et x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 11 feet per year and σ = 2 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.) (a) an escape dune will move a total distance of more than 90 feet in 7 years
Given the following which is the mean and standard deviation of the dune’s movement over one year and need to find out what the ten year mean and the standard deviation will be.
The ten-year mean is ten times the one year mean or 110 feet per decade. The ten-year standard deviation is somewhat more complicated. Multiple independent trials accumulate standard deviation as the square root of the number of trials since an unusually high level of movement ten years in a row. The decade is going to be 2 feet per year x square root of ten will result to 6.32 feet.
The answer will to question A. will be:
90 < 110 + z (6.32 feet)
-20 < z (6.32 feet)
z > - 3.16
By using the z table, it shows the probability of 0.9992. This result shows that as 90 feet is lesser than the mean travel that is expected over decade.
To find the probability that a sand dune moves more than 90 feet in 7 years, one must calculate a z-score using the mean annual movement, standard deviation, and the 7-year period, then find the corresponding probability in a standard normal distribution table or calculator.
Explanation:The question involves calculating the probability that a random variable, X, will exceed a certain value over a period using the normal distribution. The random variable X in this context represents the movement of sand dunes per year, which is assumed to be normally distributed with mean (μ) of 11 feet per year and a standard deviation (σ) of 2 feet per year.
To find the probability of the dune moving more than 90 feet in 7 years, we first calculate the mean movement for 7 years, which is 7 × μ = 7 × 11 feet = 77 feet. Next, we calculate how much more than 77 feet does 90 feet represent. This difference is 90 - 77 = 13 feet. Then, we standardize this difference by dividing by the standard deviation over the square root of 7 years to get the z-score:
Z = (90 - 7×11) / (σ × √7) = (90 - 77) / (2 × √7) = 13 / (2 × √7)
The z-score helps us find the probability that X is more than the calculated mean for 7 years. We look up this z-score in the standard normal distribution table or use a calculator to find the probability that corresponds to this z-score. This gives us the probability that a dune will move more than 90 feet in 7 years. The answer should be rounded to four decimal places as per the instruction in the question.
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the cost per month of one cell phone plan is $30 plus and additional nickel for each text. write an equation that defines the total monthly cost,c, as a function of the number of taxts,t
Write the ordered pair that describes a point 12 units down from and 7 units to the right of the origin.
A 1:35 scale model of a fishing hut is 17 cm tall, 18 cm wide, and 19.7 cm long. What are the dimensions of the actual ice fishing hut?
To determine the actual size of an ice fishing hut from a 1:35 scale model, multiply each model dimension by 35, resulting in a real hut approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.
The dimensions of the actual ice fishing hut, based on the 1:35 scale model, can be found by multiplying each dimension of the model by 35. To find the height, multiply 17 cm by 35, which gives 595 cm or 5.95 meters. To find the width, multiply 18 cm by 35, which gives 630 cm or 6.3 meters. Finally, to find the length, multiply 19.7 cm by 35, resulting in 689.5 cm or 6.895 meters. Therefore, the actual dimensions of the ice fishing hut are approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.
The plant where you work has a cylindrical oil tank that is 2.5 feet across on the inside and 10 feet high. The depth of the oil in the tank is 2 feet. About how many gallons of oil ate in the tank
Answer:
There are 73.38 gallons in the tank.
Step-by-step explanation:
The diameter of the tank is = 2.5 feet
So, the radius is = [tex]2.5/2=1.25[/tex] feet
The depth of the tank = 2 feet
The volume of the cylinder is = [tex]\pi r^{2} h[/tex]
V=[tex]3.14\times(1.25)^{2} (2)[/tex]
= 9.81 cubic feet
Now, 1 cubic feet = 7.48 gallons
So, 9.81 cubic feet = [tex]7.48\times9.81=73.38[/tex] gallons
So, there are 73.38 gallons in the tank.
A watering can dispenses water at a rate of 0.15 gallon per minute. The original volume of water in the can was 5 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y) as a function of time in minutes (x) from the first minute after the can starts dispensing water?
Answer:
The changing rate of the amount of water in the watering can is a constant rate of 0.15 gallon per minute.
The initial volume of water in the can at time = 0 is 5 gallons
The function will be a linear function in the form of where
is the volume of water in the can after minutes
is the changing rate
is the initial volume when time is 0
Substitute all the values into the form we have
Step-by-step explanation:
y=0.15x +5
Which property of real numbers is illustrated by the following statement?
6(7x) = (6 ∙ 7)x
-0.09 as a fraction , but the 09 is repeating
What is 1 3/4 - 5/6r =8/3
What is the circumference of a circle with a 7 foot diameter
In a public opinion poll,624 people from a sample of 1,100 indicated they would vote for a specific candidate.how many votes can the candidate expect to receive from a population of 40,000
1) Lee y plantea una ecuación que sea útil para resolver cada ecuación.
a. El perímetro de un jardín rectangular es de 58 m. Si el lado mayor mide 11 m mas que el lado menor.¿Cuanto mide los lados del jardín?
What value does 4 represents in the number 487.009 ?
3rd place to the left of the decimal point is the hundreds place
so the number 4 represents 4 hundred
Martina purchased a prepaid phone card for $15.00. Calls cost 5 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x minutes of calls is given by the following function.
C (x) = 15.00 -0.05x
How much credit is left on the card after Martina uses it for 20 minutes of calls?
Create a scenario that leads to an inequality of the form ax + b > c.
Answer:
Ben needs more than 200 points to unlock the next level in the game
He already has 45 points
For every win, he receives 5 points
No. of wins required: x
5x + 45 > 200
the football team offense began a drive from their 20 yard line. They gained 8 yards, lost 12 yards and lost 2 yards before having to kick the ball. What yard line were they on when they had to kick the ball
Please I have no clue
The coordinates of three vertices of rectangle are A(1,-5),B(1,3),and C(10,3). Find the coordinates of the fourth vertex. Then, find the area of the rectangle.
NEED HELP FAST!!!
2.
Two lines, C and D, are represented by the equations given below:
Line C: y = x + 10
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why? (5 points)
(5, 17), because one of the lines passes through this point
(5, 17), because the point lies between the two axes
(4, 14), because the point does not lie on any axis
(4, 14), because both lines pass through this point
Answer:
answer D
Step-by-step explanation:
make a word problem with the problem of 30 + 2d ex the outcome of 1,000 divided by x
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received 5 fewer cookies than she would have received had all of the cookies been evenly divided among the h grandchildren.
How many cookies did Cindy receive?
Write your answer as an expression.
Which of the following expressions represents the value, in dollars, of a certain number of nickels, n, and dimes, d?
value = v
v = 0.05n + 0.10d
Answer: v = 0.05n + 0.10d
Step-by-step explanation:
if x=2 , y=3 , and z=4 , what Is xyz?
Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function?
solve for w.
7w=11.2
Which of these is mostly likely to describe the change received from a cash purchase?
A.Whole Number
B.Negative Integer
C.Rational Number
D.Irrational Number
Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without tax? The cost of an item is 100% of its price. What number goes in the ? Of the additional problem
1.00-0.06 = 0.94
7.95 x 0.94 = 7.473, round to 7.47 without the tax
the height of an object dropped from the top of a 320-meter building is given by h(t)= -5t^2+320. how long will it take the object to hit the ground
Write 18/13 as a decimal.
Enter your answer as a decimal rounded to the nearest hundredth, like this: 4.25
A fraction is a way to describe a part of a whole. The given fraction 18/13 in the form of a decimal will be equal to 1.38.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The given fraction 18/13 in the form of a decimal can be written as,
18/13
= 1 5/13 (In the form of a mixed fraction)
= 1 + 0.384615
= 1.384615 ≈ 1.38 (In the form of a Decimal)
Hence, The given fraction 18/13 in the form of a decimal will be equal to 1.38.
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Silvia e Rebecca acquistano on line 10 cubi di polistirolo da rivestire di stoffa.Le dimensioni di ogni cubo riportate nel sito sono 150x150x150mm.
Possono essere sufficenti 2m^2 di stoffa?
Si perché?
No perché?