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.
a box contains 1.8*x10^24 atoms. one third of them are carbon, the other two thirds are oxygen. How many carbon atoms are in the box? use scientific notation
This should be simple but it’s Monday and my brain is fried T_T
what does “b” equal?
-10 = -b/4
to get b multiply both sides by 4
-10 *4 = -40
since b already has the negative sign the 40 would be positive
so b = 40
16 increased by twice a number is -56
What is the exact area of the base of a circular swimming pool with diameter 16 ft?
Convert 2 3/25 as a decimal/
Tim have 46 chocolate bars he eats 34.what does time have now.
A.12
B.8
C.diabetes
D.none of these
simplify this expression 7x(9x^2)
Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c.
Trigonometric area formula: Area =
Which expressions represent the area of triangle ABC? Check all that apply.
Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c.
Trigonometric area formula: Area =
Which expressions represent the area of triangle ABC? Check all that apply.
Answer:
B
C
E
Step-by-step explanation:
One-half bc sin60⁰
One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.
Start Fraction ab sin60⁰ Over 2 End Fraction
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
A triangle with equal angle and equal sides. The sum of an angle in a triangle is 180⁰ this implies that each angles have 60⁰
The area rule of triangle:
It states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle, multiplied by the sine of the angle.
Therefore, there are three options that defines the expressions to represent the area of triangle ABC:
One-half bc sin60⁰
One-half a squared sin60⁰ ; if the two opposite sides posses the same parameters.
Start Fraction ab sin60⁰ Over 2 End Fraction
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12. Find the surface area of each figure to the nearest tenth.Show your work.
e. What is a real-world example or use of surface area?
You need at least 5000 points to earn a gift card from your bank. You currently have 2700 points. What inequality represents the number of points you need to earn a gift card.
Which number is the product?
2x5=10
A.10
B.5
C.2
Graph the line for y+2=3/2(x+4) on the coordinate plane.
Please tell me the points to graph will give brainiest :)
A graph of the linear function y+2=3/2(x+4) is shown in the image attached below.
What is the point-slope form of a straight line?In Mathematics and Euclidean Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope or rate of change.Based on the information provided about the graph of this line, we can reasonably infer and logically deduce that an equation or linear function that models it can be written as follows;
y - y₁ = m(x - x₁)
y+2=3/2(x+4)
y+2=3/2(0+4)
y(0) = 4
Next, we would use an online graphing tool to plot the given linear function for the values in its domain using table, as shown in the graph attached below.
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Horatio is purchasing a computer cable for $15.49.If the sales tax rate in his state is 5.25% what is the total cost of the purchase?
which graph has a slope of 4/5?
The only graph with a slope of 4/5 is;
Graph 2
The slope of the graph is simply rise divided by run or defined as the change in y-coordinates divided by the corresponding change in x-coordinate.
Thus; m = (y₂ - y₁)/(x₂ - x₁)
Graph 1; Let us pick two coordinates;
(1, 2) and (2, 3)
m = (3 - 2)/(2 - 1)
m = 1
Graph 2; Let us pick two coordinates;
(-1, 1 ) and (4, 5)
m = (5 - 1)/(4 - (-1))
m = 4/5
Graph 3; Let us pick two coordinates;
(-2,0) and (3, 2)
m = (2 - 0)/(3 - (-2))
m = 2/5
Graph 4; Let us pick two coordinates;
(1, 1) and (4, 5)
m = (5 - 1)/(4 - 1)
m = 4/3
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Pauline spent $7.50 every day for 3 days. Which expression is the best choice to help her determine the total amount of money she spent?
A. (7.50) × (−3) = −22.50; She spent $22.50.
B. (−7.50) × (3) = −22.50; She spent $22.50.
C. (−7.50) × (−3) = 22.50; She spent $22.50.
D. (7.50) × (3) = 22.50; She spent $22.50.
Simplify.
√192
A. 8√3
B. 64√3
C. 10√6
D. 8√24
If a 30-foot tree casts a 12-foot shadow, find the length of the shadow cast by a 28-foot tree.
Final answer:
To calculate the length of the shadow cast by a 28-foot tree, we use proportional relationships, which yield a shadow length of approximately 11.2 feet.
Explanation:
Shadow Length Calculation
To find the length of the shadow cast by a 28-foot tree, we can use the concept of similar triangles. The relationship between the height of an object and the length of its shadow is proportional provided the sun's rays are coming at the same angle.
In this case, a 30-foot tree casts a 12-foot shadow.
We can set up a proportion to compare the two trees to find the unknown shadow length for the 28-foot tree.
Let's set up the proportion: Since the shadows are proportional to their respective tree heights, we can express this as follows:
(Shadow length of 28-foot tree) / 28 feet = 12 feet / 30 feet
By cross-multiplying and solving for the unknown shadow length, we would get:
(Shadow length of 28-foot tree) × 30 = 28 × 12Performing this calculation:
(Shadow length of 28-foot tree) = 336 / 30So, a 28-foot tree will cast a shadow that is approximately 11.2 feet long.
The correct answer is that the length of the shadow cast by a 28-foot tree is 11.2 feet.
To solve this problem, we can use the concept of similar triangles. The tree and its shadow form a right-angled triangle with the ground, and the angle of elevation of the sun is the same for both trees. Therefore, the triangles formed by the trees and their respective shadows are similar.
Let's denote the height of the first tree as [tex]\( h_1 = 30 \)[/tex] feet, the length of its shadow as [tex]\( s_1 = 12 \)[/tex] feet, the height of the second tree as [tex]\( h_2 = 28 \)[/tex] feet, and the length of its shadow as [tex]\( s_2 \)[/tex], which we want to find.
Since the triangles are similar, the ratios of the corresponding sides are equal:
[tex]\[ \frac{h_1}{s_1} = \frac{h_2}{s_2} \][/tex]
Substituting the known values:
[tex]\[ \frac{30}{12} = \frac{28}{s_2} \][/tex]
Now, we solve for [tex]\( s_2 \)[/tex] :
[tex]\[ s_2 = \frac{28 \times 12}{30} \][/tex]
[tex]\[ s_2 = \frac{336}{30} \][/tex]
[tex]\[ s_2 = 11.2 \][/tex]
The sales tax rate for a local county is 8.7%. If an item costs $184 (before tax), how much sales tax will be due?
Express 2.27272727273... as a rational number, in the form p
Why does the sum of -4 and 3 complain more than the sum of -3 and 5
Final answer:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The sum of two numbers depends on their signs and the rules of adding negative and positive numbers.
Explanation:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The reason why the sum of -4 and 3 is a smaller number than the sum of -3 and 5 is because of the rules of adding positive and negative numbers:
When two negative numbers add, the answer has a negative sign.When two positive numbers add, the answer has a positive sign.When two numbers with opposite signs add, the sign of the larger number is retained.In this case, -3 is larger than -4, so when adding 5 to -3, we retain the negative sign and get -1. However, when adding 3 to -4, we retain the negative sign and get -1, which is smaller than 2.
A doll maker gets laid monthly at a rate of $250 for each dol he completes. Last month he made 7 dolls and got halfway through an 8th doll. How much money was he laud last month ?
Jonah has collected 91 coins worth $7.20 in his piggy bank. his collection includes only dimes and nickels. how many dimes are there in jonah's piggy bank?
John always wears a shirt, pants, socks, and shoes. He owns 12pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Step-by-step explanation:
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.
For example If John has 2 pants and 3 shirts
he make an combination of 1 pant with 3 shirts
and another pant with 3 shirts
so total of 6 combination he can make (2*3)= 6
To find the number of combination we multiply all the shirt, pants, socks, and shoes he have
12pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.
12 * 3 * 5 * 5 = 900
So 900 different combination John can make
Combination helps us to find a number of ways. The number of ways John can wear an outfit is 900.
What is the Combination?A combination helps us to find the number of ways something can be selected from a set. It is given by the formula,
[tex]^nC_r = \dfrac{n!}{r!(n-r) ! }[/tex]
where n is the total number of choices in the set, r is the number of choices we want.
Given to us
Number of pairs of socks = 12
Number of pairs of shoes = 3
Number of pants = 5
Number of shirts = 5
The number of ways John can wear an outfit can be found out using the combination of shirt, socks, pants, and shoes. Therefore,
Number of ways John can wear an outfit
= Number of ways John wears shocks x Number of ways John wears shoes x Number of ways John wears pants x Number of ways John wears a shirt
Number of ways John can wear an outfit
[tex]= ^{12}C_1 \times ^{3}C_1 \times ^{5}C_1 \times ^{5}C_1 \\[/tex]
= 900
Hence, the number of ways John can wear an outfit is 900.
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Zach is 23 years old. Zach's age is 3 years older than twice Maya's age. Let m represent maya's age
Which equation can be used to solve for Maya's age?
A.) 23=m+3
B.) 23=2m
C.) 23=3m+2
D.) 23=2m+3
How many ways can first, second, and third place be assigned?At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
The total number of ways can first, second and third place can be assigned are:
6840
Step-by-step explanation:The total number of people that compete are: 20
Out of these 20 people we have to chose 3 people and also arrange them according to their ranks.
We know that when we have to choose and arrange r items out of total n items then we need to use the method of permutation.
Hence, the formula is given by:
[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]
Here we have:
n=20 and r=3
Hence, the number of ways first, second and third place can be assigned are:
[tex]{20}_P_3=\dfrac{20!}{(20-3)!}\\\\\\{20}_P_3=\dfrac{20!}{17!}\\\\\\{20}_P_3=\dfrac{20\times 19\times 18\times 17!}{17!}\\\\\\{20}_P_3=20\times 19\times 18\\\\\\{20}_P_3=6840[/tex]
Hence, the answer is:
6840
Answer:
The correct answer is
1. 6,840
2. 342
3. 18
At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
Be independent uniform random variables on [0, 1], and let u(n) be the maximum find the cdf of u(n) and a standardized u(n), and show that the cdf of the standardized variable tends to a limiting value.
The cumulative distribution function (CDF) of u(n), when u(n) is the maximum of n independent uniformly-distributed random variables, is given by x^n. After standardization, as n approaches infinity, the CDF of the standardized variable converges to a standard normal distribution, as per the central limit theorem.
Explanation:The subject matter relates to the field of statistics, specifically dealing with the concept of uniform distribution and standard normal distribution.
Let's denote the random variables as X1, X2, ..., Xn and they are uniformly distributed over [0, 1].Given that u(n) is the maximum of these random variables, the cumulative distribution function (CDF) of u(n) can be calculated as follows:
P(u(n) < x) = P(X1 < x, X2 < x, ..., Xn < x) = P(X1 < x) * P(X2 < x) * ... * P(Xn < x) = x^n
Given that Z = (u(n) - μ) / σ where μ is the mean and σ is the standard deviation. For the uniform distribution, μ = 0.5 and σ = √ (b - a)² / 12 = √1 / 12. Therefore, the standardized random variable Z can be calculated.
By the central limit theorem, as n increases, the standardized variable tends to a limiting value. Which means as n -> ∞ , the cumulative distribution function of Z = 1, the standardized variable converts to a standard normal distribution, and it poses bell-shaped curve form.
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Suppose a kite has diagonals of 10 and 20. Find the perimeter of the quadrilateral formed
by joining the midpoints of the kite’s sides.
(06.06)
Which of the following demonstrates the Distributive Property?
A.2(3a + 4) = 6a + 4
B.2(3a + 4) = 3a + 8
C.2(3a + 4) = 6a + 8
D.2(3a + 4) = 5a + 6
Answer:
The answer is C. Hope this helps.
Step-by-step explanation:
Rasheed needs to say $231 to earn money he plans to wash cars and charge $12 for car right to estimates Rasheed could use to determine how many cars he needs to wash
Which property is shown? (mn)^5=m^5n^5
A)Product of powers
B) power of a product property
C) power of a power property
D) power of a quotient property