[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 113\left(1+\frac{0.06}{52}\right)^{52\cdot 4} \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}[/tex]
Given x1 = x2 – x1(x1^2 + x2^2 -1) and x2 = -x1 - x2(x1^2 + x2^2 -1) as state dr do equations. Polar coordinates are r and tetha. Please prove that dr/dt = -r(r^2 -1) and dtetha/dt= -1. Then explain why r=1 is a stable limit cycle.
To solve this problem, we'll start by finding the polar coordinates r and θ in terms of x1 and x2. We have r^2 = x1^2 + x2^2, tan(θ) = x2/x1.
Taking the derivative of x1 with respect to time t, we have: dx1/dt = dx2/dt - 2x1(dx1^2 + x2^2 - 1) - x1^2(2x1dx1 + 2x2dx2)
Similarly, the derivative of x2 with respect to t is: dx2/dt = -dx1/dt -2x2(dx1^2 +x2^2 -1) - x2^2(2x1dx1 + 2x2dx2) Using the chain rule, we can write: dr/dt = (x1dx1 + x2dx2)/r dθ/dt = (1/r^2)(x2dx1 - x1dx2)
Substituting dx1/dt and dx2/dt in these equations and simplifying, we get: dr/dt = -r(r^2 -1) dθ/dt = -1 Now, to prove that r=1 is a stable limit cycle, we can use the method of linearization.
This involves finding the Jacobian matrix at the equilibrium point r=1, θ=0: Jacobian = [[-3 -1], [-1 -3]] Taking the eigenvalues of this matrix, we get -4 and -2.
Since both eigenvalues are negative, we conclude that the equilibrium point corresponds to a stable limit cycle at r=1, θ=0. In summary, we have shown that the differential equations for dr/dt and dθ/dt are -r(r^2 -1) and -1, respectively. We have also demonstrated that r=1 is a stable limit cycle.
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HELP ME IM GIVING 16 BRAINLIEST IF HELP
Answer:
277 milliliters
Step-by-step explanation:
945-668= 277
A small kiddie pool starts with 110 gallons of water. The pool is being drained at a constant rate of 4 gallons per minute. How many minutes could have passed if the pool now has less than 74 gallons of water left? Write an inequality to represent the situation. Use x to represent the number of minutes.
Thank you sooo much if you answer this I have like five missing assignments and grades are due in two days and it takes that long for my teacher to grade it. She slow.
The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The amount of water remaining in the pool after x minutes is given by:
110 - 4x
We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.
110 - 4x < 74
To solve for x, we can first subtract 110 from both sides of the inequality:
-4x < 74 - 110
Simplifying, we get:
-4x < -36
Divide both sides of the inequality by -4,
x > 9
Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.
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A 30% increase followed by a 15% decrease, is it greater than original, smaller or same as
Answer:
1.3 × .85 = 1.105
10.5% greater than original
The sum of two numbers is 72. The difference of the two numbers is 50. Let x be the larger number and ybe the smaller number. Set up and evaluate a system of equations to determine the values of x and y.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
First equation:
Write an equation that expresses the information in the sentence "The difference of the two numbers is 50."
Second equation:
Solve the system you have written above to find x and y.
x= . y= .
the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50
The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:
First equation: x + y = 72
Second equation: x - y = 50
To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:
x + y = 72
x - y = 50
--------------
2x = 122
Next, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 122/2
x = 61
Now that we know the value of x, we can plug it back into one of the equations to find the value of y:
61 + y = 72
y = 72 - 61
y = 11
So the solution to the system of equations is x = 61 and y = 11.
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Just need answers thanks alot !! Problems in picture
The quadratic equation f(x) = 3 · x² + 36 · x + 33 shows the quickest choice to determine the y-intercept. The y-intercept is equal to (0, 33).
How to find the y-intercept of a quadratic equation
In this problem we must look up for the quickest way to determine the y-intercept of a quadratic equation, this can be done by evaluating at x = 0 when the expression is of the form, that is, standard form:
f(x) = a · x² + b · x + c
Where a, b, c are real coefficients.
The standard form f(x) = 3 · x² + 36 · x + 33 may help us to determine the y-intercept quickly. The y-intercept is equal to (0, 33).
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PLEASE HURRY ITS DUE IN 24 MINUTES
A chicken breeder has chickens that are white, black or speckled. Speckled chickens have both black and white feathers. This is a co-dominant trait. The allele for white feathers is A and the allele FB for black feathers is F Determine the genotypes for the rooster and hen that the breeder should cross to produce the greatest percentage of speckled chickens. A. Place the alleles for the rooster and the hen that the breeder should cross in the blank boxes outside the Punnett square. B. Place the number that shows the percentage of speckled offspring that will result from this cross in the blank box. . You may use the allele labels more than once. • There may be more than one correct answer. • Place only one label in each blank box F F 25 50 75 100 2/5- Hen Rooster =% speckled
Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.
The Punnett square for this cross would be:
| F F
A | A F A F
A | A F A F
This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.
Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:
| F F
A | A F A F
A | A F A F
Hen Rooster
What are three equivalent ratios for 15/35
1) 3/7
2) 9/21
3) 150/350
Help, tried so many times.
Answer:
Rectangle, yes yes or no rectangle
Step-by-step explanation:
Find the domain and range for the following functions:
(3 Marks)
a) y=1/√ x2-4
y=(2x^2)-2x+5
y=
1/(1-1/(x-1))
The domain and range for the given functions are: a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞) b) Domain: (-∞, ∞), Range: [9/2, ∞) c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
The domain of a function is the set of all possible values of x that can be input into the function. The range of a function is the set of all possible values of y that can be output from the function.
a) y = 1/√(x^2 - 4)
The domain of this function is all values of x that make the denominator nonzero and the square root positive. Therefore, x^2 - 4 > 0, which means (x - 2)(x + 2) > 0. The solution to this inequality is x < -2 or x > 2. So the domain is (-∞, -2) ∪ (2, ∞).
The range of this function is all positive values of y, since the square root in the denominator is always positive. So the range is (0, ∞).
b) y = (2x^2) - 2x + 5
The domain of this function is all real numbers, since there are no restrictions on the values of x. So the domain is (-∞, ∞).
The range of this function is all values of y greater than or equal to the vertex of the parabola. The vertex of this parabola is (-b/2a, f(-b/2a)), which is (1/2, 9/2). So the range is [9/2, ∞).
c) y = 1/(1 - 1/(x - 1))
The domain of this function is all values of x that make the denominator nonzero. Therefore, 1 - 1/(x - 1) ≠ 0, which means x ≠ 2. So the domain is (-∞, 2) ∪ (2, ∞).
The range of this function is all values of y except 0, since the denominator can never be zero. So the range is (-∞, 0) ∪ (0, ∞).
In conclusion, the domain and range for the given functions are:
a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞)
b) Domain: (-∞, ∞), Range: [9/2, ∞)
c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
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A) if taxi fare (y) is 50 cents plus 20 cents per quarter mile, write the equation relating fare to number of miles traveled, m.
B) The weekly earning of a salesman are $50 plus 10 percent of the retail value of the goods he sells. Write the equation for earnings, E, in terms of sales volume, V. What is the slope of this line called?
(A) The equation relating fare to number of miles traveled, m, is y = 0.50 + 0.80m
(B) The equation for earnings, E, in terms of sales volume, V, is E = 50 + 0.10V. The slope of this line is called marginal revenue.
A) The taxi fare starts at 50 cents and increases by 20 cents for every quarter mile traveled. This means that for every mile traveled (4 quarters), the additional cost will be 80 cents per mile traveled. The equation that will relate the fare, y, to the number of miles traveled, m, is y = 0.50 + 0.80m.
B) The equation E = 50 + 0.10V shows that the weekly earning of a salesman starts at $50 and increases by 10 percent of the retail value of the goods he sells. The slope of this line is 0.10, which represents the rate of change in earnings with respect to sales volume. This slope is called the marginal revenue, as it represents the additional revenue earned for each additional unit of sales volume.
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NEED HELP DUE TODAY!!!!!!!
Express each radian measurement in degrees.
• π/3 radians
• 5π/4 radians
4. Express each degree measurement in radians.
• 30°
• 120°
5. For each pair of angle measurements, circle the one which is larger.
• π radians or 200 degrees
• 3π/2 radians or 200 degrees
• 1 radian or 90 degrees
• π/3 radians or 45 degrees
Three radians, or 45 degrees, are the greater angle between each pair of measurements.
what is angle ?An angle is a figure created in geometry by two rays or line segments that meet at the vertex of the angle. The edges of the angle are the rays or line segments. Angles are used to describe the amount of rotation or turn between two lines or objects. For instance, a 90-degree angle is equivalent to a quarter turn, while a 180-degree angle is equivalent to a half turn or a straight line. A full turn plus a smaller angle is equivalent to an angle that is larger than 180 degrees but less than 360 degrees.
given
In degrees, express each radian number.
• 3 radians equals 60 degrees (multiply the radian measurement by 180/ to transform radians to degrees).
• 225 degrees = 5/4 radians
Use radians to determine each degree.
• 30° Equals /6 radians (multiply the degree measurement by /180 to convert degrees to radians)
• 120° equals 2.3 radians
Circle the larger angle between each set of measurements.
• Radians or degrees: 200 degrees (to measure, 180 degrees are equal to one radian).
• 200 degrees or 32 radians: 200 degrees
• One radian is equal to 90 degrees.
Three radians, or 45 degrees, are the greater angle between each pair of measurements.
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a library has fiction and nonfiction books. The ration of the number of fiction books to the total number of books is 5:8. What is the ratio of the fiction to the nonfiction books in the library?
The ratio of fiction books to nonfiction books in the library is 5:3.
What are Ratios?
A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.
Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).
Then, the number of nonfiction books in the library is 8x - 5x = 3x.
Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:
5x/3x = 5/3
So, the ratio of fiction books to nonfiction books in the library is 5:3.
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please helppp!!!!!!!
Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
What is the definition of the Right Angle postulate?
The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.
Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
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Answer:
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The question is in the screenshot:
We can deduce that 3pi/4<5pi/3<2pi
The angle is in the 4th quadrant. To find the angle you just do:
[tex]2\pi -\frac{5\pi }{3}=\frac{\pi }{3}[/tex]
The answer to your question is B. I hope that this is the answer that you were looking for and it has helped you.
Simplify x^7/x^3. I need help please help and / is a fraction
Simplifying x^7/x^3 we get x^4.
We have the numerator of the given fraction x^7/x^3 as x^7, that is x raised to the power 7. We can rewrite x^7 equals to (x^4)(x^3) , that is x raised to the power 4 multiplied by x raised to the power 3 (by exponential method).
Similary, the denominator of the given fraction x^7/x^3 is x^3, that is x raised to the power 3.
Rewritting the fraction x^7/x^3 as,
(x^4)(x^3) / x^3 { using division rule}
= x^4 (that is, x raised to the power 4)
Thus after simplifying x^7/x^3 (using division rule) we get x^4.
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Find the output,
�
bb, when the input,
�
aa, is
6
66. �
=
−
1
−
7
�
b=−1−7a
Step-by-step explanation:
uuoflfjtnhgdhdurjsjueiei3io ghy
RADICALS AND CUADRATIC Solving a quadratic eque Solve (u-3)^(2)-20=0, where Simplify your answer as much : If there is more than one soluti If there is no solution, click "No
The solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.
Determine the quadratic equationTo solve the quadratic equation (u-3)^(2)-20=0, we will use the following steps:
1. Add 20 to both sides of the equation to isolate the squared term: (u-3)^(2)=20
2. Take the square root of both sides of the equation: u-3=±√20
3. Simplify the radical on the right side of the equation: u-3=±2√5
4. Add 3 to both sides of the equation to isolate the variable: u=3±2√5
5. Write the two solutions separately: u=3+2√5 or u=3-2√5
Therefore, the solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.
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2. Determine whether the seriesn=1∑[infinity](−1)n−13n+4ln(5n+2)is absolutely convergent, conditionally convergent or divergent.
The series n=1∑[infinity](−1)n−13n+4ln(5n+2) is conditionally convergent.
To determine the convergence of a series, we can use the Alternating Series Test. This test states that if the absolute value of the terms in the series decrease to zero, then the series is convergent.
First, we need to find the absolute value of the terms in the series:
| (−1)n−13n+4ln(5n+2) | = | 3n+4ln(5n+2) |
Next, we need to determine if the absolute value of the terms decrease to zero. To do this, we can use the Limit Comparison Test. We will compare the series to the series 1/n:
lim n→∞ | 3n+4ln(5n+2) | / (1/n) = lim n→∞ | 3n^2+4nln(5n+2) |
Since the limit of the series is infinity, the series is divergent. However, since the series alternates between positive and negative terms, it is conditionally convergent.
Therefore, the series n=1∑[infinity](−1)n−13n+4ln(5n+2) is conditionally convergent.
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help................................................
Answer:
I think question #1 is C
Question #2 is C
and Question #3 is A
Regular hexagons have been used to tile floors. Can a floor be tiled using only regular pentagons? Why or why not?
Select the correct answer below.
A floor can or cannot be tiled using only regular pentagons. For a regular hexagon, the measure of each vertex angle is ___nothing°, which means that 2,3,4,5 or 6 regular hexagons fit to form ____°, and the plane can be filled. For a regular pentagon, the measure of each vertex angle is ____°, so regular pentagons can or cannot be placed together to fill the plane because the measure of the plane, nothing____°,is or is not divisible by the measure of each vertex angle.
(Type integers or decimals.)
A floor cannot be tiled using only regular pentagons.
A floor cannot be tiled using only regular pentagons. For a regular hexagon, the measure of each vertex angle is 120°, which means that 3 regular hexagons fit to form 360°, and the plane can be filled. However, for a regular pentagon, the measure of each vertex angle is 108°, so regular pentagons cannot be placed together to fill the plane because the measure of the plane, 360°, is not divisible by the measure of each vertex angle. Therefore, a floor cannot be tiled using only regular pentagons.
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What is the % of the votes did MRS Naido receive write the answers to theearst whole%
With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to Gopalkrishna Gandhi, the opposition candidate, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.
According to the given information, M Venkaiah Naidu received 516 votes out of the valid votes cast in the vice-presidential election. The total number of valid votes cast was not explicitly mentioned in the statement, but we can calculate it by adding up the votes received by the two candidates. M Venkaiah Naidu received 516 votes, while his opponent Gopalkrishna Gandhi received 244 votes. Therefore, the total number of valid votes cast was 760 (516 + 244).
To calculate the percentage of valid votes that M Venkaiah Naidu received, we need to divide his number of votes by the total number of valid votes cast and then multiply by 100. Therefore, M Venkaiah Naidu received approximately 68% of the valid votes (516/760 x 100).
It's important to note that this calculation only considers the valid votes cast and not any abstentions or spoiled ballots. Additionally, this percentage reflects the support received by M Venkaiah Naidu among the MPs who voted and does not necessarily reflect the opinions of the broader public or electorate.
Complete question:
According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.
With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.
What is the % of the votes did MRS Naido receive to write the answers to the east wholw%
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Area of rectangles. Please help!
Answer:
11.35
or 11 7/20
Step-by-step explanation:
find the measures of the numbered angles in rhombus ABCD
Answer:
see explanation
Step-by-step explanation:
the diagonals of a rhombus are perpendicular to each other, then
∠ 1 = 90°
AB and CD are parallel ( opposite sides of a rhombus are parallel )
∠ 2 and 51° are alternate angles and are congruent , then
∠ 2 = 51°
the diagonals bisect the angles , then
∠ 3 = ∠ 2 = 51°
the sum of the 3 angles , in the triangle with ∠ 4 sum to 180°
∠ 1 + ∠ 3 + ∠ 4 = 180°
90° + 51° + ∠ 4 = 180°
141° + ∠ 4 = 180° ( subtract 141° from both sides )
∠ 4 = 39°
then
∠ 1 = 90° , ∠ 2 = 51° , ∠ 3 = 51° , ∠ 4 = 39°
Help me with this please
Answer:
we have to check the chemical property of the daisy perfume
Abstract Algebra (6408 Math) Homework (3) Let \( R \) be a ring. Question 1 Show that \( 0_{R} x=0_{R} \) for all \( x \in R \). Question 2 If \( a, b \in R \), show that \( -(a b)=(-a) b \). Best wis
Abstract Algebra
By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.
Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.
Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.
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the circle has a central angle of 56° as shown in the diagram. what is the length of minor arc ab
In the diagram, the length of minor arc AB is approximately 3.9 inches
Calculating the length of an arcFrom the question, we are to calculate the length of the minor arc AB
To calculate the length of an arc, we can use the formula:
Arc Length = (Central Angle / 360) x (2πr)
Where:
Central Angle is the angle formed by the two radii at the center of the circle
r is the radius of the circle
From the given information,
Central angle = 56°
r = 4 in
Substituting the given values, we get:
Arc Length = (56° / 360) x (2π x 4 in)
Arc Length = 3.9095 in
Arc Length ≈ 3.9 in
Hence, the length of minor arc AB is approximately 3.9 inches
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In this experiment you can use \( \sigma_{y}=\sigma_{y_{0}}=1 \times 10^{-3}(\mathrm{~m}) \) and \( \sigma_{m}=0.05 \times m(\mathrm{~kg}) \) as the uncertainty for the meter stick and weights, respec
The uncertainity for the meter stick and weights in this experiment are σₓ = σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg), respectively.
This means that the uncertainty in the measurement of the meter stick is 1 × 10⁻³ meters and the uncertainty in the measurement of the weights is 0.05 kg. To calculate the uncertainity of the results, one must use the appropriate formulae, taking into account the uncertainities of each measurement.
For example, if you are measuring the mass of an object, you must use the uncertainty in the measurement of the weight and the uncertainty in the measurement of the meter stick to calculate the uncertainty in the mass.
The uncertainty in the mass is then equal to the square root of the sum of the squares of the uncertainties of the measurements.
By taking into account the uncertainties in each measurement, one can accurately calculate the uncertainty of the results.
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Complete question:
In this experiment you can use σₓ = σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg) as the uncertainity for the meter stick and weights, respec.
5r^(2)-5r+2=0 How many real solutions does the equation have? no real one real two real solutions solution solutions
The equation 5r2 - 5r + 2 = 0 has two real solutions.
The two real solutions of the equation are:
x = (5 + 3i) / 10 and x = (5 - 3i) / 10
To solve this equation, you can use the Quadratic Formula:
x = (-b ± √(b2 - 4ac)) / (2a)
In this case, a = 5, b = -5, c = 2, so:
x = (-(-5) ± √((-5)2 - 4*5*2)) / (2*5)
x = (5 ± √(25 - 40)) / 10
x = (5 ± √(-15)) / 10
x = (5 ± 3i) / 10
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A hat contains three slips of paper. One of the following names is written on each slip of paper. Analise, Benjamin, and Cora
Which list gives the sample space for pulling two slips of paper out of the hat with replacement?
The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. A sample space may contain a number of outcomes that depends on the experiment.
For example if a fair die is thrown, the probability of getting an even number. This means that the sample space of even number in a fair die is 3 i.e, 2,4 and 6
Similarly, There are three names with slip, Analise, Benjamin and cora, the sample space to bring 2 slips out with replacement has this results
The slips can be;
1. Benjamin, cora
2. Analise, cora
3. Benjamine, Analise
4. Analise , Benjamin
5. cora, Analise
6. cora, Benjamin
7. cora, cora
8. Benjamin, Benjamin
9. Analise, Analise
The list that shows these result or sample space is list 4
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Answer:
The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)
Step-by-step explanation: