Let's start by setting up an equation to represent the problem.
Let's say Jake started with x amount of money.
After giving 1/3 to his wife, he has 2/3 left: (2/3)x
After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600
We can solve for x by isolating it:
(1/4)(2/3)x = $600
Multiplying both sides by 12/2 gives:
(2/3)x = $3600
Dividing both sides by 2/3 gives:
x = $5400
So Jake started with $5400.
To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:
(1/4)(2/3)($5400) = $900
So he gave his mother $900.
Step-by-step explanation:
x = original amount of money
the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.
x - (1/3)x - (1/4)x = 600
so let's bring every fractional term to .../12.
12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600
12x/12 - 4x/12 - 3x/12 = 600
5x/12 = 600
5x = 600×12
x = 600×12/5 = 120×12 = $1440
he gave to his mother
(1/4) × 1440 = $360
Harold ran a total of 4,464 miles the last 9 months. How many miles did he ride each month?
Answer:
I think 496
Step-by-step explanation:
Divide
Which of the following is the surface area of the pyramid?
36 m2
72 m2
88 m2
144 m2
please answer quick, give quick explanation please:) thanks!! 60 points!
The Surface area of Pyramid is equal to Option (B) [tex]72 m^2[/tex] when base is square and their are 4 triangles.
The surface area of a pyramid is the total area of all its faces. The formula to calculate the surface area of a pyramid depends on the shape of its base.
To find the surface area of this pyramid we should add area of all 4 triangles and 1 square base.
Area of Base = 4m * 4m
= [tex]16m^2[/tex]
Area of Triangle = 1/2 *4* 7
= [tex]14m^2[/tex]
Surface Area of Pyramid = Area of Base + 4 * (Area of Triangle)
= [tex]16m^2 + 4(14m^2)[/tex]
= [tex]72 m^2[/tex]
Therefore, Surface area of Pyramid is equal to [tex]72 m^2[/tex].
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Are these triangles similar, congruent or neither? What theorem supports your answer?
options:
Similar: SAS
Similar: AA
Similar: SSS
Congruent: ASA
Congruent: SSS
Congruent: SAS
Neither
Both of the two triangles are similar by SSS similarity postulate.
How to Identify Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.
Looking at the 2 given triangles, we can see the ratio if corresponding sides as:
39/13 = 3
39/13 = 3
21/7 = 3
Since the ratios of the corresponding sides of both triangles are the same, then they are both Similar by SSS similarity postulate.
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If the taking turns procedure takes place on this distribution of goods, who would walk away with each pile? Person A chooses first.
Pile 1
Pile 2
Pile 3
Pile 4
Pile 5
Pile 1 will go to(No answer given)
Pile 2 will go to(No answer given)
Pile 3 will go to (No answer given)
Pile 4 will go to (No answer given) + Person A views,21% 13% 22% 18% 26%
Person B views 24% 17% 14% 22% 23%
In this situation, did each person get their fair share? (No answer given)
a) Note that the distribution of piles would be:
Person A gets Pile 5
Person B gets Pile 1
Person A gets Pile 3
Person B gets Pile 4
Person A gets Pile 2.
b) No, in this situation each person did not get their fair share.
If the taking turns procedure is such that Person A chooses first and then they alternate turns, then the following would be the distribution of piles:
Person A chooses first and would likely choose Pile 5, as it has the highest percentage viewed by them.Person B chooses next and would likely choose Pile 1, as it has the highest percentage viewed by them among the remaining piles.Person A chooses next and would likely choose Pile 3, as it has the highest percentage viewed by them among the remaining piles.Person B chooses next and would likely choose Pile 4, as it has the highest percentage viewed by them among the remaining piles.Finally, Person A would choose Pile 2, as it is the only remaining pile.So the distribution of piles would be:
Person A gets Pile 5Person B gets Pile 1Person A gets Pile 3Person B gets Pile 4Person A gets Pile 2.b) No, in this situation each person did not get their fair share if the criterion for fairness is defined as each person receiving an equal share of the piles.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
A hotel has 320 rooms. Some are singles, and some are doubles. The single room cost 40$ and the double rooms cost 65$. Because of and event in town all of the hotel rooms are occupied. The sales tonight are 15,600$. How many of each type of room does the hotel have?
As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.
what is equation ?An equation in mathematics is a claim that two mathematical expressions are equivalent. In an equation, the two expressions on either side are separated by the equals sign (=). As in the following equation: 3x + 2 = 11 declares that the formula 11 is identical to the formula 3x + 2. Finding the value of x that causes the equation to be true is the first step towards solving this equation. By first removing 2 from both sides of the equation and then dividing by 3, we may find x in this situation: 3x + 2 - 2 = 11 - 2 (subtracting 2 from both sides) (subtracting 2 from both sides) .3x = 9 (simplifying the right side) (simplifying the right side) .
given
Assume that there are x single rooms and y double rooms at the hotel.
We may create an equation since we are aware that there are 320 rooms in the hotel overall:
x + y = 320 (Equation 1) (Equation 1)
We can create another equation based on sales since we also know the prices for each type of accommodation and the overall sales:
40x + 65y = 15,600 (Equation 2) (Equation 2)
We can now solve for x and y using these two equations. To accomplish this, one method is to solve for x in Equation 1 and replace it in Equation 2:
x + y = 320
x = 320 - y
Equation 2 using x = 320 - y as a replacement:
12,800 - 40y + 65y = 15,600
25y = 2,800 y = 112
40x + 65y = 15,600
40(320 - y) + 65y
= 15,600
There are 112 double rooms in the hotel. In order to determine the number of single rooms, we can reenter this value into Equation 1 as follows:
x + y = 320
x + 112 = 320
x = 208
As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.
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In analyzing hits by certain bombs in a war, an area was partitioned into 574 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 574 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Question content area bottom
Part 1
Identify the values of μ, x, and e.
x is the number of sucesses.
e = 2.71828 is the Euler number.
μ is the mean in the given interval.
The probability that a randomly selected region had exactly two hits is 0.1710.
How to identify the values of μ, x, and e and describe what each of those symbols represents?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
P(x)= (μ^x * e^-μ)/x!
Where
x is the number of sucesses
e = 2.71828 is the Euler number
μ is the mean in the given interval.
A total of 535 bombs hit the combined area of 574 regions. So the mean hits per region is:
P = 535/574 = 0.9321
Assume that we want to find the probability that a randomly selected region had exactly two hits (i.e P(x = 2)).
P(x) = (μ^x * e^-μ)/x!
P(2) = (0.9321^2 * e^-(0.9321))/2!
P(2) = 0.1710
Therefore, the probability that a randomly selected region had exactly two hits is 0.1710.
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Expand and simplify 3(3x-2)-(2x-7)
Answer:
21
Step-by-step explanation:
Answer:7x+1
Step-by-step explanation:
1). Distribute: 9x-6-2x+7
2). Combine like terms: 9x+1-2x
3). Combine like terms: 7x+1
Findthe
y -intercept
oftheparabola y = x2 + 2x + 10
The y -intercept of the parabola y = x^2 + 2x + 10 is (0, 10)
the y-intercept represents the value of y when x=0. In the equation y = x^2 + 2x + 10, the x^2 and 2x terms create a parabola that opens upwards. As x approaches infinity or negative infinity, the value of y also increases towards infinity.
The y-intercept of a graph is the point at which the graph crosses the y-axis, which is where x=0. To find the y-intercept of the parabola y = x^2 + 2x + 10, we substitute x=0 into the equation, which gives
y = 0^2 + 2(0) + 10
y = 10
Therefore, the y-intercept of the parabola is (0, 10), which means the graph crosses the y-axis at the point (0, 10).
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The given question is incomplete, the complete question is:
Find the y -intercept of the parabola y = x^2 + 2x + 10
if you have an 88, a 95, a 93, and an 80, what do you need to make on the next quiz to have a mean quiz score of 90
You would need to make a 94 on the next quiz to have a mean quiz score of 90.
If 90 is the desired mean, then you have to multiply it by the number of quizzes
5 x 90 = 450 is the total in the 5 quizzes.
Now, add the scores of the first four quizzes.
88 + 95 + 93 + 80 = 356
Then, take the amount of the 5 quizzes and subtract it from the amount of the total 4 quizzes.
450 - 356 = 94
A public opinion poll in Ohio wants to determine whether registered voters support a recent school bond. They select a simple random sample of 50
registered voters from each county in the state and ask whether they approve or disapprove of the measure.
What is the population
What is the sample
Answer:
i hope this is what you are looking for
The population is all registered voters in Ohio, and the sample is the 50 registered voters from each county in Ohio that were randomly selected
Explanation:In this case, the population refers to all registered voters in Ohio, as they are the total group being studied. The sample is the subset of the population that is being evaluated to represent the entire population. In this question, the sample is the 50 registered voters from each county in Ohio that were randomly selected for the public opinion poll.
This scenario is an example of statistical sampling, a technique used in statistics to analyze a subset of a population and extrapolate insights or findings to the entire population.
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Hector has a collection of nickels, dimes, and quarters totaling 122 coins. The number of dimes he has is 3 more than four times the number of nickels, and the number of quarters he has is 19 less than the number of dimes. How many coins of each kind does he have?
Answer: 15 nickels, 63 dimes, 44 quarters
Step-by-step explanation:
x=number of nickels
4x+3=number of dimes
4x+3-19=number of quarters
Solve the following equation:
x+4x+3+4x+3-19=122
9x-13=122
x=15
Plug x back into the expressions:
Number of nickels=15
Number of dimes:
4(15)+3
63
Number of quarters:
4(15)+3-19
44
What is the square root of 92 rounded to the nearest tenth
Answer:
answer is 2 into 2 into twenty three
Step-by-step explanation:
2×2×23
√2^2×23
2√23
Answer: The square root of 92 is approximately 9.59166304663. Rounding this to the nearest tenth gives 9.6. Therefore, the square root of 92 rounded to the nearest tenth is 9.6.
Step-by-step explanation:
PLEASEEE HELP I HAVE IT DUE TODAY
cather added the ages of a crowd of 18 year olds and 22 year olds and got a sum of 290 if there were 10 18 year olds how many 22 year olds were in the crowd?
PLEASE HELP
Answer: 5
Step-by-step explanation:
If Cather added the ages of a crowd of both 18-year-olds and 22-year-olds and got 290, we can write that as 18x+22y=290. Knowing that there were 10 18-year-olds, we can plug 10 in for x.
18 times 10 + 22y = 290
So, first, we should multiply.
18 times 10 is 180, leaving us with 180+22y=290
Next, we should subtract both sides by 180.
So, 22y=110
Finally, we need to divide both sides by 22.
Leaving us with the answer of 5.
Answer:
5
Step-by-step explanation:
10×18=180
290-180=110
110/22=5
1.5 + [ (-1) x (1/2+1/4) ] / 1/2
A) 0
B) 1
C) 3
D) -1.5
Answer:
A) 0
Step-by-step explanation:
1.5+(-1 x (.5 + .25)) / .5
1.5+(-1 x .75) / .5
1.5 + -0.75 / .5 Because of order of operations division comes first
1.5 + (-1.5)
1.5 - 1.5
0
1. Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
(i) x²-2x-8
Answer:
The zeroes are -2 and 4.
Step-by-step explanation:
x^2 - 2x - 8 = 0
(x + 2)(x - 4) = 0
x + 2 = 0 or x - 4 = 0
x = -2, 4
The general form of the equation is ax^2 + bx + c = 0.
The sum of the zeroes should be equal to -b/a:-
-2 + 4 = 2
and -(-2)/1 = 2
Verified
The product of the zeroes should be c/a = -8:-
-2 * 4 = -8.
Verified.
Please I need help
Manuel makes bird food by mixing sunflower seeds and
corn kernels. He bought 2.5 pounds of sunflower seeds. He
also bought some corn kernels. Sunflower seeds and corn
kernels each cost $2.20 per pound. The total amount
Manuel spent on the sunflower seeds and corn kernels was
$9.35.
Enter the number of pounds of corn kernels Manuel
purchased.
Manuel purchased 1.75 pounds of corn kernels.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side
In the given question,
Let's use x to represent the number of pounds of corn kernels Manuel purchased.
We know that Manuel bought 2.5 pounds of sunflower seeds, and that both the sunflower seeds and corn kernels cost $2.20 per pound.
The total amount Manuel spent on the sunflower seeds and corn kernels was $9.35, so we can write the equation: 2.2(2.5) + 2.2x = 9.35
Simplifying the left side of the equation, we get: 5.5 + 2.2x = 9.35
Subtracting 5.5 from both sides, we get: 2.2x = 3.85
Dividing both sides by 2.2, we get: x = 1.75
Therefore, Manuel purchased 1.75 pounds of corn kernels.
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what is 500 times 500
By multiplication, 500 times 500 is 250,000 using distributive property.
What is Multiplication?Multiplication is an arithmetic operation that combines two or more quantities into a single quantity. The result of multiplication is called the product. Multiplication is usually represented by the symbol "×" or "*".
For example, the product of 3 and 4 is 12, which is written as 3 × 4 = 12 or 3 * 4 = 12. In general, to multiply two numbers a and b, we write a × b or a * b, and the result is the product of the two numbers.
Multiplication is also distributive over addition, which means that a × (b + c) = (a × b) + (a × c) for any values of a, b, and c.
We are given :
500 × 500
Using distributive property
500 × 500 = 5 × 100 × 5 × 100
= (5 × 5) × (100 × 100)
= (25) × (10000)
= 250,000
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a dataset on 91 roller coasters lists the duration of the ride in seconds in addition to the drop height in feet for some of the coasters. one coaster, the tower of terror, is unusual for having a large drop but a short ride. after setting it aside, a regression to predict duration from drop for the remaining 90 coasters has r29.4%. complete parts a through c.a) What are the variable and units in this regression? The predictor variable is ___ in units of ___ and the response variable is ___ in units of ___ b) What units does the slope have? Feet, Seconds per foot, Seconds, Feet per second. c) Is the slope probably positive or probably negative? Explain. The slope is probably ____ because ___
(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.
(b) The slope is in seconds per foot.
(c) The slope may be negative, as greater drop heights generally result in longer travel times.
(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.
(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.
(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.
Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .
The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.
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factor. If the trinomial will not factor write "prime"
a²-13a-30
Answer:
( a + 2 ) ( a - 15 )
Step-by-step explanation:
a² - 13a - 30
a² + 2a - 15a - 30
( a² + 2a ) - ( 15a - 30 )
a ( a + 2 ) - 15( a + 2 )
( a + 2 ) ( a - 15 )
Find the median, mode, and range
of the data.
Birth weight (pounds) 6, 9, 8, 6, 9, 6
Answer:
answer: 7
Step-by-step explanation:
u have to find the median by finding the middle of all of those numbers which will me seven
Brian multiplies 1.098 by powers of 10.
1.098 × 101 = 10.98
1.098 × 102 = 109.8
1.098 × 103 = 1,098
1.098 × 104 = 10,980
By what power of 10 would Brian multiply 1.098 to get a product of 1,098,000?
To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to the power 6.
What is scientific notation?Powers of 10 are used in scientific notation to indicate extremely big or extremely tiny quantities. A number is written as the result of a coefficient (a number between 1 and 10) and a power of 10 when it is expressed in scientific notation. The number represented by the power of 10 is the distance the decimal point must be moved to convert a number to standard form (i.e., a number without exponents).
To get from 1.098 to 1,098,000, Brian would need to multiply by 1,000,000 that is 10 raised to 6.
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Find the indicated measure in parallelogram ABCD. State which theorem you used.
AD = 23.2 (opposite side of parallelogram are equal) and ∠D = ∠B = 188 (opposite angles are equal).
Explain the features of parallelogram:Parallelograms' characteristics
The opposing sides of a parallelogram are parallel to one another.A parallelogram has equal-length opposing sides.In a parallelogram, the measurements of the opposing angles are equal.The total of all the angles of a parallelogram, like all other quadrilaterals, is 360°.From the properties of parallelogram:
AD = BC (opposite side of parallelogram are equal)
x + 21 = 12x - 1
12x - 2x = 21 + 1
10x = 22
x = 2.2
AD = x + 21 = 2.2 + 21 = 23.2
Now,
∠A + ∠D = 180° (co interior angles are supplementary)
y - 9 + y/2 = 180
2y - 18 + y = 360
y = 360 + 18
y = 378
∠D = y/2 = 378/2 = 188
∠D = ∠B = 188 (opposite angles are equal).
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at bedtime, you read three books to your kids, walker, matthew, and dean. together, they have 43 books. if you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? assume they have different favorites. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
If we randomly choose three books, then the probability that the three we choose will consist of each of their favorite books is 0.000081.
The total number of books is = 43 books.
Now, 3 books have to be selected.
So, the number of ways of choosing 3 different books from the 43 books can be calculated as : ⁴³C₃ = 12341,
The number of ways that those 3 get their favourite book is = ³C₃ = 1.
The probability that 3 you choose will consist of each of their favorite books is = 1/12341
= 8.103×10⁻⁵,
= 0.000081
Therefore, the required probability is 0.000081.
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Write 1.1 as a mixed number.
-
You draw two marbles without replacement from a bag containing three green marbles and three black marbles. The number of possible outcomes in the sample space
Answer: There are 7 marbles in the bag and in the first attempt, all 7 marbles are there. After one marble is taken away, then we have 6 marbles to choose from. Therefore we will multiply 7*6 = 42.
Hence, there are 42 possible outcomes.
how do you find surface area on the net of a rectangular prism
Answer: The area of the rectangular prism would be S.A. = 66m²
Step-by-step explanation: :)
What is the surface area of this rectangular prism?
A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces. The surface area of this rectangular prism = l x b
We have given
4 rectangles with area
A₁ = 3m × 4m = 12 m²
2 rectangles with area
A₂ = 3m × 3m = 9 m²
Therefore the Surface Area of the rectangular prism is:
S.A. = 4A₁ + 2A₂
S.A. = 4(12) + 2(9)
= 48 + 18
= 66
Hence, the net surface area of the rectangular prism would be 66 meters sq.
Graph the function by hand using the techniques you were taught in this unit: f(x) = 2sin(x)-2. Your work and explanations must use the methods taught in this class.
• Amplitude: 2
• Period: 2pi
• Midline: y = -2
• y-intercept: (0, -2)
To graph the function f(x) = 2sin(x)-2, we can start by plotting the y-intercept (0, -2).
Next, we can use the amplitude of 2 to mark the highest and lowest points of the graph. The highest point will be 2 units above the midline at y = 0, and the lowest point will be 2 units below the midline at y = -4.
To establish the period of the function, we need to identify the distance between one complete cycle of the graph. Since sine has a period of 2pi, we can see that the period of our function is also 2pi.
Starting from the y-intercept, we can mark a point on the graph that is one-quarter of the way through a cycle, at x = pi/2. The sine function will be at its maximum value of 1 at this point, so the graph will be at y = 0 + 2
What type of function is a circle?
is a pineapple
Step-by-step explanation:this is becuase you should work it out youself you silly goose
Answer:
circle is not a function.
Step-by-step explanation:
there are certain rules to define a mapping as function, one of them is function should not have more than 1 value at a given x.
for illustration purpose consider the below diagram,
as you can see in the given circle at x = 2, there are two different values of y, therefore equation of circle doesn't qualify as a function. half circle can be defined as a function (by restricting the range to only positive or negative values).
Hopefully you found the answer helpful
solve simultaneously
[tex]44 = x - y {e}^{ - 0.7} [/tex]
[tex]18 = x - y[/tex]
Step-by-step explanation:
A component with time to failure T has failure rate z(t)= 2. 0*10-6 t/hour for t>0 1) Determine the probability that the component survives 200 hours 2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours
The probability that the component survives 200 hours is approximately 0.9802. The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
What is probability?
Probability is a numerical representation of the likelihood or chance of a specific event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
To determine the probability that the component survives 200 hours, we need to calculate the survival function, which is the probability that the component lasts longer than 200 hours. We can use the formula:
[tex]$$ S(t) = e^{-\int_0^t z(u) du} $$[/tex]
where [tex]$S(t)$[/tex] is the survival function and [tex]$\int_0^t z(u) du$[/tex] is the integral of the failure rate from 0 to [tex]$t$[/tex].
In this case, the failure rate is [tex]$z(t) = 2.0\times10^{-6}t/\text{hour}$[/tex] for [tex]$t > 0$[/tex]. Integrating this from 0 to 200 gives:
[tex]$$ \int_0^{200} z(t) dt = \int_0^{200} (2.0\times10^{-6}t) dt =[/tex] [tex]\left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{200} = 0.02 $$[/tex]
Substituting this into the survival function formula gives:
[tex]$$ S(200) = e^{-\int_0^{200} z(t) dt} = e^{-0.02} \approx 0.9802 $$[/tex]
Therefore, the probability that the component survives 200 hours is approximately 0.9802.
To determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, we need to use the conditional probability formula:
[tex]$ P(T > 400|T > 200) = \frac{P(T > 400 \cap T > 200)}{P(T > 200)} $$[/tex]
We can calculate the numerator using the survival function:
[tex]$ P(T > 400 \cap T > 200) = S(400) $$[/tex]
To find [tex]$S(400)$[/tex], we need to integrate the failure rate from 0 to 400:
[tex]$$ \int_0^{400} z(t) dt = \int_0^{400} (2.0\times10^{-6}t) dt = \left[\frac{(2.0\times10^{-6})}{2}t^2\right]_0^{400} = 0.16 $$[/tex]
Substituting this into the survival function formula gives:
[tex]$$ S(400) = e^{-\int_0^{400} z(t) dt} = e^{-0.16} \approx 0.8534 $$[/tex]
To find the denominator, we can use the survival function we found earlier:
[tex]$ P(T > 200) = S(200) = e^{-0.02} \approx 0.9802 $$[/tex]
Substituting these values into the conditional probability formula gives:
[tex]$ P(T > 400|T > 200) = \frac{S(400)}{S(200)} \approx \frac{0.8534}{0.9802} \approx 0.8703 $$[/tex]
Therefore, the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
1) The probability that the component survives 200 hours is approximately 0.9802.
2) The probability that a component, which is functioning after 200 hours, is still functioning after 400 hours, is approximately 0.8703.
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Complete question:
1. A component with time to failure [tex]$\mathbf{T}$[/tex] has failure rate[tex]$z(t)=2.0*10^{-6}$[/tex]t/hour for [tex]$t \ge 0$[/tex]
1) Determine the probability that the component survives 200 hours
2) Determine the probability that a component, which is functioning after 200 hours, is still functioning after 400 hours Note that the failure rate in this problem is not constant, but a function of time [tex]${\mathbf{}}t$[/tex].
2. Consider a computer system called [tex]$3\mathrm{P2M}$[/tex] in the following figure. The system consists of three processors and two shared memories communicating over a shared bus, as shown in the following Figure. The [tex]$3\mathrm{P2M}$[/tex] system is operational as long as at least two processors can communicate with at least one of the two memories over the bus. a) Construct the fault tree model of this system b) Find all the minimal cut sets c) Assume all the components fail exponentially with the following failure rates: processors (P1, P2, P3): 0.0001/hour; memories (M1, M2): 0.0001/hour; bus: 0.000001 /hour. Find the system reliability at mission time [tex]$t=100$[/tex] hours.