Draw n equally spaced marks between 0 and 1 on each of the x and y axes. Connect the first mark on the x-axis (closest to 0) to the last mark on the y axis (closest to 1), the second mark on the x axis to the second last on the y axis, and so on.
As n increases this process creates a curved boundary, C, as seen in this example diagram. Give an equation for this curve as n → ∞.
Answers
the equation for the curve C as n approaches infinity is y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
what is diagonal line ?
A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.
In the given question,
As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.
To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:
m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)
where the nth mark on the x-axis is given by:
nth mark = 1 - (1/n)
Substituting this expression for nth mark into the equation for m, we get:
m = (n/(n-1))
The y-intercept of the line is given by:
b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)
Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:
y = (n/(n-1))x + 1/(n-1)
Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:
y = (n/(n-2))x + 1/(n-2)
Continuing this process for all n line segments, we get:
y = (n/(n-k))x + 1/(n-k)
where k = 1, 2, ..., n.
To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:
y = x
Therefore, the equation for the curve C as n approaches infinity is:
y = x
This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
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Related Questions
someone help i really need help with this
Answers
Answer:
29
Step-by-step explanation:
she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.
please help, due in an hour !!
Answers
Answer:
Step-by-step explanation:
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound=0.640, upper bound=0.910, n=1200
Answers
The point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample are:
margin of error = 0. 135point estimate = 0. 775 x = 930 peopleHow to find the parameters ?The point estimate of the population proportion:
= (lower bound + upper bound) / 2
= (0.640 + 0.910) / 2
= 0. 775
The margin of error for the confidence level :
= p - hat - lower bound
= 0. 775 - 0. 640
= 0. 135
The number of individuals in the sample with the specified characteristic (x ) :
= n x p - hat
= 1, 200 x 0. 775
= 930 people
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what is 9v+–3v+–4v–2+1 simplified
Answers
Answer:
2v-1
Step-by-step explanation:
9v+-3v+-4v-2+1
=9v-3v-4v-1
=6v-4v-1
=2v-1
15 POINTS!! ASAP TYYY
Answers
Answer:
A
Step-by-step explanation:
She earns $15 per poinsettia.
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answers
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
what will the coordinates be if Point A (-4,-5) of the trapezoid was reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction.
Answers
Answer:
If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).
Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":
A" = (4 - 6, -5 + 7) = (-2, 2)
Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).
Step-by-step explanation:
Answer:
(-2, 2)
Step-by-step explanation:
I did the test
Hope this helps :)
The table describes the quadratic function p(x). x p(x) -4 24 -3 9 -20 -1 -3 0 2 0 What is the equation of p(x) in vertex form? Op(x) = 2(x - 1)² - 3 p(x) = 2(x + 1)² - 3 Op(x) = 3(x - 1)² – 3 p(x) = 3(x - 1)² – 3
Answers
The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.
Option C is the correct answer.
Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.
where k and n are positive integers.
We have,
From the table,
From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.
So,
The vertex is (- 1, -3).
The vertex form of p(x).
p(x) = a ( x - h)² + k
Where (h, k) is the vertex.
Now,
(-1, -3) = (h, k)
Make (- 2, 0) = (x, p(x))
0 = a (- 2 + 1)² + (-3)
0 = a x 1 - 3
a = 3
Thus, The vertex equation of p(x).
p(x) = 3(x + 1)² - 3
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Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Answers
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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Ignatio and his two friends each bought a ticket to play lazer tag and each spent $15 on game tokens at Fun Mountain. Let t represent the cost of a lazer tag ticket. Enter an expression that represents the total amount that Ignatio and his friends spent.
Answers
The expression that represents the total amount that Ignatio and his friends spent is 15t
Calculating the expression that represents the total amount
From the question, we have the following parameters that can be used in our computation:
Each spent $15 on game tokens at Fun MountainEach cost = tAfter spending on t games, we have
f(t) = Rate * t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 15 * t
Evaluate
f(t) = 15t
Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t
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Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answers
Answer:
Answer is D.
Please mark my answer as Brainliest if you found this one helpful.
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
Answers
The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²
where k is the proportionality constant.
In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.
In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:
Strength = k * width * depth² = k * x² * (d/2 - x)²
where x is the width and depth of the beam.
In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:
Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²
where θ is the angle at which the beam is cut from the log.
In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:
w = d sinθ
d = (d/2)cosθ
Then we can express the strength of the beam as:
Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²
Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.
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Complete question is:
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
The prism below is made of cubes which measure
1
4
of an inch on one side. What is the volume?
A 3D illustration view of a blank tabular with 5 rows and 2 columns.
Note: Figure is not drawn to scale.
A.
15
32
cubic in
B.
5
2
cubic in
C.
30
cubic in
D.
15
2
cubic in
Answers
The volume of the prism is B. 2.5 cubic inches.
How to calculate the volumeAccording to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:
Length = 2 × 1/4
Width = 5 × 1/4
Height = 3 × 1/4
= 2/4 + 5/4 + 3/4
= 2 2/4
= 2.5 cubic inches.
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the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answers
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
Identify the null and alternative hypotheses
Statistics!
Answers
The null and the alternate hypothesis are:
H₀: p ≤ 0.5H₁: p > 0.5How to write the hypothesisIn hypothesis testing, we take the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is the opposite of the claim , while the alternative hypothesis states the claim.
In this case, the null hypothesis is that a majority of adults would not erase their personal information online if they could (i.e., 50% or less of them would do so). The alternative hypothesis is that a majority of adults would erase their personal information online if they could (i.e., more than 50% of them would do so). In symbolic form:
H₀: p ≤ 0.5
H₁: p > 0.5
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
-3, √3, 13/3
The other zeros are
(Use a comma to separate answers.)
Answers
Answer:
{-3, √3, -√3, 13/3}
Step-by-step explanation:
Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.
We can write the polynomial with these zeros as:
p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)
where a is some constant coefficient. Multiplying out the factors, we get:
p(x) = a(x + 3)(x^2 - 3)(x - 13/3)
To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:
a(x + 3)(x^2 - 3)(x - 13/3) = 0
This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:
(x + 3)(x^2 - 3)(x - 13/3) = 0
Expanding the quadratic factor, we get:
(x + 3)(x - √3)(x + √3)(x - 13/3) = 0
Canceling out the (x - √3) and (x + √3) factors, we get:
(x + 3)(x - 13/3) = 0
Solving for x, we get:
x = -3 or x = 13/3
Therefore, the other zeros are -3 and 13/3.
The complete set of zeros is {-3, √3, -√3, 13/3}.
Hope it helps^^
Describe two trends you can find in the graph below. Use calculations and numbers to support your thinking.
Answers
The two trends on the graph are:
Positive correlationNegative correlationDescribing the two trends on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The two trends on the graph are:
Positive correlationNegative correlationFor the positive correlation, we have
Upward trend from January till August
This is because the function values increase approximately in this domain
For the negative correlation, we have
Upward trend from August till December
This is because the function values decrease approximately in this domain
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What expression is or is not equivalent, what is the answer?
Answers
Answer:
A and B
Step-by-step explanation:
-10/3= -3.33333333333
(- (-10))/(-3)= -10/3, (negative sign being erased)
=-3.33333333333
hope it helped:)
A population of values has a normal distribution with a mean of 246 and a standard deviation of 89.7. You intend to draw a random sample of size m = 158.
Answer the following, rounding your answers to three decimals where appropriate.
Find the probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4.
P(M>242.4) = ???
Answers
The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.
How to calculate the probabilityz = (x - μ) / (σ/√n)
where x is the sample mean.
Substituting the values, we get:
z = (242.4 - 246) / (89.7/√158) ≈ -0.670
We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.
P(z > -0.670) ≈ 0.751
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example of a multi-step combination problem
Answers
Answer:
A multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations
Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answers
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
Please answer if you know this one with the steps thank you.
Answers
Step-by-step explanation:
T = 5200 = .2 ( E - 10600)
5200 / .2 = E - 10600
E = 5200/.2 + 10 600 = 36600 pounds
For the following exercises,
(a) find the angle between 0 and 2π in radians that is coterminal with the given angle.
(b) find the reference angle of each one.
a)32π/13 b)-17π/6
Answers
The reference angle of given angles are -6π/13 and -5π / 6
To get coterminal angles, you simply have to add or subtract 2π.
a) 32π/13 =
= -32π/13 + 2π
= -32π + 26π / 13
= -6π/13
b) -17π/6 + 2π =
= -17π + 12π / 6
= -5π / 6
Hence the reference angle of given angles are -6π/13 and -5π / 6
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James answered 14 lems correctly
an a 16-item quiz. what percentage did he answer correctly
Answers
Answer:
14/16 = 0.875
(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
Answers
she needs to clean 15 uniforms to break even
Find the value of 11 3/8 -7/8
Answers
The value of 11 3/8 -7/8 is 10 1/2
What is subtraction?Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60
Solving 11 3/8 -7/8
= 91/8 - 7/8
= (91-7)/8
= 84/8
= 21/2
= 10 1/2
Therefore the value of 11 3/8 -7/8 is 10 1/2
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A meter in a taxi calculates the fare using the function f(x) = 2.56x + 2.40. If x represents the length of the trip, in miles, how many miles can a passenger travel for $20?
Answers
A passenger can travel 6.875 miles for $20 using the given taxi fare function.
To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.
The equation we need to solve is:
2.56x + 2.40 = 20
To solve for x, we can start by subtracting 2.40 from both sides of the equation:
2.56x = 17.60
Next, we can divide both sides by 2.56:
x = 6.875
This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.
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3. Find the solution to each equation mentally.
a. 30+ a = 40
b. 500+ b = 200
C. -1+c= -2
d. d +3.567=0
Answers
Answer:
[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]
hope it helps:)
Solve by using a system of equations.
A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?
Answers
The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:
Let the variable y represent the quantity of first alloy (30% gold).Let the variable x represent the quantity of second alloy (80% gold).Therefore, a system of linear equations to describe this situation can be written as follows;
x + y = 40 .....equation 1.
0.3x + 0.8y = 0.6(40) .....equation 2.
From equation 2, we have the following:
0.3x + 0.8y = 24
0.3x + 0.8(x - 40) = 24
0.3x + 32 - 0.8x = 24
-0.5x = -8
x = -8/-0.5
x = 16 grams.
y = 40 - x
y = 40 - 16
y = 24 grams.
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There are 6 bottles of water.
Each bottle is 1/2 full. If you
were to combine all the
water, how many full bottles
of water would there be?
Answers
Answer:3
Step-by-step explanation: 1/2 X 6 = 3
Answer:
6 x 1/2 = 3 full bottles
Step-by-step explanation:
