The distribution is symmetric. skewed. both symmetric and skewed.

a)The probability that at least 10 of the 15 randomly chosen individuals have no citations is 0.6723.  b) the probability that fewer than half of the 15 randomly chosen individuals have at least one citation is 0.3826. c) the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive, is 0.7278.

Recall that in Exercise 30 (Section 3.3) the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company, was given as follows:

Y=y 0 1 2 3 4 5

P(Y=y) 0.52 0.29 0.10 0.05 0.03 0.01

a. We can use the binomial distribution to model the number of individuals among 15 who have no citations, with the probability of success being P(Y=0)=0.52. Then, the probability of at least 10 individuals having no citations is:

P(X >= 10) = 1 - P(X < 10) = 1 - P(X <= 9)

Using a binomial table or calculator, we find that:

P(X <= 9) = 0.3277

Therefore,

P(X >= 10) = 1 - P(X <= 9) = 1 - 0.3277 = 0.6723

b. We can use the binomial distribution again to model the number of individuals among 15 who have at least one citation, with the probability of success being P(Y>0)=1-P(Y=0)=1-0.52=0.48. Then, the probability of fewer than half (less than 7) individuals having at least one citation is:

P(X < 7) = Σ P(X = k), where k = 0,1,...,6

Using a binomial table or calculator, we find that:

P(X < 7) = 0.6174

Therefore,

P(X >= 7) = 1 - P(X < 7) = 1 - 0.6174 = 0.3826

c. We need to find the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive. We can use the binomial distribution with the probability of success being P(Y>0)=0.48. Then, the probability is:

P(5 <= X <= 10) = Σ P(X = k), where k = 5,6,...,10

Using a binomial table or calculator, we find that:

P(5 <= X <= 10) = 0.7278

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Your question is incomplete, but probably the complete question is :

Exercise 30 (Section 3.3) gave the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company. What is the probability that among 15 randomly chosen such individuals

a. At least 10 have no citations?

b. Fewer than half have at least one citation?

c. The number that have at least one citation is between 5 and 10, inclusive?*

Answer:

35g^2+38g+8

Step-by-step explanation:

35g^2+38g+8

The probability of rolling a number less than 7 would be written as 1/1 or simply 1.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

Without additional information, it's impossible to determine the probability of an event being less than 7. We need to know the context of the situation and the possible outcomes that can occur to calculate the probability.

However, if we assume that the context is related to rolling a fair six-sided die, then the probability of rolling a number less than 7 is 1 because all the possible outcomes (1, 2, 3, 4, 5, and 6) are less than 7.

In fraction form, the probability of rolling a number less than 7 would be written as 1/1 or simply 1.

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The probability of getting a card less than 7 would be 0.75. So, p( less than 7) in fraction form will be 3/4.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

The given cards are numbered as:

s = [4,5,6,7]

n(s) = 4

The event here is the probability of picking the cards less than 7

Cards less than 7 i.e. 4,5,6

n(e) = 3

Probability of picking the card lesser than 7 is:

P(e) = n(e)/n(s)

P(e) = 3/4

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The complete question is as follows:

You pick a card at random. 4 5 6 7 What is P(less than 7)? Write your answer as a fraction or whole number.

p = probability.

Answer: y=6x-4

Step-by-step explanation:

Answer:

(a-b)/(b-a)

Step-by-step explanation:

The gradient = difference of y values / difference of corresponding x value

=  (a-b)/(b-a)

Step-by-step explanation:

[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]

Its like because when you try to cut down it would be

[tex] {}^{2} \sqrt{ {x}^{1} } [/tex]

So to simplify things down it would be

[tex] \sqrt{x} [/tex]

Answer:

A is definitely correct and possibly C as well

Step-by-step explanation:

Wyatt is correct so it’s not B or D and E doesn’t make sense.

Answer:

Ali will cover 1,080m altogether.

Step-by-step explanation

If the field is 80m by 100m and there are 2 sides of each of those measurements to make a whole round around the field, then one round would be (80m x 2) + (100m x 2) = 360. Since Ali wants to do three laps around the field, then you multiply 360 x 3 to get 1080m total.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. Malcolm's family travels 65 miles per hour faster than Theo's family.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. To calculate how much faster Malcolm's family travels than Theo's family, we must first know the speed of Theo's family. Let's say Theo's family travels at 25 miles per hour. To calculate the difference in speed between the two families, we must subtract 25 mph from 65 mph. The difference is then 40 mph, meaning Malcolm's family travels 40 mph faster than Theo's family.

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The surface area of the triangular prism as per the area formula is as follows:

1104m².

The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.

To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In the triangular prism given,

We have 2 triangles and 3 rectangles.

So, to find the surface area of the prism we need to find the area of the individual shapes and add them up.

Length of 1st rectangle = 20m and breadth = 19m.

Area = l × b

= 20 × 19

= 380m².

Length of 2nd rectangle = 19m and breadth = 16m.

Area = l × b

= 19 × 16

= 304m².

Length of the 3rd rectangle = 19m and breadth = 12m.

Area = l × b

= 19 × 12

= 228m².

Now coming to the triangles,

Both the triangles are equal with base = 16m and height = 12m.

Area = 1/2 × b × h

= 1/2 × 16 × 12

= 96m².

We have two triangles so, area of 2 triangles = 2 × 96 = 192m².

Therefore, total area = 380 + 304 + 228 + 192

= 1104m².

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The nth term from the quadratic sequence  "2, 8, 18, 32, 50,..." Would be 2n², where n reffers to the position of number.

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third term , n =3,                = 2*3*3 = 18

Third term, n = 4,       = 2*4*4 = 32

Fourth term, n =5,     2 * 5* 5 = 50

For nth term,        2 *n *n = 2n²

Therefore the nth term of quadratic sequence would be 2n².

Sequences with a term are referred to as quadratic sequences. The fact that the first differences between terms are not equal but the second differences between terms are can be used to identify them.

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To complete the table of equivalent ratios of lengths to widths, we need to find the missing values that make the ratios in each row equal to each other. One way to do this is to use cross-multiplication.

First, we can compare the first and second rows to find the value that makes them equivalent:

x/18 = 8/y

Multiplying both sides by 18y, we get:

xy = 144

So the missing value in the first row is 144/18 = 8, and the missing value in the second row is 144/8 = 18.

Next, we can compare the third and fourth rows:

10/30 = 12/z

Multiplying both sides by 30z, we get:

10z = 360

Dividing both sides by 10, we get:

z = 36

So the missing value in the third row is 36, and the missing value in the fourth row is 12/10 * 36 = 43.2.

Therefore, the completed table is:

8 18

8 144/10 = 14.4

10 30

12 36

Answer: {x|4<x<10}

Step-by-step explanation:

The weight of the liquid can be calculated as follows:

Weight = Volume x Density

The volume is given as 182.8 milliliters.

The density is given as 0.135 grams over milliliter.

Weight = 182.8 x 0.135 = 24.67 grams

Therefore, the weight of the liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135 grams over milliliter is 24.67 grams.

Probably this

The required probability of waiting taxi longer than one hour and waiting for one hour is equals to 0.0821 and 0.1725 respectively.

Use the exponential distribution formula,

For an exponentially distributed random variable X with mean μ, the probability density function is given by,

f(x) = (1/μ) × e^(-x/μ)

And the cumulative distribution function is ,

F(x) = P(X ≤x)

      = 1 - e^(-x/μ)

Mean time between taxi arrivals is 24 minutes,

Rate parameter

λ = 1/μ

  = 1/24.

Probability of waiting longer than one hour for a taxi,

Probability that the time between arrivals is greater than 60 minutes. Using the cumulative distribution function,

P(X > 60)

= 1 - P(X ≤ 60)

= 1 - (1 - e^(-60/24))

= e^(-2.5)

≈ 0.0821

Probability of waiting longer than one hour for a taxi is approximately 0.0821.

Already been waiting for one hour,

the time you have to wait for the next taxi to arrive is 10 minutes.

Using the cumulative distribution function,

P(X ≤70 | X > 60)

= P(60 < X ≤ 70) / P(X > 60)

= (1 - e^(-70/24) - (1 - e^(-60/24))) / e^(-60/24)

≈ 0.1725

Therefore, the probability of waiting longer than one hour for a taxi is and that a taxi arrives within the next 10 minutes waiting for one hour is equals to 0.0821 and 0.1725 respectively.

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The above question is incomplete, the complete question is:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 24 minutes. (a) What is the probability that you wait longer than one hour for a taxi? (b) Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes? Round your answers to 4 decimal places.

The predicted number of wins for a team that allowed 80 runs is 72.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

To find the predicted number of wins for a team that allowed 80 runs, we need to substitute x = 80 into the given equation:

y = 80.98 - 0.108x

y = 80.98 - 0.108(80)

y = 80.98 - 8.64

y ≈ 72.34

Rounding this to the nearest integer, we get:

y = 72

Therefore, the predicted number of wins for a team that allowed 80 runs is 72.

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Step-by-step explanation:

decimal interest = .06

$ interest = prt

                = $ 1730 * .06 * 4 = $ 415.20

From the calculations, we can see that each of the external angles of the polygon would have a measure of  60 degrees.

The external angles of a polygon are the angles formed by extending one side of the polygon and forming a new angle with the adjacent side. To find the external angle of a polygon, you can use the following formula:

External angle = 360° / number of sides

In this case we have been told that what we have is a hexagon thus;

4xternal angle is; 360/6

= 60 degrees

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Answer:

9374

Step-by-step explanation:

First add Saturday and Sunday totals (9681+8905)=18586

then subtract Friday's total from this number (18586-9212)=9374

The given expression is [tex](f+g)(x)[/tex]  so the value of this expression is [tex]= x^3 + 1/2 x^2 + 3/4 x - 5[/tex]

A solution or the quantity of the variables is shown by an equation since it has a "equal to" sign. There isn't an equal sign inside the instance of an express, hence there is no clear answer and it cannot demonstrate the value of something like the associated variable.

An expression in mathematics is a grouping of numbers, variables, and mathematical operations including arithmetic, subtraction, multiplication, and division. You may compare expressions to sentences in your mind. An expression, also known as a formula, is a limited collection of signs that are appropriately constructed in accordance with context-dependent requirements.

[tex](f+g)(x) = f(x) + g(x)[/tex]

[tex]= (x^3 - 1/2 x^2 + x) + (x^2 - 1/4 x - 5)[/tex]

[tex]= x^3 - 1/2 x^2 + x + x^2 - 1/4 x - 5[/tex]

[tex]= x^3 + 1/2 x^2 + 3/4 x - 5[/tex]

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Check the picture below.

Answer:

1080

Step-by-step explanation:

the perimeter of the field is 2(80) + 2(100) or 360

if he goes around the field 3 times then its 3*360 or 1080

~lmk if u got Qs

The length of the rope in this scenario is 33.912 meters based on given diameter.

To find the length of the rope wound around the cylindrical pipe, we need to take the circumference of the pipe and the number of times the rope is wound around it.

The diameter of the pipe is given as 600 mm, which means the radius is half of that, or 300 mm. To find the circumference, we use the formula C = 2πr, where π is pi (approximately 3.14) and r is the radius. Therefore, the circumference of the pipe is 2 x 3.14 x 300 = 1884 mm.

The rope is wound around the pipe 18 times, so the total length of the rope is 18 times the circumference of the pipe, which is 18 x 1884 = 33,912 mm or 33.912 meters.

To calculate or find the length of the rope wound around the cylindrical pipe, we multiply the circumference of the pipe by the number of times the rope is wound around it. Therefore, the length of the rope in this scenario is 33.912 meters.

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The value of the given integral function is 10 and option d is the correct answer.

Any function that may be drawn without removing the pen from the page is said to be continuous. Formally, a function f(x) is continuous at a point c if all three of the following criteria are true:

Definition of f(c) (i.e., c is in the domain of f).

When x gets closer to c, f(x) reaches its maximum.

The limit of f(x) as x gets closer to c equals f. (c).

A function is said to be continuous if it is continuous over its whole domain. In mathematics and the sciences, continuous functions have a wide range of useful features and applications.

For the given function the integral can be written as follows:

[tex]\int\limits^2_{-4} {f(x)} \, dx = \int\limits^0_{-4} {\frac{x^2}{|x|} } \, dx + \int\limits^2_0 {\frac{x^2}{|x|} \, dx[/tex]

[tex]= [\frac{x^2}{2} ]_{-4}^0 + [\frac{x^2}{2} ]_{0}^2\\= 8 + 2\\= 10[/tex]

Hence, the value of the given integral function is 10 and option d is the correct answer.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85[/tex]

The measure of arc BC is 264°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Since the triangle is isosceles, this means that angle B = angle C

therefore angle A = 180- ( 24+24)

= 180- 48

= 132°

From the theorem that says that the angle at the circumference is twice the angle at the centre.

therefore arc BC = 2 × 132

arc BC = 264°

therefore the measure of arc BC is 264°

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Based on the two-way table, it appears that there is an association between grade level and preference for school color.

As the grade level increases, there is a trend towards a greater preference for blue. Among sixth graders, there were 17 students who preferred blue and 39 who preferred green. Among seventh graders, 27 preferred blue and 27 preferred green. Finally, among eighth graders, 41 preferred blue and 14 preferred green. It is important to note, however, that this trend may not necessarily imply causation. There could be other factors at play that are contributing to this association, such as the age of the students or the characteristics of the school environment. Additionally, the sample size in each grade level is relatively small, which could lead to some variability in the results.

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Answer:

It is known as many things

Step-by-step explanation:

Kite, Dart, Arrowhead. Kites can be concave or convex. It can also be called a reflexed polygon.

Answer:

[tex]the \: shape \: above \: is \: a \\ \: concave \: polygon[/tex]

This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:= (13/4)x + y = -7

How to find standard form?

To find the standard form of the line that passes through the given points (-4, 6) and (0, -7), we need to first find the slope of the line using the slope formula:

slope = (y₂ - y₁) / (x₂- x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the given points, we get:

slope = (-7 - 6) / (0 - (-4))

slope = -13/4

Now that we have the slope of the line, we can use the point-slope form of the equation of a line:

y - y₁= m(x - x₁)

where m is the slope and (x1, y1) is one of the points on the line. Using the point (-4, 6), we get:

y - 6 = (-13/4)(x - (-4))

y - 6 = (-13/4)x - 13

y = (-13/4)x - 7

This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:

(13/4)x + y = -7

This is the standard form of the equation of the line that passes through the given points.

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