The given equation, X = 36y², represents a parabola. In standard form, the equation can be rewritten as y² = (1/36)x. The vertex (V) is located at the origin (0, 0), the focus (F) is at (0, 1/4), and the directrix (d) is the horizontal line y = -1/4.
To rewrite the equation X = 36y² in standard form, we divide both sides by 36 to get y² = (1/36)x. This form represents a parabola with its vertex at the origin (0, 0).
In standard form, the equation of a parabola can be written as y² = 4px, where p is the distance from the vertex to the focus and also the distance from the vertex to the directrix. In this case, p = 1/4.
Therefore, the vertex (V) is located at (0, 0), the focus (F) is at (0, 1/4), and the directrix (d) is the horizontal line y = -1/4.
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A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions that are needed to determine if these lines intersect.
WILL MARK BRAINLIEST
Answer:
what is this a different answer orrrr?
i’m stuck i really need help on this, thanks!
Answer:
A.) 0.25
B.) 0.125 (maybe don't trust me)
Step-by-step explanation:
convert the force in parts b from newtons to pounds. (1 lb = 4.45n). what are the chances the driver will be able to stop the child?
Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).
To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.
Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.
However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.
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can someone help me and explain this?? thanks so much!
Answer:
Step-by-step explanation:
10^7 = 1 and 7 zeros after it.
=> 10000000
or your retirement you want to have enough funds in your RRSPs to provide an income stream of $25,000 for 30 years. How much money would you need to have accumulated if your RRSPs averaged a real return of four percent per year? (Round to the nearest thousand) a. $441,000 O b. $432,000 C. $384,000 O d. $1,402,000
Money needed to have accumulated if the RRSPs averaged a real return of four percent per year is $432,000
Amount of income stream = $25,000
Time = 30 years
According to the 4% rule, a retiree can risk not having enough money for at least 30 years by comfortably withdrawing 4% of their assets in their first year of retirement and adjusting that amount for inflation each year after that.
Calculating the present value -
[tex]PV = FV / (1 + r)^n[/tex]
Substituting the values -
[tex]PV = $25,000 / (1 + 0.04)^30[/tex]
[tex]PV = $25,000 / (1.04)^30[/tex]
= 432,309
Rounded the nearest thousand the return amount comes to $432,000
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what is the distance between (6,-7) (3,-5)
Answer:
4,684 km
Step-by-step explanation:
Which statement is true? pls help :)
Answer:
The First Choice
Step-by-step explanation:
1/4 is equal to .25
.25 x 4= 1.00
25 x 4= 100
Are the ratios 2:3 and 1:2 equivalent??
Answer:
No coz 2:3 is 2+3=5
1:2 is 1+2=3 so they are not equivalent.
Need help! much appreciated
Answer:
C-D = 6
A-B = 3.25
D = 118
Step-by-step explanation:
C-D = 6 because the line is the same as B-C
A-B = 3.25 because the line is the same as A-D
D = 118 because the angle of B is vertically opposite to D
Answer this question please
Pls help ASAP. SHOW WORK
The new figure after the revolution is a cylinder of radius 5 and length 8
The volume is 200π
How to determin the new figure after the revolutionFrom the question, we have the following parameters that can be used in our computation:
The graph
The shape on the graph is a rectangle with
length = 5
width = 8
When revolved across the x-axis, we have the shape to be
A cylinder of radius 5 and length 8 (option a)
This is calculated as
V = πr²h
substitute the known values in the above equation, so, we have the following representation
V = π * 5² * 8
Evaluate
V = 200π
Hence, the volume is 200π
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what is the set of all solutions to the equation 2 = − x 2 =−xsquare root of, x, plus, 2, end square root, equals, minus, x ?
The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.
To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.
Starting with the given equation, we can simplify it step by step:
2 = -x√(x + 2) - x
Adding x to both sides:
2 + x = -x√(x + 2)
Squaring both sides to eliminate the square root:
(2 + x)^2 = (-x√(x + 2))^2
Expanding and simplifying:
4 + 4x + x^2 = x^2(x + 2)
Simplifying further:
4 + 4x = x^3 + 2x^2
Rearranging terms:
x^3 + 2x^2 - 4x - 4 = 0
Factoring the equation:
(x + 1)(x^2 + x - 4) = 0
Setting each factor to zero:
x + 1 = 0 or x^2 + x - 4 = 0
Solving the first equation, we find x = -1.
For the second equation, we can use the quadratic formula:
x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))
x = (-1 ± √(1 + 16)) / 2
x = (-1 ± √17) / 2
However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.
Hence, the set of all solutions to the equation is {x = -1}.
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NO LINKS!!! PLEASE!
You score an 86 on the first of two exams. Write and solve an equation to find the score (x) that you need on the second exam to have a mean score of 90.
Answer:
x = 94
Step-by-step explanation:
(86 + x)/2 = 90
86 + x = 180
x = 94
Please complete the table below.
Answer:
1.is 12
2. is 36
3. is 18
4. is 4.5
Step-by-step explanation:
sorry if im wrong
Simplify the following expressions to have fewer terms 5x-3+4(4x-6)+2
Answer:
(21x-25)
Step-by-step explanation:
We need to find an equivalent expression for the following.
5x-3+4(4x-6)+2
We can solve it as follows:
5x-3+4(4x-6)+2 = 5x-3+16x-24+2
= 5x+16x-3-24+2
= 21x-25
So, the equivalent expression is equal to (21x-25).
Tell whether the angles are complementary, supplementary, or neither.
Answer:
supplementary (add together to = 180°)
Step-by-step explanation:
Step-by-step explanation:
Supplementary angles add up to 180
complementary angles add up to 90
75+105=180
so the angles are supplementary
Hope that helps :)
A wallet costs $50 to produce. If the manufacturer wants a 70% markup based on cost, what should be the selling price of the wallet?
prove the following statement:
Let n be an odd positive integer then the sum of n consecutive
integers is divisible by n.
The sum of n consecutive integers, where n is an odd positive integer, is divisible by n.
To prove the statement, let's consider a set of n consecutive integers starting from a.
The sum of n consecutive integers can be expressed as:
S = a + (a+1) + (a+2) + ... + (a+n-1)
To find the sum, we can use the formula for the sum of an arithmetic series:
S = (n/2) × (2a + (n-1))
Since n is an odd positive integer, we can represent it as n = 2k + 1, where k is a non-negative integer.
Substituting this value of n into the sum formula, we get:
S = ((2k+1)/2) × (2a + ((2k+1)-1))
Simplifying further:
S = (k+1) × (2a + 2k)
S = 2(k+1)(a + k)
Since k is an integer, (k+1) is also an integer. Therefore, we can rewrite the sum as:
S = 2m(a + k)
Now, we can see that S is divisible by n = 2k + 1, where m = (k+1).
Thus, we have proven that the sum of n consecutive integers, where n is an odd positive integer, is divisible by n.
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2=5-5x (your answer must include the variable)
Answer: x=3/5
Step-by-step explanation:
10x+11=51 solve for x
Answer:
x=4
Step-by-step explanation:
in a single run of hades, zagreus has a 10% chance of catching 0 fish, 40% chance of catching 1 fish, 35% chance of catching 2 fish, and a 15% chance of catching 3 fish. calculate the standard deviation of the fish zagerus will catch.
The standard deviation of the fish Zagreus will catch is approximately 0.6833.
Given probability of catching fish by Zagreus in a single run of Hades is as follows: P(0 fish) = 0.10 P(1 fish) = 0.40 P(2 fish) = 0.35 P(3 fish) = 0.15
To calculate the standard deviation of the fish Zagreus will catch, we need to follow these steps:
Find the expected value, µ, of the fish he will catch.
Then, calculate the variance, σ², using the formula:σ² = Σ [(x - µ)² P(x)]
Finally, calculate the standard deviation, σ, which is the square root of the variance.μ = Σ [xP(x)]μ = (0 × 0.10) + (1 × 0.40) + (2 × 0.35) + (3 × 0.15)μ = 0.75
The expected value, µ, of the fish he will catch is 0.75.
To find the variance:σ² = [(0 - 0.75)² × 0.10] + [(1 - 0.75)² × 0.40] + [(2 - 0.75)² × 0.35] + [(3 - 0.75)² × 0.15]σ² = 0.4675
Finally, the standard deviation, σ, is the square root of the variance:σ = √σ²σ = √0.4675σ ≈ 0.6833
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Given: In a single run of hades, zagreus has a 10% chance of catching 0 fish, 40% chance of catching 1 fish, 35% chance of catching 2 fish, and a 15% chance of catching 3 fish. The standard deviation of the fish that Zagreus will catch is 0.49 fish.
The standard deviation of the fish that Zagreus will catch can be calculated using the following formula
σ = sqrt [∑(x-μ)²/N], where σ is the standard deviation, ∑ is the sum of, x is the fish, μ is the mean, and N is the total number of chances.
The mean value of the fish Zagreus is expected to catch is given by:
μ = (0 x 10/100) + (1 x 40/100) + (2 x 35/100) + (3 x 15/100)
μ = 0 + 0.4 + 0.7 + 0.45
μ = 1.55.
Therefore, the mean value of the fish Zagreus will catch is 1.55 fish.
To calculate the standard deviation, we first calculate the deviation of each value from the mean as shown below: Deviation = x - μ
The deviations for each value of fish that Zagreus could catch are: -1.55, -0.55, 0.45, and 1.45.
Now, we can plug in these values into the formula above to calculate the standard deviation as shown below:
σ = sqrt [(-1.55² x 10/100) + (-0.55² x 40/100) + (0.45² x 35/100) + (1.45² x 15/100)]
σ = sqrt [0.24025]
σ = 0.49
Therefore, the standard deviation of the fish that Zagreus will catch is 0.49 fish.
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Use the given values of n and p to find the minimum usual value and the maximum usual value. Round your answer to the nearest hundredth unless otherwise noted. n=267, p=0.239
a. Minimum usual value: 63.85, Maximum usual value: 90.56
b. Minimum usual value: 54.65, Maximum usual value: 79.92
c. Minimum usual value: 42.56, Maximum usual value: 72.01
d. Minimum usual value: 34.32, Maximum usual value: 68.76
Option (b) is the correct answer. Minimum usual value: 54.65
Maximum usual value: 79.92.
The given values are n = 267 and p = 0.239. The minimum usual value and the maximum usual value are to be calculated. We use the formula of the mean and the standard deviation for this purpose:
Mean = µ = np = 267 × 0.239 = 63.93Standard Deviation = σ = sqrt (npq) = sqrt [(267 × 0.239 × (1 - 0.239)] = 5.01The minimum usual value is obtained when the z-value is -2, and the maximum usual value is obtained when the z-value is +2. We use the z-score formula: z = (x - µ) / σwhere µ = 63.93 and σ = 5.01(a) When the z-value is -2, x = µ - 2σ = 63.93 - 2(5.01) = 53.91(b) When the z-value is +2, x = µ + 2σ = 63.93 + 2(5.01) = 73.95
Therefore, the minimum usual value is 53.91, and the maximum usual value is 73.95 (rounded to the nearest hundredth).
Thus, option (b) is the correct answer. Minimum usual value: 54.65Maximum usual value: 79.92.
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The given values are: n=267, p=0.239
We need to find the minimum usual value and the maximum usual value using these values of n and p.
Let X be a random variable with a binomial distribution with parameters n and p.
The mean of the binomial distribution is:μ = np
The standard deviation of the binomial distribution is:σ = sqrt(npq)where q = 1-p
Let X be a binomial distribution with parameters n = [tex]267 and p = 0.239μ = np = 267 × 0.239 = 63.813σ = sqrt(npq) = sqrt(267 × 0.239 × 0.761) = 6.788[/tex]
The minimum usual value is given by:[tex]μ - 2σ = 63.813 - 2 × 6.788 = 50.236[/tex]
The maximum usual value is given by:[tex]μ + 2σ = 63.813 + 2 × 6.788 = 77.39[/tex]
Thus, the minimum usual value is 50.24 and the maximum usual value is 77.39(rounded to the nearest hundredth).
Therefore, the answer is:Minimum usual value: 50.24, Maximum usual value: 77.39
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PLEASE HELP ITS DUE TODAY!
5. Find the length of the missing side in the figure below. a =
cm.
5.8
2.4
8.5
оо
5.3
Answer:
a=[tex]\sqrt{28.32}[/tex]≈5.3217 cm
Step-by-step explanation:
Use the Pythagorean Theorem
a^2+4.7^2=7.1^2
a^2+22.09=50.41
a^2=28.32
a=[tex]\sqrt{28.32}[/tex]
≈5.3217
Answer:
5.3
Step-by-step explanation:
Check the attached image for explanation if you are interested, as I did not feel like spending 20 minutes re-formatting the equations to work on Brainly.
Also, I did not do this
K divided by 5 = 12.4
Answer:
k=62
Step-by-step explanation:
K divided by 5 = 12.4
Multiply both sides by 5
5k/5=12.4×5
Simplify;
k=62
Hope this helped!!
Answer:
k = 62
Step-by-step explanation:
To solve we need to get k on one side alone.
To do this we can multiply buth sides by 5
[tex]\frac{k}{5} =12.4[/tex] ---> =12.4*5
This gives us x=62
You can check this by putting 62 in for k and solving the problem.
What is a brief description of a radian?
simply saying its circular measure
Plot the points D(-9,-6) E(-6,-3) F(0,-9)and dilate usinng a scale factor of 1/3 centered at the origin
Answer:
Step-by-step explanation:
Rule for the dilation of a point about the origin is,
(x, y) → (kx, ky)
Here, k = scale factor
Dilating points D, E and F about the origin by a scale factor 'k' = [tex]\frac{1}{3}[/tex]
D(-9, -6) → D'(-3, -2)
E(-6, -3) → E'(-2, -1)
F(0, -9) → F'(0, -3)
Now we can plot these points on graph.
euler's formula, v − e f = 2, relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron. solve euler's formula for e.
The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.
Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.
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Consider the system of linear equations 2- y = kx - y = k (a) Reduce the augmented matrix for this system to row-echelon (or upper-triangular) form. (You do not need to make the leading nonzero entries 1.) (b) Find the values of k (if any) when the system has (a) no solutions, (b) exactly one solution (if this is possible, find the solution in terms of k), (e) infinitely many solutions (if this is possible, find the solutions).
The system of linear equations has no solutions for any value of k except when k = 2, where it has infinitely many solutions.
(a) To reduce the augmented matrix for the system of linear equations to row-echelon form, we can write the system of equations as:
2 - y = kx
-y = k
To eliminate y in the first equation, we can multiply the second equation by (-1) and add it to the first equation:
(2 - y) - (-y) = kx - k
2 = kx - k
This gives us a new system of equations:
2 = kx - k
Now, we can represent this system in augmented matrix form:
[1 -k | 2]
(b) To find the values of k, we can examine the augmented matrix.
If the system has no solutions, it means that the rows of the augmented matrix result in an inconsistent equation, where the last row has a leading nonzero entry. In this case, for the system to have no solutions, the augmented matrix should have a row of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix [1 -k | 2] doesn't have this form, so there are no values of k that lead to no solutions.
If the system has exactly one solution, the augmented matrix should be in row-echelon form, with each row having at most one leading nonzero entry. In this case, the augmented matrix should not have any rows of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix can be reduced to row-echelon form as follows:
[1 -k | 2]
From this form, we can see that there are no restrictions on the value of k. For any value of k, the system will have exactly one solution.
If the system has infinitely many solutions, the augmented matrix should have at least one row of the form [0 0 | 0]. In our case, the augmented matrix can be reduced to:
[1 -k | 2]
From this form, we can see that if k = 2, the last row becomes [0 0 | 0]. Therefore, for k = 2, the system will have infinitely many solutions.
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The midpoint of CD is M=(2, -1). One endpoint is C=(-3,-3). Find the coordinates of the other endpoint, D. D (?, ?) M (2,-1) C (-3,-3) D = (-7, -1) Find an ordered pair (x, y) that is a solution to the equation. -x+5y=2
The ordered pair (x, y) that is a solution to the equation -x + 5y = 2 is (0, 2/5).
To find the coordinates of the other endpoint D given that the midpoint of CD is M(2, -1) and one endpoint is C(-3, -3), we can use the midpoint formula:
Midpoint formula:
The coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
Using the given information, we can substitute the known values into the midpoint formula and solve for the coordinates of D:
M(2, -1) = ((-3 + x₂) / 2, (-3 + y₂) / 2)
Simplifying the equation:
2 = (-3 + x₂) / 2
-1 = (-3 + y₂) / 2
To solve for x₂:
4 = -3 + x₂
x₂ = -3 + 4
x₂ = 1
To solve for y₂:
-2 = -3 + y₂
y₂ = -3 - 2
y₂ = -5
Therefore, the coordinates of the other endpoint D are D(1, -5).
To find an ordered pair (x, y) that is a solution to the equation -x + 5y = 2, we can choose any value for either x or y and solve for the other variable. Let's choose x = 0:
-0 + 5y = 2
5y = 2
y = 2/5
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What is 3b to the second power if b is 4