(a) The probability that X is less than 50.4 is equal to 1.
To solve the given problem, we are given that the length of time to failure for a transistor is a random variable X with a CDF of Fx = [tex]1 - e^(-x^2)[/tex] for x >= 0 and 0 elsewhere. We are also given that Ex(x) = ∫(from 0 to infinity) t * f(x) dx = a.
a) To compute P(X < 50.4), we can use the CDF as follows:
P(X < 50.4) = Fx(50.4)
= 1 - [tex]e^(-(50.4)^2)[/tex]
= 1 - [tex]e^(-2540.16)[/tex]
= 1 - 0
= 1
(b) The probability that a randomly selected transistor operates for at least 200 hours is approximately equal to [tex]e^(-40000)[/tex].
To compute the probability that a randomly selected transistor operates for at least 200 hours, we need to find P(X >= 200). We can use the complement rule and the CDF as follows:
P(X >= 200) = 1 - P(X < 200)
= 1 - Fx(200)
= 1 - (1 - [tex]e^(-200^2)[/tex])
= [tex]e^(-40000)[/tex]
(c) The PDF of this random variable is f(x) = [tex]2xe^(-x^2)[/tex].
To derive the PDF of this random variable, we can differentiate the CDF with respect to x as follows:
f(x) = d/dx Fx(x)
= d/dx (1 - [tex]e^(-x^2)[/tex])
= [tex]2xe^(-x^2)[/tex]
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Convert each of the following implicitly quantified statements
to their formally quantified statement equivalent.
Implicitly quantified statements can be converted into formally quantified statements by specifying the quantifiers and the domain of discourse.
To convert an implicitly quantified statement to its formally quantified statement equivalent, we need to determine the quantifiers and the domain of discourse.
1. For universally quantified statements, we use the universal quantifier (∀). It indicates that the statement holds for all elements in the domain of discourse. For example, if the statement is "All cats have tails," we can convert it to the formally quantified statement ∀x(Cat(x) → HasTail(x)), where Cat(x) represents "x is a cat" and HasTail(x) represents "x has a tail."
2. For existentially quantified statements, we use the existential quantifier (∃). It indicates that there exists at least one element in the domain of discourse for which the statement is true. For example, if the statement is "There is a red apple," we can convert it to the formally quantified statement ∃x(Red(x) ∧ Apple(x)), where Red(x) represents "x is red" and Apple(x) represents "x is an apple."
By explicitly stating the quantifiers and defining the predicates in the statement, we can convert implicitly quantified statements into their formally quantified statement equivalents, making the meaning and scope of the statement clear within a specific domain of discourse.
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Purple paint is made of a ratio of
16 white : 3 blue : 1 red
how much white paint is needed to make one gallon of purple paint?
plz help its important
there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint (got it from safari)
which of the following fractions converts to a repeating decimal? a. 7/16 B.5/8 C. 2/3 D.4/10
Answer:
B
Step-by-step explanation:
whats 10x10+111-21x999/999+21-111/10?
Answer:
199.9
Step-by-step explanation:
Please help Sammy buys light bulbs in pack of 8 for $20. The shipping cost is $10 regardless of the number of packs bought. Billy has only $120 to spend.
Answer:
5
Step-by-step explanation:
Shana is doing a craft project
using yarn and sticks. She
has 3 green yam pieces and
7 blue yam pieces. She has 3
times as many sticks as yarn
pieces. Write an expression.
Plz help
Answer:
3(5 + 7)
Step-by-step explanation:
Shana is carrying our a craft project
She is making use of yarns and stuck
She has three green yarn pieces and seven blue yarn pieces
She has three times as many yarn pieces
Therefore the expression can be represented as follows
3(5 + 7)
20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
Answer:
2.88 mi
Step-by-step explanation:
A cube. Point B is the top right point of the top face. Point A is the bottom left point of the bottom face and point C is the top right point of the bottom face. Diagonals are drawn from B to A and from A to C. Side B C is 10 inches long, and Side A B is StartRoot 300 EndRoot inches long. What is the length of Side A C? 14 in. StartRoot 200 EndRoot in. StartRoot 290 EndRoot in. 20 in.
Answer:
the answer is b
Step-by-step explanation:
i just did the assignment
Answer:
b
Step-by-step explanation:
12. Use Russian Peasant Multiplication to perform the following problem. Explicitly show your addition. 49 x 65
Using the Russian Peasant Multiplication, 49 x 65 is 3,185.
What is the Russian Peasant Multiplication?The Russian Peasant Multiplication method converts the problem into binary (base 2) multiplication from base 10 by halving the numbers on the first column repeatedly till the second number doesn't become 1 and doubling the numbers on the second column.
Then, add up the numbers in the second column that correspond to odd numbers in the first column to get the result.
49 65
÷ 2 24 130 x 2
12 260
6 520
3 1,040
1 2,080
Add:
65, because we ignored 1 when we divided 49 by 2
1,040, because we ignored 1 when we divided 3 by 2
2,080
= 3,185
Check:
49 x 65 = 3,185
Based on the Russian Peasant Multiplication method, the product of 49 x 65 is 3,185.
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Two sides of a triangle measure 5
units and 3 units. The perimeter
of the triangle is 12 units. What is
the measure of the third side?
Answer:
4 units
Step-by-step explanation:
5+3=8
12-8=4
Los primeros días de enero, el representante del mercado recibió cierta cantidad de di-
nero, hizo una operación y se dio cuenta que habían pagado 15 personas. ¿Cómo puede
saber la cantidad recibida?
15
425
El ejercicio completo con las opciones de respuesta está a continuación:
Los primeros días de enero el representante del mercado recibió cierta cantidad de dinero,hizo una operación y se dio cuenta que habían pagado 15 personas,cómo puede saber la cantidad recibida?
a.Multiplicando el dividendo por el divisor
b. Sumando el dividendo con el cociente y el residuo
c.Multiplicando el divisor por el cociente y sumando el residuo
d.Multiplicando el dividendo por el cociente y sumando el residuo
Answer:
La opción c es la respuesta correcta
Step-by-step explanation:
El valor de 15 corresponde al cociente es decir al total de personas que pagaron;el ejercicio nos da el valor del divisor que es 425 ; para saber cual es la cantidad exacta recibida debemos multiplicar el divisor por el cociente y si hay residuo sumarlo; el ejercicio nos queda de la siguiente manera:
425 x 15 = 6.375 (la cantidad recibida fue de 6.375)
[tex]\frac{6375}{425}[/tex] = 15 (comprobación de la división para obtener el cociente con valor de 15)
What is the slope of the line through the points (-2, -1) and (4, 3)?
2/3
2/5
5/2
Answer:
The slope is A. 2/3
HOPE THIS HELPS!!!!
Arrange in ascending order 19,654 67,923 67,397 91,945
Answer:
19654,67397,67923,91945
Step-by-step explanation:
Ascending order mean arrange the number from smaller value to bigger value
Answer:
19654,67397,67923,91945
plz mark me as brainliest
If You Have NO Explanation Than Don't Answer.
Answer: Option C
Step-by-step explanation:
C because 6+1=1+1+1+1+1+1+1
Answer:
C
Step-by-step explanation:
We want to find which model shows two equal expressions. We know that the value of x is 6. That being said, on the left side of each equation, plug in 6 for every "x" you see. Then, add the values on both sides. If they're equal, that's your answer.
For example:
In choice A, we see two x's, so we plug in 6 for them both and add them. That's 12 on the left side. On the other side of the equation, we have 7 "1" boxes, which simply just means add them, so that's 7 on the other side. 12 does not equal 7, therefore A is not the answer. However, for choice C, we are given x, which we know is 6, and a "1" box, which simply means 6 + 1, which is 7. On the other side of this equation, we have 7 "1" boxes, so that's 7. The equation becomes 7 = 7, which is true, so that is our answer.
Angela purchased a car using a simple interest loan. The loan had an interest rate of 5% and was for three years. Angela paid $450 in interest. The principal amount of the loan was for $
Answer:
$3000
Step-by-step explanation:
Given data
Rate=5%
Time=3 years
Simple interest= $450
We know that the expression for simple interest is
SI=PRT/100
Substitute
450=P*5*3/100
cross multiply
P*15= 45000
Divide both sides by 15
P= 45000/15
P=$3000
Hence the principal amount is $3000
If dy /dx is undefined for a given value of x, then the line tangent to the curve y f(x) at that value does not exist Select one:
a. true b. false
The statement "If dy/dx is undefined for a given value of x, then the line tangent to the curve y = f(x) at that value does not exist" is false.
If the derivative dy/dx is undefined at a given value of x, it means that the slope of the tangent line is undefined at that point.
However, the tangent line can still exist.
For example, consider the curve y = |x| at x = 0.
The derivative dy/dx is undefined at x = 0 since the slope changes abruptly at that point. However, we can still draw a tangent line at x = 0, which is the y-axis itself.
Therefore, even if the derivative is undefined, it does not necessarily mean that the tangent line does not exist.
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multiple 2y(6y2+4y-3)
Answer:
Step-by-step explanation:
Y- intercepts (-3 = 2 3, 0) , (-3 - 2 3, 0)
Which of the following properties is represented by the calculations in the photo?
A) multiplication property of equality
B) zero sum property
C) addition property of equality
D) zero product property
Answer:
D. zero product property
Step-by-step explanation:
Base on the Zero Product Property, if the product of factors gives us 0, either of the factors or both would equal 0.
Thus,
xy = 0, therefore,
x = 0 or y = 0
Therefore, the property that is represented by the calculation given in the photo is Zero Product Property.
Gardening Jessica is planting a garden. It has the shape of a right triangle. She wants 3
plants for each square meter of area. How many plants does she want in the garden?
Answer:
28
Step-by-step explanation:
plants in the garden = area of the garden / number of plants per square meter
the garden is in the shape of a triangle
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
Area of a triangle = 1/2 x base x height
(1/2) x 24 x 7 = 84 meters^2
plants in the garden = 84/3 = 28
Find the radius of convergence, R, of the series. Σ (-7) Vn 00 ya n=1 R= Find the interval, I, of convergence of the series.
The series converges for x values within the interval (-29/7, -27/7), and the radius of convergence is 1/7.
How do we calculate?We apply the ratio test to our series:[tex]|7^(^n^+^1^)[/tex] (x + 4)[tex]^(^n^+^1^)^) / √(n+1)] / [( (x +7^n 4))^n\sqrtn]|[/tex]
We take the limit as n approaches infinity:lim(n→∞) |[tex]7(x + 4) / √(n+1)| = |7(x + 4)|[/tex]
For the series to converge, |7(x + 4)| must be less than [tex]1.|7(x + 4)| < 1-1 < 7(x + 4) < 1-1/7 < x + 4 < 1/7-29/7 < x < -27/7[/tex]
In conclusion, the interval of convergence is (-29/7, -27/7), and the radius of convergence is the half-length of the interval, which is 1/7.
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A recent Gallup poll found large differences in the type of household chores done by wives and husbands.1 Wives still do most of the indoor household chores. Husbands still tend to do more work outside and with family cars. The simulated data in this problem are based on the results of this poll.
Suppose we wish to demonstrate that there is a difference between the proportions of wives and husbands who do laundry at home. From a random sample of 66 randomly selected wives, we observe 44 who do laundry at home. From a random sample of 46 husbands, we observe 18 who do laundry at home.
Test the claim that the proportion of wives, p1 , who do laundry at home is different from the proportion of husbands, p2 , who do laundry at home. Use a 1% significance level.
Answer : There is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
Explanation:
The null hypothesis is that the proportion of wives and husbands who do laundry at home is the same. The alternative hypothesis is that the proportion of wives and husbands who do laundry at home is different.
Mathematically, null and alternative hypotheses are given below. H0: P1 - P2 = 0H1: P1 - P2 ≠ 0 where P1 is the proportion of wives who do laundry at home and P2 is the proportion of husbands who do laundry at home. Let α = 0.01 be the significance level. Therefore, α/2 = 0.005 and the Zα/2 value for the two-tailed test is ±2.58.
The point estimate of the difference in the proportions is:Point estimate, PE = P1 - P2 = (44/66) - (18/46) = 0.6667 - 0.3913 = 0.2754
The standard error of the difference in the proportions is: SE = sqrt{(P1(1 - P1)/n1) + (P2(1 - P2)/n2)} = sqrt{[(44/66)(22/66)/65] + [(18/46)(28/46)/45]} = 0.1033
The test statistic is given by:Z = (PE - 0) / SE = 0.2754 / 0.1033 = 2.6641
Since the absolute value of the test statistic is greater than the Zα/2 value, we reject the null hypothesis and conclude that the proportion of wives who do laundry at home is different from the proportion of husbands who do laundry at home at a 1% significance level. Therefore, there is enough evidence to suggest that a higher proportion of wives do laundry at home compared to the proportion of husbands who do laundry at home.
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Please help me with the question
Answer:
the tree is 8ft long
Step-by-step explanation:
beans
3. Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, determine BY HAND what percent of the scores were 78 or less. Also, what percent of scores were 85 or better?
The percent of the scores that were 85 or better is 25.14%.
The percent of the scores that were 78 or less is 39.25%.
The percent of the scores that were 85 or better is 25.14%.
Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, we are to determine what percent of the scores were 78 or less and what percent of the scores were 85 or better.
Below are the steps to determine what percent of the scores were 78 or less.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula
Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (78 - 80) / 7.5
Z = -0.27
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie below Z = -0.27 which is 0.3925 or 39.25%
Therefore, the percent of the scores that were 78 or less is 39.25%.
Below are the steps to determine what percent of the scores were 85 or better.
Step 1: Determine the Z-score
To determine the Z-score, we use the formula Z = (X - μ) / σ
Where X is the score, μ is the mean and σ is the standard deviation
Z = (85 - 80) / 7.5
Z = 0.67
Step 2: Use the Z-table to determine the percentage
Using the Z-table, we can find the percentage of scores that lie above Z = 0.67
Which is 0.2514 or 25.14%
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The equation below has infinitely many solutions.
-3 (x – 3) – 1 = ax + b
True
False
Answer:
False
Step-by-step explanation:
tomen puntos
toy aburridoooo
Answer:
aww thank you
pls mark brainliest
Step-by-step explanation:
A variable needs to be eliminated to solve the system of equations below. Choose the
correct first step
— 5х + бу = 41
7x - 6y = -43
Answer:
6y-6y, cancel it out to find x first.
-5x+6y=41
7x-6y=-43
2x=-2
Step-by-step explanation:
i hope this helps :)
Answer:
Step-by-step explanation:
The first step is to add the 2 equations This will eliminate the y terms
( + 6y + -6y = 0).
So you are then left with 2x = -2
Priya has planted a garden shaped like a right triangle. One leg of the triangle is 5 meters long, and the angle formed by it and the hypotenuse is 50°. If Priya wants to build a fence around her garden, how many meters of fence will she need? Round your answer to the nearest meter.
Answer:
19
Step-by-step explanation:
:)
The amount of fence that Priya would need (in meters) is 19 meters approximately.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
For this case, we've to find the length of the fencing she needs to cover her garden.
Length of fencing needed = Perimeter of the considered right triangle = sum of its sides' lengths
Using the image attached below, from the perspective of angle A which is of 50 degrees from inside, we get:
|AB| = base length = 5 meters (given)|BC| = perpendicular length = p meters (say)|AC| = hypotenuse length = h meters (say)Using tangent ratio,[tex]\tan(m\angle A) = \tan(50^\circ) = \dfrac{p}{5}\\\\p = 5 \tan(50^\circ) \approx 5.96 \: \rm m[/tex]
Using sin ratio,[tex]\sin(m\angle A) = \sin(50^\circ) = \dfrac{p}{h}\\\\h = \dfrac{p}{\sin(50^\circ)} \approx \dfrac{5.96}{\sin(50^\circ)} \approx 7.78 \: \rm m[/tex]
Thus, perimeter of the triangle = 5 + p + h ≈ 18.74 m ≈ 19 m
Thus, the amount of fence that Priya would need (in meters) is 19 meters approximately.
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evaluate each of the following
205 x 195
Answer:
39,975
Step-by-step explanation:
There u go
Answer:
39,975
Step-by-step explanation:
Caculater
Let f(x) = 9+√2-3. Find f(x).
The value of the function f(x) = 9 + √2 - 3 is a constant and can be simplified as f(x) = 6 + √2.
The given function f(x) = 9 + √2 - 3 is an expression that does not depend on the variable x. Therefore, it represents a constant value.
To evaluate the function, we can simplify the expression by combining like terms:
f(x) = 9 + √2 - 3
Combining the constants 9 and -3, we have:
f(x) = 6 + √2
Thus, the value of the function f(x) is a constant, which is 6 + √2.
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En san pedro de atacama, un dia de septiembre a las 7a.M., la temperatura fue de 6°c, la que fue aumentando 2,3°c en promedio por hora hasta que alcanzo su maxima de 30,15 °c ¿ a que hora alcanzo su temperatura maxima
Answer:
5:30 p.m.
Step-by-step explanation:
30.15 - 6 = 24.15
24.15 / 2.3 = 10.5 hrs
7 + 10.5 = 17.5 = 5:30 p.m.