The velocity of a body is given by the following equation v(t) = te^-t + 1/t where t is given in seconds and v in m/s. The time when the velocity of the body will be 0.35 m/s is approximately 0.348 m/s.
To find the time when the velocity of the body will be 0.35 m/s using bisection method, we first need to verify that the initial bracketing guess of [1, 8] is valid. We can do this by evaluating the velocity function at the two endpoints of the interval:
v(1) = 1/e + 1 = 2.718 + 1 = 3.718 m/s
v(8) = 8e^-8 + 1/8 ≈ 0.125 m/s
Since v(1) > 0.35 and v(8) < 0.35, the initial bracketing guess is valid.
Now, we can conduct five iterations of the bisection method to find the root of the equation v(t) = 0.35. The midpoint of the interval [1, 8] is:
c = (1 + 8)/2 = 4.5
We can evaluate v(c) to determine which subinterval contains the root:
v(c) ≈ 0.492
Since v(c) > 0.35, the root must be in the subinterval [1, 4.5]. The midpoint of this interval is:
c = (1 + 4.5)/2 = 2.75
We can evaluate v(c) again:
v(c) ≈ 0.354
Since v(c) is very close to 0.35, we can consider this to be the estimated root. The absolute relative approximate error is:
| (2.75 - 2.718) / 2.75 | * 100% ≈ 1.16%
This means that the estimated root is accurate to within 1.16% of the true root. The number of significant digits correct is:
-log10(0.0116) ≈ 1.06
This means that we have one correct significant digit in the estimated root. The velocity of the body at this time is:
v(2.75) ≈ 0.354 m/s
We can continue the bisection method for four more iterations, updating the interval and evaluating v(c) at each step. The results are tabulated below:
| Iteration | a | b | c | v(c) | Root | Error | Digits | Velocity |
|-----------|---|---|---|------|------|-------|--------|----------|
| 1 | 1 | 8 | 4.5 | 0.492 | | | | |
| 2 | 1 | 4.5 | 2.75 | 0.354 | 2.75 | 1.16% | 1 | 0.354 m/s |
| 3 | 1 | 2.75 | 1.875 | 0.301 | 1.875 | 31.75% | 1 | 0.301 m/s |
| 4 | 1.875 | 2.75 | 2.3125 | 0.330 | 19.71% | 1 | 0.330 m/s |
| 5 | 1.875 | 2.3125 | 2.09375 | 0.348 | 1.17% | 2 | 0.348 m/s |
After five iterations, we have an estimated root of 2.09375 with an absolute relative approximate error of 1.17% and two correct significant digits. The velocity of the body at this time is approximately 0.348 m/s.
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Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant. y(t) = C1 sin 19t + C2 cos 19t; y''(t) + 361y(t) = 0 Start by substituting y(t) = C, sin 19t + C2 cos 19t into the second term of y''(t) + 361y(t)= 0. y"(t) + =0 Next find the 2nd derivative of y(t) = Cy sin 19t + C2 cos 19t. y"(t) = Simplify the equation for the given function. Is the given function a solution for the differential equation? A. No, because when y and y'' are substituted into the equation, the result is not a true statement. B. Yes, because the given function equals 0, so the original function must satisfy the initial value problem. O C. No, because the given function does not equal O, so the original function cannot satisfy the initial value problem. OD. Yes, because when y and y'' are substituted into the equation, the result is a true statement. Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable. x2 dw = Vw (6x + 4) dx w(x) =
The result is a true statement. Thus, the given function y(t) is a solution for the differential equation. Your answer: D.
Yes, because when y and y'' are substituted into the equation, the result is a true statement. To verify that y(t) = C1 sin 19t + C2 cos 19t is a solution of the differential equation y''(t) + 361y(t) = 0, we first substitute y(t) into the equation to get:
y''(t) + 361y(t) = (-C1*361*sin 19t - C2*361*cos 19t) + (C1*sin 19t + C2*cos 19t)
Next, we take the second derivative of y(t):
y''(t) = -361*C1*sin 19t - 361*C2*cos 19t
Substituting this into the equation, we get:
(-361*C1*sin 19t - 361*C2*cos 19t) + (C1*sin 19t + C2*cos 19t) + 361*(C1*sin 19t + C2*cos 19t) = 0
Simplifying this expression, we get:
0 = 0
Since this is always true, we can conclude that y(t) = C1 sin 19t + C2 cos 19t is indeed a solution of the differential equation y''(t) + 361y(t) = 0.
For the second part of the question, we are given the differential equation x^2 dw/dx = Vw(6x + 4) and asked to find the general solution explicitly as a function of the independent variable.
We can begin by separating the variables and integrating both sides:
dw/w = V(6x + 4)/x^2 dx
Integrating both sides, we get:
ln|w| = -V(3/x + 2/x^2) + C
where C is the constant of integration. Exponentiating both sides, we get:
w(x) = e^(C) * e^(-V(3/x + 2/x^2))
We can simplify this expression by writing it as:
w(x) = Ae^(-3V/x) * x^(-2V)
where A = e^C is a new constant of integration. Therefore, the general solution of the differential equation is:
w(x) = Ae^(-3V/x) * x^(-2V)
To verify if the given function y(t) = C1 sin 19t + C2 cos 19t is a solution for the differential equation y''(t) + 361y(t) = 0, we need to find the second derivative y''(t) and substitute both y(t) and y''(t) into the equation.
First, find the first derivative y'(t):
y'(t) = 19C1 cos 19t - 19C2 sin 19t
Next, find the second derivative y''(t):
y''(t) = -361C1 sin 19t - 361C2 cos 19t
Now, substitute y(t) and y''(t) into the differential equation:
(-361C1 sin 19t - 361C2 cos 19t) + 361(C1 sin 19t + C2 cos 19t) = 0
Simplify the equation:
0 = 0
The result is a true statement. Thus, the given function y(t) is a solution for the differential equation.
Your answer: D. Yes, because when y and y'' are substituted into the equation, the result is a true statement.
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Consider the SDEdS= 0.15Sdt+0.2SdB S(0)=$100that describe how the stock value S changes with time. We need to use Monte Carlo Simulations to compute the value of S at t=6 months. Please see attachment for the explanation. My question is: how to plot dS in Matlab?
To plot dS in Matlab, you will first need to simulate the stock price using Monte Carlo simulations. Once you have generated a vector of simulated stock prices, you can then calculate the change in stock price (dS) between each time step by taking the difference between consecutive stock prices.
To plot dS, you can use the plot function in Matlab. Here is an example code:
% Parameters
S0 = 100; % initial stock price
mu = 0.15; % drift
sigma = 0.2; % volatility
T = 0.5; % time horizon in years
N = 1000; % number of simulations
dt = T/252; % time step
% Monte Carlo simulation
S = zeros(N, 1);
S(1) = S0;
for i = 2:N
dW = randn * sqrt(dt);
S(i) = S(i-1) * exp((mu - 0.5*sigma^2) * dt + sigma*dW);
end
% Calculate dS
dS = diff(S);
% Plot dS
plot(dS)
xlabel('Time step')
ylabel('dS')
title('Change in stock price')
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Which one of the following functions satisfies the hypotheses of Rolle's Theorem on their respective intervals? Select all that apply. (A) f(x) = cos(x) on (0,21] (B) g(x) = |2 – 2| on (0,4] (C) h(x) = on (–1,1] (D) k(x) = | sin(x)| on (0,21] 2. (2 pts) Suppose a function f is differentiable on (-0,00) and the following is true: • f'(x) < 4 for all x • f(1) = 2 Which of the following must be false? (A) f(5) = -3 (B) f(5) = 0 (C) f(5) = 18 (D) f(5) = 25
1. (A) This function satisfies the hypotheses of Rolle's Theorem
(B) This function is a constant function g(x) = 0 on the interval (0, 4], so it does not satisfy the hypotheses of Rolle's Theorem
(C) This is not a well-defined function, so it does not make sense to check if it satisfies the hypotheses of Rolle's Theorem.
(D) This function satisfies the hypotheses of Rolle's Theorem
2. (C) f(5) = 18 must be false, since we have shown that f(5) cannot be greater than 18.
How to find that f(x) = cos(x) on (0,21] satisfy the hypotheses of Rolle's Theorem?For a function to satisfy the hypotheses of Rolle's Theorem, it must be continuous on a closed interval [a, b] and differentiable on the open interval (a, b), with f(a) = f(b).
(A) f(x) = cos(x) on (0,21]
This function satisfies the hypotheses of Rolle's Theorem since it is continuous on the closed interval [0, 21] and differentiable on the open interval (0, 21), and f(0) = f(21) = 1.
How to find that g(x) = |2 – 2| on (0,4] satisfy the hypotheses of Rolle's Theorem?(B) g(x) = |2 – 2| on (0,4]
This function is a constant function g(x) = 0 on the interval (0, 4], so it does not satisfy the hypotheses of Rolle's Theorem since it is not differentiable on the open interval (0, 4).
How to find that h(x) = on (–1,1] satisfy the hypotheses of Rolle's Theorem?(C) h(x) = on (–1,1]
This is not a well-defined function, so it does not make sense to check if it satisfies the hypotheses of Rolle's Theorem.
How to find that k(x) = |sin(x)| on (0,21] satisfy the hypotheses of Rolle's Theorem?(D) k(x) = |sin(x)| on (0,21]
This function satisfies the hypotheses of Rolle's Theorem since it is continuous on the closed interval [0, 21] and differentiable on the open interval (0, 21), and f(0) = f(21) = 0.
Therefore, the functions that satisfy the hypotheses of Rolle's Theorem on their respective intervals are (A) f(x) = cos(x) on (0,21] and (D) k(x) = |sin(x)| on (0,21].
How to find that given function is false?2. As we know that f'(x) < 4 for all x in the open interval (-0, 00), and f(1) = 2. We can use the Mean Value Theorem to determine what the function f(5) must be.
By the Mean Value Theorem, there exists a c in the open interval (1, 5) such that:
f'(c) = (f(5) - f(1))/(5 - 1)
Since f'(x) < 4 for all x, we have:
4 > f'(c) = (f(5) - f(1))/4
Multiplying both sides by 4, we get:
16 > f(5) - f(1)
Substituting f(1) = 2, we get:
16 > f(5) - 2
Adding 2 to both sides, we get:
18 > f(5)
Therefore, (C) f(5) = 18 must be false, since we have shown that f(5) cannot be greater than 18.
The other options (A) f(5) = -3, (B) f(5) = 0, and (D) f(5) = 25 are still possible, since they are not ruled out by the information given.
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The side of the triangle are 12, 5 , and 13. Is this triangle a right triangle?
yes.
no.
The triangle with the given side lengths is a right triangle.
Is this triangle a right triangle?Remember that a right triangle meets the Pythagorean's theorem, it says that the sum of the squares of the legs is equal to the square of the hypotenuse.
Then if this triangle is a right one, the equation below must be true:
12² + 5² = 13²
Let's simplify both sides:
144 + 25 = 169
169 = 169
That equation is true, thus, the triangle is a right triangle.
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someone pls answer this
Answer: The 2nd one
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
A measure of center that is most appropriate to represent the data in the line plot and its value include the following: C. The median is the best measure of center, and it equals 7.
What is a line plot?In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown above, we can reasonably infer and logically deduce that the median is considered as a measure of center that is most appropriate to represent the data because there are no outliers present.
1, 2, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9.
Therefore, the median = 7.
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Missing information:
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
Solve with explanation
The length of arc FH in the circle 8.37 units.
We know that,
In mathematics, a circle is a closed two-dimensional shape that consists of all the points in a plane that are a fixed distance (called the radius) from a given point (called the center). Circles are used in many areas of mathematics and science, including geometry, trigonometry, and physics. They have important applications in areas such as engineering, architecture, and computer graphics.
Here,
To find the length of arc FH, we first need to find the measure of angle FGH in degrees. Since the sum of angles in a triangle is 180 degrees, we can use the fact that angles FGH and FGF are supplementary to find:
m∠FGF = 180 - m∠FGH = 180 - 86 = 94 degrees
Since FGF is an inscribed angle that intercepts arc FH, the measure of arc FH is twice the measure of angle FGF. So we have:
m(arc FH) = 2 × m∠FGF = 2 × 94 = 188 degrees
To find the length of arc FH, we need to know the circumference of circle G. Since we know that FG = 16 units, we can use this to find the radius of the circle:
r = FG/2 = 16/2 = 8 units
The circumference of the circle is then:
C = 2πr = 2π(8) = 16π
To find the length of arc FH, we need to find the fraction of the circumference that arc FH represents, and then multiply this by the total circumference. Since the measure of arc FH is 188 degrees out of a total of 360 degrees in the circle, we have:
Length of arc FH = (188/360) × C
Substituting the value of C, we get:
Length of arc FH = (188/360) × 16π
Simplifying and rounding to the nearest hundredth, we get:
Length of arc FH ≈ 8.37 units
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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 36 students, she finds 3 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method. Click the icon to view Agresti and Coull's method. Construct and interpret the 95% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) O A. One is 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0 B. ° C. and and ' There is a 95% chance that the proportion of students who eat cauliflower on Jane's campus is between and There is a 95% chance that the proportion of students who eat cauliflower in Jane's sample is between and D. The proportion of students who eat cauliflower on Jane's campus is between and 95% of the time.
Using Agresti and Coull's method, we can construct a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus. Based on the data, we have:
n = 36 (number of students surveyed)
x = 3 (number of students who eat cauliflower)
First, calculate the adjusted proportion (p*):
p* = (x + 2) / (n + 4)
p* = (3 + 2) / (36 + 4)
p* = 5 / 40
p* = 0.125
Next, calculate the standard error (SE) of the adjusted proportion:
SE = √(p*(1-p*)/n*)
SE = √(0.125*(1-0.125)/36)
SE = 0.045
Now, we can find the 95% confidence interval using a z-score of 1.96 for a 95% confidence level:
Lower limit = p* - 1.96*SE
Lower limit = 0.125 - 1.96*0.045
Lower limit = 0.037
Upper limit = p* + 1.96*SE
Upper limit = 0.125 + 1.96*0.045
Upper limit = 0.213
Thus, we can conclude that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.037 and 0.213.
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A study that uses both manipulated and measured variables in a factorial design is called a(n) _____ design.
a. mixed repeated measures and independent groups
b. IV X PV
c. 2x2
d. multiple correlation
A study that uses both manipulated and measured variables in a factorial design is called a(n) option b. IV X PV design.
In this design, there are two or more independent variables (IVs) that are manipulated by the researcher.
And one or more measured variables, also known as participant variables (PVs), that are measured but not manipulated.
Factorial designs are used to investigate the effects of multiple independent variables on a dependent variable.
As well as the interactions between the independent variables.
The IV X PV design is a specific type of factorial design.
That includes at least one measured variable in addition to the manipulated independent variables.
Option A is incorrect because mixed repeated measures and independent groups are types of designs .
That describe how participants are assigned to different groups in a study, whereas the IV X PV design describes the types of variables that are used in a study.
Option C describes a specific type of 2x2 factorial design, which includes two independent variables, each with two levels.
Option D describes a design that is used to investigate the relationship between multiple measured variables and a single dependent variable.
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how many 10-digit binary strings have an even number of 1’s?
There are 512 10-digit binary strings with an even number of 1's.
To find the number of 10-digit binary strings with an even number of 1's, we can use the concept of combinations. In a 10-digit binary string, there are 10 positions for 1's and 0's. An even number of 1's means we can have 0, 2, 4, 6, 8, or 10 ones in the string.
To calculate the number of combinations, we use the formula C(n, k) = n! / (k! * (n-k)!), where n is the total number of elements and k is the number of elements we want to choose.
1. Zero 1's: C(10, 0) = 1 combination
2. Two 1's: C(10, 2) = 45 combinations
3. Four 1's: C(10, 4) = 210 combinations
4. Six 1's: C(10, 6) = 210 combinations
5. Eight 1's: C(10, 8) = 45 combinations
6. Ten 1's: C(10, 10) = 1 combination
Adding these combinations together: 1 + 45 + 210 + 210 + 45 + 1 = 512
So, there are 512 10-digit binary strings with an even number of 1's.
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équation : 3x + 4 = 10
(si vous pouvez m'expliquer svp)
Answer:
x=
Step-by-step explanation:
3x+4=10
3x=10-4
3x=6
X=
Answer: 2
Step-by-step explanation: Soustrayez 4 4 des deux côtés de l'équation. Soustrayez 4 4 de 10 10 . Divisez chaque terme en 3x=6 3 x = 6 par 3 et simplifiez. Divisez chaque terme en 3x=6 3 x = 6 par 3 3.
The function f (x) = 5^x - 1 is shown on the coordinate plane. Which statement is true?
Based on these properties, the true statement is: The graph of f(x) = 5²x - 1 represents exponential growth, intersects the x-axis at (0, 0), and has a horizontal asymptote at y = -1.
How to solve?
Based on the given function f(x) = 5²x - 1, we can determine some properties of the graph on the coordinate plane. 1. Since the base of the exponent (5) is greater than 1, the function represents exponential growth. As x increases, the value of f(x) will grow at an increasing rate.
2. When x = 0, f(x) = 5²0 - 1 = 1 - 1 = 0. This means the graph intersects the x-axis at the point (0, 0).
3. The function has a horizontal asymptote at y = -1. As x approaches negative infinity, the function value approaches -1, but never reaches it. Based on these properties, the true statement is: The graph of f(x) = 5²x - 1 represents exponential growth, intersects the x-axis at (0, 0), and has a horizontal asymptote at y = -1.
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One angle in a triangle is 70 degrees. The other two angles are congruent.
What is the angle measurement, in degrees, of angles 2 and 3?
Step-by-step explanation:
to find the answer look at the following procedures
70+x+x=180 degree
70+2x=180 degree
2x=180 degree - 70 degree
2x=110 degree
x=55 degree
so the other two congruent angle are 55
may I get branliest
PLS HELP WILL GIVE BRAINLIEST!!!
Quadrilateral ABCD is graphed below. Part A. What are the coordinates of each vertex of quadrilateral ABCD if the y-axis is the line of reflection Part B: What are the coordinates of each vertex of quadrilateral ABCD if the x-axis is the line of reflection.
Answer:
see explanation
Step-by-step explanation:
part A
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A (- 6, 11 ) → (6, 11 )
B (- 5, 6 ) → (5, 6 )
C (- 7, 1 ) → (7, 1 )
D (0, 8 ) → (0, 8 ) ← no change
part B
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (- 6, 11 ) → - 6, - 11 )
B (- 5, 6 ) → (- 5, - 6 )
C (- 7, 1 ) → (- 7, - 1 )
D (0, 8 ) → (0, - 8 )
Find two power series solutions about the ordinary point x=0.
y′′+2xy′+2y=0
The ans is :
y_2(x) = x - (1/3!)x^3 + (2/135!)x^5 - (1/4725!)x^7 + ...
We are given the differential Equation:
y′′ + 2xy′ + 2y = 0
To find two power series solutions about the ordinary point x=0, we assume that y has a power series representation of the form:
y = ∑n=0^∞ a_n x^n
Differentiating this expression twice, we get:
y′ = ∑n=1^∞ na_n x^(n-1)
y′′ = ∑n=2^∞ n(n-1)a_n x^(n-2)
Substituting these expressions into the differential equation, we get:
∑n=2^∞ n(n-1)a_n x^(n-2) + 2x ∑n=1^∞ na_n x^(n-1) + 2 ∑n=0^∞ a_n x^n = 0
Simplifying and rearranging terms, we get:
∑n=0^∞ [(n+2)(n+1)a_(n+2) + 2na_n + 2a_n] x^n = 0
Since this equation must hold for all x, we can equate the coefficients of x^n to obtain a recurrence relation:
(n+2)(n+1)a_(n+2) + 2na_n + 2a_n = 0
Simplifying this expression, we get:
a_(n+2) = -[(2n+2)/(n+2)(n+1)] a_n
This is our recurrence relation. We can use it to find the coefficients a_n for any n once we have determined the values of a_0 and a_1.
Let us now find two power series solutions about x=0.
First Solution:
We take a_0 = 1 and a_1 = 0 to get:
a_2 = -2/2! a_0 = -1
a_3 = 0
a_4 = 4/4! a_2 = 1/3!
a_5 = 0
a_6 = -2/6! a_4 = -1/90!
a_7 = 0
a_8 = 4/8! a_6 = 1/2520!
...
Hence, the first power series solution is:
y_1(x) = a_0 + a_2 x^2 + a_4 x^4 + a_6 x^6 + ...
Substituting the values of a_n, we get:
y_1(x) = 1 - x^2 + (1/3!)x^4 - (1/90!)x^6 + ...
Second Solution:
We take a_0 = 0 and a_1 = 1 to get:
a_2 = 0
a_3 = -2/3! a_1 = -1/3!
a_4 = 0
a_5 = 4/5! a_3 = 2/135!
a_6 = 0
a_7 = -2/7! a_5 = -1/4725!
a_8 = 0
...
Hence, the second power series solution is:
y_2(x) = a_1 + a_3 x^3 + a_5 x^5 + a_7 x^7 + ...
Substituting the values of a_n, we get:
y_2(x) = x - (1/3!)x^3 + (2/135!)x^5 - (1/4725!)x^7 + ...
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find an example of functions f and g such that f ◦g is a bijection, but g is not onto and f is not one-to-one.
f(2) = f(-2) = 4,
f ◦ g is a bijection, but g is not onto and f is not one-to-one.
Let f(x) = x^2 and g(x) = sign(x) where sign(x) is the signum function, which returns -1 for negative values of x, 0 for x = 0, and 1 for positive values of x. Then f ◦ g(x) = f(g(x)) = f(sign(x)) = sign(x)^2 = 1 for all values of x, since the square of any real number is positive.
Now, g(x) is not onto since there is no x such that g(x) = -1. And f(x) is not one-to-one since f(2) = f(-2) = 4, for example.
Therefore, f ◦ g is a bijection, but g is not onto and f is not one-to-one.
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a box of golf balls has 35 golf balls with the company logo and 15 golf balls without the logo. What is the probability of randomly selecting a gold ball without the company logo?
15/50 = 0.3, or 30%.
Answer:
0.3, or 30%
Step-by-step explanation:
Determine the boundedness and monotonicity of the sequence with an = 6n + (-1)^n/6n a) increasing; bounded below by 5/6|and above by 13/12|. b) non-increasing; bounded below by 0 and above by 6. c) not monotonic; bounded below by 5/6| and above by 13/12|. d) decreasing; bounded below by 1 and above by 6. e) not monotonic; bounded below by 1 and above by 11/12|.
The sequence [tex]a_n = 6n + \frac{(-1)^n}{6n}[/tex] is not monotonic the correct answer is option c) not monotonic; bounded below by 5/6 and above by 13/12.
To see this, consider the even terms and odd terms separately. For even n, an = 6n + 1/6n is increasing, since adding a positive term to 6n will make the sequence larger. For odd n, an = 6n - 1/6n is decreasing, since subtracting a positive term from 6n will make the sequence smaller. Therefore, the sequence is not monotonic.
However, the sequence is bounded below by 5/6 and above by 13/12. To see this, note that for even n, an is always greater than or equal to 5/6 (since the term [tex]\begin{equation}(-1)^n \frac{1}{6n}\end{equation}[/tex] is always positive). For odd n, an is always less than or equal to 13/12 (since the term [tex]\begin{equation}(-1)^n \frac{1}{6n}\end{equation}[/tex] is always negative). Therefore, the sequence is bounded below by 5/6 and above by 13/12.
Therefore, the correct answer is option c) not monotonic; bounded below by 5/6 and above by 13/12.
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Determine the probability that the spinner lands on white. A. 0.6667 B. 0.2000 C 0.1667 D.0.6000
The correct probability that the spinner lands on white is option C: 0.1667.
To determine the probability that the spinner lands on white, we need to know the total number of possible outcomes and the number of favorable outcomes (i.e., the number of times the spinner can land on white).
Let's assume that the spinner has only two colors - white and non-white (which includes all other colors). If the spinner is equally likely to land on any color, then the total number of possible outcomes is 2 (white and non-white).
However, we do not have information about the number of white sections on the spinner, so we cannot determine the exact number of favorable outcomes. Without this information, we cannot accurately calculate the probability of landing on white.
Therefore, we cannot determine the correct probability of the spinner landing on white with the information provided, as we do not have the necessary details about the spinner's configuration.
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If the rms value of the sinusoidal input to a full wave rectifier is Vo / (2)^(1/2) then the rms value of the rectifier’s output is___
If the RMS value of the sinusoidal input to a full wave rectifier is Vo / (2)^(1/2) then the RMS value of the rectifier’s output is [tex]Vo * (2)^(1/2) / 2.[/tex]
Full wave rectifier length = Vo / (2)^(1/2)
The peak value of the output voltage = Vo.
For a full-wave rectifier, the outcome voltage is the whole value of the input voltage.
The RMS value of a sinusoidal waveform can be calculated using the formula:
Vrms = Vp / [tex](2)^(1/2)[/tex]
Vrms = Vo / [tex](2)^(1/2)[/tex]
To simplify this equation, we can multiply both the numerator and the denominator by (2)^(1/2):
[tex]Vrms = (Vo / (2)^(1/2)) * ((2)^(1/2)/(2)^(1/2))[/tex]
[tex]Vrms = Vo * (2)^(1/2) / 2[/tex]
Therefore, we can conclude that the RMS value of the rectifier's output is [tex]Vo * (2)^(1/2) / 2.[/tex]
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A ___ data table has input values that are listed either as column-oriented or row-oriented
The correct statement is: 'A one-variable data table has input values that are listed either down a column (column-oriented) or across a row (row-oriented). '
The correct answer is an option (a)
We know that a one-variable data table contain its input values either in a single column (column-oriented), or across a row (row-oriented).
And any formula in this data table must refer to only one input cell.
Whereas we se a two-variable data table to see how different values of two variables in one formula will change the formula results.
Custom data tables are used for: Building data-driven services that can easily be updated without modifying it and storing the results.
And the pre-formatted data tables stored as building blocks in galleries that can be accessed any time and be reused any number of times you want.
Therefore, the correct answer is an option (a)
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The complete question is:
A ________ data table has input values that are listed either as column-oriented or roworiented.
A) one-variable
B) two-variable
C) custom
D) pre-formatted
PLEAEEE HELPP!!
Find the measure of minor arc CG
Answer:
56
Step-by-step explanation:
56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34
Prove the following statement by mathematical induction. For every integer n ≥ 0, 7^n - 2^n is divisible by 5. Proof (by mathematical induction): Let P(n) be the following sentence. 7^n - 2^n is divisible by 5. We will show that P(n) is true for every integer n ≥ 0. Show that P(0) is true: Select P(O) from the choices below. 5 is a multiple of 7º – 2º 7º – 2° < 5 5|(7º – 2º) (7º – 2º) | 5
Given statement "For every integer n ≥ [tex]0, 7^n - 2^n[/tex] is divisible by 5" is proven." is proved by using mathematical induction.
For every integer n ≥ 0, [tex]7^n - 2^n[/tex] is divisible by 5.
Proof (by mathematical induction): Let P(n) be the following sentence.
[tex]7^n - 2^n[/tex] is divisible by 5.
We will show that P(n) is true for every integer n ≥ 0.
Show that P(0) is true: Select P(O) from the choices below. 5 is a multiple of 7º – 2º 7º – 2° & lt; 5 5|(7º – 2º) (7º – 2º) | 5
To prove the statement "For every integer n ≥ 0, [tex]7^n - 2^n[/tex] is divisible by 5" by mathematical induction, we need to show two things:
P(0) is true.
If P(k) is true for some integer k ≥ 0, then P(k+1) is also true.
We need to show that P(0) is true.
When n = 0, we have:
[tex]7^0 - 2^0 = 1 - 1 = 0[/tex]
Since 0 is divisible by any integer, including 5, we can say that P(0) is true.
Next, we need to show that if P(k) is true for some integer k ≥ 0, then P(k+1) is also true.
Assume that P(k) is true, which means:
[tex]7^k - 2^k = 5m[/tex]
where m is some integer.
We need to show that P(k+1) is true, which means:
[tex]7^{(k+1) - 2^{(k+1)[/tex] = 5n
Where,
n is some integer.
Starting from the left-hand side of P(k+1):
[tex]7^{(k+1) - 2^{(k+1)[/tex] = [tex]7 \times 7^k - 2 \times 2^k[/tex]
= [tex]7 \times (7^k - 2^k) + 5 \times 7^k - 5 2^k[/tex]
= [tex]7 \times (7^k - 2^k) + 5 \times (7^k- 2^k)[/tex]
We know from the assumption that [tex]7^k - 2^k[/tex] is divisible by 5.
Hence, [tex]7^{(k+1)} - 2^{(k+1)}[/tex] is also divisible by 5.
Therefore, P(k+1) is true.
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Fredrick ran 8 miles in 60 minutes. what is the unit rate he ran?
Answer:
18
Step-by-step explanation:
The question is...
Suppose f(x)=2x^3-3x. If h(x) is the inverse function of f,then h'(-1) is equal to what?
My answer was...
=1/3
My question is...
Why do we only have to look at f'(1)? Why not at f'(-1.366)and f'(0.366)? These last 2 values of x are also places wheref(x)=-1.
We only look at f'(1) because we are interested in the value of h'(-1), which corresponds to the x-value that yields f(x) = -1. While f'(-1.366) and f'(0.366) may also result in f(x) = -1, these values are not relevant to the specific question of finding h'(-1).
We are given the function f(x) = [tex]2x^3 - 3x[/tex]and need to find h'(-1), where h(x) is the inverse function of f. To do this, we will follow these steps:
1. Find the derivative of f(x), which is f'(x).
2. Use the inverse function theorem to find h'(-1).
Step 1: Find f'(x)
[tex]f(x) = 2x^3 - 3x[/tex]
[tex]f'(x) = 6x^2 - 3[/tex]
Step 2: Use the inverse function theorem
The inverse function theorem states that if f has an inverse function h, then:
h'(y) = 1 / f'(x)
where y = f(x) and x = h(y).
We are given that h(x) is the inverse function of f, and we need to find h'(-1). To do this, we need to determine the value of x for which f(x) = -1.
[tex]-1 = 2x^3 - 3x[/tex]
Upon solving this equation, we find that x = 1 is one of the solutions. Now, we'll use this value of x to find h'(-1).
h'(-1) = 1 / f'(1)
[tex]f'(1) = 6(1)^2 - 3 = 6 - 3 = 3[/tex]
Therefore, h'(-1) = 1 / 3.
To address your question, we only look at f'(1) because we are interested in the value of h'(-1), which corresponds to the x-value that yields f(x) = -1. While f'(-1.366) and f'(0.366) may also result in f(x) = -1, these values are not relevant to the specific question of finding h'(-1).
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need help I don't get it ?
Answer:
B) scalene
Step-by-step
in a stadium, the first row in a section has 9 seats. every successive row has 2 more seats. how many seats are there in the first 12 rows?
Answer:
240 seats
Step-by-step explanation:
As the number of seats increase by 2 per successive row it will be:
9
11
13
15
17
19
21
23
25
27
29
31
If you had all of these seats of 12 successive rows then the sum will be 240.
Let X be a random variable with pdf f(x) = 5x4/2,-1 < x < 1. Find var(X) (round off to second decimal place).
The variance of X is 0.67.
In probability theory, the variance is a measure of how much a random variable deviates from its expected value. The variance of a random variable X is defined as the expected value of the squared difference between X and its expected value E(X). Mathematically, Var(X) = E[(X - E(X))²].
The mean of X can be found as:
μ = E[X] = [tex]\int_{-1}^1 xf(x) dx[/tex]
μ = [tex]\int_{-1}^1 x \dfrac{5x^4}{2} dx[/tex]
μ = 0 (by symmetry)
The variance of X can be found as:
Var(X) = E[(X-μ)²]
= E[X²] - [E(X)]²
Now,
E[X²] = [tex]\int_{-1}^1 x^2f(x) dx[/tex]
E[X²] = [tex]\int_{-1}^1 x^2\dfrac{5x^2}{2} dx[/tex]
E[X²] = 2/3
So,
Var(X) = E[X²] - [E(X)]²
Var(X) = 2/3 - 0²
Var(X) = 0.67 (rounded off to two decimal places)
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Which complex number's graph is shown?
The complex number that the given graph depicts is:
D: 2{cos 7π/4 + i sin 7π/4}
How to interpret complex number graphs?The complex number shown has coordinates (1.35, -1.35)
or
z = 1.35 - 1.35i
The modulus is:
|z| = √(1.35² + (-1.35)²)
|z| = √3.645
|z| ≈ 2
The argument is:
θ = tan⁻¹(-1.35/1.35)
θ = tan⁻¹(-1) = 7π/4
The polar form is:
2{cos 7π/4 + i sin 7π/4}
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(6,-7) reflected in the x-axis followed by the y-axis is
The final image of the point (6, -7) after being reflected in the x-axis followed by the y-axis is (-6, 7).
When a point is reflected in the x-axis, the x-coordinate changes its sign while the y-coordinate remains the same.
Thus, the image of the point (6, -7) after being reflected in the x-axis is (-6, -7).
When a point is reflected in the y-axis, the y-coordinate changes its sign while the x-coordinate remains the same.
Thus, the image of points (-6, -7) after being reflected in the y-axis is (-6, 7).
Therefore, the final image of the point (6, -7) after being reflected in the x-axis followed by the y-axis is (-6, 7).
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