A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload
Answers
Answer:
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n values of a distribution, the mean is \(\mu \times n\) and the standard deviation is \(\sigma\sqrt{n}\)
An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.
This means that \(\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300\)
If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload
Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{20000 - 20000}{300}\)
\(Z = 0\)
\(Z = 0\) has a pvalue of 0.5
1 - 0.5 = 0.5
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload
Related Questions
What equation of the line which passes through the point (-1, 2) and is parallel to the line y=x+4
Answers
Answer:
Thus, the equation of line for point (-1, 2) is y = x + 3.
Step-by-step explanation:
Answer:
The equation of the line is y = x + 3.
Step-by-step explanation:
A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.
y = mx + b
y = 1 * -1 + b
y = -1 + b
b = y + 1
b = 2 + 1
b = 3
Thrice a number increased by 5 exceeds twice the number by 11 . Find the number.
Answers
I think
A city currently has a population of 72,300 people the population will grow at a rate of 0.8% per year determine an exponential equation that can be used to predict c the miner of years it will take the population to reach 100,000 people
Answers
Answer:
Step-by-step explanation:
72,300 × 1.008^c = 100,000
1.008^c = 1,000/723
\(\huge\colorbox{pink}{An§wer}\)
72,300 × 1.008^c = 100,000
1.008^c = 1,000/723
Can someone help me on 6?
Answers
Answer:
66600 ft
Step-by-step explanation:
First draw a rectangle and draw a diagonal line in the middle. The line makes two triangles, and the line itself is the hypotenuse. So, to find hypotenuse, the formula is:
a^2 + b^2 = c^2
The variable c defines the hypotenuse. Therefore:
a = 150
b = 210
Let's solve:
150^2 + 210^2 = c^2
22500 + 44100 = c^2
66600 = c^2
Therefore, in conclusion, the result we are getting is 66600 ft.
Hope This Helps!
Answer:
30√74 ft or 258.070 ft rounded to three decimal places.
Step-by-step explanation:
To find the length of a diagonal, add the square of the width and the square of the length together and find the square root of the sum.
d = √210² + 150²
d = √44100 + 22500
d = √66600
d = 258.069758 ft (This is the answer I got in six decimal places. Rounding it to three, as it says in the question, would be 258.07 ft, as 7 is greater than 5 (the third digit was 9 by the way).)
An exact answer to that, in radical form, is 30√74 ft.
select the point that is a solution to the system of inequalities
Answers
This point is below both the red diagonal line and the blue parabola. We know that the set of solution points is below both due to the "less than" parts of each inequality sign.
In contrast, a point like (2,2) is above the parabola which is why it is not a solution. It does not make the inequality \(y \le x^2-3x\) true. So this is why we can rule choice A out.
Choice C is not a solution because (4,1) does not make \(y \le -x+3\) true. This point is not below the red diagonal line. We can cross choice C off the list.
Choice D is similar to choice A, which is why we can rule it out as well.
Can someone please help awnser these.
Answers
The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm
Given are the circles and the circular items we need to find their circumference,
Circumference of a circle = 2π × radius = Diameter × π
4. a) Circumference = 5 × 3.14 = 15.7 cm
b) Circumference = 8.36 × 3.14 = 26.25 m
5. a) Circumference = 41 × 3.14 = 128.74 cm
b) Circumference = 13 × 3.14 = 40.82 mm
c) Circumference = 14.3 × 3.14 = 45 cm
6.
The perimeter of the cloth = circumference of the circular ends plus length in the middle,
= 76 × 2 × 3.14 + 150 × 2
= 477.28 + 300
= 777.28 cm
Learn more about Circumference click;
https://brainly.com/question/28757341
#SPJ1
A convex lens with focal length f centimeters will project the image of an object on a
point behind the lens. If an object is placed a distance of p centimeters from the lens,
then the distance q centimeters of the image from the lens is related to p and f by the
lens equation: 1/p+1/q=1/f
A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is
formed 7 cm from the lens, find the distance from the lens to the object, p. (It’s not necessary to simplify your answer.)
B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.
C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a
constant of 5 centimeters. Show any important features of the graph.
D. Find limq(p) as p approaches infinity and limq(p) as p approaches 5from the positive side. What do these limits represent physically? What must
happen to the distance of the image and the object?
Answers
Answer:
A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:
1/p + 1/7 = 1/5
Multiplying both sides by 35p, we get:
35 + 5p = 7p
Simplifying and rearranging, we get:
2p = 35
Therefore, the distance from the lens to the object, p, is:
p = 35/2 cm
B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:
1/q = 1/f - 1/p
Substituting f = 5 cm, we get:
1/q = 1/5 - 1/p
Multiplying both sides by 5qp, we get:
5p = qp - 5q
Simplifying and rearranging, we get:
q = 5p / (p - 5)
Therefore, the expression that gives q as a function of p is:
q = 5p / (p - 5)
C. Here is a sketch of the graph of q(p):
The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.
D. Taking the limit of q as p approaches infinity, we get:
lim q(p) = 5
This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.
Taking the limit of q as p approaches 5 from the positive side, we get:
lim q(p) = -infinity
This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.
In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.
How are zero identified in a rational expression??? Please help
Answers
0x0
Step-by-step explanation:
Answer:
look at the y and x intercept
Step-by-step explanation:
The linear function y = 145 + 30x represents the cost y (in dollars) of an airline ticket after adding x checked
bags. At most 5 bags can be checked.
a. Interpret the terms and coefficient in the equation.
Answers
From the given parameters to determine the cost of the airline ticket, we can interpret that that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.
How to interpret Equation of a line in slope intercept form?
We are given the linear equation that represents the cost of an airline ticket after adding a number of checked bags as;
y = 145 + 30x
where;
y is the cost (in dollars) of an airline ticket after adding a number of checked bags
x is the number of checked bags
Thus, if there is a maximum of 5 bags that can be checked, then we have;
y = 145 + 30(5)
y = $295
This means that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.
Read more about Equation of a Line in Slope Intercept Form at; https://brainly.com/question/1884491
#SPJ1
12 is ____ % of 200.
Answers
Answer:
12 is 6% of 200
Step-by-step explanation:
I just used a little mental math
pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee help mwah. will give brainliest
Answers
Answer:
its 0.4 :)
Step-by-step explanation:
Answer:
this is the answer :))
0.4
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
Answers
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
To know more about Intersection points visit,
https://brainly.com/question/29248863
#SPJ4
Dr. Weinstein took 50 ounces of a 20% silver
alloy and mixed it with a 40% silver alloy to get
a 30% silver alloy. How many ounces of the 40%
silver alloy did he use?
Answers
Answer:
I think it is 100
Answer:
Step-by-step explanation:
The answer is 50 ounces
Because 30% silver is right in between 20% silver and 40% silver, it would have to be the same amount to be 30%
what is the difference between ANOVA and Z-test Hypothesis
Answers
The difference between ANOVA and Z-test Hypothesis is the Z-test is employed to contrast the averages of single or dual populations, whereas ANOVA is utilized for assessing the means across three or more clusters.
How to determine the differenceThe Z-test becomes possible in the comparison of the mean of a sample to that of the population. It evaluates if there is statistical relevance in the difference between the mean of a sample and the mean of the whole population
In contrast, ANOVA is employed to contrast the averages of three or more separate groups. This assesses if there is a noteworthy distinction in the averages of said groups. The F-statistic in ANOVA is computed by assessing the disparity in variability between groups and the variability within groups.
In a nutshell, the Z-test is employed to contrast the averages of single or dual populations, whereas ANOVA is utilized for assessing the means across three or more clusters.
Learn more about ANOVA at: https://brainly.com/question/25800044
#SPJ1
Which of the following methods will solve the equation (5x – 7)3 = 42
a) Divide the left side of the equation by 3, add 7 to the right side of the
equation, and multiply both sides by 3.
b) Divide both sides by 3, add 7 to both sides, and multiply both sides by 3.
c) Add 7 to both sides, divide both sides by 3, and multiply the left sides by 3.
d) Multiply both sides by 3, add 7 to both sides, and then divide both sides by 3.
Answers
Answer:
Divide both sides by 3, Add 7 to each side ,Divide each side by 5
Step-by-step explanation:
(5x – 7)3 = 42
Divide both sides by 3
(5x – 7)3/3 = 42/3
5x-7 = 14
Add 7 to each side
5x-7+7 = 14+7
5x = 21
Divide each side by 5
5x/5 = 21/5
x = 21/5
I need some help pls! I'm getting stuck!
Answers
Answer: 3 pounds.
Step-by-step explanation:
We have two metals:
One that contains 20% nickel, let's call it metal A.
One that contains 80% nickel, let's call it metal B.
We have 6 pounds of metal B, in those 6 punds we have:
0.80*6lb = 4.8lb of nickel.
Now, if we add X pounds of metal A, then we will have:
X + 6lb in total weight.
4.8lb + 0.2*X of nickel.
And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6
(4.8lb + 0.2*X)/(6lb + X) = 0.6
now we solve it for X:
(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X
4.8lb - 3.6lb = 0.6*X - 0.2*X
1.2lb = 0.4*X
1.2lb/0.4 = 3lb = X
We should use 3 pounds of the metal with 20% of nickel.
a package of marbles contains 20 blue marbles, 38 red marbles, 48 green marbles, and 16 yellow marbles. which color of marbles can be divided evenly between 6 people?
Answers
the answer would be 48 green marbles
Step-by-step explanation:
48/6=8
So, each person would get 8 marbles each
Which is the graph of F(x)= sqrt 4x
Answers
The graph of f(x) = sqrt(4x) looks like this
So choose the one that looks like the image attached
The graph has been plotted.
What is a Graph?Graph is a mathematical representation of relation between two objects.
A graph is plotted between two variables that depicts the relation between them which is helpful in prediction of the pattern of the function that it is following.
A function is a relation between a dependent and an independent variable.
The domain and range of a function is always defined.
A domain is the value that can be an input to the function and a range is all the possible output value that can be obtained from the function.
The function is
F(x)= √4x
A square root is the factor of a number when multiplied by itself gives the number itself.
A square root function is also called as a radical function represented by
y = √x
the domain of f(x)=√x is x≥0 and the range is y≥0
The graph of the function is plotted and attached with the answer.
To know more about Graph
brainly.com/question/14375099
#SPJ2
A______ is a value, usually in the form of a letter or symbol, that can change or that represents an unknown quantity.
Answers
Answer:
Variable
Step-by-step explanation:
a sphere has a volume of 36tt in3 find the radius of the sphere
Answers
3•36π=4π • r^3
108 π=4 π • r^3
r^3 =108 π/4 π
r=3 inch
Answer:
r=3 inch
Step-by-step explanation:
i need help on these please
Answers
The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.
How to calculate the constant rate of gas?From the given table;
The volume of the first gas Layla bought = 3 gallons.
The cost of the 3 gallons = 9.45
Therefore the cost of 1 gallon = ?
That is:
3 gallons = $9.45
1 gallon = X
Make X the subject of formula:
X = 9.45/3 = $3.15
Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.
Learn more about division here:
https://brainly.com/question/25289437
#SPJ1
What is the x and y intercepts
Answers
Answer:
Y= 2 X= None
Step-by-step explanation:
There is no X-interecpt because the line does not cross through x. Y-intercept is 2 because the line crosses through 2.
What is the surface area of this prism?
Answers
Answer:
Step-by-step explanation:
front side: 6x3 = 18
back : 6x3 = 18
right:6x2 = 12
left:6x2 = 12
top: 3x2 =6
bottom: 3x2 =6
18 + 18 + 12 + 12 + 6 + 6
= 72
The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answers
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
\((-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\\)
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
\((-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\\)
\(= \frac{3440}{160}\)
= $21.5
b. Now The maximum profit could be determined by the following equation
\(f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\\)
= $980
c. The price that would enable the company to break even that is
f(p) = 0
\(f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0\)
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
- A certain forest covers an area of 30 square kilome-
ters. In 2018, the number of pine trees in this
particular forest was 75,000. In 2019, the number
of pine trees had decreased so that there was an
average of 2,000 pine trees per square kilometer in
the forest. What was the total percent decrease in
the number of pine trees in this forest from 2018 to
2019?
E. 20%
F.24%
G. 25%
H. 30%
Answers
Answer:
E
Step-by-step explanation:
2018 : 75 000 pines
2019 : 2000 pines / km^2 * 30 km^2 = 60 000 pines
(75 000 - 60 000) / 75 000 = .2 or 20 %
Which expression is equivalent to
36x^2 - 84x
answer choices
A. 12x (3x + 7)
B. 12 (3x + 7)
C. 12x (3x -7)
D 12 (3x -7)
Answers
Trinagle ABC has vertices at A(0,5), B(-3,3), and C(0,-5) Classify the triangle according to the side lengths
Answers
The classification of the triangle according to its side lengths and vertices would be scalene triangle.
How to classify the triangle?To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.
To find the vertices, the formula is:
= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )
The length of AB is therefore 3.61 units
The length of BC is 8.54 units
The length of AC is 10 units.
None of the side lengths of this triangle are the same so it is a scalene triangle.
Find out more on triangle classification at https://brainly.com/question/21535569
#SPJ1
Give the slope of the graph and the unit rate.
Answers
I need help with MY MATH jejehee
A bag contains 10 green,8 blue, and 2 white balls. Naomi seclets 2 balls from the bag at random, one at a time, without replacing them. What is the probability that she selects all two white balls?
E.) 2/95
F.) 1/95
G.) 1/190
H.) 1/380
Answers
To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:
Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190
Number of favorable outcomes:
Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:
Favorable outcomes = C(2, 2) = 1
Probability = Favorable outcomes / Total outcomes = 1/190
Therefore, the correct answer is (G) 1/190.
I need help! Does anyone understand?
Answers
Answer:
the answer should be G or H