construct the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall. assume the population is approximately normal. step 3 of 4: find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

It is proved that, for every positive integer n, there are n consecutive composite integers.

Given statement,

For every positive integer n, there are n consecutive composite integers.

Proof:

Assume that m is less than n and that both m and n are positive integers. When m is less than n,

n! = 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n,

which is to say that m is a factor of n!

So,

m + n! = m + ( 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n )

          = m ((1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n) / m + 1)

Since m is a multiple of n!, n!/m is still an integer. Since the integer m is bounded between 1 and n, it follows that any number you choose up to n can divide m + n!, making it composite until the nth integer.

However, since n! contains the nth integer, the nth integer is also composite, meaning you can choose any integer between 1 and n inclusively and it will be composite.

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William must make 1806 copies before his total cost is less than the photocopy store.

Let William made x copies from his home photocopier.

Now total cost of x copies = 0.12 x + 162.5

Total cost of x copies from the store = 0.21 x

Now his cost needs to be lower, so we form an inequality to solve this problem.

0.12x + 162.5 < 0.21x

or, 0.12x - 0.21x < -162.5

or, -0.09x < -162.5

or, x > 1805.56

Hence the minimum value of x will be 1806.

Therefore we can say that he needs to make at least 1806 copies.

The two sides of a mathematical equation having an inequality must be equal. In inequality, we compare several values in contrast to equations. The equal sign can be substituted with the less than (or less than as well as equal to), larger above (or greater to), or is not equal to signs.

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The value of x and y is 19 and 132.

What is equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables. More than one variable may be present in a linear equation. An equation is said to be linear if the highest power of a variable is consistently 1. Another name for it is a one-degree equation.

Sol- as per the given question y= 8x -20

We have to add the equations

(2x+10)° + (8x-20)°= 180°

= (10x-10)° = 180°

= (10x)° = 190°

= X= 19

= Y = 8.19-20 = 132

Thus,

X = 19 and Y = 132.

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The common multiple of 14 and 28 is 28.

Common multiple:

A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.

Here we have to find the common multiple of 14 and 28.

Data given:

Two numbers = 14 and 28

We can also write these numbers as:

14 = 2 × 7

28 = 2² × 7

The common multiple of these numbers is 2² × 7

Therefore the common multiple of these numbers is 28.

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Answer:

Step-by-step explanation:

The correct option is “C” protesters were driven out by force.

This is after President Hoover ordered an army regiment into the city to quash their protests.  Under the leadership of General Douglas MacArthur, the army, rolled into Anacostia Flats forcing the Bonus Army to flee

The mean has a value of 8 minutes and a standard deviation of 0.9736.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics. The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including basic arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Here,

X= attention span of the 2 year old

μ=8

σ=8

m=1/8

X=exp(1/8)

mean=N(8,8/√60)

Mean is normally distributed with value about 8 minutes and difference being 0.9736.

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∠(x+20)° and ∠(4x-5)° are the same side interior angles or supplementary angles thus x will be 33.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given angles,

∠(x+20)° and ∠(4x-5)° are supplementary angles.

∠(x+20)° + ∠(4x-5)° = 180°

x + 20 + 4x - 5 = 180

5x + 15 = 180

5x = 165

x = 33

Hence "∠(x+20)° and ∠(4x-5)° are the same side interior angles or supplementary angles thus x will be 33".

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The technique reduces at the training time t = 0.709.

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic.

Given that,

Population mean = 11.1 hrs

Sample mean = 10.9 hrs

Sample size , n = 26

α = 0.025

Sample standard deviation = 1.44

Therefore the null and alternate hypothesis will become,

H₀ : μ = 11.1 hrs

Hₐ : μ ≠ 11.1 hrs

here we have to use two tailed test to [perform above hypothesis,

t = (x - μ)/ (s/[tex]\sqrt{n}[/tex])

= (10.9 - 11.1) /(1.44/[tex]\sqrt{26}[/tex] )

 = - 0.2/ 0.282

t = 0.709.

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b1, is higher when: I. there is a lot of scatter around the regression line.

I is higher. The more scatter around the regression line, the higher the uncertainty associated with the slope estimate, b1. If there is a lot of scatter, the estimated slope is less reliable than if there is very little scatter.

The uncertainty associated with the slope estimate, b1, is higher when there is a lot of scatter around the regression line. This is because the estimate of the slope is based on the data points, and when there is a lot of scatter, the data points are more spread out and the estimate of the slope is less reliable.

In regression analysis, the scatter of data points around the regression line is important in determining the uncertainty of the slope estimate. When there is a lot of scatter, the data points are more spread out and the estimate of the slope is less reliable. This is because the estimate of the slope is based on the data points, and when there is more scatter, the data points are more spread out and the estimate of the slope is less reliable.

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A Quadratic function is non-Linear.

Answer:

nonlinear

Step-by-step explanation:

Quadratic functions are non-linear. A linear function produces a straight line while a quadratic function produces a parabola

Answer:

40

Step-by-step explanation:

You can always look it up but that is the answer

The value of x for the given triangle by a similar triangle rule will be 5.

If two figures look an exact shape but their size could be small or big then both figures are called similar figures.

When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.

As per the given triangles,

By a similar triangle rule,

(2x - 8)/(5x - 19) = (x + 2)/(3x + 6)

(2x - 8)/(5x - 19) = (x + 2)/3(x + 2)

(2x - 8)/(5x - 19) = 1/3

6x - 24 = 5x - 19

x = 5

Hence "The value of x for the given triangle by a similar triangle rule will be 5".

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

The shopping times were recorded for 64 randomly selected customers from a local supermarket. The average and variance of the 64 shopping times were 33 minutes and 256, respectively.

Estimate the true average shopping time per customer, with a confidence coefficient of 1- = 0.90.

x-bar = 33 min

ME = 1.645 = 3.29

90% CI: 33-3.29 < u < 33+3.29

Population Means – You can use this calculator to find the confidence interval for your sample mean if you are estimating the mean of a population trait (e.g., the mean blood pressure of a group of patients).

The estimate is your "best guess" at the unknown mean, and the confidence interval displays how reliable the estimate is. You may determine a range of values within which the population mean is expected to fall using the confidence interval.

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The 90% confidence interval is ( 992.053088, 1119.946912 ).

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ. The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

As per the question,

⇒  degree of freedom ( df )   =   n - 1

                                                =   64 - 1

                                        df   =   63

⇒ α   =   0.05

⇒ t    =   1.998341 ( Calculated using excel functions )

At 90% confidence, the confidence interval is

( μ - t ) ( s / √n )  ≤  x  ≤  ( μ + t ) ( s / √n )

( 33 - 1.998341 ) ( 256 / √64 )  ≤  x  ≤  ( 33 + 1.998341 ) ( 256 / √64 )

( 31.001659 ) ( 256 / 8 )  ≤  x  ≤  ( 34.998341 ) ( 256 / 8 )

( 31.001659 ) ( 32 )  ≤  x  ≤  ( 34.998341 ) ( 32 )  

992.053088   ≤  x  ≤    1119.946912

Therefore, ( 992.053088   ≤  x  ≤    1119.946912 ) is the 90% confidence interval for the true population mean.

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The 3 types of solutions to a system of linear equations are Unique Solution, No Solution and Infinitely Many Solutions.

In the given question we have to find the 3 types of solutions to a system of linear equations.

The 3 types of solutions to a system of linear equations are:

(1) Unique Solution: There is only one solution to a linear equation including one variable. The one and only position at which LHS and RHS are similar on substitution is the unique solution of a linear equation.

(2) No Solution: The system of linear equations has no solution if the graphs of the linear equations are parallel. There is no point in this situation when no lines cross one another.

(3) Infinitely Many Solutions: There are infinite solutions to a 2 linear equation. There is a set of infinite solution points for the linear equation system when each equation's L.H.S changes to its R.H.S

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The plane's average speed is 602 miles/hour.

What is the average speed?

The overall distance the object covers in a given amount of time is its average speed. It can be calculated by:

Average Speed = (Total distance)/(Total Time)

Given, Total distance traveled = 3010 miles

Total time taken = 5 hours

Now, the average speed is given by:

average speed = (3010/5) miles/hour

                         = 602 miles/hour

Hence, the plane's average speed is 602 miles/hour.

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Two angles are considered to be congruent if their measures match. You are already aware that the vertical angles created when two lines connect are congruent.

A = B if A and B are both complements of C. We should investigate additional angle correlations. When you reveal these angle correlations, you will formally prove their veracity. For instance, you were given the concept of an angle bisector. It turns out that an angle's bisector separates it into two angles, each of which has a measure equal to half that of the original angle.Two angles are considered to be congruent if their measures match. You are already aware that the vertical angles created when two lines connect are congruent.

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Answer:

576

Step-by-step explanation:

48 {[2 x (1 + 3)] + 4}​

48 ((2x4)+4)

48(8+4)

48 x 12

= 576

In short form we can write the word Cubicle as a word, Cube. However, both the words can be used for different purposes or having different interpretation.

Given, a word Cubicle

we have to write the given word in short form.

now to write any word in short form, we have to make its length or abbreviate the word.

As, the word is Cubicle.

Then, the word Cubicle can be written in as Cube in short form.

However, both the words can be used for different purposes or having different interpretation. Such as, Cube is used for a Particular shape or figure in Geometry i.e. the 3-D shape of the cube. Whereas, Cubicle is used for the small small cabins of the employees in the corporate offices.

Hence, the word Cubicle can be written in as Cube in short form, but may be with different meaning.

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If andre lives with his wife and three children. 22 pounds of municipal solid waste his family generates each day.

It is defined as the ratio of the population to the total area. The population density represents the average number of people living in each square unit.

It is given that and lives with his wife and three children.

We have to find the mass of municipal solid waste Andre and his family generate each day.

From the data research 22 pounds of municipal solid waste, his family generates each day.

Thus, if Andre lives with his wife and three children. 22 pounds of municipal solid waste his family generates each day.

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The probability that it weighs less than 29 kilograms is 0.625.

How likely is it that a box will weigh less than 29 kilograms?

according to the histogram( image attached )

A box could weigh any one of 8 different amounts, all of which have the same chance of happening.

thus, the equal probability is:

= 1/8

= 0.125

According to the probability distribution, The probability that a box weighs less than 29 kilograms is represented by the probability below 27. There are 5 weights below 29 which makes the probability :

= 5 × 0.125

= 0.625

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The amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of rainfall in 2 minutes = 75 mm

So , the amount of rainfall in 1 minute = amount of rainfall in 2 minutes / 2

                                                              = 75 / 2

                                                              = 37.5 mm

And , 1 hour = 60 min

So ,

The amount of rainfall in 1 hour = amount of rainfall in 1 minute x 60

                                                    = 37.5 mm x 60

                                                    = 2250 mm

Hence , the amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm

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50 m  is dimensions will require the least amount of fencing .

What is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.

                                          Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x = length of the side parallel to the river

     y = length of each of the other two sides

Then xy = 5,000, so y = 5,000/x

Minimize:  L = length of the fence

L = x + 2y

 = x + 10,000/x, where x > 0

L' = 1 - 10,000/x2 = (x2 - 10,000)/x2

L' = 0 when x = 100 or -100

Since x can't be negative, x must be 100.

When 0 < x < 100, L' < 0.  So, L is decreasing.

When x > 100, L' > 0.  So L is increasing.

Therefore, L has a relative and absolute minimum when x = 100 m

                                                                                    y = 5,000/x = 50 m

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The worth of the factory is $97580.17.

Given data;

Cost of $460,000 for the factory. You project that it will bring in $150,000 in the first year, $210,000 in the second, and $360,000 in the third. The 12% discount rate applies.

To know the factory's worth;

Let,

[tex]NPV = \frac{C_0}{(1 + r)^0} + \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3}[/tex]

Here,

C₀ = -460,000, C₁ = 150,000, C₂ = 210,000, C₃ = 360,000

[tex]NPV = \frac{-460,000}{(1 + 0.12)^0} + \frac{150,000}{(1 + 0.12)^1} + \frac{210,000}{(1 + 0.12)^2} + \frac{360,000}{(1 + 0.12)^3}[/tex]

NPV = $97,580.17

Therefore, the factory's worth is $97580.17.

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∂v⃗ ∂t+(v⃗ ⋅∇⃗⃗) v⃗ +1ρ∇⃗ p=g. The viscosity leads to frictional forces within the fluid. Taking the viscosity into account in the Euler equation finally leads to the Navier-Stokes equation.

For the derivation of the Navier-Stokes equations we consider a fluid element and the forces acting on it. At first we will consider only the motion of the fluid in x-direction. The motion of the fluid element is influenced by the pressure forces acting on the front and back surface of the cubic volume element.

    These pressure forces basically represent normal stresses and are therefore denoted in the following by the Greek symbol σ instead of p. We will see later that in addition to the pressure forces, viscosity-related forces also act perpendicular to the surfaces and contribute to the normal stress.

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An angle GHI measures 28° degrees.

What is the angle sum property of a triangle?

The triangle's inner angles can be added up to 180°, according to the triangle's "angle sum property."

For example, in a triangle, ABC, the sum of angles A, B, and C will be 180°.

Given, ∡G = 62°

∡I = 90° and ∡ H = ?

From the angle sum property of a triangle,

∡G + ∡ H + ∡I = 180°

or, 62° + ∡ H + 90° = 180°

or, ∡ H + 152° = 180°

or, ∡ H = 180° - 152° = 28°

or, Angle GHI = 28°

Hence, the required value of Angle GHI is 28°.

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The tip of the shadow is moving at  [tex]4.8\frac{ft}{sec}[/tex]

Consider the image , as depicted below

Based on similar triangle , we have

[tex]\frac{s(t)}{6} =\frac{s(t)+w(t)}{16}[/tex]

⇒ 10s(t) = 6w(t)

⇒ w(t) = [tex]\frac{10}{6} s(t)[/tex]

we are told that a certain time t,

[tex]\frac{d(w(t))}{dt} = 8\frac{ft}{sec}[/tex]

[tex]\frac{d(w(t))}{dt} = \frac{d(\frac{10}{6}.s(t)) }{dt}[/tex]

          [tex]= \frac{10}{6}\frac{d(s(t))}{dt}[/tex]

Therefore,

[tex]\frac{10}{6} \frac{d(s(t))}{dt} = 8\frac{ft}{sec}[/tex]

[tex]\frac{d(s(t))}{dt} = 4.8\frac{ft}{sec}[/tex]

Hence, The tip of the shadow is moving at  [tex]4.8\frac{ft}{sec}[/tex]

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The possible length of the region after solving the quadratic equation is either 170ft or 50ft.

What is a quadratic equation?

A quadratic equation in algebra is any equation that can be written in the simpler form where x stands for an unknown value and a, b, and c are known quantities. The assumption is that a > 0; an equation with a = 0 is thought to be degenerate because they become linear or even simpler.

Solution Explained:
Lets assume, length = x and width = y

So we know, the area and perimeter is supposed to be 8500 and 440 respectively

we form the equations,

1) 8500 = xy , and                       [Area = length*width]

2) 440 = 2(x + y)                           [ Perimeter = 2(length +width)]

   220 = x + y

So, x = 8500/y (from equation 1) and put the value of x in 2

220 = x + (8500/x)

After solving this we get the quadratic equation,

x^2 - 220x + 8500 = 0

Solving the equation, we get

x = 170 or, x = 50 which are the two possible lengths of the region.

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The two third can be written as 2/3 which in decimal means 0.6667 and when expressed as a percentage it is 66.67%

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The two third can be written as 2/3. It basically means 2 parts of 3 total parts.  Here the numerator is 2 and demominator is 3.

It can be written in decimal as 2/3 = 0.666

This is an irrational fraction when converetd into decimal system, it becomes a recurring decimal.

The equivalent fraction of 2/3 is 4/6 or 20/30 etc

Therefore, The two third can be written as 2/3 which in decimal means 0.6667 and when expressed as a percentage it is 66.67%

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