2.192 repeating to a rational Number?
Answer:
no
Step-by-step explanation:
Answer:
rational number
o((>ω< ))o help plsv
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
Answer:
0.625 liters
Step-by-step explanation:
Given data
volume drained= 2.5Liters
Time= 4 days
Now the if 4 days leakage will produce a volume of 2.5Liters
Then 1 day will produce a volume of x liters
cross multiply
4x= 2.5
x= 2.5/4
x= 0.625 liters per day
Hence, each day will produce 0.625 liters
what is a irrational number minus a irrational number?
Answer:
They won't both be rational but that's about it. If one is rational and the other is not then the result is certainly irrational. Subtracting two irrational numbers might produce a rational value but it might also not. Consider: a=1+2–√, b=2–√ and a=3–√, b=2–√.
Step-by-step explanation:
Answer:
Rational number minus irrational number will result in an irrational number respectively : 2 - √3 is an irrational number. And it's consequent results [ Addition ] will also result the same : Aslike : 2 + √3 is also an irrational number. If you dig deep into the question it is similar to the basic odd minus odd or even minus even.
Hope this helps <3
Create a line parallel to ABand passes thru point C
First, the definition of parallel lines is:
Lines on a plane that never meet. They are always the same distance apart.
Considering the definition we draw the parallel line as a line that has all its points at the same distance of the one that passes through A and B.
Im not sure how to do this, could one of you give me the answer on how to do this?
Answer:
2x+4=52
2x+19=67
2x+13=61
(I gotta be honest I can’t fully remember how to name the angles but to not set you astray I just put the equation each angle goes to)
x=24
Step-by-step explanation:
the sum of all three angles is equal to 180 degrees
So we can add all of these angles and set it equal to 180 like this
(2x+19)+(2x+4)+(2x+13)=180
Simplify by adding common terms
6x+36=180
-36. -36
6x=144
/6. /6
x=24
So now to find the angles we just fill in x with 24
2(24)+4
48+4
52
2(24)+19
48+19
67
2(24)+13
48+13
61
Hopes this helps please mark brainliest
(10 points) Give the design of a counter. Use five JK flip/flops. Assuming the value inside the counter is 00100, what will be the value of the counter after two clock ticks
This is because each clock tick will cause the counter to increment by one, and the binary value of 00100 incremented twice becomes 00110.
To design a counter using five JK flip-flops, we can cascade them in a "ripple" configuration. The output of the first flip-flop will be connected to the clock input of the second flip-flop, the output of the second flip-flop will be connected to the clock input of the third flip-flop, and so on. The input to the first flip-flop will be the clock signal, and the J and K inputs of all five flip-flops will be connected to a common input (such as a switch or another logic gate) that can be used to set the initial value of the counter. Assuming the value inside the counter is 00100, after two clock ticks the value of the counter will be 00110.
Learn more about binary value here
https://brainly.com/question/30583534
#SPJ11
Pls help
WILL MARK BRAINLIEST!!
Answer:
Technically, there is a proportionality because there will always be more road bikes than mountain bikes rented, but the proportionality is not completely constant as the ratio is 300/425 which is 0.75 compared to 575/680 which is 0.84.
During the summer break from school, Eric is going to work 25 hours a week for eight weeks babysitting for a family in his neighborhood. Eric will be paid $10 an hour for his babysitting job. In addition, Eric's family gives him a weekly allowance of $15. What will Eric's income be for the eight weeks he is babysitting?
Answer:
$2120.
Step-by-step explanation:
So first off he will be working for 25 hours a week for eight weeks.
He's getting paid $10 an hour. For one week, 25*10=$250. He would have $250 after one week.
Let's find out how much money for 8 weeks. $250*8=$2000.
Eric will have $2000 for babysitting.
On top of that, his family is also giving a $15 allowance each week.
15*8=$120.
$2000+$120=$2120.
Eric's income for the eight weeks he is babysitting will be $2120.
A group of students has a total of 29 pencils and everyone has at least one pencil. six students have 1 pencil each ,five students have 3 and the rest have 2 .how many student shave only 2pencils
Answer:
18 students have only 2 pencils
Step-by-step explanation:
There is 29 students. six + five is eleven. Subtract 29 - 11 which is 18
What value of k makes the equation below true?
k - 2k + 3k - 4k + 5k - 6k + 7k - 8k + 9k - 10k = 100.
What does k equal?
Answer:
k=-20
Step-by-step explanation:
We move all terms to the left:
k-2k+3k-4k+5k-6k+7k-8k+9k-10k-(100)=0
We add all the numbers together, and all the variables
-5k-100=0
We move all terms containing k to the left, all other terms to the right
-5k=100
k=100/-5
k=-20
Suppose that, in a probability experiment, there are three independent events A, B and C. Furthermore, P(A) = 0.2, P(B) = 0.24, and P(C) = 0.32. What is the probability that at least one of A, B, or C happens?
The probability that at least one of A, B, or C happens is approximately 0.5968, or 59.68%.
To calculate the probability that at least one of A, B, or C happens, we can use the principle of inclusion-exclusion.
The probability that at least one of the events occurs is equal to the sum of the probabilities of the individual events minus the sum of the probabilities of the intersections of any two events plus the probability of the intersection of all three events. This can be expressed mathematically as:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Since A, B, and C are independent events, we know that the probability of any intersection of two or more of them is simply the product of their individual probabilities. Therefore, we can substitute the given probabilities into the equation:
P(A ∪ B ∪ C) = 0.2 + 0.24 + 0.32 - (0.2 x 0.24) - (0.2 x 0.32) - (0.24 x 0.32) + (0.2 x 0.24 x 0.32)
Simplifying the expression gives:
P(A ∪ B ∪ C) = 0.5968
In other words, in about 60% of the trials, at least one of the events A, B, or C will occur. This probability can be useful in determining the likelihood of a certain outcome in a probability experiment or in making decisions based on uncertain events.
To learn more about probability click on,
https://brainly.com/question/14051468
#SPJ4
gritical in equation (3) is referred to as a pseudo-order rate constant, or apparent 5. rate constant. Using grammatically correct sentences define pseudo-order rate constant. constant. 6. The rate law for the reaction cC+dD→ products has an expected rate law of the form: rate =k(C)
α
(D)β The orders α and β are unknown. a) Under what conditions will the rate law for this reaction be a pseudo β-order law in (D)? b) Assume that β is equal to either 1 or 2 . Using grammatically correct English sentences, explain how the value of β could be obtained from a series of experiments using the method of isolation. Include a discussion of both the experiments which would be done and how the data would be analyzed.
The pseudo-order rate constant, or apparent rate constant, in equation (3) refers to a rate constant that appears in a pseudo-order rate law. It is called "pseudo" because it does not represent the true reaction order but is an effective rate constant obtained under specific conditions.
In the rate law for the reaction cC + dD → products, the rate is expressed as rate = k(C)^α(D)^β, where α and β are the unknown reaction orders.
a) The rate law for this reaction will be a pseudo β-order law in (D) when the concentration of D remains much larger than the concentration of C throughout the reaction. In other words, if the concentration of D is in excess compared to C, then the rate becomes solely dependent on the concentration of C, resulting in a pseudo β-order rate law.
b) To determine the value of β using the method of isolation, a series of experiments can be conducted.
If β is equal to 1, the reaction rate would be directly proportional to the concentration of D. By varying the concentration of D while keeping the concentration of C constant, multiple experiments can be performed, and the corresponding rates can be measured. Plotting the rate versus the concentration of D on a graph would yield a straight line with a slope of β, indicating that β is equal to 1.
If β is equal to 2, the reaction rate would be proportional to the square of the concentration of D. Similar to the previous case, different experiments can be carried out by changing the concentration of D while keeping C constant. The obtained rates can be plotted against the square of the concentration of D. If the resulting graph shows a straight line with a slope of β, it indicates that β is equal to 2.
Analyzing the experimental data and observing the relationship between the rate and the concentration of D in each case allows the determination of the value of β in the rate law.
To know more about the method of isolation, refer here:
https://brainly.com/question/5082157#
#SPJ11
How do you solve the equation 4a+b=12
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*a+b-(12)=0
Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 4a+b-12 = 0 and calculate its properties
Notice that when a = 0 the value of b is 12/1 so this line "cuts" the b axis at b=12.00000
b-intercept = 12/1 = 12.00000
When b = 0 the value of a is 3/1 Our line therefore "cuts" the a axis at a= 3.00000
a-intercept = 12/4 = 3
Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is 12.000 and for a=2.000, the value of b is 4.000. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 4.000 - 12.000 = -8.000 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -8.000/2.000 = -4.000
Geometric figure: Straight Line
Slope = -8.000/2.000 = -4.000 a-intercept = 12/4 = 3 b-intercept = 12/1 = 12.00000Answer:
Step-by-step explanation:
Without having a numerical value for a (or b), you can't "solve this equation."
You can, however, solve it for either a or b, but not both.
For a: Subtract b from both sides. This results in 4a = 12 - b. Dividing both sides by 4 isolates a:
12 - b
a = --------------
4
For b: Subtract 4a from both sides. Then: b = 12 - 4a
View Policies Current Attempt in Progress Using the information provided in the table, the network diagram and the project completion time = 25 weeks, reduce the completion time of the project by 5 we
Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.
To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.
To achieve a reduction of 5 weeks, we can consider several strategies:
1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.
2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.
3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.
4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.
It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.
To know more about project management techniques and strategies, refer here:
https://brainly.com/question/32653641#
#SPJ11
Evaluate for a = 2 and b = 3.
(a + b)2
\(\sf\fbox\red{Answer:-}\)
(2+3)²
=(5)²
=25
\(\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}\)
In the figure, line v is parallel to line r . If m∠2=(11x+3)° and m∠8=(13x−19)° , what are the measures of ∠2 and ∠8?
Answer:
The measures of <2 and <8 are 124 degrees
Step-by-step explanation:
<2 is congruent to <4 by the Vertical Angles Theorem, and <4 is congruent to <8 by the corresponding angles theorem. <2 is congruent to <8 by the Transitive Property so we get <2 is congruent to <8, and it follows that m<2 equals m<8 by the definition of congruence. We can substitute <2 and <8 with 11x+3 and 13x-19 respectively, so we get 11x+3=13x-19. Solve for x, and we get that x=11, and plug in 11 for x into 11x+3, 11(11)+3=121+3=124.
The measure of angle ∠2 is 124.
The measure of angle ∠8 is 124.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
∠2 and ∠8 are alternate exterior angles.
This means,
∠2 = ∠8
We can write it as,
11x + 3 = 13x - 19
3 + 19 = 13x - 11x
22 = 2x
x = 11
Now,
∠2 = 11x + 3 = 11 x 11 + 3 = 121 + 3 = 124
∠8 = 13x - 19 = 143 - 19 = 124
Thus,
The measures of ∠2 and ∠8 are 124.
Learn more about corresponding angles here:
https://brainly.com/question/1597341
#SPJ2
What is the equation of the line through 1 2 which makes equal intercepts on the axis?
The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)
The equation of the line through (1,2) makes an equal intercept on the axis
The formula of the intercept form is
\(\frac{x}{a} +\frac{y}{b} =1\)
If they make an equal intercept
\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)
Put the value of the point in the axis, and we get.
\(1+2=a\\a=3\)
Put the value in the equation, and we get.
\(x+y=3\)
Learn more about equations from
https://brainly.com/question/29657983
#SPJ4
Identify a product/service that is currently in the decline stage. Use the Product Lifecycle Concept to explain why you believe the product/service is at that stage .
Describe the strategic options for companies that are competing in a declining market. Provide specific examples too illustrate what these strategic options entail and how they differ .
One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.
DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.
In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.
Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.
To learn more about discounts click here: brainly.com/question/15060398
#SPJ11
if p(x) = -2x²-3x+1, find p( -2)
help me please
\(\large{\mathcal{QUESTION:}}\)
if p(x) = -2x²-3x+1, find p( -2)
\(\large{\mathcal{ANSWER:}}\)
the answer is on the photo
9. An interior designer is decorating a bedroom and plans on placing a bookcase in the corner. The bookcase has three shelves, and each shelf has a diameter of 28 inches. What is the total shelf area of the bookcase?
The total shelf area of the bookcase is given as follows:
A = 1846.32 in².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The radius is half the diameter, hence it is given as follows:
r = 14 inches.
There are three shelves, hence the total shelf area of the bookcase is given as follows:
A = 3 x 3.14 x 14²
A = 1846.32 in².
(there are 3 bookcases, hence we obtain the area of one bookcase and then multiply by 3 to obtain the total area).
More can be learned about the area of a circle at https://brainly.com/question/15673093
#SPJ1
In this diagram, lines AC and DE are parallel and line DC is perpendicular to each of them. What is a reasonable estimate for the length of side DE
The reasonable estimate for the length of side DE is 3 units
Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.
Using the similarity theorem of a triangle, this is expressed as:
AC = DE
Using the pythagoras theorem to get the length of AC:
AB^2 = AC^2 + BC^2
5^2 + AC^2 + 4^2
AC^2 = 25 - 16
AC^2 = 9
AC= 3
Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units
Learn more on similar shapes here: https://brainly.com/question/14285697
Answer:
5/3
Step-by-step explanation:
satara was having fun playing poker. she needed the next two cards dealt to be hearts so she could make a flush (five cards of the same suit). there are 10 cards left in the deck, and three are hearts. what is the probability that the two cards dealt to satara (without replacement) will both be hearts? answer choices are in percentage format, rounded to the nearest whole number. 30% 7% 60% 26%
the probability that the two cards dealt to Satara (without replacement) will both be hearts is 7%
Total Number of cards left in the deck = 10
Number of hearts left in the deck = 3
Probability = (required outcome / Total possible outcomes)
Required outcome = hearts card in the deck
Without replacement, deal Satara two cards as follows:
The chance that the first card is a heart:
P(first card being hearts) = necessary result / all possible results
P(first card is a heart) equals 3/10.
The probability that the second card is a heart:
It cannot be replaced because:
Required result = (3 - 1). = 2
The total number of outcomes is (10 - 1) = 9 P(the second card is a heart) = 2 /9
The likelihood that the two cards are hearts is (3/10 x 2/9) = 6/90 = 0.0666 x 100% = 6.66%
= 7% (nearest whole number)
learn more about probability here: https://brainly.com/question/24756209
#SPJ4
A bouquet of flowers weighs approximately 4. 3 × 104 milligrams. The bouquet has two daisies, each weighing 7. 5 × 102 milligrams.
If the daisies were removed from the bouquet, the bouquet would weigh p × 10q grams, where p is
and q is
A bouquet of flowers weighs approximately 4.3 × 10⁴ milligrams. The bouquet has two daisies, each weighing 7.5 × 10² milligrams.
If the daisies were removed from the bouquet, the bouquet would weigh p × 10q grams, where p is 4.3 × 10¹ and q is 2. First, subtract the weight of two daisies from the weight of the bouquet to find the remaining weight of the bouquet as follows:
Weight of two daisies = 2 × 7.5 × 10² milligrams
= 1.5 × 10³ milligrams
Weight of the bouquet without the daisies = Weight of the bouquet - Weight of two daisies
= (4.3 × 10⁴) - (1.5 × 10³) milligrams
= 4.15 × 10⁴ milligrams
Convert milligrams into grams as follows: 1 gram = 10³ milligrams
Hence, 1 milligram = (1/10³) grams
Multiply the weight of the bouquet without the daisies by this conversion factor to get the weight of the bouquet in grams as follows:
Weight of the bouquet in grams= (4.15 × 10⁴) × (1/10³) grams
= 4.15 × 10¹ grams
Therefore, the bouquet would weigh p × 10q grams, where p is 4.3 × 10¹ and q is 2, if the daisies were removed from the bouquet.
To know more about milligrams visit:-
https://brainly.com/question/29798259
#SPJ11
What is the probability that a standard normal random variable will be between 0.3 and 3.2?
A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.
What is probability?The probability is calculated by dividing the total number of outcomes by the total number of events.
Odds and probability are two different concepts.
Divide the probability of an event occurring by the probability that it won't happen to calculate chances.
The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.
So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.
First, a mean and standard deviation are introduced for a standard normal random variable.
The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.
Therefore, it should be more likely that:
P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)
Using the usual value of z:
P(0.3<z<3.2)=0.9993−0.6179
Justify by saying:
P(0.3<z<3.2)=0.3814
Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.
Know more about probability here:
brainly.com/question/24756209
#SPJ4
Determine whether each vector can be written as a linear combination of vectors S 1) 8= {(2₁-1₁3), (5,0,4)} a) 2- (-1₁-2.2); c) w = (1₁-8, 12) b) v = (8,-14, 27/4) d) (1,1,-1)
We are given a set of vectors S and we need to determine whether each given vector can be written as a linear combination of the vectors in S.
(a) For vector (2, -1, -2), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (2, -1, -2). By solving the system of equations, we find that k₁ = -1 and k₂ = 0, so the vector can be written as a linear combination of the vectors in S.
(b) For vector (8, -14, 27/4), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (8, -14, 27/4). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.
(c) For vector (1, -8, 12), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, -8, 12). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.
(d) For vector (1, 1, -1), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, 1, -1). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.
Learn more about vectors here: brainly.com/question/29740341
#SPJ11
from a population of size 500, a random sample of 50 items is selected. the mode of the samplea. can be larger, smaller or equal to the mode of the population. b. must be equal to the mode of population, if the sample is truly random. c. must be equal to the mean of the population, if the sample is truly random. d. must be 500.
The mode of a sample is the value that appears most often in the data set. It can be larger, smaller or equal to the mode of the population, depending on the sample size and the distribution of the population.
The mode of a sample is not necessarily equal to the mode of the population if the sample is truly random, as there is no guarantee that the most frequent value in the population will appear in the sample.
For example, let’s say the population has a mode of 10. If the sample size is 50, the probability of the sample having a mode of 10 is 0.2. The probability of the sample having a mode of 11 or larger is 0.4. The probability of the sample having a mode of 9 or smaller is also 0.4.
This means that the mode of the sample can be larger, smaller or equal to the mode of the population. It does not have to be equal to the mean of the population, as the mean is an average of all the values in the population and is not necessarily the most frequent value. Furthermore, the mode of the sample cannot be 500, as this is the size of the population, not a value that appears in the data set.
The mode of the sample can be larger, smaller or equal to the mode of the population, and cannot be equal to the mean of the population or equal to the size of the population.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
4. Find a polynomial function of degree 3 with the given zeros. Write your answer in the form:
Ax) = ax + bx² + cx+d
x= -2, x=-1, x=2
Answer:
I'm assuming the equation "Ax) = ax + bx² + cx+d" is really meant to read:
A(x) = ax^3 + bx² + cx+d
A(x) = x^3 + x^2 -4x -4
Step-by-step explanation:
(x+2)*(x+1)*(x-2) [This reflect the fact that x= -2, x=-1, x=2 all result in a zero]
Multiply this out to get A(x) = x^3 + x^2 -4x -4
A recent report from the Postal Rate Commission Office of the Consumer Advocate concluded that 23% of three-day Priority mail was not delivered by the end of the third day. Suppose an impartial inspector checks the on-time delivery of a random sample of Priority packages at the time of the report.
Required:
a. If the inspector randomly checks ten packages, what is the probability that at least one package did not arrive on time (by the end of the third day?
b. What is the probability that the first Priority package delivered on time is the fourth package checked?
c. What is the expected number of packages that need to be checked to find the first that doesn't arrive on time?
d. What is the expected number of packages that need to be checked to find the first that does arrive on time?
a. The probability that at least one package did not arrive on time is 0.92. b. The probability that the first Priority package delivered on time is the fourth package checked is 0.04. c. 4.35. d. 1.30.
a. The given information suggests that 23% of three-day Priority mail was not delivered by the end of the third day. If the inspector randomly checks ten packages, the probability that at least one package did not arrive on time (by the end of the third day) is the complement of the probability that all packages arrived on time. Hence, P(at least one) = 1 - P(all arrived on time). The probability of one package arriving on time is given by 1 - 0.23 = 0.77. Hence, the probability that all ten packages arrived on time is 0.77 × 0.77 × ... (ten times) ≈ 0.08. Therefore, the probability that at least one package did not arrive on time is 1 - P(all arrived on time) ≈ 1 - 0.08 = 0.92.
b. The probability that the first Priority package delivered on time is the fourth package checked is given by: P(3 on time, then 1 not on time) = (0.77)³ × 0.23 ≈ 0.04
The probability that the first Priority package delivered on time is the fourth package checked is obtained by finding the probability of having three packages delivered on time and the fourth not delivered on time. Since the probability of any package arriving on time is 1 - 0.23 = 0.77, the probability of having three packages delivered on time is (0.77)³. Then, the probability of having the fourth package not delivered on time is 0.23. Hence, the probability that the first Priority package delivered on time is the fourth package checked is P(3 on time, then 1 not on time) = (0.77)³ × 0.23 ≈ 0.04.c. The expected number of packages that need to be checked to find the first that doesn't arrive on time is given by: Expected value = 1 / P(first not on time) = 1 / 0.23 ≈ 4.35
The expected value is the number of trials needed to get the first success. In this case, the success is to have a package that does not arrive on time. The probability of having a package that does not arrive on time is 0.23. Then, the probability of the first package not arriving on time is 0.23, the probability of the second package not arriving on time is (0.77)(0.23), and so on. Hence, the expected value is obtained by summing the products of the probability of having the first failure (not on time) and the number of trials needed to get the first failure, which are the integers from 1 to infinity. This sum is known to be equal to 1 / P(first not on time). Therefore, the expected number of packages that need to be checked to find the first that doesn't arrive on time is 1 / P(first not on time) = 1 / 0.23 ≈ 4.35. d. The expected number of packages that need to be checked to find the first that does arrive on time is given by: Expected value = 1 / P(first on time) = 1 / 0.77 ≈ 1.30.
Learn more about probability here:
https://brainly.com/question/32575884
#SPJ11
A diver went 24 feet below the surface of the ocean, and then 47 feet down. What is the diver's new position relative to the surface?
Write an expression to represent the problem, and solve.
Answer:
71 feet below the water.
Step-by-step explanation:
x=the divers position relative to the surface
when x=0, the diver is at the surface.
when x=-24, the diver is 24 feet below the surface, therefore -24-47=-71.