The probability that the average of 49 marathons is between 143 and 147 minutes is 0.5980. The 60th percentile is 148.25 minutes, and the median is 146 minutes.
The average of a sample of 49 marathons will be approximately normally distributed with mean = 146 minutes and standard deviation = 15/sqrt(49) = 15/7.
To find the probability that the average of the sample will be between 143 and 147 minutes, we can standardize the values:
z1 = (143 - 146) / (15/7) = -1.4
z2 = (147 - 146) / (15/7) = 0.4667
Then, using a standard normal distribution table or calculator, we find:
P(-1.4 < Z < 0.4667) = P(Z < 0.4667) - P(Z < -1.4)
= 0.6788 - 0.0808
= 0.5980
So the probability that the average of the sample will be between 143 and 147 minutes is 0.5980.
To find the 60th percentile for the average of these 49 marathons, we need to find the z-score such that the area to the left of the z-score is 0.6. Using a standard normal distribution table or calculator, we find:
P(Z < z) = 0.6
z = 0.25
Then, we can solve for the corresponding value of X:
0.25 = (X - 146) / (15/7)
X = 148.25
So the 60th percentile for the average of these 49 marathons is 148.25 minutes.
To find the median of the average running times, we note that the median of a normal distribution is equal to its mean. Therefore, the median of the average running times is 146 minutes.
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(4) Practice: Using Visual Cues
Step-by-step explanation:
Refer to pic..........
10. You buy a 1-pound box of oatmeal. You use of the box, then divide the
remainder into 4 equal portions. How many pounds are in each portion?
Therefore, each portion will be (1-x)/4 pounds.
What are pounds?Pounds (lb) is a unit of measurement of weight or mass commonly used in the United States, United Kingdom, and other countries that have adopted the Imperial system of measurement. One pound is equal to 0.453592 kilograms (kg). The symbol for pound is "lb", which comes from the Latin word libra. In everyday use, pounds are often used to measure the weight of objects, people, and animals, as well as food and other goods sold by weight.
Given by the question.
If you have used x pounds of the 1-pound box of oatmeal, then the remaining amount is 1 - x pounds.
You then divide this remainder into 4 equal portions, which means each portion will be (1-x)/4 pounds.
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Maximize z = 3x₁ + 5x₂
subject to: x₁ - 5x₂ ≤ 35
3x1 - 4x₂ ≤21
with. X₁ ≥ 0, X₂ ≥ 0.
use simplex method to solve it and find the maximum value
Answer:
See below.
Step-by-step explanation:
We can solve this linear programming problem using the simplex method. We will start by converting the problem into standard form
Maximize z = 3x₁ + 5x₂ + 0s₁ + 0s₂
subject to
x₁ - 5x₂ + s₁ = 35
3x₁ - 4x₂ + s₂ = 21
x₁, x₂, s₁, s₂ ≥ 0
Next, we create the initial tableau
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 -5 1 0 35
s₂ 3 -4 0 1 21
z -3 -5 0 0 0
We can see that the initial basic variables are s₁ and s₂. We will use the simplex method to find the optimal solution.
Step 1: Choose the most negative coefficient in the bottom row as the pivot element. In this case, it is -5 in the x₂ column.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 -5 1 0 35
s₂ 3 -4 0 1 21
z -3 -5 0 0 0
Step 2: Find the row in which the pivot element creates a positive quotient when each element in that row is divided by the pivot element. In this case, we need to find the minimum positive quotient of (35/5) and (21/4). The minimum is (21/4), so we use the second row as the pivot row.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 4/5 0 1/5 1 28/5
x₂ -3/4 1 0 -1/4 -21/4
z 39/4 0 15/4 3/4 105
Step 3: Use row operations to create zeros in the x₂ column.
Basis x₁ x₂ s₁ s₂ RHS
s₁ 1 0 1/4 7/20 49/10
x₂ 0 1 3/16 -1/16 -21/16
z 0 0 39/4 21/4 525/4
The optimal solution is x₁ = 49/10, x₂ = 21/16, and z = 525/4.
Therefore, the maximum value of z is 525/4, which occurs when x₁ = 49/10 and x₂ = 21/16.
I need help with this question.. :')
The equation of the line passing through A and B is y = (4/5)x - (2/5).
What is the line example's equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.
The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:
y - y1 = m(x - x1) (x - x1)
where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.
To calculate the slope, we can use points A (3, 2) and B (8, 6).
m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5
So the equation for the line connecting A and B is:
y - 2 = (4/5)(x - 3) (x - 3)
This equation can be simplified by multiplying both sides by 5:
5y - 10 = 4x - 12
Then we can rearrange it to form the slope-intercept equation, y = mx + b:
5y = 4x - 2
y = (4/5)x - (2/5)
As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).
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The sum of the ages of father and son at present is 45 years. If both live on until the son's age becomes equal to the father's present age, the sum of their ages then will be 95 years. Find their present ages.
Answer:
father age 45 son age 0 this is answer
a homogeneous wire is bent into the shape shown. determine the x coordinate of its centroid by direct integration. express your answer in terms of a.
The x coordinate of the centroid of the wire with y=kx^(3/2) and x and y intercept a is 0.546a. The y coordinate is 8a/5.
To find the centroid of the wire, we need to find the area and first moments of the wire, which are given by:
Area, A = ∫y dx, where x ranges from -a to a
First moment with respect to x, Mx = ∫xy dx, where x ranges from -a to a
Then the x coordinate of the centroid is given by:
xc = Mx / A
We can start by finding the area:
A = ∫y dx = ∫kx^(3/2) dx = (2/5)kx^(5/2) + C
At x = a, y = 0, so C = - (2/5)ka^(5/2)
At x = -a, y = 0, so A = 2(2/5)ka^(5/2) = (4/5)ka^(5/2)
Now we need to find the first moment with respect to x:
Mx = ∫xy dx = ∫kx^(5/2) dx = (2/7)kx^(7/2) + C'
At x = a, y = 0, so C' = - (2/7)ka^(7/2)
At x = -a, y = 0, so Mx = 0
Therefore, the x coordinate of the centroid is:
xc = Mx / A = 0 / [(4/5)ka^(5/2)] = 0
This means that the centroid lies on the y-axis. To find its y coordinate, we can use the formula:
yc = ∫x dy / A = ∫x (dy/dx) dx / A
Using the equation y = kx^(3/2), we can find dy/dx:
dy/dx = (3/2)kx^(1/2)
Substituting this into the formula for yc and simplifying, we get:
yc = (4/5)ka^(5/2) / (5/8)ka^(5/2) = (8/5)a
Therefore, the coordinates of the centroid are (0, 8/5 a), and the y coordinate is (8/5)a.
To find the x coordinate of the centroid, we need to use the formula:
xc = (1/A) ∫x y dx
We already found the expression for the area A, so we just need to evaluate the integral:
xc = (1/A) ∫x y dx = (1/A) ∫x kx^(3/2) dx
Integrating this by substitution with u = x^(1/2), we get:
xc = (2/5a^(5/2)) ∫u^4 du = (2/5a^(5/2)) (u^5/5) + C
where C is a constant of integration.
At x = a, y = 0, so u = a^(1/2) and C = -(2/25)a^(5/2).
At x = -a, y = 0, so the contribution to the integral is zero.
Therefore, the x coordinate of the centroid is:
xc = (2/5a^(5/2)) (u^5/5) - (2/25a^(5/2)) = (2/25)a(5√2 - 1)
Plugging in a = 1, we get:
xc = 0.546a
So the x coordinate of the centroid is 0.546 times the x and y intercept value a.
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_____The given question is incomplete, the complete question is given below:
a homogeneous wire is bent into the shape shown of graph y = kx^(3/2), x and y intercept is 'a'. determine the x coordinate of its centroid by direct integration. express your answer in terms of a. Also find y- coordinate.
Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.
a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.
b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.
c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.
An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.
To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have
(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)
using the fact that ψ and φ are automorphisms. Similarly,
(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹
using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.
To show that Aut(G) is a group, we need to show that it satisfies the four group axioms
Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.
Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.
Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).
Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.
Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.
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PLEASE HELP !
Use the figure below to answer the questions
From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.
What are rays, line segment and line?A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.
The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.
A line is a collection of points that extends in two opposing directions and is endlessly long and thin.
From the given figure we observe that,
1. Two line segments are LA and EP.
2. Two rays are EC and AH.
3. Two lines are b and AP.
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Milly took a loan of N$900 with simple interest for as many years as the rate of interest. If she paid N$324 as
interest at the end of the loan period, what was the rate of interest?
Answer:
Let's assume that the rate of interest is r (in decimals), and the time period is also r years. Then we can use the simple interest formula:
I = P * r * t
where I is the interest paid, P is the principal amount (the loan amount in this case), r is the rate of interest per year, and t is the time period in years.
Substituting the given values, we get:
324 = 900 * r * r
Simplifying, we get:
r² = 324/900
r² = 0.36
Taking the square root of both sides, we get:
r = ±0.6
Since the rate of interest cannot be negative, we can take r = 0.6. Therefore, the rate of interest is 0.6 or 60% per year.
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Answer:
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Step-by-step explanation:
The total surface area of the pyramid can be calculated using the formula for the lateral surface area of a pyramid:
Lateral surface area = (1/2) × perimeter of base × slant height
Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:
Perimeter of base = 3 × 40 feet = 120 feet
Lateral surface area = (1/2) × 120 feet × 50 feet = 3000 square feet
To paint 75% of the pyramid, the painter needs to paint:
0.75 × 3000 square feet = 2250 square feet
Since the painter can paint 100 square feet in 18 minutes, the time required to paint 2250 square feet can be calculated as:
2250 square feet ÷ 100 square feet per 18 minutes = 225 ÷ 10 × 18 minutes = 405 minutes
Therefore, the painter would need 405 minutes or 6 hours and 45 minutes to paint 75% of the pyramid.
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If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (_____, _____) such that f'(c)>_______
If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (1, 2) such that f'(c)> 0.
How do we know?Applying the Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
In the scenario above, we have that f is differentiable, and that f(1) < f(2).
choosing a = 1 and b = 2.
Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:
f'(c) = (f(2) - f(1)) / (2 - 1)
f'(c) = f(2) - f(1)
We have that f(1) < f(2), we have:
f(2) - f(1) > 0
We can conclude by saying that there exists a number c in the interval (1, 2) such that:
f'(c) = f(2) - f(1) > 0
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An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?
To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.
Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.
We need to find the score which is at the 10th percentile of the distribution.
Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.
From the table, we can see that the z-score is approximately -1.28.
Using the formula for standardizing a normal distribution:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have:
-1.28 = (x - 70) / 10
Solving for x, we get:
x = (-1.28 * 10) + 70
x = 82.8
Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.
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John plans to practice piano at least 2 hours this weekend.
If he practices 1 hours on Saturday and 14 hours on Sunday, will he meet his goal?
Answer:
Yes
Step-by-step explanation:
Yes because 1+14=15 hours and that is more than two
Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x) = g(x). f: initial value of 500 decreasing at a rate of 6% g: initial value of 90 increasing at a rate of 6%
The value of x that makes f(x)g(x) is x
Answer:
Step-by-step explanation:
u got this
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A concave polygon can never be classified as a regular polygon.
A) True
B) False
Answer:
False.
Step-by-step explanation:
A concave polygon can never be a regular polygon as it can never be equiangular. Each side of a regular polygon must be the same length, and all interior angles must also be equal.
12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)
Answer:
height = 7 yards
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the 2 parallel bases
here b₁ = 12 , b₂ = 9 and A = 73.5 , then
[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )
h(21) = 147
21h = 147 ( divide both sides by 21 )
h = 7 yards
A home has gone up in value over several
decades and is now worth 1354% of its
original sale price of $23,000. What is the
value now?
Answer:
$31,142
Step-by-step explanation:
To convert a percentage into a decimal, you move the decimal two places to the left. 1354% converted into a decimal is 13.54.
$23,000 * 13.54 = $31,142
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = x^3 - x^2 - 37x - 35 Find the real zeros of f. Select the correct choice below and; if necessary, fill in the answer box to complete your answer. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers as needed.) There are no real zeros. Use the real zeros to factor f. f(x)= (Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)
By using rational zeros theorem, we find that there are no real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, so we cannot factor f(x) over the real numbers.
To find the real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, we can use the rational zeros theorem, which states that any rational zeros of the function must have the form p/q, where p is a factor of the constant term (-35) and q is a factor of the leading coefficient (1).
The possible rational zeros of f are therefore ±1, ±5, ±7, ±35. We can then test each of these values using synthetic division or long division to see if they are zeros of the function. After testing all of the possible rational zeros, we find that none of them are actually zeros of the function.
Therefore, we can conclude that there are no real zeros of the function f(x) = x^3 - x^2 - 37x - 35.
However, we could factor it into linear and quadratic factors with complex coefficients using the complex zeros of f(x). But since the problem only asks for factoring over the real numbers, we can conclude that the factored form of f(x) is:
f(x) = x^3 - x^2 - 37x - 35 (cannot be factored over the real numbers)
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(√3 + √3)²=
F) 12
G) 9
H) 6
J) 3
K) None of these
Answer:
F) 12
Step-by-step explanation:
To answer, we use the perfect square formula:
(a + b)² = a² + 2ab + b²
(√3 + √3)² = (√3)² + 2(√3)(√3) + (√3)²
Simplify:
√3² = 3
2(√3)(√3) = 2 x (√3)² = 2 x 3 = 6
Plug in:
(√3 + √3)² = 3 + 6 + 3 = 12
Correct to 3 significant figures, the of 18.75-(2.11)2
Answer: 14.5
Step-by-step explanation:
When there is a decimal point, you start counting from the left any number that is not zero. If the zero is at the end, then you count it.
For example, if the answer is 0.000145 then the number of significant figures is still three because you start counting from the first nonzero number from the left.
If the answer is 14.50, then the number of significant figures is four because you start counting from the first nonzero number from the left.
14.53 is the answer to the equation but because you want to correct it to 3 significant figures, you round down because 3 is less than 5 and 14.5 ends up being the final answer.
Question 25 (2 points)
Suppose the Math Department has 17 full-time faculty members. If 3 are selected to
attend a conference in Las Vegas, in how many different ways can you selected the 3
individuals?
3
17
680
4080
Answer:
680 ways
Step-by-step explanation:
C(17, 3) gives 17! / (14! 3!), or (17*16*15)/6 = 680 ways to select the 3 individuals.
Hope this helped!
how do you find the simplest radical form for this please help me i got a (f) and i really need help that’s why i’m up this late trying to do all of my missing assignments.
Answer:
[tex]14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} }[/tex]
Step-by-step explanation:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} }= \sqrt{196} \times \sqrt{ {x}^{3} } \times \sqrt{ {y}^{4} } \times \sqrt{ {z}^{9} } \\ \sqrt{196} = 14 \\ \sqrt{ {x}^{3} } = {x}^{ \frac{3}{2} } \\ \sqrt{ {y}^{4} } = {y}^{2} \\ \sqrt{ {z}^{9}} = {z}^{ \frac{9}{2} }[/tex]
A fractional exponent is not necessarily simpler so just take out the 1st and 3rd parts of the term which simplify nicely:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} } = 14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} } [/tex]
Find the difference. 2.1 0.25 = ?
Answer: 1.85
Step-by-step explanation:
Help please! I have no idea!!!! PLEASEE
To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.
What is graph?
In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.
Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:
To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.
To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.
To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.
Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.
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I need help on these equations
In the graph, Student B and C are both 10 years old and student C has a shoe size of 5. The coordinates of D are (12,6)
What is a graph?In graph theory, a graph is a framework that consists of a collection of objects, some of which are paired together to form "related" objects. The objects are represented by mathematical abstractions known as vertices (also known as nodes or points), and each set of connected vertices is known as an edge (also called link or line). A graph is typically shown diagrammatically as a collection of dots or circles representing the centres and lines or curves representing the edges.
Both directed and undirected lines are possible. For instance, if the edges between two individuals are handshakes, then the graph is undirected because any individual A can only shake hands with an individual B if B also holds hands with A. The graph is directed, however, if an edge from person A to person B indicates that A owes money to B because borrowing money is not always returned.
In the given graph,
Student B and C are both 10 years old and student C has a shoe size of 5.
The coordinates of D are (12,6)
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The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 30 minutes, what is the probability that X is less than 38 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
Answer:
0.718 = 71.8% probability that X is less than 38 minutes
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x)=\mu e^{-\mu x}[/tex]
In which [tex]\mu=\frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X\leq x)=\int\limits^a_0f ({x)} \, dx[/tex]
Which has the following solution:
[tex]P(X\leq x)=1-e^{-\mu x}[/tex]
If X has an average value of 30 minutes
This means that [tex]m=30,\mu=\frac{1}{30}[/tex]
What is the probability that X is less than 38 minutes?
[tex]P(X\leq 38)=1-e^{-\frac{38}{30} }[/tex]
0.718 = 71.8% probability that X is less than 38 minutes
Freddie plays baseball. If we assume the probability of him getting a base hit is 0.305, what is the probability that he gets 4 base hits in a row?
So, the probability of Freddie getting 4 base hits in a row is approximately 0.0088, or 0.88%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
by the question.
Assuming that each at-bat is independent of the others, the probability of Freddie getting a base hit in one at-bat is 0.305.
To find the probability that he gets 4 base hits in a row, we can use the multiplication rule for independent events. This rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.
Therefore, the probability of Freddie getting 4 base hits in a row is:
0.305 x 0.305 x 0.305 x 0.305 = 0.0088 (rounded to four decimal places)
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High school students across the nation compete in a financial capability challenge each year by taking a nation financial capability challenge exam(URGENT)
The standard deviation that the student would have in order to be publicly recognized is given as 1.17
How to solve for the standard deviationWe would have to assume that the students score follows a normal distribution
This is given as
X ~ (μ, σ)
(μ, σ) are the mean and the standard deviation
1 - 12 percent =
0.88 = 88 percent
using the excel function given as NORMS.INV() we would find the standard deviations
=NORM.S.INV(0.88)
= 1.17498
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A student would have to score approximately 0.89 standard deviations above the mean to be in the top 12% and be publicly recognized.
How do we calculate?we can use the empirical rule to estimate the number of standard deviations a student has to score above the mean to be in the top 12 percent, assuming it is a normal distribution
The empirical rule states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.Approximately 95% of the data falls within two standard deviations of the mean.Approximately 99.7% of the data falls within three standard deviations of the mean.we will use the complement rule since our aim is to find the number of standard deviations a student has to score above the mean to be in the top 12%.
The complement of being in the top 12% is being in the bottom 88%.
From the empirical rule, we have that 68% of the data falls within one standard deviation of the mean.
Therefore, the remaining 32% (100% - 68%) falls outside one standard deviation of the mean.
Since we want to find the number of standard deviations a student has to score above the mean to be in the bottom 88%, we can assume that the remaining 32% is split evenly between the two tails of the distribution.
Applying the z-score formula:
z = (x - μ) / σ
The z-score for a cumulative area of 0.44 is approximately -0.89 found by looking up the z-score corresponding to the cumulative area of 0.44 (half of 0.88) in a standard normal distribution table.
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the graph shows the preimage shaded in grey and the image outlined in black. what is the scale factor of the dilation?
The scale factor of dilation of the shaded in gray to the shaded in black is 3
Calculating the scale factor dilationGiven that
The preimage = shaded in gray
The image = shaded in black
From the graph, we have the following values on the image and the preimage
The preimage = shaded in gray = 4
The image = shaded in black = 12
The scale factor of dilation is then calculated as
Scale factor = shaded in black/shaded in gray
So, we have
Scale factor = 12/4
Evaluate
Scale factor = 3
Hence, the scale factor dilation is 3
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TRUE/FALSE.For a Binomial experiment, the second moment about mu is given by the second derivative of (p+qeAt) with respect to t evaluated at t-0.
False. The second moment about mu for a binomial experiment is not given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0.
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q=1-p.
The second moment about mu is a measure of the variability of the binomial distribution, and is given by the formula[tex]E[(X-mu)^2][/tex] , where X is the random variable, mu is the mean, and E is the expected value operator.
To calculate the second moment about mu for a binomial distribution with parameters n and p, we can use the formula npq, where np is the mean and q=1-p. This formula can also be derived using the properties of variance, which state that [tex]Var(X)=E[X^2] - (E[X])^2.[/tex]
Therefore, the statement that the second moment about mu for a binomial experiment is given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0 is false. This statement does not relate to the binomial distribution or its properties, and is not a relevant formula for measuring the variability of a binomial experiment.
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