In a 4-year period, expect around 2 loads (Poisson model). Over 11 loads is likely (80% chance). No loads for 5.8 years or more guarantees under 30% chance.
In a Poisson process with a mean time between occurrences of λ = 0.4 years, we can answer your questions as follows:
**(a) Expected number of loads in 4 years:**
The expected number of events in a Poisson process is the product of the mean occurrence rate (λ) and the time interval (t). Therefore, in a 4-year period, you can expect:
Expected loads = λ * t = 0.4 years/load * 4 years ≈ 1.6 loads
However, since the Poisson process deals with discrete events, the expected value doesn't necessarily translate to an exact number of occurrences. It represents the average number of loads you would expect to see over many repetitions of the same 4-year period.
**(b) Probability of more than 11 loads in 4 years:**
To calculate the probability of more than 11 loads, we need to find the probability of 12 or more loads. In a Poisson process, the probability of k events occurring in a time interval t is given by:
P(k events) = (e^(-λt) * (λt)^k) / k!
For k = 12 and λt = 4 * 0.4 = 1.6:
P(more than 11 loads) = 1 - P(0 loads) - P(1 load) - ... - P(11 loads)
≈ 1 - (e^(-1.6) * 1.6^0) / 0! - (e^(-1.6) * 1.6^1) / 1! - ... - (e^(-1.6) * 1.6^11) / 11!
≈ 1 - 0.1995 ≈ 0.8005
Therefore, the probability of having more than 11 loads in a 4-year period is approximately 0.801 (rounded to three decimal places).
**(c) Time period for at most 0.3 probability of no loads:**
We want to find the time period (t) where the probability of no loads (P(0 loads)) is at most 0.3. In other words, we need to solve:
P(0 loads) = e^(-λt) ≤ 0.3
Taking the natural logarithm of both sides and rearranging:
t ≥ -ln(0.3) / λ ≈ 2.303 / 0.4 ≈ 5.76 years
Therefore, the time period must be at least 5.76 years (rounded to four decimal places) for the probability of no loads to be at most 0.3.
The probable question may be:
An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year.
(a) How many loads can be expected to occur during a 4-year period?
(b) What is the probability that more than eleven loads occur during a 4-year period? (Round your answer to three decimal places.)
(c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.3? (Round your answer to four decimal places.)
Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1
Answer:
399.21 newtons or 40.73 kg
Step-by-step explanation:
In order to solve this you first have to do a rule of threes to calculate how much would the fish will weight compared with the stretching of the spring:
[tex]\frac{21}{162} =\frac{62.1}{weight} \\weight=\frac{62.1*162}{21}=399.21 Newtons[/tex]
So the weight would be 399.21 newtons and it would have 40.73 kilograms in mass.
What's the circumference of a circle with a diameter of 30 cm
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting
Answer:
the rate is equal to [tex]3.2\frac{inches}{week}[/tex]
Step-by-step explanation:
we have
[tex]h-15=3.2t[/tex]
where
h is the height of a plant
t is the number of weeks after planting
so
Find the rate at which the plant's height is increasing
we know that
The given formula is a linear equation
The rate is equal to the slope of the linear equation
Isolate the variable h
[tex]h=3.2t+15[/tex]
the slope is equal to [tex]m=3.2\frac{inches}{week}[/tex]
therefore
the rate is equal to [tex]3.2\frac{inches}{week}[/tex]
The height was 31 inches in (D) Some time between 3 and 7 weeks.
To find out when the height of the plant was 31 inches using the formula given, we start with the equation:
h - 15 = 3.2t
We want to find the value of ( t ) when the height ( h ) is 31 inches. First, substitute ( h ) with 31 in the equation:
31 - 15 = 3.2t
Now, simplify the left side:
16 = 3.2t
Next, divide both sides by 3.2 to isolate ( t ):
t = [tex]\frac{16}{3.2}[/tex]
Calculating this gives:
t = 5
Therefore, the height of 31 inches was reached at 5 weeks.
So, the answer is: D. Some time between 3 and 7 weeks.
The full question is:
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting
When was the height 31 inches?
A. Some time between 11 and 18 weeks
B. Some time between 7 and 12 weeks
C. Some time between 6 and 10 weeks
D. Some time between 3 and 7 weeks
An integer is 1 less than twice that of another. If their sum is 20, find the integers
Answer:7,13
Step-by-step explanation:
Pizza planet is running a special: 3 pizzas for $16.50. What is the unit rate for one pizza?
Answer:
$5.5
Step-by-step explanation:
16.5 ÷ 3= 5.5
Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0). The fourth vertex is point
1.)(2, -1)
2.)(10, 2)
3.)(8, 4)
Answer:
Option 3 - (8,4)
Step-by-step explanation:
Given : Three consecutive vertices of a parallelogram are points (2, 4), (0, 0), and (6, 0).
To find : The fourth vertex is point ?
Solution :
We have given that points are forming a parallelogram.
Let the fourth coordinate is (x,y)
Now, we draw a rough image of the given situation.
Refer the attached figure below.
Draw a parallelogram ABCD with mid point O.
Applying the mid point between two points (2,4) and (6,0).
[tex]O=\frac{2+6}{2}, \frac{4+0}{2}\\\\ O=4,2[/tex]
Now, Applying mid point between points (0,0) and (x,y)
[tex](4,2)=\frac{x+0}{2}, \frac{y+0}{2}[/tex]
[tex]\frac{x+0}{2}=4, \frac{y+0}{2}=2[/tex]
[tex]x=8 ,y=4[/tex]
Therefore, The fourth vertex point is (8,4).
Hence, Option 3 is correct.
Suppose w=xy+yzw=xy+yz, where x=e2t, y=2+sin(4t)x=e2t, y=2+sin(4t), and z=2+cos(5t)z=2+cos(5t).
a. use the chain rule to find dwdtdwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2te2t as x.
To find dw/dt for w = xy + yzw, we use the chain rule, yielding dw/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt). The derivatives dx/dt, dy/dt, dz/dt are calculated using derivative rules. The question-specific parameters are then substituted back into these functions.
Explanation:Let's denote w as a function of x, y, and z, where x, y, and z are functions of t. We will use the chain rule to find dw/dt as a function of x, y, z, and t.
Given the function: w = xy + yzw, using the chain rule, we get the derivative dw/dt as:
dw/dt = x * dy/dt + y * dx/dt + y * dz/dt + z*dy/dt + z * dy/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt)
To particularize this expression for our given parameter values, we need to find dx/dt, dy/dt, and dz/dt. Each derivative can be calculated using the derivative rules. In this case we are to leave the equations x=e^2t, y=2+sin(4t), z=2+cos(5t) as they are, not rewriting them in terms of t, and also not rewriting e^2t as x. This results in dw/dt as a function of x, y, z, and t.
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Write four decimals with the digit four in a different place in each ones, tenths , hundredths, and thousandths .Then write a statement that compares the value of the digit 4 in the different decimals
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
5,280 feet = 1 mile
40 miles x 5280 = 211200 feet per hour
1 hour = 3600 seconds
211200 / 3600 = 58.67 feet per second
Answer:
The answer is 59 feet per second (B)
Step-by-step explanation:
edge hope ya do well
A construction crew needs to build a road that will be 20 miles long. The crew already completed a stretch that is 6.44 miles long and another that is 8.62 miles long.
How much more road does the construction crew need to build?
(A) 2.18 miles
(B) 4.94 miles
(C)11.38 miles
(D)13.56 miles
solve 3x=12? 5,36,4,or 3
How do you find the corresponding ordered pair of f(23)=2?
A person's blood glucose level and diabetes are closely related. let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean m 85 and standard deviation s 25 (diagnostic tests with nursing implications, edited by s. loeb, springhouse press). note: after 50 years of age, both the mean and standard deviation tend to increase. what is the probability that, for an adult (under 50 years old) after a 12-hour fast,
Help!!!!!!
A sporting goods store marks up the cost s of soccer balls by 250%. Write an expression that represents the retail cost of the soccer balls. The store buys soccer balls for $5.00 each. What is the retail price of the soccer balls?
(you have to do a expression)
1.all real numbers that are less than -3 or greater than or equal to 5
A.x < -3 or x≥5
B.x < 5 or x ≥-3
C.x ≤ -3 or x >5
D.x ≤-3 or x ≤ 5
2.The time a cake must bake is between 25 minutes and 30 minutes, inclusive.
A.25 < x < 30
B.25 ≤ x ≤ 30
C.25 ≤x ≥ 30
D.25 < x > 30
3. Solve. 5 < x -2 <11
A.5 < x < 11
B.7 < x < 13
C.7 < x < 11
D.5 < x < 16
4. Which graph shows the solution of 9 - c < 2 or -3c > 15?
1 is a
2 is b
3 is b
hope it helped
Find the average rate of exchange for the function. x=-6 and x=0
[tex]f(x)= \frac{1}{x-1} [/tex]
How would you Evaluate. 5⋅4 ^0
A survey of 240 families showed that.. 91 had a dog 70 had a cat 31 had a dog and a cat 91 had neither a cat nor a dog nor a parakeet 7 had a cat and a dog and a parakeet how many had a parakeet
There were 30 families that had a parakeet.
By using the concept of Sets :
- Total number of families surveyed (denoted as N) = 240.
- Number of families with dogs (denoted as D) = 91.
- Number of families with cats (denoted as C) = 70.
- Number of families with both dogs and cats (denoted as D ∩ C) = 31.
- Number of families with neither cats nor dogs nor parakeets (denoted as neither) = 91.
- Number of families with cats, dogs, and parakeets
(denoted as D ∩ C ∩ P) = 7.
We want to find the number of families that had parakeets
(denoted as P).
To find the number of families with parakeets, we can use the principle of inclusion-exclusion. It states that:
N(D ∪ C ∪ P) :
= N(D) + N(C) + N(P) - N(D ∩ C) - N(C ∩ P) - N(D ∩ P) + N(D ∩ C ∩ P).
Substitute the given values:
240 = 91 + 70 + P - 31 - N(C ∩ P) - N(D ∩ P) + 7.
Now, we can calculate the number of families with both cats and parakeets (C ∩ P) and the number of families with both dogs and parakeets (D ∩ P):
C ∩ P + D ∩ P = (C + D + P) - (N(D) + N(C) + N(P)) = 240 - 91 - 70 - P = 79 - P.
From the given information, we also know that the number of families with neither cats nor dogs nor parakeets is 91. Therefore, we can write:
neither + N(D ∩ P) + N(C ∩ P) + N(D ∩ C ∩ P) = 91.
Substitute the values:
91 + N(D ∩ P) + C ∩ P + 7 = 91.
Now, we can solve for C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
Substitute the value of C ∩ P we found earlier:
79 - P = 91 - N(D ∩ P) - 7.
Now, we can find N(D ∩ P):
N(D ∩ P) = 79 - P - 91 + 7 = -P - 5.
However, we know that the number of families cannot be negative. So, we ignore this solution. Instead, we use the previously calculated value of C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
91 - (79 - P) - 7 = 91 - 79 + P - 7 = P - 7.
P - 7 = 30.
Finally, we get the value of P:
P = 30.
Therefore, there were 30 families that had a parakeet.
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1.5 4.5 13.5 40.5.... what is the seventh term in the sequence?
The seventh term in the sequence is 1093.5.
What is Sequence?A sequence in mathematics is a ordered set od objects or numbers which are related with something.
For example, 1, 3, 5, ..... is a sequence of odd numbers.
Given sequence is,
1.5, 4.5, 13.5, 40.5....
There must be a predictable relation between the numbers in order for them to form in a sequence.
It is clear that,
First term = 1.5
Second term = 3 × 1.5
Third term = 3 × 3 × 1.5 = 1.5 (3)²
............
nth term = 1.5 (3)ⁿ⁻¹
seventh term = 1.5 (3)⁷⁻¹ = 1.5 (3)⁶ = 1093.5
Hence the seventh term is 1093.5.
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How do I complete an exponential growth table which does not give enough information?
Ava's heart rate is 65 beats per minute. If this is her average heart rate, how many times will her heart beat in 10 years.
Answer:
Ava's heart will beat for 341640000 beats in 10 years.
Step-by-step explanation:
Heart rate of Ava is = 65 beats per minute
We have to calculate the heart beat in 10 years.
Since Ava's heart beats in 1 minute = 65 times
Heart beat in 1 hour = 65 × 60
= 3900 beats
Heart beats in 24 hours or one day = 3900 × 24
= 93600 beats
Heart beats in 365 days or 1 year = 93600 × 365
= 34164000 beats
Heart beats in 10 years = 34164000×10
= 341640000 beats
Therefore, Ava's heart will beat for 341640000 beats in 10 years.
Use technology to find the p-value for a right-tailed test about a mean with nequals=66 and test statistic t equals 3.624 .
The ratio of red poms to yellow poms on a float is 5 to 7. If there are 392 yellow poms on the float, how many red poms are there? *
In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family, and want to sit together. How many ways can this happen?
Since 3 members want to sit together, we'll calculate total ways for it and then for remaining seats in each of its case, we'll see in how many ways can those rest of 5 people wants to sit.
The total number of ways those 8 people can sit is 3,991,680 ways.
Given that:Total 14 seats are there in a row in a doctor's waiting room.8 people are waiting to be seated.3 people are of same family and want to sit together.To find:In how many ways can those people sit?
Number of ways in which 3 family members can sit:Since 3 people wants to sit together, then suppose seats are numbered 1,2,3,...,14.
Then those 3 people can choose seats as:
1,2,3
2,3,4
...
...
12,13,14
Total 12 ways.
In each way, those three can sit on those 3 chairs in any order. The number of ways 3 people will arrange themselves is 3! = 6 ways.
Thus:
Total ways those 3 people can sit in = 12 times 6 = 72 ways.
( i did multiplication since for each of 3 seat chosen they were sitting in 6 ways, and this repeated 12 times would end up on 12 times 6 = 72 ways).
Number of ways those remaining 5 people can sit on remaining 11 seats:On remaining seats (14-3 = 11), we have 5 people to sit.
Those people can choose any seat they want to sit on.
Total ways(combinations) they together choose 5 seats is given by: [tex]^11C_5 = 462 [/tex]
For each of those choice of seats, they can arrange themselves in 5! = 120 ways.
Thus, those 5 people can sit in 120 times 464 = 55440 ways.
Since on each choice of those 3 family members , we have 55440 ways of 5 people sitting on remaining 11 seats, thus in total we have:
55440 times 72 = 3,991,680 ways.
Thus, in total, those 8 people can sit in 3,991,680 number of ways in that row of the doctor's waiting room.
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1 3/4 in a decimals
what is m<4? I tryed to do the work but I just can't get it can someone help me plz
F(x)=5(3-x)^2 What is f(-4)
A grocer has two kinds of tea, one selling for 80 cents per pound and the other selling for 60 cents per pound. How many pounds of each kind must he use to make 50 pounds of tea that will sell for 74 cents per pound?
Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
here, we have,
Imagine what x is tea grocer selling for 80 cents per pound
y is tea grocer selling for 60 cents per pound
{80x+60y
=50*74
=3700
{x+y=50 //*60
{80x+60y=3700
-{60x+60y=3000
20x=700
x=35
y=50-35=15
hence, Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
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I'm not quite sure where to start, help and answers would be appreciated !:)
What is 1/5 + 2/3 plz answer this