Evaluate the definite integral of: ∫_0^π (sin(x))^3 dx

the expected value for the given data set will be 0.423

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, a data set gives prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery.

We have to determine the expected value of winnings when buying one ticket. This can be computed using the expected value formula.

Recall the formula for the expected value E for events A and B whose probabilities of occurring are P(A) and P(B), respectively:

E  = (P(A)×value for A)+(P(B)×value for B)

​Using the formula above and extending it to 99 events yields:

E(x) = (1/ 292, 201,338 * 30,000,000) + (1 / 11,688,053 * 1,000,000) + (1/913,129 * 50,000) + (1/ 36,525 * 100) + (1/14,494 * 100) + (1/ 580 *7) + (1 /701 * 7) + (1/92 * 4) + (1/ 38 * 4)

E = 0.423

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If the car’s average tire pressure is on target, the probability that the TPMS will trigger a warning is 0.0000.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 31 psi (pounds per square inch.)

Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Target pressure = 31 psi

So, 26% of 31,

31 x 0.26 = 8.06

TPMS warns at below (31 - 8.06) = 22.94

Let X be tire pressure.

µ = 31, σ = 2

P(X < 22.94)

= P(x-µ / σ < (22.94 - 31) / 2)

= P(Z < -4.03)

= 0.0000 {from the z-score table}

Hence, the probability is zero.

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Answer:

see below

Step-by-step explanation:

a. amount of time = t

Value = 32000*(1-16.3%)^t

b. in 35 years Value = 32000*(1-16.3%)^35 = 63.17

The ordered pair (4, 1) is not a solution to the system,

- x + y = - 3 and x + 3y = 6.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, A system of linear equations - x + y = - 3 and x + 3y = 6.

An ordered pair must satisfy both equations simultaneously.

For, - x + y = - 3

- 4 + 1 = - 3.

- 3 = - 3 (satisfied).

For, x + 3y = 6.

4 + 3(1) = 6.

4 + 3 = 6.

But, 7 ≠ 6.

Therefore, the ordered pair is not a solution.

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Answer:

50

Step-by-step explanation:

To find the number of students, we can use the formula: average = (sum of marks) / (number of students).

Substituting the given values: 40 = 2000 / number of students

Solving for the number of students: number of students = 2000 / 40 = 50

So, there are 50 students in the series.

The surface area of figure is 784 ft² and the volume of the figure is 576 ft³.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The shape created by Jeff is a cube + square pyramid.

The height of square pyramid is = 3 ft

The sides of cube = 8 ft

The formula for volume of cube = (side)³

Volume of cube = (8)³

Volume of cube = 512 ft³

The formula for volume of square pyramid = (base)² × height / 3

Volume of square pyramid = (8)² × 3/3

Volume of square pyramid = 64 × 1

Volume of square pyramid = 64 ft³

Total volume of the figure -

Volume of cube + Volume of square pyramid

Total volume = 512 + 64

Total volume = 576 ft³

The formula for surface area of cube = 6(side)²

Surface Area of cube = 6 × (8)²

Surface Area of cube = 6 × 64

Surface Area of cube = 384 ft²

The formula for surface area of square pyramid = 6(side)²

Surface Area of square pyramid = (side)² + 2(side) √[{(side)²/4} + (height)²]

Surface Area of square pyramid = (8)² + 2(8) √[{(8)²/4} + (3)²]

Surface Area of square pyramid = 64 + 16 √[{64/4} + 9]

Surface Area of square pyramid = 80 √[16 + 9]

Surface Area of square pyramid = 80 √25

Surface Area of square pyramid = 80 × 5

Surface Area of square pyramid = 400 ft²

Total surface area of the figure -

Surface Area of cube + Surface Area of square pyramid

Total Surface Area = 384 + 400

Total Surface Area = 784 ft²

Therefore, the volume and surface area of the figure is 576 ft³ and 784 ft² respectively.

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Answer:

24

Step-by-step explanation:

You multiply the number of positions (2), by the number of people (12).

Answer:

... correct answer is 77 inches...

Answer:

A = 77 inches squared

Step-by-step explanation:

To find the area of a triangle, we use the formula

A = 1/2 bh where b is the base and h is the height

A = 1/2 (14) * 11

A = 77 inches squared

The exact values of two trigonometric functions are listed below:

- 2√2 / 3 and ± √6 / 3

In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.

Since sin(π/3-a) if cos(a)=-0.6 and π < a < 3π/2

Then, by the fundamental formula:

cos α = - √(1 - sin² α)

cos α = - √[1 - (1 / 3)²]

cos α = - √(8 / 9)

cos α = - 2√2 / 3

sin (π/3-a):

sin (π/3-a) = ± √[(1 - cos a) / 2]

sin (π/3-a) = ± √[[1 - (0.6)] / 2]

sin (π/3-a) = ± √6 / 3

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The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

a) P(Z < -1.35) =0.8708

b) P(Z > 1.48) =0.5714

c) P(-0.4 < Z < 1.5) =0.000

d) P(| Z | >2)=0.3830

Z-Score Table. A z-table, also known as the standard normal table, provides the area under the curve to the left of a z-score. This area represents the probability that z-values will fall within a region of the standard normal distribution.

Given:

The given condition is Z~N(μ = 0,σ = 1).

(a)

Find the value for .P(Z < -1.35)

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(Z < -1.35) =0.8708

(b)

Find the value for .P(Z > 1.48)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of  .P(Z > 1.48) =0.5714

(c)

Find the value for .) P(-0.4 < Z < 1.5)

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .) P(-0.4 < Z < 1.5) =0.000

(d)

Find the value for .P(| Z | >2)

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

Now,

Thus, the value of .P(| Z | >2)=0.3830

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The probability distribution is calculated z-table.

Z-table is also known as standard normal table which is used to find the area under the curve to the left of a z-score.

(a)P(Z<-1.35)

Here Z value negative so it is lies left of the curve, using standard normal table , P(Z<-1.35) = 0.0885

(b)P(Z>1.48)

z value is positive it lies right of the curve, using standard normal table, area under the curve P(Z>1.48)= 0.9306

(c)P(-0.4 < Z < 1.5) = P(Z<1.5) - P(-0.4<Z)

                             = 0.9332 - 0.3446

                             = 0.5886

(d)P(| Z | >2), |Z| is both positive and negative we have,

  P(| Z | >2) = P(-2 < Z <2)

                  = P(Z<2) - P(-2<Z)

                  = 0.9772 - 0.0228

                 = 0.9544.

Hence, (a)P(Z<-1.35) = 0.0885

(b)P(Z>1.48) = 0.9306

(c)P(-0.4<Z<1.5) = 0.5886

(d)P(|Z|>2)  = 1.9544

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According to the information, the order of the numbers would be 1, 3, 5, 8, 12.

To organize the numbers from smallest to largest we must use a number line in which we organize the numbers according to their position with respect to zero.

According to the above, the numbers closest to zero go first and then those that are further away from this number. Therefore, the sequence would look like this:

Since none of the numbers is negative, it can be inferred that they all go to the right of zero and are located in ascending order.

Note: This question has incomplete and disorganized information. Here is the complete and organized information.

Question/Task: Arrange the numbers from least to greatest.

Options:

3

8

5

1

12

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A polygon with seven congruent sides and angles is called HEPTAGON. In this case

A polygon is a two-dimensional closed figure with three vertices, three angles, and at least three straight sides. The words "Poly" and "gon" both mean many and angle, respectively. A triangle, for instance, has three vertices, three sides, and three angles. Therefore, it qualifies as a polygon.

Chantal "draws a polygon with seven congruent sides and angles," according to the statement. Heptagon is the name for a polygon with seven identical sides and angles. This polygon is a regular one because all of its sides and angles are equal. A regular polygon must have equal side lengths and angles by definition.

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In each case, the response variable, the explanatory variables, and the probability distribution is specified.

Before answering this question, let's us understand the Generalized linear models

Generalized linear models (GLMs) are used to model a response variable that has a non-normal distribution by linking the mean of the response variable to a linear combination of explanatory variables through a link function.

The Identification of cases are given below:

a) Response variable: number of trips per week to the supermarket for a household

Explanatory variables: number of people in the household, household income, distance to the supermarket

Probability distribution: Poisson

Justification: The response variable "number of trips per week" is count data and can be modeled using a Poisson distribution.

Linear component: log(μ) = β0 + β1 * number of people in the household + β2 * household income + β3 * distance to the supermarket

b) Response variable: person's weight

Explanatory variables: age, sex, height, mean daily food intake, mean daily energy expenditure

Probability distribution: Gaussian (Normal)

Justification: The response variable "person's weight" is continuous and approximately normally distributed.

Linear component: μ = β0 + β1 * age + β2 * sex + β3 * height + β4 * mean daily food intake + β5 * mean daily energy expenditure

c) Response variable: proportion of mice infected after exposure to bacteria

Explanatory variables: exposure level

Probability distribution: Binomial

Justification: The response variable "proportion of mice infected" is binary (yes/no) and can be modeled using a binomial distribution.

Linear component: logit(p) = log(p/(1-p)) = β0 + β1 * exposure level

The linear component represents the relationship between the mean of the response variable and the explanatory variables.

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____ The given question is incomplete, the complete question is given below:-

The following associations can be described by generalized linear models. For each one, identify the response variable and the explanatory variables, select a probability distribution for the response (justifying your choice) and write down the linear component.

a. The association between the number of trips per week to the supermarket for a household and the number of people in the household, the household income and the distance to the supermarket.

b. The effect of age, sex, height, mean daily food intake and mean daily energy expenditure on a person’s weight.

c. The proportions of laboratory mice that became infected after exposure to bacteria when five different exposure levels are used and 20 mice are exposed at each level.

Answer: The range rule of thumb is used to estimate the standard deviation by taking the range of the data and dividing it by 4:

s = (max - min) / 4

In this case, the range is 191.1 cm - 150.0 cm = 41.1 cm.

s = 41.1 cm / 4 = 10.275 cm

This estimate of the standard deviation is 10.275 cm, which is close to the actual standard deviation of 10.84 cm. Since the difference between the two is less than 1.4 cm, we can say that the estimate is accurate.

Answer: 0.47, 4.07,  4.70, 7.40, 74

Step-by-step explanation:

0.47, 4.07,  4.70, 7.4, 74

Answer:

0.47,4.07, 4.70, 7.40, 74

Step-by-step explanation:

In order the numbers from smallest to biggest, you can compare them pair-wise. For example, 0.47 is smaller than 4.07, so 0.47 is the smallest number. You can continue comparing the remaining numbers pair-wise to find the next smallest number, and so on.

Here is a more detailed explanation of how to order the numbers from smallest to biggest:

1. Compare 0.47 and 4.07. 0.47 is smaller than 4.07, so 0.47 is the smallest number.

2. Compare 4.07 and 4.70. 4.07 is smaller than 4.70, so 0.47, 4.07, and 4.70 are the smallest three numbers.

3. Compare 4.70 and 7.40. 4.70 is smaller than 7.40, so 0.47, 4.07, 4.70, and 7.40 are the smallest four numbers.

4. Compare 7.40 and 74. 74 is larger than 7.40, so 0.47, 4.07, 4.70, 7.40, and 74 are the smallest five numbers.

When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.

In Geometry and trigonometry, an aspect is a shape made up of two rays, referred to as the angle's sides, that converge at a center point termed as the angle's vertex. Two rays can create an angle in the region where they are arranged. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible structure for two rays or lines with only a common end in planar geometry. The English term "angle" originated from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the opposite rays, also known as the side of the angle.

given

distance between two observer = 300 ft

angle of elevation to top pole = 17° and 16°

height of the flagpole = ?

now,

Let x be the distance of the pole

tan17° = h /x

x = h / tan17°

now,

tan20° = h / 500 - x

500 - x = h / tan16°

again applying

500 - 3.49h = 2.75h

h = 48.077 ft

When two observers on opposing sides of a flagpole are 500 feet apart, the height of the flagpole is 48.077 feet.

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Answer:

If m∠1=95°, then m∠8 can be found by using the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, m∠8 = 180 - (m∠1 + m∠3) = 180 - (95° + 55°) = 30.

Two equivalent fractions is 16/4, 100/25

Equivalent fractions are two or more fractions that are all equal even though they have different numerators and denominators. For example, the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000. Each time the fraction in its simplest form is 'one half'.

Given here : The two fractions 40/

Now the quotient is 40/10=4

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½

Thus two equivalent fractions here are 16/4,100/25 both will equal to 4

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The regression equation is linear in the explained and explanatory variables.

In order for Ordinary Least Squares (OLS) estimates to be unbiased, the regression equation must be linear in both the explained and explanatory variables. This means that the relationship between the dependent variable (what is being explained) and the independent variables (what is being used to explain the dependent variable) must be linear. This is important because it ensures that the estimated coefficients of the regression equation accurately reflect the true relationship between the variables. Additionally, the error term must have an expected value of 0, given any value of the explanatory variable, and have the same variance given any value of the explanatory variable. This ensures that the estimated coefficients do not suffer from bias and that the OLS estimates are unbiased.

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In a unit rate, the denominator is always 1.

The marginal revenue when q = 29 is 510 dollars.

To find the marginal revenue we need to differentiate the revenue equation, here we know that:

R(q) = -5q² + 800q

Differentiating that, we will get:

R'(q) = MR(q) = 2*(-5)*q + 800

                     = -10q + 800

The marginal revenue when q = 29 is

MR(29) = -10*29 + 800 = 510

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Step-by-step explanation:

a) Find the angular speed of the blade in radians per minute:

The formula for angular speed is given by:

ω = 2 * π * f

where f is the frequency of rotation in revolutions per minute, and π is approximately equal to 3.14159.

Plugging in the values, we get:

ω = 2 * 3.14159 * 4300 revolutions per minute

ω = 26,957.1 radians per minute

Rounding to three decimal places, the answer is:

ω = 26,957.1 radians per minute = 26,957.1 radians/minute

b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut:

The formula for linear speed (v) is given by:

v = ω * r

where ω is the angular speed in radians per minute, and r is the radius of the blade (half of the diameter).

Plugging in the values, we get:

v = 26,957.1 radians/minute * 4.125 inches

v = 111,542.7 inches per minute

Rounding to one decimal place, the answer is:

v = 111,542.7 inches per minute = 111,543 inches/minute

The solution is, the minute hand will be 87.7 degrees ahead of the hour hand.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Let's call the current position of the hour hand H and the current position of the minute hand M.

At the start, we have H = 0 and M = -20 degrees.

After 18 minutes, the minute hand will have moved 18 * 6 = 108 degrees, while the hour hand will have moved 18 * (6/60) = 0.3 degrees.

So the new position of the minute hand is M + 108 = 88 degrees,

and the new position of the hour hand is H + 0.3 = 0.3 degrees.

Therefore, the minute hand will be 88 - 0.3 = 87.7 degrees ahead of the hour hand.

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The value of the functions are (f o g) (2) = 0 and  (g o f) (2) = 4.

What are functions?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x). In other words, for the same x value, there cannot be more than one value for f(x).

We are given two functions, f(x) and g(x).

Their graphs are also given.

We are asked to solve the following questions using the given graphs.

1) (f o g) (2) = f( g(2) )

To solve this we have to first start with inner functions.

g(2) = value of y when x = 2  

    From the g(x) graph it is given that g(2) = 2 when x = 2

Now we substitute this in f( g(2) )

i.e f(2) = value of y when x = 2 = 0

From the f(x) graph it is given that f(2) = 0 when x = 2.

So (f o g) (2) = 0

2) (g o f) (2) = g( f(2) )

  f(2) = 0 ( as mentioned above)

Substituting,

 g( f(2) = g (0) = 4

So (g o f) (2) = 4

Therefore the value of the functions are (f o g) (2) = 0 and

(g o f) (2) = 4.

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Answer:

4 1/5

Step-by-step explanation:

6/10 = 3/5

2+1=3

3+6/5 = 4 1/5

The value of a and c in the right triangle are 38.28 and 66.89 respectively.

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.

From the diagram:

sin(55.0892) = 54.855/c

c = 66.89

Also:

tan(55.0892) = 54.855/a

a = 38.28

The value of a and c are 38.28 and 66.89 respectively.

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Answer:

Step-by-step explanation:

Total students = 275
Boy students = 150
So, girl students = (275-150) = 125

Percentage of boy students = (150/275)% = 54.55%

Answer:

5425.92

Step-by-step explanation:

radius(r)=d/2

=24/2

=12ft

So,

Volume=πr^3

=(3.14*12^3)cubic feet

=5425.92cubic feet

Answer:

V≈7238.23 [ft³].

Step-by-step explanation:

1. formula of the required volume is

[tex]V=\frac{4}{3} \pi R, \ where \ R-radius.[/tex]

2. if diameter is 24 ft., then R=12 [ft] and the required volume is:

[tex]V=\frac{4}{3} *3.1415*12^3=7238.2294[ft^3].[/tex]

On a dot plot, the statement saying that Four people said they rode a Ferris wheel five times would be represented with four dots above the input five.

A dot plot shows the number of times that each observation was accrued in a data-set, which the number of dots representing the number of observations of each input.

The parameters for this problem are given as follows:

Hence the statement would be represented with four dots above the input five.

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Answer:

a) The two variables in this table are "students" and "parents".

b) The observational unit in this study is a student-parent pair.

c) The total number of students who do not use drugs is 141.

d) The total number of student-parent pairs in this study is 445.

Step-by-step explanation:

a) The two variables in this table are "students and parents" who do not use drugs and those who use drugs.

b) The observational unit in this study is a student-parent pair.

c) The total number of students who do not use drugs is 141.

d) The total number of student-parent pairs in this study is 445.

An observational unit is described as an entity for which data is collected and analyzed and enables conclusions to be drawn about its characteristics.

An observational unit is assigned a value based on the collected data.

On the other hand, we define a variable as the piece of information being collected from each observational unit.

                Does not use    Uses    Total

Students          141               94        235

Parents            110              100        210

Total               251              194        445

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