The probability distribution of X is as follows:P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31.
Given function: f(x)={0x<10.51≤x<313≤xTo verify that the given function is a cumulative distribution function, we have to check the following conditions:1. f(x) is non-negative for all x.2. f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1. Now, let's verify these conditions one by one.1. f(x) is non-negative for all x. This condition is satisfied, as the given function f(x) is defined only for x ≥ 1, and is non-negative for all x in this domain. Therefore, f(x) is non-negative for all x.2. f(x) is continuous from the right for all x. This condition is also satisfied, as the given function f(x) is defined piecewise as a continuous function for all x. Therefore, f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x. This condition is satisfied, as the given function f(x) is non-decreasing for all x in its domain.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1.
Using the definition of f(x) for x < 10, we have f(x) = 0 for x < 10. Therefore, lim{x → -∞} f(x) = 0. Using the definition of f(x) for x ≥ 31, we have f(x) = 1 for x ≥ 31. Therefore, lim{x → ∞} f(x) = 1. Hence, all four conditions are satisfied. Therefore, the given function is a cumulative distribution function. To find the probabilities of the intervals, we use the formula: P(a ≤ X ≤ b) = F(b) - F(a)where P(a ≤ X ≤ b) is the probability that X lies between a and b, and F(x) is the cumulative distribution function of X. Furthermore, the probability of the interval (a, b] is: P(a < X ≤ b) = F(b) - F(a)Therefore, the probabilities of the intervals are: P(1 < X ≤ 10.5) = F(10.5) - F(1) = 0 - 0 = 0P(10.5 < X ≤ 31) = F(31) - F(10.5) = 1 - 0 = 1P(X > 31) = F(∞) - F(31) = 1 - 1 = 0Therefore, we have: P(1 < X ≤ 10.5) = 0P(10.5 < X ≤ 31) = 1P(X > 31) = 0
Hence, the probability distribution of X is as follows: P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31. Therefore, the given function is a cumulative distribution function, and the probability distribution of X is as above.
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Isaiah is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
What is the surface area of the box, in square meters, that
Isaiah decorates
Answer:
389.19 m²
Step-by-step explanation:
The surface area of the box = area of the two equal triangles + area of the 3 different rectangles
✔️Area of the two equal triangles:
Area = 2(½*base*height)
base = 7 m
height = 8 m
Area of the two triangles = 2(½*7*8) = 56 m²
✔️Area of rectangle 1:
Area = Length*Width
L = 13 m
W = 7 m
Area of rectangle 1 = 13*7 = 91 m²
✔️Area of rectangle 2:
L = 13 m
W = 8 m
Area of rectangle 2 = 13*8 = 104 m²
✔️Area of rectangle 3:
L = 13 m
W = 10.63 m
Area of rectangle 3 = 13*10.63 = 138.19 m²
✅Surface Area of the box = 56 + 91 + 104 + 138.19 = 389.19 m²
Caitlin ate 20 pieces of candy on Monday and 17 pieces on Tuesday. by what percent did she decrease her candy intake
She decreased her candy intake by 15%
Rewrite the expression using a DIVISION SYMBOL: "The quotient of m and 7."
Answer:
m ÷ 7
Step-by-step explanation:
"Quotient" means you're dividing, so this just means you're dividing m by 7.
According to a 2014 poll by the American Academy of Ophthalmology, Americans break down like this when it comes to eye color:
• Brown eyes: 45 %
• Blue eyes: 27 %
• Hazel eyes: 18%
• Green eyes: 9%
• Other: 1%
Consider a random group of 20 American people. Let a random variable X be the number of Americans in this group with green eyes.
(a) Argue that this is a binomial experiment.
(b) Find the probability that
i. None have green eyes
ii. Nine have green eyes
iii. At most three have green eyes
iv. At least four have green eyes
v. If four people out of twenty have green eyes. Is it unusual?
(c) What is the mean and standard deviation of this distribution?
This is a binomial experiment because it meets all the necessary conditions: a fixed number of trials (20 people in the group), independence of each trial (assuming eye color is independent), two possible outcomes (green eyes or not), a constant probability of success (9% for having green eyes), and the random variable representing the count of successes (number of Americans in the group with green eyes, denoted as X).
To argue that this is a binomial experiment, we need to check if the following conditions are met:
1. The experiment consists of a fixed number of trials: In this case, we are considering a fixed number of trials equal to 20, as we have a random group of 20 American people.
2. Each trial is independent: We assume that the eye color of each person in the group is independent of the others.
3. There are only two possible outcomes for each trial: The outcomes are either having green eyes or not having green eyes.
4. The probability of success is constant for each trial: The probability of an American having green eyes is fixed at 9% for each individual in the population.
5. The random variable X represents the count of successes: In this case, X represents the number of Americans in the group with green eyes.
Since all these conditions are satisfied, we can conclude that this is a binomial experiment.
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Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming, is $605. This claim is being challenged by the Association of Travel Agents, who believe the median price is less than $605. A random sample of 25 round-trip tickets from Chicago to Jackson Hole revealed 11 tickets were below $605. None of the tickets was exactly $605. State the null and alternate hypotheses.
Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.
The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605.
The median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.As per the given question, Central Airlines claims that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. But, this claim is being challenged by the Association of Travel Agents, who believes that the median price is less than $605. Hence, we need to test whether the median price is less than $605 or not.Hence,Null hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is $605. Alternative hypothesis is that the median price of a round-trip ticket from Chicago, Illinois, to Jackson Hole, Wyoming is less than $605.
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Can someone help me on this
Answer:
Y = 10 I believe
Step-by-step explanation:
To solve this we need to find what number, times 6, equals 18 - it's fairly easy to find the answer is three.
So what, minus seven, equals 3?
Find the value of X for which the following fraction is undefined
2x²+x-15
________
2/3x²-6
Answer: ±√2
Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!
Solve the system by graphing
y = -3/4x + 6
y = 2x - 5
Answer:
X= 4. Y = 3.
Step-by-step explanation:
If you have a graphing calculator, put the first equation into Y1. And second equation into Y2. Then, find the intersection of the two equations. That's how you find your answer.
Find the median of the data.
93,81,94,71,89,92,94,99
Answer: 92.5
So to find median all we have to do is rearange it from low - high and get the middle number
71 81 89 92 93 94 94 99
So take this and you know the middle is right in between 92 and 93
71 81 89 92 | 93 94 94 99
All you have to do then is take the mean of 92 and 93 (so do [92+93]/2)
Answer is 92.5
ABM Services paid a $4.15 annual dividend on a day it closed at a price of $54 per share. What
was the yield?
Answer:
the yield is 7.68%
Step-by-step explanation:
The calculation of the yield is given below:
we know that
Yield is
= Annual dividend ÷ Price per share
= $4.15 ÷ $54
= 7.68%
Here we divide the annual dividend by the price per share in order to determine the yield
hence, the yield is 7.68%
And, the same would be considered
What is the simplified form of the following expression? Assume x>0. 4 square root 3 over 2x
Answer:
the answer is B)
4√24x^3/2x
Solution:
The answer is B
Step-by-step explanation:
I just took the test.
In 3^6, 6 is called ___.
base
exponent
Step-by-step explanation:
the correct answer is exponent because 6 is its power.
hope this answer will help u.
have a great time.
What is the simplified form of the expression below?
3+ 4i
4 - 2i
Answer:
7 + 2i is the simplified form
Step-by-step explanation:
HELP
4(x-2+y)=???????
Answer:
4+4−8
Step-by-step explanation:
The graph of which function(s) will contain the point (4, 12)?
y = x + 8
y = 3x
y = 2x
y = x + 6
(one or more than one)
Answer:
y=3x
Step-by-step explanation:
Write a function trapezium_integrator(f, start, end, num_traps) that uses the Trapezium Rule to evaluate the integral ∫endstartf(x)dx where f, start, and end are defined in the formula above, and num_traps is the number of trapeziums that the integration interval should be divided into.
Notes:
You may assume num_traps >= 1
Hint: This should be a simple modification of your code from the last question.
We are still expecting you to compute the width of each trapezium and then use a for loop to solve this problem, iterating over the trapeziums to sum their areas. A more efficient approach, using numpy and avoiding any explicit loops, is the topic of one of the challenge questions.
The function trapezium_integrator uses the Trapezium Rule to approximate the value of a definite integral. It takes four parameters: f, which represents the function to be integrated, start and end, which specify the interval of integration, and num_traps, the number of trapeziums used to approximate the integral.
In the Trapezium Rule, the interval of integration is divided into multiple trapeziums of equal width. The area of each trapezium is calculated as the sum of the lengths of its parallel sides divided by 2, multiplied by its height (the difference between the function values at the two endpoints of the trapezium). The areas of all trapeziums are then summed to obtain an approximation of the integral.
The function calculates the width of each trapezium by dividing the interval length by the number of trapeziums. It then uses a for loop to iterate over the trapeziums, accumulating their areas. The final result is returned as the approximation of the integral.
By dividing the interval into smaller trapeziums, the Trapezium Rule provides a reasonably accurate estimate of the integral. However, for highly oscillatory or irregular functions, a large number of trapeziums may be required to achieve sufficient accuracy. In such cases, more sophisticated numerical integration methods may be more appropriate.
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how do you solve for the x ?
Answer:
x = -8
Step-by-step explanation:
these angles are vertical, therefore they are equal
x + 78 = 70
x = -8
Point (2.-3) on glx) is transformed by -g[4(x+2)]. What is the new point? Show your work
After considering the given data we conclude that the new point generated is (2,3), under the condition that g(x) is transformed by [tex]-g[4(x+2)][/tex].
To evaluate the new point after the transformation of point (2,-3) by -g[4(x+2)], we can stage x=2 and g(x)=-3 into the expression [tex]-g[4(x+2)][/tex]and apply simplification to get the new y-coordinate. Then, we can combine the new x-coordinate x=2 with the new y-coordinate to get the new point.
Stage x=2 and g(x)=-3 into [tex]-g[4(x+2)]:[/tex]
[tex]-g[4(2+2)] = -g = -(-3) = 3[/tex]
The new y-coordinate is 3.
The new point is (2,3).
Hence, the new point after the transformation of point (2,-3) by [tex]-g[4(x+2)][/tex] is (2,3).
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44% of what number is 400?
Answer:
909.09
Step-by-step explanation:
400 divided by 44% is about 909.09.
What is the range for the following data?
52, 32, 61, 82, 63
Answer:
The range would be 50.
Step-by-step explanation:
Range is found by putting a list or set of numbers in order, then subtracting the lowest number from the highest.
32, 61, 63, 52, 82
82 - 32 = 50
ht
Which of the following is an equivalent expression to the expressione,
А
B
D
ANSWER QUICK PLZ
i’m lost on this help would be nice
Answer:
3x - 4 = 14
+4. +4
3x = 18
÷3. ÷3
x = 6
Can someone state the range of this function pleaseee?
Answer:
Range = [0, ∞)
Step-by-step explanation:
Range is the y-values
For this question y starts at 0 and just continually goes up so:
Range = [0, ∞)
7. An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Using a .05 level of significance test the claim that the proportion is at least 34%.
The calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.
Hence, the claim that the proportion is at least 34% is rejected.
Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.
Null hypothesis:
H0: p ≥ 0.34
Alternative hypothesis:
Ha: p < 0.34
where:p = proportion of Littleton fathers who do not help with childcare
Here, the level of significance, α = 0.05
Level of significance = α = 0.05
The test statistics for a proportion is given as z-test.
The formula for calculating z-score for a proportion is: z = (p - P) / sqrt[P(1 - P) / n]
where:
P = Population proportion
p = Sample proportion
n = Sample size
The calculated value of z-statistics can be compared with the critical value of z-score from the standard normal distribution table at a particular level of significance.
If the calculated value of z is greater than the critical value of z, then we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Calculating the z-statistic:
Here, Sample size n = 225
Sample proportion
p = 97/225
= 0.4311
Population proportion
P = 0.34z
= (p - P) / sqrt[P(1 - P) / n]z
= (0.4311 - 0.34) / sqrt[(0.34)(0.66) / 225]z
= 2.80
Since the alternative hypothesis is one-tailed (Ha: p < 0.34), the critical value of z at α = 0.05 can be found as follows:
The critical value of z = zα
= -1.645
Since the calculated value of z = 2.80 > the Critical value of z = -1.645, we reject the null hypothesis.
Hence, the claim that the proportion is at least 34% is rejected.
Therefore, the researcher's claim is true that the figure is higher for fathers in Littleton.
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Find the zeros of the following quadratic functions.
3) x2 + 5x + 6 = 0
Sammy counts the number of people in one section of the school auditorium. He counts 18 female students, 16 male students, and 6 teachers. There are 720 people in the auditorium. Consider the probability of selecting one person at random from the auditorium
Correct Question:
He counts 18 female students, 16 male students, and 6 teachers. There are
720 people in the auditorium. Consider the probability of selecting one person
at random from the auditorium.
Which of these statements are true?
Choose all that apply.
A: The probability of selecting a teacher is 6%.
B : The probability of selecting a student is 85%.
C : The probability of selecting a male student is 32%.
D : The probability of selecting a female student is 45%.
Step-by-step explanation:
Option B and D are correct because
The total number of people in one cross section = 18 + 16 + 6 = 40.
A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %
B = The probability of selecting a male student is = (34/40)x100 = 85%
C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %
D : The probability of selecting a female student is = (18/40)x100= 45%
Given the definitions of f(x) and g(x) below, find the value of (gof)(1).
f(x) = 2x² – 2x – 4
g(x) = -5x + 14
Answer:
[tex](g*f)(x) = 34[/tex]
Step-by-step explanation:
For sake of clarity, [tex](g * f)(x) = g(f(x))[/tex]
First, find [tex]f(1)[/tex]
[tex]f(1) = 2(1)^2 - 2(1) - 4\\f(1) = 2-2-4 \\f(1)=-4[/tex]
Then, take what you got for [tex]f(1)[/tex] and plug that into [tex]g(x)[/tex]. In this case, [tex]f(1) = -4[/tex]
[tex]g(-4) = -5(-4) + 14\\g(-4)= 20 + 14\\g(-4) = 34[/tex]
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Find the solution to the linear system of differential equations { 146 +24y 12x + 20y satisfying the initial conditions X(0) = 3 and Y(0) = 3. x(t)=__ y(t)=__
Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:
x_(t) = 146t + 24yt + 3
y_(t) = (876t + 21) / ((-144) - 10t)
To solve the given linear system of differential equations, let's rewrite the system in a more standard form:
dx/dt = 146 + 24y
dy/dt = 12x + 20y
We'll use the initial conditions x_(0) = 3 and y_(0) = 3 to find the specific solution.
To solve the system, we can use the method of integrating factors.
Solve the first equation:
dx/dt = 146 + 24y
Rearrange the equation to isolate dx/dt:
dx = (146 + 24y) dt
Integrate both sides with respect to x:
∫dx = ∫(146 + 24y) dt
x = 146t + 24yt + C_(1) ---(1)
Solve the second equation:
dy/dt = 12x + 20y
Rearrange the equation to isolate dy/dt:
dy = (12x + 20y) dt
Integrate both sides with respect to y:
∫dy = ∫(12x + 20y) dt
y = 6x + 10yt + C_(2) ---(2)
Now, we'll apply the initial conditions x_(0) = 3 and y_(0) = 3 to find the values of C_(1) and C_(2).
From equation (1), when t = 0, x = 3:
3 = 146(0) + 24(3)(0) + C_(1)
C_(1) = 3
From equation (2), when t = 0, y = 3:
3 = 6(0) + 10(3)(0) + C_(2)
C_(2) = 3
Now, substituting the values of C_(1) and C_(2) back into equations (1) and (2), we get:
x = 146t + 24yt + 3
y = 6x + 10yt + 3
Simplifying further:
x = 146t + 24yt + 3
y = 6(146t + 24yt + 3) + 10yt + 3
x = 146t + 24yt + 3
y = 876t + 144y + 18 + 10yt + 3
x = 146t + 24yt + 3
y - 154y - 10yt = 876t + 18 + 3
(-144y) - 10yt = 876t + 21
y = (876t + 21) / (-144 - 10t)
Therefore, the solution to the given system of differential equations, with the initial conditions x(0) = 3 and y(0) = 3, is:
x_(t) = 146t + 24yt + 3
y_(t) = (876t + 21) / ((-144) - 10t)
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A rectangular prism has a volume of 600 cubic inches lf the height of the prism is 5 inches and the width is 10 inches what is the length of the prism? Enter your answer in the box.
Answer:
3 inches
Step-by-step explanation:
got it right on edg
Find the area bounded by the curves y= and y= x2 Round the answer to two decimal places. Question 4 3 pts A company's marginal cost function is given by MC(x)= VX + 30 Find the total cost for making the first 10 units.
The total area of the regions between the curves is 1/3 square units
The total cost for making the first 10 units is 7.79
Calculating the total area of the regions between the curvesFrom the question, we have the following parameters that can be used in our computation:
y = √x and y = x²
With the use of graphs, the curves intersect at
x = 0 and x = 1
So, the area of the regions between the curves is
Area = ∫x² - √x
Integrate
[tex]Area = \frac{x^3}{3} - \frac{2x^\frac32}{3}[/tex]
Recall that x = 0 and x = 1
So, we have
[tex]Area = (\frac{0^3}{3} - \frac{2 * 0^\frac32}{3}) - (\frac{1^3}{3} - \frac{2 * 1^\frac32}{3} )[/tex]
Evaluate
Area = 0 + 1/3
Evaluate
Area = 1/3
Hence, the total area of the regions between the curves is 1/3 square units
Calculating the total costGiven that
MC(x) = √(x + 30)
Integrate to calculate the cost function
So, we have
[tex]C(x) = \frac{2}{3}(x + 30)^\frac23[/tex]
For the first 10, x = 10
So, we have
[tex]C(10) = \frac{2}{3}(10 + 30)^\frac23[/tex]
Evaluate
C(10) = 7.79
Hence, the total cost for making the first 10 units is 7.79
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