3. Suppose the average amount of apples per tree in a large orchard is 600 pounds with a standard deviation of 70 pounds. a. Assuming the necessary conditions are satisfied, give the mean and standard deviation of the Normal model that would be used to approximate the sampling distribution of the sample mean for a sample of 40 trees. Include units in your answers. b. Sketch and clearly label the sampling model for a sample of 40 trees, based on the 68-95-99.7 Rule. c. Find the probability that a random sample of 40 trees has an average amount of apples of 620 pounds or higher. (To show your work: Write down which calculator/program you are using and what values you are entering into the calculator.)
Answers
Answer:
a) The sampling distributio will be normal with mean 600 and standard deviation 11.07.
b) - 68% of the samples will have means between 589 and 611 apples per tree.
- 95% of the samples will have means between 578 and 622 apples per tree.
- 99.7% of the samples will have means between 567 and 633 apples per tree.
c) The probability that a random sample of 40 trees has an average amount of apples of 620 pounds or higher is 0.035.
Step-by-step explanation:
a) The sampling distribution for a population with mean of 600 pounds and standard deviation of 70 pounds, with a sample size of 40 trees, will have the following parameters:
\(\mu_s=\mu=600\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{70}{\sqrt{40}}=\dfrac{70}{6.325}=11.07\)
b) Using the 68-95-99.7 rule for the sampling distribution, we can tell that:
- 68% of the samples will have means between 589 and 611 apples per tree.
\(X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-1\cdot 70\sqrt{40}=600-11=589\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+1\cdot 70\sqrt{40}=600+11=611\)
- 95% of the samples will have means between 578 and 622 apples per tree.
\(X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-2\cdot 70\sqrt{40}=600-22=578\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+2\cdot 70\sqrt{40}=600+22=622\)
- 99.7% of the samples will have means between 567 and 633 apples per tree.
\(X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-3\cdot 70\sqrt{40}=600-33=567\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+3\cdot 70\sqrt{40}=600+33=633\)
c) We can calculate the probability with the z-score for X=620.
\(z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{620-600}{70/\sqrt{40}}=\dfrac{20}{11.068}=1.807\\\\\\P(X>620)=P(z>1.807)=0.035\)
The probability that a random sample of 40 trees has an average amount of apples of 620 pounds or higher is 0.035.
Related Questions
We are interested in determining the probability that a retail store will meet its daily revenue goal of $100. Analysis of sales history indicates that daily demand, D is random and independent of the demand on other days. Assume D follows the distribution below
P(D=d) =
0.3, d=0
0.3, d=1
0.2, d=2
0.1, d=3
0.1, d=4
Furthermore, due to a complicated discount structure, the shop has determined that their revenue per day can be modeled as R(s) = â100 cos(20s) + 100 where s is the number of jeans sold that day and R(s) is in dollars. Assume that this retail store will always have enough inventory to meet demand. What is the probability the retail store will generate a revenue of at least 100 dollars?
Answers
Answer:
Assume D follows the distribution below
P(D=d) =
So the probability of getting revenue of 100 dollars is 0.
Step-by-step explanation:
Ans - The cumulative probability for demand is given below
d 0 1 2 3 4
P(D=d) 0.3 0.3 0.2 0.1 0.1
C(D=d) 0.3 0.6 0.8 0.9 1.0
Now the Revenue function is
R(s-100cos(20s) 100
As per the question the retail store always has inventory to meet demand D
Now to get the revenue at least 100 dollars ---
1cos(20s) <0
As cos heta is a continuously decreasing function within 0 degree to 180 degree withcos(0)1 and cos 180)-
and cos (90)0.
Hence 20s90
s-4.5
As s is an integer s must be 5 to get revenue of at least 100 dollars.
Now the maximum demand for a particular day is 4.
So the probability of getting revenue of 100 dollars is 0.
O y=
y = cos(x + 1)
O y = cos(x+ 2x)
y-con~+5 )
Oy= cos(x+8)
©
Answers
Option C - y = cos(x + 5π) is the equation that most closely represents the graph. See attached graph.
What is an equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.
The graph of y = cos(x + 5π) is a cosine function that is shifted horizontally 5 units to the left compared to the standard cosine function.
The function is a periodic function that oscillates between -1 and 1, with each cycle shifted 5 units to the left compared to the standard cosine function.
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Suppose the domain of f is restricted to {1,2}.State the domain of the inverse function.Separate your answers with a comma.
Answers
The domain of f is restricted to {1, 2}
The domain of the inverse function
Find the value of x when 5 - x = 12x + 4
Answers
Answer:
5-4=12x+x
1=13x
1/13=×
consider a political discussion group consists of 6 democrates, 3 republicans, and 5 independents. suppose that two group members are randomly selected, in succession, to attend the political convention. find the probability of selecting a independent then a democrat
Answers
Answer:
16.48%
Step-by-step explanation:
6 democrates
3 republicans
5 independents
Total number: 6+3+5=14
Probability of selecting an independent:
#of independents/ Total number
5/14= 0.3571
Probability of selecting a democrat:
# of democrats/ Total number-1
6/13= 0.4615
Probability of independent then democrat:
0.3571x0.4615=0.1648
0.1648x100= 16.48%
Thomas got a haircut from the barber. If the
haircut costs $32 and he wants to leave a
18% tip, how much will he pay in total?
Answers
The diagram shows EFG. Which term describes point H?
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Answers
Point H is the ortho-center of our given triangle and option c is the correct choice.
We have been given an image of a triangle. We are asked to find the term that describes point H.
We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.
We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.
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what is 4million 2hunderd thousand 6 hundred 52 in digitss
Answers
Answer:
one thousand, seven hundred twenty-eight
The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
Answers
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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What is f(g(x)) when f(x) = x ^ 2 + 5 , and g(x) = 10 - 5x ?
Answers
A function f (x) and g (x) then:
(f + g) (x) = x² - x + 6
Further explanation
Like the number operations we do in real numbers, operations such as addition, installation, division or multiplication can also be done on two functions.
Suppose a function f (x) and g (x) then:
(f + g) (x) = f (x) + g (x)
(f + g) (x) is a new function of the sum of f (x) and g (x)
Likewise with other function operations:
(f-g) (x) = f (x) - g (x)
(fg) (x) = f (x) x g (x)
(f / g) (x) = f (x) / g (x)
In addition to the above operations we can combine two functions using the function composition with the symbol o
(fog) (x) = f ((g (x))
Known on the question
f (x) = x² + 1
g (x) = 5 x
Summing the two functions f (x) and g (x):
(f + g) (x) = f (x) + g (x)
(f + g) (x) = x² + 1 + 5 - x
(f + g) (x) = x² - x + 6
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 2 ft by 2 ft by 12.5 ft. If the container is entirely full and, on average, its contents weigh 0.22 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answers
Answer:
38.81 pounds
Step-by-step explanation:
Considering the definition of right rectangular prism and its volume, the total weight of the contents is 38.81 pounds.
Right rectangular prism
A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
Volume of right rectangular prism
To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.
That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.
Volume of the container
In this case, you know that:
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
7.5 ft× 11.5 ft× 3 ft= 258.75 ft³
Then, the total weight of the contents is calculated as:
258.75 ft³× 0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds
Finally, the total weight of the contents is 38.81 pounds.
Find x intercepts y=(x+3) (6x-2)
Answers
Answer:
x = - 3 , x = \(\frac{1}{3}\)
Step-by-step explanation:
to find the x- intercepts let y = 0 , that is
(x + 3)(6x - 2) = 0
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
6x - 2 = 0 ( add 2 to both sides )
6x = 2 ( divide both sides by 6 )
x = \(\frac{2}{6}\) = \(\frac{1}{3}\)
the x- intercepts are then x = - 2 and x = \(\frac{1}{3}\)
Question 14 of 44
Which of the following represents the diameter of the circle below?
A. TH
B. H
C. O
D. OH
O
H
Answers
Katie made 6 times as many baskets as Tiffany during basketball practice today.
Answers
Answer:
6(x) (not much info is known to get a full answer)
Step-by-step explanation:
"Katie made 6 times as many baskets" this shows that you need to multiply how much baskets tiffany made by 6 thus making the equation 6(x)
The ratio for the number of baskets made by Katie and Tiffany is 6:1.
What is the ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.
Given Katie made 6 times as many baskets as Tiffany during basketball practice,
let the basket done by Tiffney be x
basket made by Katie is 6x
the ratio of the number of baskets made by Katie and Tiffany,
= 6x/x
= 6/1
or ratio = 6:1
Hence the ratio is 6:1.
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The complete question is,
Katie made 6 times as many baskets as Tiffany during basketball practice write a ratio
What is the IQR for 10, 14, 15, 15, 16, 18, 19, 21
Answers
Answer:
15-18
Step-by-step explanation:
The IQR is the middle 50% of a set of numbers
There are 8 numbers, so its the middle 4
The middle 4 consists of 15,15,16,18
The range is 15-18
On Monday it was 70 degrees. On Tuesday it dropped to 45 degrees. What was the percent of change?
Answers
Answer:
The answer is 64.29% hope it helps
Answer:
35.71 percent
Step-by-step explanation:
Percentage change= \(\frac{Old value-New value}{Old value}\)x100
= \(\frac{70-45}{70}\)x100
= \(\frac{25}{70}\)x100 = 35.71 percent (rounded to 2 decimal places)
There are 5 burgers in burger world. A cowboy at 2, a lawyer ate 3, and a chef ate 9. How many burgers left?
Answers
Answer:
Step-by-step explanation:
Answer:
Mathematically -9, but the chef likely made new burgers so the answer is undetermined as the chef could have made any amount of burgers when he made his 9.
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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Qs =-20+ 3p
Qd = 220- 5p
Answers
Answer:
The answer is below
Step-by-step explanation:
What is the equilibrium price and the quantity for the market whose quantity demanded and quantity supplied are given: Qd=220-5P and Qs= -20+3P?]
Solution:
The equilibrium price of a goods is the price at which the quantity of goods supplied is equal to the quantity of goods demanded. The equilibrium price can be determined by the supply and demand curve. The equilibrium price is the price at which the point of intersection of the supply and demand curve.
At equilibrium:
\(Q_s=Q_d\\\\-20+3p=220-5p\\\\220+20=3p+5p\\\\8p=240\\\\p=30\)
The equilibrium price is 30.
The equilibrium quantity = 220 - 5p = 220 - 5(30) = 70
Which one of the following correctly states the VaR for a 3-year period with a 2.5 percent probability?
a) Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
b) Prob[Rp, I S E(Rp) x 13 - 1.645 x Op 3]
c) Prob[Rp, T = E(Rp) x V3 - 1.960 x Op 3]
Answers
Answer: Option A
Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]
Step-by-step explanation:
It should be noted that, the VaR for a 3-year period with a 2.5 percent probability is Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]. Therefore, option A only is correct while other options are wrong
Answer:
A: Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
Step-by-step explanation:
Which of the following is the correct factorization of the polynomial below?
p^3 - 125q^3
A. (p - 5q)(p^2 + 5pq + 25q^2)
B. (p - 25q)(p^2 + 25pq + 25q^2)
C. (p^2 + 10q)(p^3 + 25pq + 5q^2)
D. The polynomial is irreducible.
Answers
The correct factored form of the expression p³ - 125q³ is,
(p - 5q)(p² + 5pq + 25q²).
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
We know, a³ - b³ = (a - b)(a² + ab + b²).
Given, An expression p³ - 125q³.
= p³ - (5q)³.
= (p - 5q)(p² + p.5q + (5q)²).
= (p - 5q)(p² + 5pq + 25q²).
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What is the likelihood of throwing a 4 with a single throw of a die?
asap needed please help
select an answer
thanks
Answers
Answer:
1 in 6 chance
Step-by-step explanation:
This is do to the fact that a die has only 6 sides with 6 different numbers so each has a equal chance of being landed on.
The probability or likelihood of throwing a 4 with a single throw of a die will be 1 in 6 thus option (B) is correct.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given die,
The number of sample space = 6 {1,2,3,4,5,6}
Number of choice = 1 {4}
The likelihood or probability is the same.
Probability = (number of choice)/(total sample space)
Probability = 1/6
Hence "The probability or likelihood of throwing a 4 with a single throw of a die will be 1 in 6".
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Mickey and Minnie Mouse are purchasing a new home. Their annual property taxes are estimated to be $5,467, and their homeowner's insurance policy has an annual cost of $1,440. They must also purchase flood insurance, since they live in below sea level, at an additional cost of $1,262 per year. How much will they be required to put into their escrow account each month to cover these costs?
Answers
Result:
Mickey and Minnie Mouse will need to put $680.75 into their escrow account each month to cover the property taxes, homeowner's insurance, and flood insurance costs.
What is an escrow account?An escrow account is like a savings account that is managed by a mortgage servicer. The portion deposited into an escrow account usually covers estimated property taxes and your homeowners and mortgage insurance premiums.
To calculate the monthly amount Mickey and Minnie Mouse need to put into their escrow account for property taxes, homeowner's insurance, and flood insurance, we will first add up the total annual costs for these expenses:
Property taxes: $5,467
Homeowner's insurance: $1,440
Flood insurance: $1,262
Total annual costs = $5,467 + $1,440 + $1,262 = $8,169
Next, we divide the total annual costs by 12 to get the monthly escrow amount:
$8,169 / 12 = $680.75
Therefore, $680.75 is the amount they will need to put into their escrow account each month.
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permieter of 2 rectangles is 54 cm.
work out the area of a square
Answers
The Area of Square is 81 cm².
let the side of the square which is length for both rectangles be a.
let the width of rectangle be x and y.
So, x+ y= a
sum of perimeters= 54
2 (a +x ) + 2 (a+ y) = 54
2a+ 2x + 2a+ 2y = 54
2a + 2a + 2(x+ y) = 54
4a + 2 (a) = 54
4a + 2a = 54
6a = 54
a= 54/6
a= 9
So, area of square
= 9 x 9
= 81 cm²
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Decide which of the two given prices is the better deal and explain why. You can fill a 12-gallon tank of gas for $39.43 or buy gas for $3.20/gallon.
Answers
Answer:
$3.20/gallon
Step-by-step explanation:
to fill up your tank at $3.20/gallon only costs $38.40
Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (2,-4). A) y = 1/2x-4 - 15 B) y = -2x-4 + 15 C) y = -2x-5 D) y = 1/2x - 5
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = \(\frac{1}{2}\) x + 3 ← is in slope- intercept form
with slope m = \(\frac{1}{2}\)
• Parallel lines have equal slopes , then
y = \(\frac{1}{2}\) x + c ← is the partial equation
to find c substitute (2, - 4 ) into the partial equation
- 4 = \(\frac{1}{2}\) (2) + c = 1 + c ( subtract 1 from both sides )
- 5 = c
y = \(\frac{1}{2}\) x - 5 ← equation of parallel line
mZB = xo, what is the measure of a
supplement of LB?
Answers
9514 1404 393
Answer:
supplement of ∠B = 180° -x°
Step-by-step explanation:
The supplement of an angle is the difference between 180° and that angle.
supplement of ∠B = 180° - m∠B
supplement of ∠B = 180° -x°
A car rental costs $50 per day plus an additional $0.20 for each mile driven. The daily cost y is given by the equation
y = 0.20x + 50
where x is the number of miles driven. Find the y-intercept of the graph of the equation.
(x, y) =
Answers
Answer:
(0, 50)
Step-by-step explanation:
The y-intercept is when x=0.
\(y=0.20(0)+50=50\)
59) When scrap iron in a boat is thrown overboard in a swimming pool, the pool level
A) rises.
B) falls.
C) remains unchanged.
Answers
As rain drop and sink through the rock, it often solvates some of the iron. It conveys that iron along with it as it continues to seep through the rock and soil.
When the rainwater becomes groundwater or dart into freshwater sources like lakes and rivers, it may become the part of the local water supply.
Municipal water systems that get their water from these sources can end up with high levels of iron in their water, and the riddle they have set up to remove bacteria and other harmful contaminants may not always riddle it out.
Wells that portray water from aquifers with high iron content may contain high iron concentrations as well.
Iron in water generally takes two types of ferrous iron, which is soluble in water, and next one is ferric iron, which is insoluble.
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5. This graph shows the outside temperature (in degrees Celsius) over the course of 12 hours, starting at midnight (x = 0). 2 Temperature (in degrees Celsius) Time in hours)
Part 1:
a. what is the domain?
b. what does the domain mean in terms of the problem
Part 2:
a. what is the range
b. what does the range mean in terms of the problem
Part 3:
a. when is the fuction decreasing?
b. what does the decreasing interval mean in terms of the problem?
Answers
Answer:
PART 1
a. The domain of the graph is the set of all possible input values, which in this case is time in hours. From the graph, we can see that the time range is from 0 to 12 hours.
b. In terms of the problem, the domain represents the time period over which the outside temperature was recorded. It tells us that the temperature was measured over a 12-hour period, starting at midnight (x=0) and ending at noon (x=12).
PART 2
a. The range of the temperature in degrees Celsius can be determined by finding the difference between the maximum and minimum values on the y-axis. From the graph, it appears that the highest temperature is around 20°C while the lowest temperature is around 5°C. Therefore, the range of temperatures is 15°C.
b. The range in this context means that there is a variation of 15°C in the outside temperature over the course of 12 hours. This could indicate that there are fluctuations in weather patterns or that there are different times of day where temperatures are typically higher or lower.
PART 3
a. The function is decreasing between 4 AM and 8 AM.
b. The decreasing interval means that the temperature is decreasing during that time period. In other words, the outside temperature is getting colder between 4 AM and 8 AM. This could be due to a variety of factors such as the time of day, weather patterns, or location.
Tell me if this is correct.