Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x = the average of the 49 races. Part (a) two decimal places.) Give the distribution of X. (Round your standard deviation to two decimal places)Part (b) Find the probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) __ min Part (d) Find the median of the average running times ___ min

Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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The maximum of a graph is found on the y axis. Considering the given interval, the point on the y axis is 4. Thus, the maximum of the graph over the interval is 4.

Answer:

2(-3x+2)^2 -1

Step-by-step explanation:

so first you would find that f(g(x)) = f(-3x+2)

next plug in

f(-3x+2) = 2x^2-1

to every x

f(-3x+2) = 2(-3x+2)^2-1

Answer:

HOI

Step-by-step explanation:

Answer: Probably negative 69

The coordinates of the vertex are (0, 27).

A parabola is a symmetrical, U-shaped curve that can be formed by intersecting a cone with a plane that is parallel to one of its sides. In mathematics, a parabola is a type of quadratic function that can be written in the standard form y = ax² + bx + c, where x and y are variables, a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term. The coefficient a determines the shape of the parabola: if a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.

To find the vertex of the parabola, we need to use the formula:

x = -b / 2a

where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c), which describes the parabola.

In this case, the equation of the parabola can be written as:

h = -0.045t² + 27

where h is the height of the cable (in meters) above the deck of the bridge, and t is the distance (in meters) from the first tower.

By comparing this equation with the standard form, we can see that a = -0.045 and b = 0. To find the vertex, we can substitute these values into the formula:

x = -b / 2a = 0 / (-2 * 0.045) = 0

So the x-coordinate of the vertex is 0. To find the y-coordinate, we can substitute this value back into the equation:

h = -0.045(0)² + 27 = 27

So the coordinates of the vertex are (0, 27).

The correct interpretation of the vertex is that it represents the highest point on the parabola, which in this case is the highest point of the cable above the deck of the bridge. The vertex is also the axis of symmetry of the parabola, which means that the distance from the first tower to the vertex is the same as the distance from the vertex to the second tower.

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Answer:

x + 10 = 24

Step-by-step explanation:

In the figure attached,

There are two external points A and B.

Fro point A two tangents AD and AE have been drawn and From point B tangents BE and BC have been drawn.

Since AD = 10 units,

Therefore, AE = 10 units

(Since tangents drawn from a point to a circle are same in measure, therefore, AD = AE)

Therefore,

BE = AB - AE

Since BE = BC

So BC = AB - AE

       x = 24 - 10

x + 10 = 24

Therefore, (x + 10) = 24 will be the equation to be used to solve for x.

There are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

The system of equations is:

y = 3x - 3

y = -x^2

To determine which point from a specified set satisfies the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

Substituting y = 3x - 3 into the second equation, we get:

3x - 3 = -x^2

Rearranging this equation, we get:

x^2 + 3x - 3 = 0

Using the quadratic formula, we can solve for x:

x = (-3 ± sqrt(3^2 - 41(-3))) / (2*1) = (-3 ± sqrt(21)) / 2

Therefore, there are two possible values of x that satisfy the system of equations:

x = (-3 + sqrt(21)) / 2 ≈ 0.79

x = (-3 - sqrt(21)) / 2 ≈ -3.79

To find the corresponding values of y, we can substitute these values of x into either equation. For example, if we use y = 3x - 3, we get:

y ≈ 0.37 (when x ≈ 0.79)

y ≈ -12.37 (when x ≈ -3.79)

Therefore, there are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

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Answer:

P = 0.545

Step-by-step explanation:

Here we can find the probability Q, in which you need one or two spins to win the game, and then:

P = 1 - Q

Will be the probability that it takes 3 or more spins to win.

Case where you need only one spin:

There are 3 out of 12 possible outcomes, then the probability of winning with only one spin is:

p = 3/12.

Case where you need two spins to win:

Here we should get a normal sushi roll in the first spin and a wasabi bomb in the second.

The probability of getting a sushi roll in the first spin is equal to the quotient between the number of sushi rolls (9) and the total number of possible outcomes (12), then:

p1 = 9/12

For the second spin we need to get a wasabi bomb, assuming that the susi roll is not replaced (so now there are 8 sections with sushi rolls and 3 with wasabi bombs, if you get the empty section you roll again or something like that)

Now the probability of getting a wasabi bomb is equal to the quotient between the number of wasabi bombs remaining (3) and the total number of outcomes remaining (11), this is:

p2 = 3/11

The joint probability is the product of the two individual probabilities:

p = p1*p2 = (9/12)*(3/11)

Now, the total probability of winning with one or two spins is equal to the sum of the probabilities for each case, then:

Q = (9/12)*(3/11)  + 3/12 = 0.455

Then the probability of needing 3 or more spins to win is:

P = 1 - Q = 1 - 0.455 = 0.545

The probability that it takes 3 or more spins for the contestant to get a wasabi bomb is 0.545 and this can be determined by using the given data.

Given :

The probability to win the game in the first spin is:

\(\rm P_1=\dfrac{3}{12}=\dfrac{1}{4}\)

The probability to win the game in the second spin is:

\(\rm P_2 = \dfrac{9}{12}\times \dfrac{3}{11}\)

\(\rm P_2=\dfrac{9}{44}\)

The probability to win in 1 or 2 spins is given by:

\(\rm Q = P_1+P_2=\dfrac{9}{44}+\dfrac{1}{4}\)

Q = 0.455

So, the probability that it takes 3 or more spins for the contestant to get a wasabi bomb is:

P = 1 - Q

P = 1 - 0.455

P = 0.545

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A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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Answer:

$80 is the 100% original price

The sale price is $56 with 30% off and $24 in savings.

Step-by-step explanation:

We can write a proportion. We know that $24 is a 30% off discount of an unknown original price. Let's call it x. We write equal ratios of  comparing percent and  comparing the 24 to the original price. We then set them equal.

We then cross multiply across the equal sign from numerator to the opposite numerator.

30(x)=24(100)

30x=2400

We divide to find x.

x=80.

Since we saved $24 as a discount, the sale price would be 80-24=56.

The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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Answer:

84

Step-by-step explanation:

70% of 120= 84

The composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.

Given the function y = 3(1 + 4x), we need to write it in the form f(g(x)) by identifying the inner function g(x) and the outer function f(u).

First, let's identify g(x), which is the inner function. In this case, g(x) = 1 + 4x.

Next, let's identify the outer function f(u). Since y = 3(1 + 4x), we can rewrite this expression as y = 3u, where u = 1 + 4x. So, f(u) = 3u.

Now, we can write the composite function in the form f(g(x)): f(g(x)) = f(1 + 4x) = 3(1 + 4x).

So, the composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.

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Answer:

9cm<x<17cm

Step-by-step explanation:

your welcome

The range of the possible lengths for the third side is 9 cm < x < 17 cm.

A triangle is a geometrical shape which has three vertices, three edges and three angles. In other words, in Euclidean geometry, a triangle is defined as a two dimensional shape which is three non-collinear points lying on a unique plane.

The sum of the interior angles of a triangle is 180 degrees.

Here we have lengths of two sides of a triangle which are 4 cm and 13 cm.

If the length of two sides of a triangle are given, then the length of third side will lie in the range between the difference of the other two sides and the sum of the other two sides.

Let x represents the third side of the triangle.

So, here the third side lies between 13 cm - 4 cm and 13 cm + 4 cm.

13 - 4 < x < 13 + 4

9 < x < 17

Hence the range of possible lengths for the third side of the triangle is in between 9 cm < x < 17 cm.

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Answer:

C, the third choice

Step-by-step explanation:

Answer:

384 square inches

Step-by-step explanation:

The side is 10×5=50

There are 4 sides of equal surface area so we are at 200

The floor is 8×10=80 so we are at 280

The front is 8×5=40 and the back is the same so add another 40 so we are at 360

Add the little triangles which are 4×3=12 and you add the back as well so we get 384 square inches

Answer:

I think it is the first one because it shows 18 but it says the nearest tenth so it will become 20

A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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On solving the provided question, we got to know that - 40/155 adults will not have hypertension (70%),

The probability is calculated by dividing the total number of outcomes by the total number of possible ways an event may occur. Probability and odds are two different ideas. The chances are calculated by dividing the likelihood that a certain event will occur by the likelihood that it won't.

Probabilities are mathematical explanations of the chance that an event will happen or that a proposition is true. The probability of an occurrence is a number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty.

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Answer: SOLN,

let,<FHC be x

<GHC+<FHC( sum of  angle of triangle=180 degree

 x+6m+55+8m+55=180

 x+ 14m+110=180

  x+14m=180-110

  x+14m=70

    x=70 divied by 14m  

     x=5m

therefore,the value of <FHC is 5m.      

Answer:

The following statement, “Children are typically introduced to video games between the ages of six to eight” is a true statement. The graph shows that a very small percentage of children from birth to five years old play video games, but suddenly, once they have turned 6, there is practically a 60% increase in how many kids are playing video games one hour a week. It is from the age 6 that the kids start off and are introduced to the video games, as more and more kids end up playing as well as the grow older.

Step-by-step explanation:

change wording

We can easily conclude from the column chart that children at the age group of 6-8 are introduced to video games typically.

''A column chart is a data visualization where each category is represented by a rectangle, with the height of the rectangle being proportional to the values being plotted. Column charts are also known as vertical bar charts.''

From the column chart, it is clear that children of age groups of 0-2 and 3-5 are using almost minimum amount of video games. The percentage is near about (0 - 5%).

After that, the children of the age group of 6-8 are using video games for a much longer period as compared to the previous two groups. The percentage is 60%.

After that, the next children of the age group of 9-11 are using video games for a much slightly more as compared to the previous group. The percentage is around 65%

The children of the age group of 12-14 are using video games for a slightly longer period as compared to the previous group. The percentage is about 75%.

The children of the age group of 15-17 are using video games for a maximum period in this graph. The percentage is 80%.

We can easily conclude from the column chart that children at the age group of 6-8 are introduced to video games typically. Because, before that age there were not much playing of video games as per the given column chart .

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Answer:

362,880 different

Step-by-step explanation:

Use the permutation 9*8*7*6*5*4*3*2*1. Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.

The dimension of the rectangular closet are as follows:

A rectangular closet has an area of 36 square feet and a perimeter of 24 feet. The dimension of the closet is as follows:

perimeter of the rectangular closet = 2(l + w)

where

24 = 2(l + w)

l + w = 12

l = 12 - w

Area of the rectangular closet = lw

where

Therefore,

36 = lw

Using substitution,

36 = (12 - w)w

36 = 12w - w²

w² - 12w + 36 = 0

w² - 6w - 6w + 36 = 0

w(w - 6) - 6(w - 6) = 0

(w - 6)(w - 6) = 0

Therefore,

w = 6

l = 36 / 6

l = 6

Hence,

length = 6ft

width = 6 ft

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Answer:

Step-by-step explanation: since the 1.5 is suppose to be on the x axis, you plot the point between 1 and 2. Ten you go down to the y axis since it is negative and plot it between -2 and -3.

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The statement that is not true about a rational function of the form f(x) where g and h are polynomial functions is D. A rational function may have many horizontal asymptotes.

A rational function is defined as the ratio of two polynomial functions, where g and h are polynomials and h is not the zero polynomial. The graph of a rational function can have vertical asymptotes, which occur when the denominator of the function is equal to zero. However, a rational function can intersect a vertical asymptote if the numerator is also equal to zero at that point.

Regarding vertical asymptotes, statement A is true. The graph of a rational function will never intersect a vertical asymptote, as long as the function is defined at that point.

Statement B is also true. A rational function may have multiple vertical asymptotes if the denominator has multiple factors that result in the function being undefined at different points.

Statement C is also true. If the degrees of g and h are m and n, respectively, and m is less than or equal to n, then the rational function will have a horizontal asymptote with an equation of y = (a/b).

However, statement D is not true. A rational function can have at most one horizontal asymptote, and this occurs when the degree of g is equal to the degree of h. The equation of the horizontal asymptote is y = (a/b), where a is the leading coefficient of g and b is the leading coefficient of h.

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Answer:

Probability of drawing an odd number.

Number of odd numbers = 5

Number of numbers in the set = 10

So it's a 5 in 10 chance or 1 in 2 chance.

Probability of drawing a multiple of 3.

Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3

Number of numbers in the set = 10

So it's a 3 in 10 chance

The problem involves finding the maximum value of the function F(z) = 2z² + z/(2 - z²) - z² - 1 for |z| = 1 and determining if there exists a point z₀ in the disk B₂(0) such that |F(z₀)| = M. We will explore whether this contradicts the maximum modulus principle.

To find the maximum value of F(z) on the circle |z| = 1, we need to evaluate the function F(z) along the curve parameterized by z = e^(iθ), where θ ranges from 0 to 2π. By substituting z = e^(iθ) into F(z), we obtain a function in terms of θ. Taking the absolute value of this function yields |F(z)|.

To find the maximum value of |F(z)| on the unit circle, we can evaluate |F(z)| at different points along the circle and determine the maximum. Let M be the maximum value of |F(z)| obtained in this manner.

Next, we consider the disk B₂(0) and seek a point z₀ in the disk such that |F(z₀)| = M. If such a point exists, it would imply that |F(z)| takes its maximum value on the boundary of the disk, violating the maximum modulus principle. However, it is unclear from the given information whether such a point exists.

In summary, we determine the maximum value M of |F(z)| on the unit circle |z| = 1. We then consider the disk B₂(0) to check if there exists a point z₀ in the disk such that |F(z₀)| = M. This analysis will help us ascertain if there is any contradiction with the maximum modulus principle, which states that a holomorphic function cannot attain its maximum on the interior of its domain.

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The number of $0.50 increases to maximize the profit is X = 1.

First of all, we need to write the linear function which represents the price of the ticket for each increase of $0.50:

P - Price of each ticket.

x - number of increases.

We know that the current price is $5.00, so:

    \(P(x) = 0.5x + 5.00\)

After that, let's build a linear function which shows the number of tickets sold for each price increase:

    T - number of tickets.

    x - number of increases.  

    \(T(x) = -100x + 1200\)

With all this done, we can finally build the quadratic function which represents the money earned:

M - money earned

\(M = Tickets Sold \times TicketPrice\\\\M = T(x) \times P(x)\\\\M = (0.5x + 5) \times (-100x + 1200)\\\\M = -50x^{2} + 600x -500x + 6000\\\\M(x) = -50x^{2} + 100x + 6000\\\\\)

Now, to finish, we only have to calculate the value of X(number of increases) which can give us the maximum value of this function:

the X coordinate for the maximum value of a quadratic is expressed by:

   \(Xmax = \frac{-b}{2a} \\\\\)

In our equation, b = 100 and a = - 50 :

\(Xmax = \frac{-(100)}{2(-50)} \\\\Xmax = \frac{-100}{-100} \\\\Xmax = 1\)

Thus, the number of increases which maximizes the profit is 1.

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