Answer:
Additive law, also known as the law of addition, is a principle in probability theory that states that the probability of the occurrence of two or more mutually exclusive events is the sum of their individual probabilities. In other words, if events A and B are mutually exclusive (meaning that they cannot occur simultaneously), the probability of either event A or event B occurring is equal to the sum of their individual probabilities: P(A or B) = P(A) + P(B).
Step-by-step explanation:
Answer:
The Additive Law states that when two vectors have the same direction but different magnitudes, then the sum of their magnitudes will be equal to the magnitude of the resultant vector. In other words, if two vectors have the same direction, then adding them together will give you the magnitude of the resultant vector in the same direction as the original two vectors. This can also be expressed mathematically by saying that r = |a| + |b| where r is the resultant vector and a and b are the two given vectors.
Brainliest?
Help pls will give brainlyiest
Note that the tangents of the acute angles in the right triangle are:
tan(θ) = 35/12tan(α) = 12/35.What is the explanation for the above response?In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
Let's label the acute angles in the triangle as follows:
Angle NMP: θ
Angle NPM: α
Then we can use the given side lengths to find the tangents of these angles:
Tangent of angle θ: tan(θ) = opposite/adjacent = MN/MP = 35/12
Tangent of angle α: tan(α) = opposite/adjacent = MP/MN = 12/35
Therefore, the tangents of the acute angles in the right triangle are:
tan(θ) = 35/12
tan(α) = 12/35
Both of these answers are fractions, as requested.
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a qualitative researcher might pose which question relating to sampling? to which group will i be able to generalize my findings? will my sample be representative of the target population? who would be a rich information source for my study? how many people do i need to achieve adequate power?
A researcher will pose all of these related to sampling. So, the correct answer is all of the questions
The first question is related to the applicability of the findings of study which are typically beyond the data sources that are selected for study
The second question is related to the fact that sample of participants selected for the study reflects the diversity of the actual population to which extent
The third question relates to identifying the individuals which will be available for the study and it will consider different factors such as their experiences
The fourth question is not that much relevant as it as related with depth and the precision of the findings of the study
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Let f and g be functions from the positive integers to the positive integers defined by the equations f(n) = 2n + 1, g(n) = 3n - 1. Find the compositions f of, g 0 g,f 0 g,and g o f
We can find the compositions f o g, g o g, and f o g by plugging the function expressions into each other and simplifying.
f o g(n) = f(g(n)) = f(3n - 1) = 2(3n - 1) + 1 = 6n - 1
g o g(n) = g(g(n)) = g(3n - 1) = 3(3n - 1) - 1 = 8n - 4
f o g(n) = f(g(n)) = f(3n - 1) = 2(3n - 1) + 1 = 6n - 1
g o f(n) = g(f(n)) = g(2n + 1) = 3(2n + 1) - 1 = 6n + 2
Therefore, the compositions are:
f o g(n) = 6n - 1
g o g(n) = 8n - 4
f o g(n) = 6n - 1
g o f(n) = 6n + 2
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. Identify the corresponding frequency table with intervals of 5. 3, 18, 6, 14, 8, 10, 1, 10, 4, 17, 8, 11, 17, 4, 8, 14, 14, 10
The library had 200 visitors over the weekend, 150 of whom were female.The library expects to have 500 visitors this week. Using the information given, how many of visitors are expected to be female? Enter your answer in the box.
Answer:
375 females
Step-by-step explanation:
150/200 = 75%
375/500 = 75%
16. Which equation represents a linear function of x?
A. y = x²/3 B. y = -3/x² C. y = x/3 -2 D. y = 3/x+2
Answer:
C. y = x/3 -2
Step-by-step explanation:
A linear function is a function of x.
A. is a function of x^2
B. is a function of 1/ x^2
C. is a function of x
D is a function of 1/x
The only linear function is C.
Please help now ASAPppp please we
find an equation of the curve whose tangent line has a slope of f'(x)=2x^-8/9 given that the poing (-1,-6) is on the curve
To find the equation of the curve whose tangent line has a slope of f'(x) = 2x^(-8/9) and given that the point (-1, -6) is on the curve, follow these steps: Integrate the derivative to find the original function: f(x) = ∫(2x^(-8/9))dx.Apply the power rule for integration: f(x) = (2/(1 - (-8/9)))x^(1 - (-8/9)) + C = (2/(17/9))x^(17/9) + C = (18/17)x^(17/9) + C.
Use the given point (-1, -6) to find the value of C: -6 = (18/17)(-1)^(17/9) + C. Solve for C: C = -6 - (18/17)(-1) = -6 + (18/17) = (-104 + 18)/17 = -86/17.Write the equation of the curve with the value of C: f(x) = (18/17)x^(17/9) - 86/17. We know that the slope of the tangent line at any point on the curve is equal to the value of the derivative of the curve at that point. So, we can use the given derivative to find the equation of the curve.f'(x) = 2x^(-8/9).Integrating both sides with respect to x, we get:f(x) = ∫2x^(-8/9) dxf(x) = -9x^(1/9) + C (where C is the constant of integration)Now, we can use the given point (-1,-6) to find the value of C:f(-1) = -9(-1)^(1/9) + C = -6C = -6 + 9(1)^(1/9) = -6 + 9 = 3Therefore, the equation of the curve is:f(x) = -9x^(1/9) + 3.
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A glider soars upward along the helix r(t) = costi+sintj+tk. How far does the glider travel from t 8-0.6-0-4-0.20.0 0.20.4 0.6 0.8 1 o -0.r0.0.40.20.00.2 0.40.6 Select one: a. 2T b. O c. 27r/2 O d. T2 e. 47 t2 4 7 (6,19)
The glider travels along the helix r(t) = costi + sintj + tk. We want to find the distance traveled by the glider from t = 0 to t = 8. We can use the arc length formula to find this distance: s = ∫√[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt.
We have r(t) = costi + sintj + tk, so, dx/dt = -sint, dy/dt = cost, dz/dt = 1, Substituting into the arc length formula, we get: s = ∫√[(-sint)^2 + (cost)^2 + 1^2] dt, s = ∫√(2) dt, s = √(2)t + C. Evaluating s at t = 8 and s = 0, we get: s = √(2)8 + C
s = √(2)0 + C, C = 0, Therefore, the distance traveled by the glider from t = 0 to t = 8 is: s = √(2)8 = 4√(2), So the answer is (e) 47t^2.
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to find demand, we use the condition that the mrs will be equal to the price ratio at an interior optimal bundle. set the mrs from part 1 equal to −pxpy and then solve the resulting equation for y.
The demand function for good y is y* = -(p2/p1) * (x*/2)
How to find the demand for good y?To find the demand for good y, we can set the MRS (marginal rate of substitution) from part 1 equal to the price ratio at an interior optimal bundle.
Let's call the optimal bundle (x*, y*) and the prices of goods x and y as px and py, respectively. Then the condition for optimal consumption is given by:
MRS = -px / py = p1 / p2 (assuming a two-good model)
where p1 and p2 are the prices of goods x and y, respectively, and px/py is the price ratio.
Solving this equation for y, we get:
y* = -(p2/p1) * (x*/2)
This gives us the demand function for good y in terms of its price (p2) and the price of good x (p1) and the optimal quantity of good x (x*).
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Find the volume of a cone with a base diameter of 9 yo and a height of 7yd. Write the exact volume in terms of pi
since it has a diameter of 9, that means its radius is half that, or 4.5.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4.5\\ h=7 \end{cases}\implies V=\cfrac{\pi (4.5)^2(7)}{3}\implies V=47.25\pi[/tex]
Answer:
Step-by-step explanation:
r= the radius of base
h=height
volume of cone=1/3*r^2*pi*h
1/3*(4.5)^2*pi*7
=1/3*81/4*7*pi
=567/12 pi
Let C be the circle relation defined on the set of real numbers. For every x, y ϵ R, x Cy <=> x^2 + y^2 = 1. (a) Is C reflexive justify your answer. C is reflexive for a very real number x, x C x. By definition of C this means that for every real number x, ____ -1. This is ____.
Find an example x and x^2 + x^2 that show this is the case. (x, x^2 + x^2) = ( ____ ) Since this ____ 1, C ____ reflexive
About the circle relation C on the set of real numbers:
To determine if circle (C) is reflexive, we need to examine if for every real number x, x C x holds true. By definition of C, this means that for every real number x, x^2 + x^2 = 1.
Now, let's simplify this equation: x^2 + x^2 = 2x^2, so we get 2x^2 = 1. To satisfy this equation, x^2 must equal 1/2. However, there is no real number x for which x^2 = 1/2.
As we cannot find an example of x such that (x, x^2 + x^2) = (x, 1), we conclude that since this does not equal 1, C is not reflexive.
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How do i solve this ?
Answer:
2) x=11
Step-by-step explanation:
1) u got the first one right x=90°
2)
2x-1+69=90
2x-1=21
2x=22
x=11
a poll is given, showing 70 re in favor of a new building project. if 10 people are chosen at random, what is the probability that exactly 2 of them favor the new building project?
The probability of 2 people out of 10 chosen at random favoring the new building project: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where n = 10, p = 0.7, and k = 2. The resulting probability is approximately 0.00005349 or 0.005%.
To solve this problem, we need to use the binomial distribution formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where P(X = k) is the probability of getting exactly k successes (people who favor the new building project),
n is the total number of trials (people chosen at random),
p is the probability of success in each trial (proportion of people in favor of the project), and
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.In this case, n = 10, p = 0.7 (since 70% of the polled people are in favor of the project), and k = 2 (we want to find the probability of exactly 2 people favoring the project).Using the formula, we get:Learn More About Probability: https://brainly.com/question/13604758
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Damian has a bag that contains pineapple chews, lemon chews, and watermelon chews. He performs an experiment. Damian randomly removes a chew from the bag, records the result, and returns the chew to the bag. Damian performs the experiment 68 times. The results are shown below:
A pineapple chew was selected 39 times.
A lemon chew was selected 24 times.
A watermelon chew was selected 5 times.
Based on these results, express the probability that the next chew Damian removes from the bag will be lemon chew as a decimal to the nearest hundredth.
There is a 0.35 percent chance that the next chew Damian takes out of the bag will be a lemon chew.
Define ProbabilityThe possibility or chance of an event occurring is quantified by probability. A number between 0 and 1, with 0 signifying impossibility and 1 signifying certainty, is used to symbolize it.
probability of selecting a lemon chew = number of times a lemon chew was selected / total number of experiments
In this case, the number of times a lemon chew was selected is 24, and the total number of experiments is 68:
probability of selecting a lemon chew = 24 / 68
To express this probability as a decimal to the nearest hundredth, we can divide 24 by 68 using a calculator or by long division:
24 ÷ 68 = 0.35294117647...
Rounding this decimal to the nearest hundredth gives:
0.35
Therefore, the probability that the next chew Damian removes from the bag will be a lemon chew is approximately 0.35 or 35% to the nearest hundredth.
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Find the acceleration for the piecewise defined velocity function v(t) = { mt) _ St2 – 4,0 st<2 14 ln(t – 1),t > 2 when the velocity equals zero.
To find the acceleration when the velocity equals zero, we need to differentiate the velocity function with respect to time, t.
For the first piece of the velocity function where st<2, the derivative of mt is simply m since t is not a variable in this expression. For the second piece of the velocity function where t>2, we need to use the chain rule to differentiate the natural logarithmic function. The derivative of ln(t-1) with respect to t is 1/(t-1).
Therefore, the derivative of v(t) with respect to t is:
a(t) = m - 2St for st<2
a(t) = 1/(t-1) for t>2
To find the acceleration when the velocity equals zero, we need to set v(t) equal to zero and solve for t.
For the first piece of the velocity function where st<2, we have:
0 = mt - St2 - 4
St2 = mt - 4
t = sqrt((m-4)/S)
For the second piece of the velocity function where t>2, we have:
0 = 14 ln(t-1)
t = e+ 1
Now, we can substitute these values of t into the acceleration function to find the acceleration when the velocity equals zero:
For the first piece of the velocity function where st<2, we have:
a(sqrt((m-4)/S)) = m - 2S(sqrt((m-4)/S))
For the second piece of the velocity function where t>2, we have:
a(e+1) = 1/(e-1)
Therefore, the acceleration when the velocity equals zero depends on the values of m, S, and e.
To find the acceleration for the piecewise defined velocity function when the velocity equals zero, we first need to identify when v(t) = 0 within the given function. The function is defined as follows:
v(t) = { mt - St^2 - 4, for 0 ≤ t < 2
14 ln(t - 1), for t > 2
1. For the first part of the function (0 ≤ t < 2), set v(t) = 0 and solve for t:
mt - St^2 - 4 = 0
2. For the second par of the function (t > 2), set v(t) = 0 and solve for t:
14 ln(t - 1) = 0
After finding the values of t when the velocity is zero, you can then calculate the acceleration for each case. Acceleration is the derivative of the velocity function with respect to time (a(t) = dv(t)/dt). Compute the derivatives for both parts of the piecewise function and evaluate them at the values of t where the velocity is zero.
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:
[tex]\large\boxed{\textsf{See Below.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for the values of x, given values to select from.}[/tex]
[tex]\textsf{Instead of using the FOIL Method, we can simply substitute in the given options}[/tex]
[tex]\textsf{then identify if the two expressions are actually equal to each other. This is}[/tex]
[tex]\textsf{the \underline{Substitution Property of Equality}.}[/tex]
[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]
[tex]\textsf{The Substitution Property of Equality is a property that allows us to substitute in}[/tex]
[tex]\textsf{a known value for a placeholder, or an unknown variables and the equation will}[/tex]
[tex]\textsf{still remain equal. However for our problem we are given the value of x, but we're}[/tex]
[tex]\textsf{not certain that the value will make the equation true. That's why we should}[/tex]
[tex]\textsf{check every option provided.}[/tex]
[tex]\large\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]
[tex]\textsf{Our first option given is -46. Substitute that value in for x.}[/tex]
[tex]\tt (-46 - 3)^{2} = 49[/tex]
[tex]\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}[/tex]
[tex]\tt (-46 -3)^{2}=(-49)^{2}=(-49 \times -49)=2401.[/tex]
[tex]\tt 2401 \neq 49.[/tex]
[tex]\textsf{-46 is not a value of x.}[/tex]
---------------------------------------------------
[tex]\textsf{Our second option given is -4. Substitute that value in for x.}[/tex]
[tex]\tt (-4 - 3)^{2} = 49[/tex]
[tex]\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}[/tex]
[tex]\tt (-4 -3)^{2}=(-7)^{2}=(-7 \times -7)=49.[/tex]
[tex]\tt 49 = 49. \large\checkmark[/tex]
[tex]\large\boxed{\textsf{-46 is a value of x.}}[/tex]
---------------------------------------------------
[tex]\textsf{Our third option given is 10. Substitute that value in for x.}[/tex]
[tex]\tt (10 - 3)^{2} = 49[/tex]
[tex]\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}[/tex]
[tex]\tt (10 -3)^{2}=(7)^{2}=(7 \times 7)=49.[/tex]
[tex]\tt 49 = 49. \large\checkmark[/tex]
[tex]\large\boxed{\textsf{10 is a value of x.}}[/tex]
---------------------------------------------------
[tex]\textsf{Our last option given is 52. Substitute that value in for x.}[/tex]
[tex]\tt (52 - 3)^{2} = 49[/tex]
[tex]\textsf{Follow Order of Operations (PEMDAS), and simplify inside the parentheses first.}[/tex]
[tex]\tt (52 -3)^{2}=(49)^{2}=(49 \times 49)=2401.[/tex]
[tex]\tt 2401 \neq 49.[/tex]
[tex]\textsf{52 is not a value of x.}[/tex]
Which equation represents a line that has a slope of 3/4 and passes through the point ( 2, 1)
The equation of the line with a slope of 3/4 passing through the point (2,1) is y = (3/4)x - 1/2.
Define slopeIn mathematics, slope refers to the measure of steepness or incline of a line, usually denoted by the letter m.It is the ratio of the vertical change in position of two points on a line to their horizontal change.
The equation of a line with a slope of 3/4 passing through the point (2,1) can be found using the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁,y₁) are the coordinates of the given point on the line.
Substituting the given values, we get:
y - 1 = (3/4)(x - 2)
Multiplying both sides by 4 to eliminate the fraction, we get:
4y - 4 = 3(x - 2)
Expanding the right-hand side, we get:
4y - 4 = 3x - 6
Adding 4 to both sides, we get:
4y = 3x - 2
Dividing both sides by 4, we get the final equation in slope-intercept form:
y = (3/4)x - 1/2
Therefore, the equation of the line with a slope of 3/4 passing through the point (2,1) is y = (3/4)x - 1/2.
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construct a grammar over [a, b, c}whose language is [anb2ncm \n, m >0).
S is the start symbol, and A, B, and C are non-terminal symbols. These rules generate the desired language by allowing you to create strings with n a's, 2n b's, and m c's.
To construct a grammar for the language [anb2ncm \n, m >0] over the set {a, b, c}, we can follow these steps:
1. Start with the start symbol S.
2. For every a in the language, add an A to the grammar.
3. For every b in the language, add two Bs to the grammar.
4. For every c in the language, add a C to the grammar.
5. Add a production rule for S that generates an A and a B pair, followed by a C. This ensures that the language has at least one a, two b's, and one c.
6. Add a production rule for A that generates another A, followed by an a. This allows for the generation of any number of a's in the language.
7. Add a production rule for B that generates two more B's, followed by a b. This allows for the generation of any even number of b's in the language.
8. Add a production rule for C that generates another C, followed by a c. This allows for the generation of any number of c's in the language.
The resulting grammar would be:
S -> ABBC
A -> aA | a
B -> BBb | bb
C -> cC | c
This grammar generates strings such as "abbc", "aabbcc", "aaaabbbbbbcccccc", and so on, which are all in the language [anb2ncm \n, m >0].
To construct a grammar for the language L = {anb2ncm | n, m > 0} over the alphabet {a, b, c}, you can use a context-free grammar with the following production rules:
1. S → ABC
2. A → aA | a
3. B → bbBc | bbc
4. C → cC | c
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Determine which sets in Exercises 1-8 are bases for R3. Of the sets that are not bases, determine which ones are linearly independent and which ones span R'. Justify your answers. 1. 0 . 2 038 0 0 L TI |-77 5 O | 17 | 37 -37 27 [ 17 3. | 0.1 2 . 5 (4.) 1-2 , -3 [-2] L-4] L 1] L1 L2 I 2 4 17 T-27 ToT07 T 17 I-4 9 . O . -3 6. I 2 1 -5 LOJ LOJ[5] L-3] L 6] T 17 07 | 37 | 07 3. -4 . 3 . -5 . 2 13 L-1] [ 4 ] [-2] - 67
To determine which sets are bases for R3, we need to check if they are linearly independent and if they span R3. The set {0, 2 038 0; 0, 0, 5; -77, 17, 37; -37, 27, 17} is a basis for R3.
This can be seen by putting the set in row echelon form and observing that all columns have pivots, which means they are linearly independent. Furthermore, every vector in R3 can be expressed as a linear combination of the vectors in this set, which means they span R3.Learn More About Sets: https://brainly.com/question/13458417
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Suppose you are offered a job with a relatively low starting salary but with a $4000 raise for each of the next 6 years. How much more than your starting salary would you be making in the 7th year?
In the 7th year, you would be making $24,000 more than your starting salary from the job offer.
To calculate how much more than your starting salary you would be making in the 7th year after receiving a $4,000 raise for each of the next 6 years, follow these steps:
1. Determine the total raises you will receive in 6 years: $4,000 raise per year * 6 years = $24,000 total raise.
2. Subtract your starting salary from your 7th-year salary to get the difference: (starting salary + $24,000) - starting salary = $24,000.
In the 7th year, you would be making $24,000 more than your starting salary from the job offer.
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If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
According to given information, the value of cos θ is (3sqrt(5))/7.
What is cos?
In trigonometry, cos (short for cosine) is a mathematical function that relates the angle of a right triangle to the ratio of the length of its adjacent side to its hypotenuse.
We can start by using the Pythagorean identity:
[tex]sin^2[/tex] θ + [tex]cos^2[/tex] θ = 1
Since we know sin θ, we can solve for cos θ:
[tex]cos^2[/tex] θ = 1 - [tex]sin^2[/tex] θ
[tex]cos^2[/tex] θ = 1 - [tex](2/7)^2[/tex]
[tex]cos^2[/tex] θ = 1 - 4/49
[tex]cos^2[/tex] θ = 45/49
Taking the square root of both sides, we get:
cos θ = ±[tex]\sqrt{(45/49)[/tex]
Since we know that tan θ is positive, we can deduce that cos θ must be positive as well. Therefore:
cos θ = [tex]\sqrt{(45/49)[/tex] = [tex](3\sqrt{(5)})/7[/tex]
So the value of cos θ is (3sqrt(5))/7.
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justify the following equality: dim row a nullity at = m, the number of rows of a
The justification for the equality "dim row a nullity at = m" lies in the fact that the row space and null space of a matrix A have dimensions that add up to the number of columns in A, i.e., dim row A + dim nullity A = n, where n is the number of columns of A.
Now, considering the transpose of A, denoted as A^T, we know that the row space of A is the same as the column space of A^T, and the null space of A is the same as the left null space of A^T.
Therefore, we have dim row A = dim col A^T and dim nullity A = dim nullity (A^T)^L, where (A^T)^L denotes the left null space of A^T.
Since A has m rows, A^T has m columns. Hence, by the above equation, we have dim row A^T + dim nullity (A^T)^L = m.
Substituting dim row A^T = dim row A = dim row a and dim nullity (A^T)^L = dim nullity at, we get dim row a + dim nullity at = m, which is the desired equality.
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Solve the given differential equation. (6x+1) y^2 dy/dx + 4x^2 + 2y^3 = 0.
To solve the given differential equation (6x+1)y^2 dy/dx + 4x^2 + 2y^3 = 0, we can rearrange the terms to make it an explicit equation for dy/dx: dy/dx = -(4x^2 + 2y^3) / ((6x+1)y^2)
Now, separate the variables by moving all the x terms to one side and y terms to the other side: (dy / (y^2 - 2y^3)) = - (4x dx / (6x + 1))
Next, integrate both sides of the equation: (dy / (y^2 - 2y^3)) = -∫(4x dx / (6x + 1))
To solve the given differential equation (6x+1) y^2 dy/dx + 4x^2 + 2y^3 = 0, we can rearrange the terms to get:
(6x+1) y^2 dy = - (4x^2 + 2y^3) dx
Now, we can integrate both sides:
∫ (6x+1) y^2 dy = - ∫ (4x^2 + 2y^3) dx
Integrating the left-hand side with respect to y and the right-hand side with respect to x, we get:
2y^3 (3x + 1) = - (4/3)x^3 - y^4 + C
where C is the constant of integration.
To solve for y, we can isolate y^4 on one side of the equation and take the fourth root:
y^4 = (4/3)x^3 - 2y^3 (3x + 1) + C
y^4 + 6y^3 x + (4/3)x^3 - C = 0
This is a quartic equation in y^4, which can be difficult to solve. However, if we substitute z = y^3, we can rewrite the equation as:
z^2 + 6xz + (4/3)x^3 - C = 0
This is a quadratic equation in z, which can be solved using the quadratic formula:
z = (-6x ± sqrt(36x^2 - 4(4/3)x^3 + 4C)) / 2
Simplifying and substituting back for y, we get:
y = (z)^(1/3)
y = [(-6x ± sqrt(36x^2 - 4(4/3)x^3 + 4C)) / 2]^(1/3)
This is the general solution to the given differential equation. To find a particular solution, we need to know the initial condition, such as y(0) = 1.
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At batting practice Alexis hit 8 balls out of 15 into the outfield. Which equation below can be
used to determine the percentage of balls hit into the outfield?
The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.
How to calculate the percentage of balls the hit the outfield?The total number of balls that that where present at the battling practice by Alexis = 15.
The number of balls that hit into the outfield = 8
The number of balls that hit outside the outfield = 15-8= 7
The percentage (x) of the balls that are outside the outfield;
X = 8/15 × 100/1
x ×15 = 8 × 100
15/8 = X/100.
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PLEASE HELP need great assistance. The problem is in the picture below.
The correct option is:
She cannot reject the null hypothesis at α = 0.05 because 7.5 is not contained in the 95% confidence interval.
Option B is correct
What is a confidence interval ?
A confidence interval is described as a range of estimates for an unknown parameter. A confidence interval is also computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
For the true population mean, a confidence interval provides a range of likely values, and in this instance, the 95% confidence interval is (5.8, 6.4).
Thus, if we were to conduct this study repeatedly, we could anticipate that the genuine population mean would, 95% of the time, fall between 5.8 and 6.4.
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given a box of 12 identical looking chocolates, six with nuts and six with strawberries, what is the probability of picking and eating three chocolates in this order: nut, nut, strawberry?
The probability of picking strawberry chocolate as the third chocolate is 6/10 or 3/5. So the overall probability of picking and eating three chocolates in the order nut, nut, strawberry is (1/2) x (5/11) x (3/5) which equals 15/110 or approximately 0.136 or 13.6%.
To find the probability of picking and eating three chocolates in the order of nut, nut, and strawberry, we'll use the concept of probability.
The probability of picking nut chocolate from the box is 6/12 or 1/2. Once a nut chocolate has been chosen and eaten, there are now 5 left in the box out of which 5/11 or approximately 0.45 are nut chocolates. So the probability of picking another nut chocolate is 5/11. Finally, once the second nut chocolate has been eaten, there are 4 left in the box out of which 6/10 or 0.6 are strawberry chocolates.
There are 12 chocolates in total: 6 with nuts and 6 with strawberries.
1. Probability of picking a nut on the first attempt: 6/12 (6 nuts out of 12 chocolates)
2. Probability of picking a nut in the second attempt: 5/11 (5 nuts out of 11 remaining chocolates)
3. Probability of picking a strawberry on the third attempt: 6/10 (6 strawberries out of 10 remaining chocolates)
To find the overall probability, multiply the individual probabilities:
Probability = (6/12) * (5/11) * (6/10) = 1/2 * 5/11 * 3/5 = 3/22
So, the probability of picking and eating three chocolates in the order of nut, nut, and strawberry is 3/22.
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if 3n + 2 is an odd integer, then n is odd. • Proof : Assume that n is even. This implies that n = 2k for some integer k.
If 3n + 2 is an odd integer, then n must be odd.
The proof starts by assuming that n is even, which means it can be expressed as 2k for some integer k.
Substituting this value in the expression 3n + 2, we get:
3n + 2 = 3(2k) + 2 = 6k + 2
Simplifying further, we can factor out 2 from the expression:
3n + 2 = 2(3k + 1)
Since 3k + 1 is an integer, we can see that 3n + 2 is even, which contradicts our original assumption that it is odd. Therefore, our initial assumption that n is even is false, and we conclude that n must be odd.
This proof follows the method of proof by contradiction, where we assume the opposite of what we want to prove and show that it leads to a contradiction, hence proving the original statement.
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3,495 rounded to the nearest hundred
Answer:
3500
Step-by-step explanation:
9 rounds up the number 4 to 5
3500
Answer:
3,500
Step-by-step explanation:
because 9 is greater than 5 so u would round upward and that 495 would become a 500 but theres also the 3,000 so add the two together and you would get 3,500
consider the following. f(x) = { −4 −x if x ≤ 4 x^2 -8x + 8 if x > 4
is f differentiable at 4?
a. yes
b. no
b.) No, f is not differentiable at x=4. This is because the left and right limits of the function at x = 4 are not equal, and hence the function has a sharp corner or cusp at that point.
To demonstrate this, determine the left and right derivatives of f(x) at x = 4. The limit of (f(4 - h) - f(4)) / h as h approaches 0 from the left can be used to calculate the left derivative. We receive the following results after plugging in the values from the first portion of the function:
lim h→0- [(-4 - (4 - h)) - (-4)] / h
= lim h→0- [-h / h]
= -1
Similarly, finding the right derivative is as simple as taking the limit of (f(4 + h) - f(4)) / h as h approaches 0 from the right. We receive the following results after plugging in the values from the second portion of the function:
lim h→0+ [(4 + h)^2 - 8(4 + h) + 8 - (4^2 - 8(4) + 8)] / h
= lim h→0+ [(h^2 + 16h) / h]
= 16
Since the left and right derivatives are not equal (i.e., -1 ≠ 16), the function is not differentiable at x = 4.
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