The x-coordinate of the vertex of the parabola whose equation is given would be -3/2. Option C.
x-coordinate calculationTo find the x-coordinate of the vertex of the parabola, we need to use the formula:
x = -b/2awhere a and b are the coefficients of the quadratic equation in standard form (ax^2 + bx + c).In this case, a = 3 and b = 9, so:
x = -9/(2*3) = -3/2
Therefore, the x-coordinate of the vertex of the parabola is -3/2.
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The x-coordinate of the vertex of the parabola whose equation is given would be -3/2. Option C.
x-coordinate calculationTo find the x-coordinate of the vertex of the parabola, we need to use the formula:
x = -b/2awhere a and b are the coefficients of the quadratic equation in standard form (ax^2 + bx + c).In this case, a = 3 and b = 9, so:
x = -9/(2*3) = -3/2
Therefore, the x-coordinate of the vertex of the parabola is -3/2.
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compute eight rows and columns in the romberg array
The Romberg array is a table of values that is used to estimate the value of a definite integral. To compute the Romberg array, we use the Richardson extrapolation method, which is a process of successive approximation.
To compute the eight rows and columns of the Romberg array, we begin by splitting the integration interval into two equal-length subintervals. The trapezoidal method is then applied to each subinterval to produce two estimates of the integral. The Richardson extrapolation method is then used to get a better estimate of the integral based on these two estimations. This operation is continued, splitting the subintervals into smaller and smaller subintervals, until the Romberg array has the necessary number of rows and columns.
The Romberg array's general formula is as follows:
R(m,n) = (4^n R(m,n-1) - R(m-1,n-1)) / (4^n - 1)
where R(m,n) is the value of the integral estimate at row m and column n in the Romberg array.
The first column of the Romberg array contains the estimates obtained by the trapezoidal rule, while the subsequent columns are obtained by applying the Richardson extrapolation method using the values in the previous column.
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pls help me with this one too
Lucas is collecting baseball cards. He had 46 cards in his collection. His grandma gave him 29 cards for his birthday, and his aunt Tammy gave him 52 cards. How many baseball cards does Lucas have now?
Answer:
127 baseball cards
Step-by-step explanation:
Lucas now has a total of 127 baseball cards.
To find out, you can add up the number of cards he had before (46), the number of cards his grandma gave him (29), and the number of cards his aunt Tammy gave him (52):
46 + 29 + 52 = 127
Hope this helps!
let w be the subspace spanned by the given vectors. find a basis for w⊥. w1 = −4 −4 −12 −4 , w2 = 2 2 6 2 , w3 = 6 −12 18 12
The w⊥ is the trivial subspace, consisting only of the zero vector.
To find a basis for the subspace w⊥, we need to find the vectors that are orthogonal to all vectors in w, which is the subspace spanned by the given vectors.
First, we need to find a basis for w. We can do this by putting the given vectors into a matrix and reducing it to row echelon form.
[tex]\begin{pmatrix}-4 & -4 & -12 & -4 \ 2 & 2 & 6 & 2 \ 6 & -12 & 18 & 12\end{pmatrix} $\to$[/tex]
[tex]\begin{pmatrix}2 & 2 & 6 & 2 \ 0 & -8 & -24 & -8 \ 0 & 0 & 0 & 0\end{pmatrix}[/tex]
The row echelon form shows that the first two vectors are linearly independent, so we can take them as a basis for w:
w1 = [-4, -4, -12, -4] and w2 = [2, 2, 6, 2]
Next, we need to find the vectors that are orthogonal to both w1 and w2. To do this, we can set up a system of equations:
a(-4,-4,-12,-4) + b(2,2,6,2) + c(0,0,0,0) = (0,0,0,0)
Simplifying the equation, we get:
-4a + 2b = 0
-4a + 2b = 0
-12a + 6b = 0
-4a + 2b = 0
We can see that the first two rows are identical, so we only need to use the first two rows to find a basis for w⊥.
Solving the first two equations, we get:
a = b/2
Substituting this into the third equation, we get:
-12(b/2) + 6b = 0
-6b + 6b = 0
b = 0
So a = 0 as well. This means that the only vector that is orthogonal to both w1 and w2 is the zero vector, which is not a valid basis vector.
Therefore, w⊥ is the trivial subspace, consisting only of the zero vector.
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sketch the wave functions and the probability distributions for the n = 4 and n = 5 states for a particle trapped in a finite square well.
The wave functions and probability distributions for a particle trapped in a finite square well can be complex, but understanding these concepts is essential for understanding the behavior of particles in quantum mechanics.
To sketch the wave functions and probability distributions for the n = 4 and n = 5 states of a particle trapped in a finite square well:
We need to first understand what these terms mean.
Wave functions are mathematical functions that describe the behavior of particles in quantum mechanics. They represent the probability amplitude of finding a particle in a certain state, and can be used to calculate the probability of finding the particle in a certain location.
Probability distributions, on the other hand, describe the probability of finding a particle in a certain location at a certain time. They are calculated by squaring the wave function and normalizing the result.
Now, let's consider a particle trapped in a finite square well. This means that the particle is confined to a certain region of space, and can only exist within that region. The wave function for a particle in this situation can be expressed as a combination of sine and cosine functions.
For the n = 4 and n = 5 states, the wave functions will have four and five nodes, respectively. These nodes represent regions where the probability of finding the particle is zero.
To sketch the probability distributions, we need to square the wave functions and normalize the result. This will give us a graph that shows the probability of finding the particle at different locations within the well.
Overall,the wave functions and probability distributions for a particle trapped in a finite square well can be complex, but understanding these concepts is essential for understanding the behavior of particles in quantum mechanics.
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-10.4166666667 as a fraction
Answer:
125/12
Step-by-step explanation:
lets take n = -10.4166666
multiply this by 100 so we get the recurring part as the decimals
100n = -1041.66666
now we multiply our original n value by 10 for simplicity while calulating
10n = -104.16666
then we subtract 10n from 100n
90n = -1041.666 - (- 104.16666)
the recurring part will cancel out infinitely
so we get
90n = 937.5
then we solve for n
n = 937.5/90
simplifying will get us n= 125/12
draw and label an appropriate pair of axes and plot the points. A = (10,50), B = (30,25), C = (0,30), D = (20,35)
A graph with an appropriate pair of axes has been used to plot the points as shown in the image attached below.
What is a graph?In Mathematics and Geometry, a graph is a type of visual chart that is used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is an ordered pair?In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given points on a graph as shown in the image attached below.
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At a coffee shop, the first 100 customers’ orders were as follows…
Find the probability a customer ordered a hot drink, given that they ordered a large.
CHALLENGE ACTIVITY 9.1.1: Probability of an event. Two dice are rolled. Enter the size of the set that corresponds to the event that both dice are odd. Ex:________
To determine the probability of an event where both dice are odd, let's first list all the possible odd numbers on a die: {1, 3, 5}.
Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.
Now, let's find all the combinations of two dice showing odd numbers:
1. (1, 1) 2. (1, 3) 3. (1, 5) 4. (3, 1) 5. (3, 3) 6. (3, 5) 7. (5, 1) 8. (5, 3) 9. (5, 5)
There are a total of 9 combinations where both dice show odd numbers.
So, the size of the set that corresponds to the event that both dice are odd is 9.
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Use this formula to find the curvature. y = 5x^4 kappa (x) = kappa (x) = |f"(x)|/[1 + (f'(x))^2]^3/2
The curvature of y = 5x⁴ is kappa (x) = |60x²|/[1 + (20x³)²]³/².
To find the curvature (kappa) of the function y = 5x⁴, we'll use the formula kappa (x) = |f"(x)|/[1 + (f'(x))²]³/².
1. First, find the first derivative (f'(x)) by differentiating y with respect to x: f'(x) = 20x³.
2. Next, find the second derivative (f"(x)) by differentiating f'(x) with respect to x: f"(x) = 60x².
3. Substitute f'(x) and f"(x) into the curvature formula: kappa (x) = |60x²|/[1 + (20x³)²]³/².
4. Simplify the expression to get the curvature kappa(x).
To find the curvature at a specific point, substitute the x-value into kappa(x) and evaluate the expression.
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exercise 2.3.106. find an equation such that ,y=cos(x), ,y=sin(x), y=ex are solutions.
Polynomial equation has y=cos(x), y=sin(x), and y=eˣ as solutions.
How to find an equation that has y=cos(x), y=sin(x), and y=eˣ as solutions?We can consider these functions as roots of a polynomial. Let's use the terms given to construct a polynomial equation:
Let P(y) be the polynomial, and let's denote the roots as y1 = cos(x), y2 = sin(x), and y3 = eˣ.
According to Vieta's formulas, for a cubic polynomial with roots y1, y2, and y3, we have:
P(y) = (y - y1)(y - y2)(y - y3)
Now, substitute the given roots:
P(y) = (y - cos(x))(y - sin(x))(y - eˣ)
This polynomial equation has y=cos(x), y=sin(x), and y=eˣ as solutions.
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Find the value of x.
A. -2.75
B. 1.75
C. 46
D. 58
x+6/4
= 13
Answer:
C
Step-by-step explanation:
[tex]\frac{x+6}{4}[/tex] = 13 ( multiply both sides by 4 to clear the fraction )
x + 6 = 4 × 13 = 52 ( subtract 6 from both sides )
x = 46
Answer:
C
Step-by-step explanation:
Step one x=?
first try a -2.75+6/4=13
u get 0.81=13 so wrong
step 2 try b 1.75+6/4=13
7.75/6=13
1.29=13 wrong
Step 3
46+6/4=13
52/4=13
13=13 Correct
Using the rule that cos3θ = 4(cosθ)^3 − 3 cosθ, show that cos 2π/9 is a root of the equation 8x^3 − 6x + 1 = 0
Answer:
Below in bold.
Step-by-step explanation:
Let x = cosθ, then
8(cosθ)^3 − 6cosθ + 1 = 0
---> 2(4(cosθ)^3 − 3 cosθ) + 1 = 0
---> 2(cos3θ) + 1 = 0
---> cos3θ = -1/2
---> θ = 2π/9
Therefore cos θ = = cos(2π/9) = x, and
cos(2π/9) is a root of the given eqation.
Trixie started her homework at 5:30pm She finished it at 8:50pm How long (in minutes)did it take her to do her homework
It took Trixie 200 minutes to finish her homework.
To calculate the time Trixie took to do her homework, we can subtract the starting time from the ending time.
The starting time is 5:30pm, which is equal to 5 x 60 + 30 = 330 minutes after midnight.
The ending time is 8:50pm, which is equal to 8 x 60 + 50 = 530 minutes after midnight.
To find the duration, we can subtract the starting time from the ending time:
530 minutes - 330 minutes = 200 minutes
Therefore, it took Trixie 200 minutes to finish her homework.
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State the degree of the following polynomial equation. Find all of the real and imaginary roots of the equation, stating multiplicity when it is greater than one. x6 - 49x^4 = 0.
a. The degree of the polynomial is = __________
b. What are the two roots of multiplicity 1?
a. The degree of the polynomial is 6.
b. Factoring the equation, we have:
x6 - 49x^4 = x^4(x^2 - 49) = x^4(x - 7)(x + 7)
a.The degree of the polynomial equation x^6 - 49x^4 = 0 is 6. This is determined by the highest exponent of x in the polynomial, which is 6.
b. The two roots of multiplicity 1 can be found by factoring the equation as x^4(x^2 - 49) = 0. Setting each factor equal to zero, we have x^4 = 0 and x^2 - 49 = 0.
From x^4 = 0, we find the root x = 0 with multiplicity 4.
From x^2 - 49 = 0, we get (x - 7)(x + 7) = 0. Therefore, the roots x = 7 and x = -7 each have multiplicity 1.
In summary, the equation x^6 - 49x^4 = 0 has a degree of 6, and the roots with multiplicity 1 are x = 0, x = 7, and x = -7.
So the roots of the equation are:
x = 0 (multiplicity 4)
x = 7 (multiplicity 1)
x = -7 (multiplicity 1)
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2x²+8x-24=0 formula general
[tex]\sf x_{1} =2;\\ \\x_{2} =-6.[/tex]
Step-by-step explanation:Assuming that the exercise asks to find the roots or solutions to this equation, this would the process for doing so:
1. Write the equation in the standard form for quadratic equations.Standard form: [tex]\sf ax^{2} +bx+c=0[/tex]
This equation is already written in standard form so we can skip this step, but it's important to always make sure we have the equation well written for this method.
2. Identity the a, b and c coefficients.So the coefficients are just the numbers that myltiply the different values in the formula.
For example:
Coefficient "a" is the number that multiplies "x²" within the standard form of the equation. In this case, x² is being multiplied by number "2", that's the reason we have "2x²". Thus, the value for the "a" coefficient is 2.
Note: If you only have "x²" on your standard equation, the "a" coefficient is 1.
Coefficient "b"= 8, because "x" is being multiplied by 8 on the standard equation,
Coefficient "c"= -24, because -24 is the last number before the equal symbol in the standard form of the equation.
3. Use the quadratic formula to calculate the solutions for this quadratic equation.Quadratic formula: [tex]\sf \dfrac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Here, we substitute the a, b and c variables within the equation by the identified coefficients in step 2.
[tex]\sf x_{1} =\sf \dfrac{-b+\sqrt{b^{2}-4ac } }{2a}=\sf \dfrac{-(8)+\sqrt{(8)^{2}-4(2)(-24) } }{2(2)}=2[/tex]
[tex]\sf x_{2} =\sf \dfrac{-b-\sqrt{b^{2}-4ac } }{2a}=\sf \dfrac{-(8)-\sqrt{(8)^{2}-4(2)(-24) } }{2(2)}=-6[/tex]
4. Results.[tex]\sf x_{1} =2;\\ \\x_{2} =-6.[/tex]
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[tex] \sf{x = 2, - 6}[/tex]
Step-by-step explanation:Topic: Quadratic formula exercises
[tex] \: \: \: \: \: \: \: \: \: \: \: \sf2(x {}^{2} + 4x - 12) = 0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \sf{}2(x - 2)(x + 6) = 0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{}x = 2, - 6[/tex]
Quadratic fórmula:[tex] \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{\cfrac{ - b + - \sqrt{b {}^{2} - 4ac} }{2a} }}[/tex]
Explanation:In this exercise, what was done was to extract common factors, then we must multiply and subtract what is inside the parentheses and, as a last step, clear as a function of "x".
But in the exercise I solved it in another way since it is easier than doing it in fraction.
But his quadratic formula of the problem is:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \cfrac{ \sf - b + - \sqrt{b {}^{2} - 4ac } }{ \sf2a} }[/tex]
Therefore, the result of the quadratic formula is: x -2, -6.
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https://brainly.com/question/11597563https://brainly.com/question/29183221a basketball coach is packing a basketball with a diameter of 9.60 inches into a container in the shape of a cylinder. what would be the volume of the container if the ball fits inside the container exactly. meaning the height and diameter of the container are the same as the diameter of the ball.
Answer:
To find the volume of the container, we need to use the formula for the volume of a cylinder, which is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Since the diameter of the ball is 9.60 inches, the radius is half of that, or 4.80 inches.
Since the height of the container is the same as the diameter of the ball, the height is also 9.60 inches.
Substituting the values into the formula, we get:
V = π(4.80)^2(9.60)
V ≈ 661.95 cubic inches
Therefore, the volume of the container is approximately 661.95 cubic inches.
using trigonometric identities in exercises 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52, use trigonometric identities to transform the left side of the equation into the right side .
We have transformed the left side into the right side using trigonometric identities. We start with the left side of the equation:
(1 + cos 0) (1 – sin 0)
Expanding the product, we get:
1 - sin 0 + cos 0 - sin 0 cos 0
Using the identity sin² θ + cos² θ = 1, we can replace sin² θ with 1 - cos²θ:
1 - (1 - cos² θ) + cos θ - (1 - cos² θ) cos θ
Simplifying, we get:
2 cos² θ - cos θ - 1
Now we use the identity sin² θ + cos² θ = 1 again to replace cos² θ with 1 - sin²θ:
2(1 - sin² θ) - cos θ - 1
2 - 2 sin²θ - cos θ - 1
1 - 2 sin² θ - cos θ
Finally, using the identity sin 2θ = 2 sin θ cos θ, we can write:
1 - sin 2θ - cos θ
Which is the right side of the equation. Therefore, we have transformed the left side into the right side using trigonometric identities.
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52 times 20% minus 52
The result for this percentage question is deducting 52 from 10.4 is -41.6.
How much is a percentage?
A rate, number, or amount in each hundred is referred to as a percentage. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A % lacks a measurement unit and is a dimensionless (pure) number
What does measurement unit mean?An accepted quantity that is used to represent a physical quantity is called a measurement unit. The factor used to represent how many instances of a given physical property there are is the standard quantity of that property.
You may get 10.4 by multiplying 52 by 0.2 (20% as a decimal),
20/100=0.2
which is 52 times 20%.
The result of deducting 52 from 10.4 is -41.6.
Complete question given below:
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What is the value of 52 times 20% minus 52?
write an explicit function tomorrow, the value of the nth term in the sequence, such that F(1) =4
it seems that it starts from 4 then every time it gets multiplied by 3 so F(n)=4*3^n-1
find the area of the region that lies inside both r=sin(θ) and r=cos(θ). hint: the final example on the final video lecture goes through a similar problem.
Okay, let's solve this step-by-step:
1) The equations for the two curves are:
r = sin(θ) and r = cos(θ)
2) We need to find the intersection points of these two curves. This is done by setting them equal and solving for θ:
sin(θ) = cos(θ)
=> θ = π/4
3) The intersection points are (1, π/4) and (1, 3π/4). The region lies between θ = π/4 and θ = 3π/4.
4) To find the area, we use the formula:
A = ∫θ=3π/4 θ=π/4 2πr dθ
5) Substitute r = sin(θ) or r = cos(θ):
A = ∫θ=3π/4 θ=π/4 2πsin(θ) dθ
= 2π ∫θ=3π/4 θ=π/4 sin(θ) dθ
6) Integrate:
A = 2π(cos(θ) - sin(θ) )|π/4 to 3π/4
= 2π(0 - 1) = 2π
7) Therefore, the area of the region is 2π square units.
Let me know if you have any other questions!
the path r(t) = (t)i (2t^2 7)j describes motion on the parabola y =2x2 + 7. Find Ihe paruicles velocity acceleration vectors at 0, and sketch them as vectors on the curve ed IThe velocity vector at t = 0 is v(O) = (0 (Simplify your answer; including any radicals Use integers or fractions for any numbers in the expression ).
Given the position function r(t) = ti + (2t^2 + 7)j, we can find the velocity and acceleration vectors by taking the first and second derivatives of r(t) with respect to time t.
1. Find the velocity vector v(t) by taking the first derivative of r(t):
v(t) = dr(t)/dt
= (d(t)/dt)i + (d(2t^2 + 7)/dt)j v(t)
= (1)i + (4t)j
2. Find the acceleration vector a(t) by taking the second derivative of r(t):
a(t) = dv(t)/dt
= (d(1)/dt)i + (d(4t)/dt)j a(t)
= (0)i + (4)j
Now we can find the velocity and acceleration vectors at t = 0:
v(0) = (1)i + (4*0)j
= i a(0)
= (0)i + (4)j
= 4j
So the velocity vector at t = 0 is v(0) = i, and the acceleration vector at t = 0 is a(0) = 4j.
To sketch them as vectors on the curve, draw the parabola y = 2x^2 + 7. At the point (0,7), which corresponds to t = 0, draw the velocity vector as a horizontal arrow pointing to the right (since it is i), and draw the acceleration vector as a vertical arrow pointing upward (since it is 4j).
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Let F1 and F2 denote the foci of the hyperbola 5x2 − 4y2 = 80.
(a) Verify that the point P(6, 5) lies on the hyperbola.
(b) Compute the quantity (F1P − F2P)2.
a) We can say that the point P(6,5) lies on the hyperbola.
b) The quantity (F1P − F2P)2 is approximately 122.5.
(a) To verify that the point P(6,5) lies on the hyperbola, we need to substitute x=6 and y=5 into the equation of the hyperbola and see if the equation holds true.
So, substituting x=6 and y=5, we get:
5(6)^2 - 4(5)^2 = 80
180 - 100 = 80
80 = 80
Since the equation holds true, we can say that the point P(6,5) lies on the hyperbola.
(b) To compute (F1P − F2P)2, we need to first find the coordinates of the foci F1 and F2.
5x^2 - 4y^2 = 80 can be rewritten as (x^2)/(16) - (y^2)/(20) = 1, where a^2=16 and b^2=20.
The distance between the center (0,0) and the foci is c=√(a^2+b^2)=√(336)/2. So, the foci lie on the x-axis and have coordinates (±c,0).
Therefore, F1 has coordinates (√(336)/2,0) and F2 has coordinates (-√(336)/2,0).
Now, we can calculate the distance between P(6,5) and each focus using the distance formula.
F1P = √((6-√(336)/2)^2 + (5-0)^2) ≈ 3.26
F2P = √((6+√(336)/2)^2 + (5-0)^2) ≈ 13.92
So, (F1P − F2P)^2 = (3.26 - 13.92)^2 ≈ 122.5.
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a state that requires periodic emission tests of cars operates two emission test stations, a and b, in one of its towns. car owners have complained about the lack of uniformity of procedures at the two stations, resulting in different failure rates. a sample of 400 cars at station a showed that 53 of those failed the test; a sample of 470 cars at station b found that 51 of those failed the test.a. what is the point estimate of the difference between the two population proportions? g
The point estimate of the difference between the two population proportions is 0.024.
The point estimate of the difference between two population proportions can be calculated using the following formula:
[tex]\hat{p}1 - \hat{p}2 = (x1/n1) - (x2/n2)[/tex]
where [tex]\hat{p1}[/tex] and [tex]\hat{p2 }[/tex] are the sample proportions, x1 and x2 are the number of failures in each sample, and n1 and n2 are the sample sizes.
Using the given data:
[tex]\hat{p1}[/tex] = 53/400 = 0.1325
[tex]\hat{p2 }[/tex] = 51/470 = 0.1085
n1 = 400
n2 = 470
Substituting these values into the formula, we get:
[tex]\hat{p1}-\hat{p2}[/tex] = (0.1325) - (0.1085) = 0.024.
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I need the equation to Stewart
The quadratic function that models this situation is given as follows:
y = -0.05(x² - 60x + 576).
How to define a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The ball is kicked 12 yards from the goal and lands 48 yards from the goal, hence, the roots are given as follows:
x = 12, x = 48.
Thus the function is defined as follows:
y = a(x - 12)(x - 48)
y = a(x² - 60x + 576).
The x-coordinate of the vertex is given at the mean of the roots, hence:
x = (12 + 48)/2 = 30.
The maximum height means that when x = 30, y = 17, hence the leading coefficient a is obtained as follows:
17 = a(30² - 60 x 30 + 576)
a = 17/(30² - 60 x 30 + 576)
a = -0.05
Hence the equation is:
y = -0.05(x² - 60x + 576).
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1. Solve the differential equation by variation of parameters. y'' y = sin^2(x) y(x) = _______2. The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population p_0, has doubled in 4 years, how long will it take to triple? (Round your answer to one decimal place.) _____ yrHow long will it take to quadruple? (Round your answer to one decimal place.)_____ yr
Refer to the attached images. Comment any questions you may have.
Homework, 17.3-using proportional relationships
Solve for X
Step-by-step explanation:
5x/20 = 45/36
x/4=5/4
x=5×4/4
x=5
hope it helps
determine the number of years it will take to recoup the extra cost of buying the prius. format as a number to 2 decimal places.
It will take 5 years to recoup the extra cost of buying the Prius.
The number of years it will take to recoup the extra cost of buying the Prius will depend on several factors such as the price of the car, the cost of gas, and the average number of miles driven per year. However, according to a study by Consumer Reports, the Prius has an average payback period of about 4 years compared to a similar gas-powered vehicle. This means that if the extra cost of buying the Prius is $4,000, for example, it would take about 4 years to recoup that cost through fuel savings. Keep in mind that this is just an estimate and individual results may vary.
To determine the number of years it will take to recoup the extra cost of buying the Prius, follow these steps:
1. Identify the extra cost of buying the Prius compared to a similar non-hybrid vehicle.
2. Determine the annual fuel cost savings of the Prius compared to the non-hybrid vehicle.
3. Divide the extra cost by the annual fuel cost savings.
For example, let's say the extra cost of buying the Prius is $5,000 and the annual fuel cost savings is $1,000.
Number of years to recoup extra cost = Extra cost / Annual fuel cost savings
Number of years = $5,000 / $1,000
Number of years = 5.00
So, it will take 5.00 years to recoup the extra cost of buying the Prius.
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A tablecloth has a circumference of 220 inches. What is the radius of the tablecloth? Round to the nearest hundredth.
Answer:
35.03 inches
Step-by-step explanation:
We Know
A tablecloth has a circumference of 220 inches.
Circumference of circle = 2 · r · π
C = 220 inches
π = 3.14
What is the radius of the tablecloth?
We Take
220 = 2 · r · 3.14
110 = r · 3.14
r ≈ 35.03 inches
So, the radius of the tablecloth is about 35.03 inches.
Suppose a curve is traced by the parametric equations x=2(sin(t)+cos(t)) y=36−10cos2(t)−20sin(t) as t runs from 0 to π . At what point (x,y) on this curve is the tangent line horizontal?
The two points on the curve where the tangent line is horizontal are (2,26) and (-2,26).
To find where the tangent line is horizontal, we need to find where the derivative of y with respect to x (dy/dx) equals 0.
First, we need to express y in terms of x. We can do this by eliminating t from the two parametric equations.
From x=2(sin(t)+cos(t)), we get sin(t) = (x/2) - cos(t).
From y=36−10cos2(t)−20sin(t), we substitute sin(t) with the above expression and get:
y = 36 - 10cos²(t) - 20((x/2) - cos(t))
Simplifying this expression, we get:
y = -10cos²(t) - 10x + 36
Next, we need to find the derivative of y with respect to x:
dy/dx = -10sin(2t)/(dx/dt)
From x=2(sin(t)+cos(t)), we get dx/dt = 2(cos(t)-sin(t))
Substituting this into the above equation for dy/dx, we get:
dy/dx = -5sin(2t)/(cos(t)-sin(t))
Setting dy/dx equal to 0, we get:
0 = -5sin(2t)/(cos(t)-sin(t))
This means sin(2t) = 0, or t = 0 or t = π/2.
Plugging these values into the parametric equations for x and y, we get:
When t=0: x = 2, y = 26
When t=π/2: x = -2, y = 26
Thus, the two points on the curve where the tangent line is horizontal are (2,26) and (-2,26).
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