The baggage limit for an airplane is set at 100 pounds per passenger. thus, for an airplane with 200 passenger seats there would be a limit of 20,000 pounds. the weight of the baggage of an individual passenger is a random variable with a mean of 95 pounds and a standard deviation of 35 pounds. if all 200 seats are sold for a particular flight, what is the probability that the total weight of the passengers' baggage will exceed the 20,000-pound limit?
At a mean of 95 pounds per passenger and standard deviation of 35 pounds, multiplying this with the total number of passengers = 200, results in:
absolute mean = 95 * 200 = 19,000
absolute std dev = 35 * 200 = 7,000
Calculating for the z score:
z = (x – u) / s
where x is sample value = more than 20,000; u is the sample mean = 19,000; s is std dev = 7,000
z = (20,000 – 19,000) / 7,000
z = 0.143
From the distribution tables,
P (z = 0.14) = 0.5557
Therefore a 55.57% chance that it will be more than 20,000 pound limit
Final answer:
Using the Central Limit Theorem, we calculate the probability that the total weight of passengers' baggage exceeds 20,000 pounds for an airplane with 200 passengers to be approximately 0.0217.
Explanation:
To solve this problem, we use the Central Limit Theorem which states that if we have a large enough sample size, the distribution of the sample means will be approximately normally distributed regardless of the original distribution's shape. Given that the mean weight of an individual passenger's baggage is 95 pounds with a standard deviation of 35 pounds, and that there are 200 passengers, we can calculate the mean and standard deviation of the total baggage weight.
The mean total weight, μtotal, is calculated as the product of the mean individual weight and the number of passengers, so μtotal = 95 pounds × 200 = 19,000 pounds. The standard deviation of the total weight, σtotal, is calculated as the standard deviation of the individual weight multiplied by the square root of the number of passengers, so σtotal = 35 pounds × √200 ≈ 494.97 pounds.
Using the standard normal distribution, we find the z-score for the probability that the total weight exceeds 20,000 pounds by subtracting the mean from the limit and dividing by the standard deviation: z = (20,000 - 19,000) / 494.97 ≈ 2.02.
Looking up this z-score in a standard normal table or using a calculator, we find that the probability of the total baggage weight exceeding 20,000 pounds is approximately 0.0217.
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The exponential function in the graph shows the population of Greeville in the years since 2010. What real-world information is given by the point (6, 2707)?
options:
The population in 2006
The population in 2010
The population in 2016
The year in which the population is twice the population in 2010
If rectangle DEFG is dilated by a scale factor of 1/2 with a dilation center of (0, 0), what will be the coordinates of point F'?
The equation of line m is 5x−3y=2. What is the slope of a line that is perpendicular to line m? Enter your answer in the box.
Step 1
Find the slope of the line M
we have
[tex]5x-3y=2[/tex]
isolate the variable y
[tex]3y=5x-2 \\ \\y=\frac{5}{3}x-\frac{2}{3}[/tex]
the slope of the line is [tex]\frac{5}{3}[/tex]
Step 2
Find the slope of the line perpendicular to line M
we know that
if two lines are perpendicular , then the product of their slopes are equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=\frac{5}{3}[/tex]
Find m2
[tex]m2=-1/m1[/tex]
[tex]m2=-1/(5/3)[/tex]
[tex]m2=-\frac{3}{5}[/tex]
therefore
the answer is
[tex]-\frac{3}{5}[/tex]
The function f(x)=3(2.5)x is shown on the coordinate plane.
Select from the drop-down menus to correctly describe the end behavior of f(x) .
As x decreases without bound, the graph of f(x) .
As x increases without bound, the graph of f(x) .
An exponential curve on a coordinate plane with horizontal x axis ranging from negative 4 to 4 in increments of 1. The vertical y-axis ranges from negative 1 to 7 in increments of 1. The curve begins infinitely close to the x axis in the second quadrant. The curve increases through begin ordered pair 0 comma 3 end ordered pair. DO NOT DELETE THIS PLZ HOEFULLY SOMEONE CAN TRY TO ANSWER IT
As x increases without bound, the graph of f(x) approaches y=0 increases without bound .
We have function [tex]f(x)=3(2.5)^x[/tex]
From the graph we can see that as x decreases without bound the graph of f(x) approaches y=0.
Also the exponential function in the graph is approaching y=0 as x decreases on the left side of the curve.
Here as the exponential function here the power is x variable and the exponential function cannot be negative for any value of x.
Therefore as x increases without bound, the graph of f(x) approaches y=0 increases without bound .
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Step-by-step explanation:
i took the test :)
can someone help answer and explain to me how to solve this? log (lowercase 6) 1/36
The expression on the left side of an equation is shown below.
-5(x+2) +3x =___
If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
A. -5(x-3) +2x
B. -5x-10
C. x-2x +2 +3x
D. -2(x +5)
After solving the equation, the equivalent equation obtained which has an infinite solution will be equal to -2(x + 5). Hence, option D is correct.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-5(x + 2) + 3x
Now, solve the equation,
-5x - 10 + 3x
= -5x + 3x - 10
= - 2x - 10
So, the equivalent equation will be,
-2(x + 5), it has an infinite solution because it is the same equation.
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Randy solved the following problem: 7/8 + 9/15. He said, "I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. " Is Randy correct? Explain your answer.
What is the remainder of the following division problem? in the pic?
A. x
B.1
C. 0
D.–1
Answer : Option B is correct.
Explanation :
Since we have given that
f(x) = x+1
and
g(x) =x
and when we divide f(x) with g(x) i.e.
[tex]\frac{f(x)}{g(x)}[/tex]
And we know the division algorithm , i.e.
[tex]f(x)=g(x).q(x) +r(x)[/tex],
Where q(x) represents quotient and r(s) denotes remainder
So, we write it in this manner ,
[tex]x+1=x.1+1\\\\\text{Remainder becomes 1}[/tex]
Hence, Remainder = 1
So, Option B is correct.
Which is an example of a function?
the time it takes to mow a lawn and the age of the person mowing the lawn
the distance to school and the time you spend at school
the price of a movie ticket and the height of the customer
the price of a piece of cloth and the length of the cloth
The example of a function is:
The price of a piece of cloth and the length of the cloth.
Step-by-step explanation:We know that a function is a relation in which each element of a set is mapped to a single element of the other set.
i.e. an element has just one image.
1)
The time it takes to mow a lawn and the age of the person mowing the lawn.
This is not a example of function since, the time taken by two person's of different age may be same to mow a lawn.
This means that there is more than one image of a single element i.e. time.
2)
The distance to school and the time you spend at school.
The time one spend at school at different days may be different even if the distance to school is same.
3)
The price of a movie ticket and the height of the customer.
Two person's with different height will buy a movie ticket at the same cost.
Hence, this relation won't be a function.
4)
The price of a piece of cloth and the length of the cloth.
As we know that the price of a cloth is fixed according to the length.
Hence, the relation is a function.
( As corresponding to each price we have a unique length if a piece of clothing )
Tyson and his friends go ice skating. Tyson must pay an initial fee of $18.30 plus $4.80 per hour. Write an equation for the cost c Tyson must pay after skating h hours. Solve the equation to find the cost to go ice skating for four hours. Write your answer as an ordered pair.
A, c = 4.80h – 18.30 (4, 0.9)
B. c = 4.80 + 18.30h (4, 78.00)
C. c = 18.30 + 4.80h (4, 37.50)
D. c = 18.30 + 4.80 + h (4, 27.10)
Ben's date of birth is a prime number between 15 and 25. This number has 57 as a multiple.
What date is Ben's birthday?
How can sums and differences of cubes be identified for factoring?
M(8, 5) is the midpoint of JK. The coordinates of point J are (5, −6) . What are the coordinates of point K?
The midpoint is the exact middle of a line segment which divides the line into two equal lengths. Hence, the coordinate of K is (11, 16)
We can obtain the distance between the coordinates of JM thus :
Distance = y2 - y1 ; x2 - x1
Distance = (8 - 5) ; (5 - (-6) = (3, 11)
Hence, the change in the coordinates is (3, 11)
Therefore, the coordinates of K can be obtained thus :
(8 + 3) ;(5 + 11) = (11, 16)
Hence, the coordinate of K is (11, 16)
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holly and melanie were playing a video game. the ratio of holly's score to melanie's score was 8:3. after melanie scored 34 points, the ratio of their scores became 2:5. what were their scores at the end?
Sergio is S years old. Which expression shows how old will he be 7 years from now?
A. 7s
B. 7-s
C. s+7
D. 7s+7
Jill has 8.75. Jack has three times as much as Jill, but he spent 5.00 to buy a book. How much money does jack have ?
True or false: the regression sum of squares (ssr) can never be greater than the total sum of squares (sst).
There are 18 players on the baseball team. Of these players 1/3 are girls. How many girls play on the baseball team?
divide 18 by 3
18 / 3 = 6
there are 6 girls on the team
Which property justifies this statement?
If 4x=20, then x=5.
What does y and z equal. I already got x
Davis knows that the area of his square shaped bag is 81 ft sq. What is the length of any side of the bag
A rectangle has an area of 16 ft2. every dimension is multiplied by a scale factor, and the new rectangle has an area of 64 ft2. what was the scale factor?
The product of two numbers is 40. if one of the numbers is 5/11, what is the other number?
Final answer:
To find the other number when the product of two numbers is 40 and one of the numbers is 5/11, we divide 40 by 5/11 to solve for the unknown number. The other number is found to be 88.
Explanation:
The question asks to find the other number when the product of two numbers is 40 and one of the numbers is given as 5/11. To do this, we can set up an equation where the product of 5/11 and the unknown number (which we can call 'x') is equal to 40.
The equation would be: (5/11) × x = 40. To solve for x, we need to do some algebraic rearrangement by dividing both sides of the equation by 5/11. This brings x into the numerator on the left side and shifts the 5/11 to the denominator on the right side. Therefore, we get x = 40 × (11/5).
Next, we multiply 40 by 11/5. This calculation results in x = 88. Thus, the other number is 88.
What is the answer to: jason has 4 tiles. each tile has a number printed oon it. the numbers are 2,3,6, and 8, a decimal number is formed using the titles and the clues. be a math detective and find the number.?
I believe this problem has the following clue:
digit in the tens place is the largest number. digit in tenths place is less than the digit located in the hundredths place. the digit in the ones place is greater than the digit in the hundredths place
From this clue, we can say that the number is:
86.23
How to factor this:
6x² + 7x - 5
Please give an explanation on how you did it
Alexandra bought a $90000 life insurance policy at $10.98 for a 20 year term. She will pay ___ over 20 years for the premium
Solve for x.
x2(^) + 9x = 0
Maria works for an automobile dealership. She earns a 10% commission on each motorcycle she sells and a 15% commission on each car she sells.
Maria sells a motorcycle for $5,000 and a car for $25,000. What is the total commission that she will earn on the sale of these two vehicles?
The total commission that she will earn on the sale of these two vehicles is $4,250.
You have already saved $55 you earn $9 per hour babysitting you ate saving for a camera that costs $199