question
Percentage:
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
For example, 45% (read as "forty-five per cent") is equal to the fraction
45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.
now we need to find 80% of a 25 question test
80% of 25 can be written as 80% × 25
= 80/100 × 25
= 20
To get 80% you need to attempt 20 question
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CAN SOMEONE HELP ME WITH ALGEBRA 2?
The solution set is for the given inequality is (-∞, -2.25]
How to solve the inequality?Here we want to solve the following inequality:
-11 - 8k ≥ 23 - (7 - 4k)
To solve this, we need to isolate the variable k in one side of the equation.
First we can expand the right side so we get:
-11 - 8k ≥ 23 - (7 - 4k)
-11 - 8k ≥ 23 - 7 + 4k
Group like terms:
-11 - 23 + 7 ≥ 4k + 8k
-34 + 7 ≥ 12k
-27 ≥ 12k
-27/12 ≥ k
-2.25 ≥ k
Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]
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If F1 + F2 = 100 and F1 - F2 = 20 then how F1 = 60 ?? I need the solution
To find the value of F1, we can start by writing out the given equations in a more standard form.
First, we can rewrite the equation "F1 + F2 = 100" as "F1 = 100 - F2".
Then, we can rewrite the equation "F1 - F2 = 20" as "F1 = 20 + F2".
If we set these two equations equal to each other, we get "100 - F2 = 20 + F2".
If we simplify this equation, we get "80 = 2 * F2".
If we divide both sides of the equation by 2, we get "40 = F2".
Substituting this value back into either of the original equations, we can find that "F1 = 100 - F2" or "F1 = 100 - 40" which gives us "F1 = 60".
Therefore, the value of F1 is 60.
The superintendent of a large school district is curious about the relationship between students' grades and their participation in extracurricular activities. They take a random sample of 500500500 students and find that students with more participation in extracurricular activities are far more likely to have high grades than students with little or no participation.
What conclusion can they draw from this study?
There was an association between extracurricular participation and grades, but it's not necessarily a causal relationship.
Activities in which students participated in sports benefit in a variety of ways, including greater grades and test scores, higher academic achievements, more regularity in class attendance, and an increase in self.
Since the students also weren't assigned to a therapy group at random, the study was an observation one.It is a connection between extra curricular and academics.We don't know if extracurricular engagement resulted in higher grades since this wasn't a controlled experiment.There had been a link between extracurricular involvement and grades, but there was not definitely a causal relationship, thus they cannot make any conclusions from this research.
This was an observational study since students were not randomly assigned to treatment groups—so we can say that there is an association or a relationship extracurricular participation and grades. Since this wasn't an experiment, we don't necessarily know that extracurricular participation caused higher grades.
Hence we get the required answer.
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What is Y=2000(1.25)^12
Answer:
y+29103.83045673370361328125
use the extended euclidean algorithm to find the greatest common divisor of 8,406 and 1,242 and express it as a linear combination of 8,406 and 1,242. step 1: find q1 and r1 so that 8,406
Using Euclid's Algorithm, the greatest common divisor or 8406 and 1242 is 18
The first number = 8406
The second number = 1242
We have to find the greatest common divisor of the given numbers 8406 and 1242 using the Euclid's Algorithm
8406 / 1242 = 6 R 954
8406 = 6 × 1242 + 954
1242 / 954 = 1 R 288
1242 = 1 × 954 + 288
954 / 288 = 3 R 90
954 = 3 × 288 + 90
288 / 90 = 3 R 18
288 = 3 × 19 + 18
90 / 18 = 5 R 0
90 = 5 × 18 + 0
The remainder became zero, so the greatest common divisor 18
Therefore, the greatest common divisor of 8406 and 1242 is 18
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