The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
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Sarun is thrice as old as his sister Anita. If five years is subtracted (5) from Anita’s age and seven years added to Sarun’s age , then
Sarun will be five times Anita’s age. How old were they three years ago?
Answer: Let's start by using algebra to represent the given information.
If we let "a" be Anita's current age, then we know that Sarun's current age is 3a (since he is thrice as old as Anita).
According to the problem, if we subtract 5 years from Anita's age and add 7 years to Sarun's age, then Sarun will be 5 times Anita's age. In other words, we have the equation:
3a + 7 = 5(a - 5)
Simplifying and solving for a, we get:
3a + 7 = 5a - 25
32 = 2a
a = 16
So Anita is currently 16 years old, and Sarun is 3 times as old, or 48 years old.
To find out how old they were three years ago, we simply subtract 3 from their current ages:
Anita was 13 years old three years ago (16 - 3), and Sarun was 45 years old (48 - 3).
Step-by-step explanation:
Part A Which solution do you get when you use the quadratic formula to solve the equation –4x2 – 12x – 9 = 0?
Answer:
A: -3/2
Step-by-step explanation:
-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9
-4x²-6x-6x-9=0 Factor by grouping
(-2x-3)(2x+3)=0 Solve for x
x= -3/2
Write an equation for the line on a graph below.
Check the picture below.
Answer:
x=-3
Step-by-step explanation:
this isnt making any sense i need help please!
The value οf sin F is 5/6.
What is meant by trigοnοmetry?The branch οf Mathematics which helps in dealing with measure οf three sides οf a right-angled triangle is called Trigοnοmetry.
What are the different Trigοnοmetric Ratiο?sin θ = Perpendicular/Hypοtenuse
cοs θ = Base/Hypοtenuse
tan θ = Perpendicular/Base
cοsec θ = Hypοtenuse/Perpendicular
sec θ = Hypοtenuse/Base
cοt θ = Base/Perpendicular
Cοs D = 5/6 (given)
We knοw, cοs θ =Base / Hypοtenuse
Thus, base = 5 and hypοtenuse = 6
Therefοre, DE = 5 and DF = 6
Sin θ = Perpendicular / Hypοtenuse
Sin F = DE / DF
Sin F = 5/6
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In Drosophila, the allele for normal-length wings is dominant over the allele for vestigial wings. In a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?1:2:1 :1:2:1 is the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes. This also means that the phenotypic ratio should be 3 dominant phenotype:1 recessive phenotype. From the phenotypic class "3", 2/3 are represented by the heterozygotes, while the remaining 1/3 by the dominant homozygotes.
The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.
The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?
In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:
Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360
This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:
Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals
Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.
Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):
Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals
And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):
Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals
Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.
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Suppose that the domain of discourse of the propositionalfunction P(x) is {1,2,3,4}. Rewrite each propositional function below using only negation, disjunction, and conjunction. (a) Vx P(x) (b) -(Vx P(x)) (c) 3x P(x) (d) -(E. P(x))
The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:
a) "there does not exist an x in the domain for which P(x) is false."
b) "there exists an x in the domain for which P(x) is false."
c) "there exist exactly three x's in the domain for which P(x) is true."
d) -(E. P(x)) can be rewritten as “Every x is not P(x)”
We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.
a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:
-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."
b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:
Ex -P(x).
c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:
There exists at least three x's in the domain for which P(x) is true.There does not exist a fourth x in the domain for which P(x) is true.Using the symbols for negation, disjunction, and conjunction, we can write this as:
(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).
d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:
Ax -P(x),
which means "for all x in the domain, P(x) is false."
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a biased dice was rolled and the probability distribution of the outcomes are as follows. what will be the possible probability of getting 3 and of getting 5 when rolling this dice?
The possible probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice is 0.2.
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
A biased dice was rolled and the probability distribution of the outcomes are as follows then the outcomes are [tex] 1, 2, 3, 4, 5, 6[/tex]
Probability: [tex]0.2, 0.1, 0.3, 0.1, 0.2, 0.1[/tex]
To find the probability of getting [tex]3[/tex] and of getting [tex]5[/tex] when rolling this dice.
Probability of getting [tex]3[/tex]:
Outcome = [tex]3[/tex]
Probability of getting = [tex]^3P(3) = 0.3[/tex]
So, the possible probability of getting [tex]3[/tex] is [tex]0.3[/tex].
Probability of getting [tex]5[/tex]
So, the outcome of [tex]5[/tex]
Probability of getting [tex]^5P(5) = 0.2[/tex]
So, the possible probability of getting 5 is 0.2.
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In the diagram below, what is the measure of ∠x?
Answer:<x=105
Step-by-step explanation:
180-75=105
PLEASE HELP ASAP!!!!!!!!!!!! 100 POINTS!!!
Prove that the angle bisector of the the angle opposite the base of an isosceles triangle is also the following:
A) the altitude to the base
B) the median to the base
(MUST BE A CORRECT EXPLANATION)
Answer:
We need to prove that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.
Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from A to BC and call the point where it intersects BC as D.
Now, we need to prove that AD is the angle bisector, median, and altitude to the base BC.
To prove AD is the angle bisector:
We need to prove that the angle ADB and ADC are equal. We know that angle ABD and angle ACD are right angles because BD and CD are altitudes. We also know that AB = AC because the triangle is isosceles. Therefore, the triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion.
Thus, angle ADB = angle ADC, which means that AD is the angle bisector of angle BAC.
To prove AD is the median:
We need to prove that BD = CD. Since AB = AC and AD is perpendicular to BC, triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion. Therefore, BD = CD, which means that AD is also the median to the base.
To prove AD is the altitude:
We need to prove that angle BAD and angle CAD are right angles. This is true because AD is perpendicular to BC, and BD and CD are also perpendicular to BC. Therefore, AD is also the altitude to the base BC.
Hence, we have proved that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.
0
2
Given the function f(x) = x-2, draw a line from the value of
to the corresponding value of f(x).
16
undefined
The graph of the function f(x) = x - 2 is a straight line that passes through the origin and has a slope of 1.
What is function in math?Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
This means that for every unit increase in x, the value of f(x) increases by 1 unit. Therefore, when x is equal to 0, the value of f(x) is equal to -2. When x is equal to 1, the value of f(x) is equal to -1. When x is equal to 2, the value of f(x) is equal to 0. When x is equal to 16, the value of f(x) is equal to 14. As you can see, for every increase in x, the value of f(x) increases by 2 units. This is the reason why the line drawn from the value of x to the corresponding value of f(x) increases by 2 units when x is increased by 1 unit.
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In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).
What is function ?Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
In this example, the function f(x) = x-2 is being represented by a line that connects each value of x to the corresponding value of f(x).
When x = 4,
then f(x) = 4-2
f(x) = 2,
so the line extends from (4, 2) to the origin (0, 0).
Similarly, when x = 0,
then f(x) = 0-2
f(x) = -2,
so the line extends from (0, -2) to (4, 2).
When x = 1,
then f(x) = 1-2
f(x) = -1,
so the line extends from (1, -1) to (4, 2).
Finally,
when x = 2,
then f(x) is undefined.
In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).
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Plot the points A(3,1), B(-2, 6), C(6, 4) on
the coordinate axes below. State the
coordinates of point D such that A, B, C,
and D would form a parallelogram.
(Plotting point D is optional.)
To form a parallelogram, the opposite sides of the quadrilateral should be parallel. Let's find the coordinates of point D such that AB is parallel to DC.
The slope of line AB = (yB - yA) / (xB - xA) = (6 - 1) / (-2 - 3) = -1
Therefore, the slope of line DC should also be -1.
Let's assume the x-coordinate of point D is xD.
The slope of line CD = (yD - yC) / (xD - xC)
Since the slope of CD is -1, we can write:
(yD - yC) / (xD - xC) = -1
yD - yC = -(xD - xC)
yD = -(xD - xC) + yC
Substituting the coordinates of points C and A, we get:
yD = -(xD - 6) + 4
yD = -xD + 10
Therefore, the coordinates of point D are (xD, -xD + 10).
To find the x-coordinate of point D, we can use the fact that BC is parallel to AD.
The slope of line BC = (yC - yB) / (xC - xB) = (4 - 6) / (6 + 2) = -1/4
Therefore, the slope of line AD should also be -1/4.
The slope of line AD = (yD - yA) / (xD - xA)
Substituting the coordinates of points A and D, we get:
(yD - 1) / (xD - 3) = -1/4
yD - 1 = -(xD - 3) / 4
yD = -(xD - 3) / 4 + 1
yD = -xD/4 + 5/4
Substituting the equation we found for yD in terms of xD, we get:
-xD/4 + 5/4 = -xD + 10
3/4 xD = 35/4
xD = 35/3
Therefore, the coordinates of point D are (35/3, -35/3 + 10) = (35/3, 5/3).
We can now plot the points A, B, C, and D on the coordinate axes, and verify that they form a parallelogram.
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uessing on an exam: in a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers. what is the probability that: (please round all answers to four decimal places)
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977
How to calculate the probability?In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.
The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:
Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977
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Calculator may be used to determine the final numeric value, but show all steps in solving without a calculator up to the final calculation. The surface area A and volume V of a spherical balloon are related by the equation A’ = 364V? where A is in square inches and Vis in cubic inches. If a balloon is being inflated with gas at the rate of 18 cubic inches per second, find the rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches
In the equation A’ = 364V relating the surface area A and the volume V of a spherical balloon. We are also given that the volume is increasing at a rate of 18 cubic inches per second.so the rate at which the surface area of the balloon is increasing is 6552 square inches per second
We want to find the rate at which the surface area is increasing when A = 153.24 square inches and V = 178.37 cubic inches.
To find the rate of change of A with respect to time, we can use the chain rule of differentiation:
dA/dt = dA/dV × dV/dt
We know that dV/dt = 18 cubic inches per second, so we just need to find dA/dV and then we can find dA/dt.
To find dA/dV, we differentiate the equation A’ = 364V with respect to volume V:
dA/dV = 364
Now we can find dA/dt:
dA/dt = dA/dV × dV/dt ⇒ 364 × 18 ⇒ 6552 square inches per second
So the rate at which the surface area of the balloon is increasing is 6552 square inches per second when A = 153.24 square inches and V = 178.37 cubic inches.
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A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet long. How tall is a man who can cast a shadow that is 14 feet long?
Answer:
Step-by-step explanation:
We can set up a proportion to solve this problem:
(height of boy) / (length of boy's shadow) = (height of man) / (length of man's shadow)
We are given that the boy is 3 feet tall and his shadow is 7 feet long. Let's use "h" to represent the height of the man. We are also given that the man's shadow is 14 feet long. Substituting these values into the proportion, we get:
3/7 = h/14
To solve for h, we can cross-multiply and simplify:
3 × 14 = 7h
42 = 7h
h = 42/7
h = 6
Therefore, the man is 6 feet tall.
Use the equation, 8^2x = 32^x+3, to complete the following problems.
(a) Rewrite the equation using the same base.
(b) Solve for x. Write your answer in simplest form.
Given: ,8^2x= 32^x+3
a: (2³)^2x = (2⁵)^x+3
b: Solving, we get
2^6x = 2^5x+15
Since bases are same, we have
=>6x=5x+15
=> x = 15
4.1.60-(15)+(-13 4.2.-2(3)+27 ÷(-3)
Answer:
-15
Step-by-step explanation:
4.1.60 - (15) + (-13) = 32
4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15
A printer manufacturer obtained the following probabilities from database of test results. Printer failures are associated with three types of problems: hardware, software, and other (such as connectors) , with probabilities 0.1_ 0.6, 0.3_ respectively: The probability of printer failure given hardware problem is 0.9 given a software problem is 0.2, and given any other type of problem is 0.5. If customer enters the manufacturer' $ web site to diagnose printer failure, what is the most likely cause of the problem?
The probability of a printer failure given hardware problems is 0.9, given software problems are 0.2, and given any other type of problem is 0.5. The customer should diagnose the printer failure by looking for a hardware issue.
The probability of printer failure is dependent on three problem types, hardware, software, and others (like connectors). The respective probabilities are 0.1_, 0.6, and 0.3_.
We have hardware problems, the probability of printer failure is 0.9, given software problems the probability is 0.2, and given any other problem type the probability is 0.5. By using Bayes' theorem, the most probable cause of the failure can be determined.
Let A represent the cause of the problem, and B is the evidence that the customer sees. Let's calculate the probability that A = hardware given B, which is P(A|B) = P(B|A)*P(A)/P(B).
Here, P(A) is the prior probability of the cause being hardware,
P(B|A) is the likelihood of observing the evidence given the cause being hardware, and P(B) is the probability of observing the evidence.
Given hardware problems, the probability of printer failure is 0.9, while the probability of observing this evidence given hardware problems is 0.9. Since there are three problem types, each of them having a prior probability of 1/3, we get P(A) = 1/3.
The probabilities of observing the evidence in the case of other types of problems and software problems are 0.5 and 0.2, respectively. Therefore, the most likely cause of printer failure is hardware problems.
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A square field has a side length of 6x10³ meters. Which of the following is its area in square meter
(1) 6x106
(3) 36x106
(2) 36×10⁹
(4) 6x10⁹
Answer:
36 × 10^6 m²
Step-by-step explanation:
Given the side length of a square = 6 × 10³m,
To solve for the area of a square, use the following formula:
A = S² where:
S = side of the square
Substitute the given value for the side into the formula:
A = S²
A = (6 × 10³)²
A = 36000000 or 36 × 10^6 m²
NOTE:
6 × 10³ is also the same as 6 × 1000 = 6000,
(6 × 10³)² is essentially 6,000² = 36,000,000
Therefore, its area in square meters is 36 × 10^6
If the radius of the circle is 8 cm, what would the area of the square that is around it be? Use 3.14 as π.
Answer: 201.06
Step-by-step explanation:
A=πr2=π·8^2≈201.06193
Here is a hanger that is in balance. We don't know how much any of its shapes weigh. How
could you change the number of shapes on it, but keep it in balance? Describe in a couple
sentences
We can change the number of shapes on it by putting one rectangle to the right and put two triangles to the left.
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let's say the circle is A, Triangle is B, and Rectangle is C.
2A + 4C = 2A + 4B + 2C
So, C = 2B ( 4C = 4B + 2C, 2C = 4B, C = 2B)
That one rectangle and two triangles are equally weighed. So, put one rectangle to the right and put two triangles to the left. The hanger is still in the balance.
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Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is true. B. The statement is false. A sampling distribution is normal only if n≥30. C. The statement is false. A sampling distribution is normal if either n≥30 or the population. D. The statement is false. A sampling distribution is never normal.
A sampling distribution is normal only if the population is normal. This statement is false because A sampling distribution is normal only if n≥30.
If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values above 30, but after a certain threshold the x(bar) distribution is effectively "normal".
Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.
A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.
In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.
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Urgent Help! 100 points to whoever is willing ^-^
Noise-canceling headphones have microphones to detect the ambient, or background, noise. They interpret those noises as sinusoidal functions. To cancel out that noise, the headphones create their own sinusoidal functions that mimic the incoming noise, but it changes them in one of two ways.
1. The mimic function is the negative of the noise's function.
2. The mimic function is the noise function shifted one-half period.
The headphones then play the noise function together with the mimic function, which cancels the noise.
Instructions
• Find the frequency of any musical note in hertz (Hz).
• Use the frequency to write f(x), the sine function for the note. For example, [tex]A_4[/tex] has a frequency of 440 Hz. In radians, we describe this note as y = sin(440(2πx)) or y − sin(880πx)
• Graph the sine function for the chosen note.
• Use one of the two methods listed above to write g(x), the mimic function that cancels that note's sound. Graph that function.
• Write a third function, h(x), that is the sum of f(x) and g(x). Graph it.
• Use your three graphs to explain why g(x) cancels out f(x).
Which angles would the Alternate Exterior Angles Theorem state are congruent?
Which angles would the Alternate Exterior Angles Theorem state are congruent?
Answer:
Choice 2
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
This is a good example of a problem that can be solved by POE(process of elimination)
First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°
The same applies for ∠3 and ∠4 (third choice)
The same applies for ∠1 and ∠4 (fourth choice)
That leaves choice 2
We can prove ∠1 ≅ ∠7 as follows:
∠1 ≅ ∠3 since they are vertically opposite angles
∠3 ≅ ∠7 since they are exterior angles
So ∠1 ≅ ∠7
By similar reasoning,
∠2 ≅ ∠8
So correct choice is Choice 2
Suppose X and Y are independent N(0; 1) random variables.
(a) Find P(X^2 < 1).
(b) Find P(X^2 + Y^2 < 1)
The required probability is obtained as:
(a) P(X^2 < 1) = 0.8413.
(b) P(X^2 + Y^2 < 1) = 0.7854.
(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:
P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))
Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:
P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))
Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.
(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.
We can use polar coordinates to express X and Y as:
X = Rcosθ
Y = Rsinθ
where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).
Therefore, we can find P(X^2 + Y^2 < 1) as:
P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))
Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:
P(R^2 < 1) = 0.7854
Therefore, P(X^2 + Y^2 < 1) = 0.7854.
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ADEF-AABC. What is the sequence of transformations that maps AABC to ADEF?
A reflection across the y-axis and a translation 4 units down
A rotation of 180* about the origin and a dilation with center (0,0) and scale factor 2
A reflection across the y-axis and a translation 2 units down.
A rotation of 90° about the origin and a translation 2 units down
The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.
What is transformation?The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.
The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.
ADEF and AABC are not in the same location, even if they are the same height and shape.
The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.
A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.
Therefore, A reflection across the y-axis and a translation 2 units down.
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-14+7m <7h, please answer this I need help
Each pair of numbers (m, h) which meet the inequality is the answer to the inequality. m < h plus 2.
Pairs of numbers: what are they?A factor pair is a collection of two factors that, when multiplied together, produce a certain result in mathematics. In those other words, it's a pair of integers that we multiply to produce a result. For instance, the factor pair that yields the result in the multiplication formula 6 7 = 42 is composed of the numbers 6 and 7. 42
By adding 14 to both sides, starting with -14 + 7m 7h, we may simplify the left side:
-14 + 7m plus 14 < 7h plus 14
Even more condensed, we get at:
7m < 7h plus 14
The inequality can then be divided by 7 on both sides: m h + 2.
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suppose that a will be randomly selected from the set {-3, -2, -1, 0, 1} and that b will be randomly selected from the set {-2, -1, 0, 1}. what is the probability that a*b>0
Answer:
1
----
20
Step-by-step explanation: Total there are 20 Combinations as 5*4 = 20 ab>0 when b
one hundred students were asked whether they liked certain candy flavors. it was found that liked cherry, liked coconut, and liked both flavors. what's the probability that a randomly selected student...
The probability that a randomly selected student likes coconut is 0.6.
Step-by-step explanation:
Given that,
Now we have to find the probability that a randomly selected student likes coconut.
P (student likes coconut) = the number of students who liked coconut / total number of students
= 60/100
= 0.6
Therefore, the probability that a randomly selected student likes coconut is 0.6.
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Amy, Beth, and Cassandra were carpeting 4 identically sized rooms. It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room. Together, how long would it take them to carpet the 4 rooms (round to the nearest thousandth of an hour;
It would take the three of them about 6 hours to paint the four rooms.
How to solve an equation?Let t represent the time that it would take all three of them to paint one room.
It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.
Therefore:
(1/6 + 1/4 + 1/8)t = 1
(2/3)t = 1
t = 1.5 hours
It would take all of them 1.5 hours each to paint one room.
For 4 rooms:
Total time = 1.5 hours * 4 = 6 hours
It would take the three of them about 6 hours to paint the four rooms.
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Evaluate
(
3
7
)
−
2
Give your answer as an improper fraction in its simplest form
The value of (37)-2 is 1/1369, in its simplest form as an improper fraction.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that is larger than a whole number.
When an expression is written in the form of [tex]x^{(-n)[/tex], it means the reciprocal of [tex]x^n.[/tex] In this case, we have the expression[tex](37)^{(-2)[/tex] which means the reciprocal of 37².
The expression (37)-2 means 37 raised to the power of -2, or 1/(37²). To simplify this fraction, we can multiply the numerator and denominator by 1,296 (37²):
1/(37²) = 1 * 1 / (37 * 37)
= 1/1369
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