In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between ________and_________ miles.

The level of confidence for this estimate is ________%

The transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis

The complete question is added as an attachment

From the graph, we have the following highlights:

This means that parallelogram LMNO is reflected across the x-axis to get parallelogram L'M'N'O'

Hence, the transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis

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The missing length of given right triangle is equal to 25.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean  Theorem.

The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x),  cos (x) and tan (x) , where:

[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]

There is another important property, where h²=m*n. See the attached image.

From the previous informations presented, you can solve the given question.

From Pythagorean Theorem you can find h (heigth). Thus,

15²=9²+h²

h²=225-81

h²=144

h=12

If h=12 and m=9, from  h²=m*n you can find n.

h²=m*n

12²=9*n

144=9n

n=144/9

n=16

Therefore, x= m+ n= 9+16=25.

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Answer:

D

Step-by-step explanation:

In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:

Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.

One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.

Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.

Options for this question include:

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Answer:

a)(x+h+2)²=x²+2xh+h²+4x+4h+2

b)(x+h+2)²–(x+2)²=2xh+h²+4h

c)2x+4+h

Step-by-step explanation:

f(x)=x²+4x+2

Aight so for part a you have to replace x with x+h

a)f(x+h)=(x+h)²+4(x+h)+2=x²+2xh+h²+4x+4h+2

and then for part b you need to subtract f(x) from part a:

b)f(x+h)–f(x)=x²+2xh+h²+4x+4h+2–x²–4x–2===>

2xh+h²+4h

and for part c divide the answer by h:

c)

[tex] \frac{f(x + h) - f(x)}{h} = = = > \\ \frac{2xh + 4h + {h}^{2} }{h} = = = > \\ 2x + 4 + h[/tex]

and if you limit h by 0 you'll get the derivative of f(x)

The height of the right pyramid is 48.53 cm.

A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.

Height = ( 3 x Volume of a pyramid) /( area)

Height = (3 x 21452) / 1326 = 48.53 cm

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Binomial

First Degree

Naming and giving the degree of a polynomial can help people understand the different properties of an expression.

Naming Polynomials

Polynomials are named based on the number of terms in the expression.

For example, the expression above has 2 terms. The first being 2x and the second being 4. There are 2 separate terms being subtracted.

There are 3 main types of polynomials

This specific expression is a binomial.

Degree

The degree of a polynomial is the highest exponent in the expression. For example, if the largest exponent is a 6, then the degree is also 6.

In the binomial above, there is no written exponent; however, it can be assumed that the variable "x" has an exponent of 1. Thus, this binomial is of the first degree.

Additionally, when writing a polynomial in standard form, the terms should be written in descending order of exponents.

Answer:

B

Step-by-step explanation:

5x+y=10

-5x -5x

y= -5x+10

Answer:

x = 73

x = -35

Step-by-step explanation:

Here are the 8 numbers:

34, 31, 15, x, 17, 4, 20, 25

Here are the 8 numbers in ascending order with x as the greatest number:

4, 15, 17, 20, 25, 31, 34, x

x - 4 = 69

x = 73

Here are the 8 numbers in ascending order with x as the smallest number:

x, 4, 15, 17, 20, 25, 31, 34

34 - x = 69

-x = 69 - 34

-x = -35

x = -35

Answer:

x = 73

x = -35

Answer:

800

Step-by-step explanation:

zero percent is just no percent...

800 - (0% × 800) =

800 - (0 ÷ 100 × 800) =

800 - (0 × 800) =

800 - 0 =

800

lol

The 0% of 800 is 800

Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Calculating percentage means to find the share of a whole, in terms of 100. There are two ways to find a percentage:

Given:

800 - (0% × 800)

=800 - (0 ÷ 100 × 800)

=800 - (0 × 800)

=800 - 0 =800

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When both expressions have the same value,  then they are equal to each other.

The equivalent is the expressions that are in different forms but are equal to the same value.

Consider the expressions 5 + 8k and 8k + 5.

Using k = 3

5 + 8k = 8k + 5

5 + 8(3) = 8(3) + 5

5 + 24 = 24 + 5

29 = 29

Using k = 5

5 + 8k = 8k + 5

5 + 8(5)= 8(5) + 5

5 + 40 = 40 + 5

45 = 45

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Complete question:

Consider the expressions 5 + 8k and 8k + 5. Determine why the expressions are equivalent.

Using k = 3 5 + 8k 8k + 5 5 + 8(3) 8(3) + 5 5 + 24 = 29 24 + 5 = 29

Using k = 5 5 + 8k 8k + 5 5 + 8(5) 8(5) + 5 5 + 40 = 45 40 + 5 = 45

Complete the statements.

If both expressions have the same value after substituting and simplifying two different values for the variable, then they are.

The value of both expressions when k = 3 is and when k = 5 is 45, so the expressions are.

Answer:

[tex]4a^{4} -11a^{3} + 6a^{2}[/tex]

The function that's illustrated in the graph is function D.

First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.

Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.

The answer that illustrates the information explained is D.

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Answer:

B.

Step-by-step explanation:

An open circle means to exclude the point.

A closed circle means to include the point.

In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.

A parabola has an x squared in the equation.

The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.

The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.

The answer is B.

The probability of selecting two prime numbers is 1/6.

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers  = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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Since both np > 5 and n(1 - p) > 5, the normal curve can be used as an approximation to the binomial distribution.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The normal approximation can be used if:

In this problem, the parameters are:

n = 107, p = 0.25.

Hence:

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The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)

A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31

Median = 24

First quartile = 1/4 x (7 + 1) = 2nd term =13

Third quartile = 3/4 x (7 + 1) = 6th term = 27

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Answer: D

Step-by-step explanation:

There are vertical asymptotes at x=7 and x=-3, so the denominator should have factors of (x-7) and (x+3).

This eliminates everything except for D.

The average rate of change of f(x) from x = 5 to x = 8 would be gotten by; B: Substituting 5 for x and 8 for h in the expression x + one-half h + 15

The difference quotient is defined as a measure of the average rate of change of a function over an interval.

The limit of the difference quotient which is the derivative is the instantaneous rate of change.

This differential quotient in calculus is usually expressed as;

[f(x + h) - f(x)]/h

We are given the differential quotient as;

f(x) = x + ¹/₂h + 15

Thus, the average rate of change of f(x) from x = 5 to x = 8 would be gotten by;

Substituting 5 for x and 8 for h in the expression x + one-half h + 15

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The interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

What is the formula for simple and compound interest?

Simple interest = (P× r× t)

Compound interest = P(1+r/n)^nt - P

We will find the interest as shown below:

P=$4,000

t=25 years

a) r=7%=0.07

Simple interest = (P× r× t)

= (4000×0.07×25)

= $7000

b) r=7%=0.07

Compound interest = P(1+r)^t - P

= 4000(1+0.07)^25-4000

= $17709.73056

rounding to nearest cents

= $17709.73

c) r=7%=0.07

n=4

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/4)^(25*4)-4000

= $18672.62375

rounding to nearest cent

= $18672.62

d) r=7%=0.07

n=12

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/12)^(25*12)-4000

= $18901.6728

rounding to nearest cent

= $18901.67

Hence, the interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

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The tires can be arranged in 24 ways. Computed using permutation.

The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.

For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:

nPr = n!/(n - r)!.

In the question, we are asked the number of ways in which the four tires can be arranged on a car.

As we need to select 4 tires, from 4 tires, with any order, we will use permutation.

Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.

Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.

Thus, the tires can be arranged in 24 ways. Computed using permutation.

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The expression which is equivalent to the given expression in the task content is; 1/x²⁴.

It follows from the task content that the given expression is; ((x)^-6/x²)³.

Hence, it follows from the laws of indices that the expression can be evaluated as follows;

= (x^-8)³

= x^-²⁴

= (1/x²⁴).

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The slope of a line parallel to this line is -5 and the slope of a line perpendicular to this line is 1/5

The slope is given as:

m = -5

Parallel line have the same slope.

So, the slope of a line parallel to this line is -5

However, perpendicular lines have their slopes to be opposite reciprocal

This means that:

The slope of a line perpendicular to this line is 1/5

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Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.

Sabemos que trabajando 8 horas, en 5 dias producen 2000 ruedas.

El número total de horas que trabajan en esos 5 dias es:

(8 horas)*5 = 40 horas

Entonces se producen 2000 ruedas en 40 horas, es decir, la razon de trabajo es:

(2000 ruedas)/(40 horas) = 50 ruedas por hora.

Ahora, sí en la fabrica trabajan 10 horas al día, entonces van a producir:

10h*(50 ruedas por hora) = 500 ruedas por día.

El número x de días que deben trabajar para producir 3000 ruedas es:

x*(500 ruedas por dia) = 3000 ruedas

x = (3000 ruedas)/(500 ruedas por dia) = 6 dias.

Trabajando 10 horas por día, en 6 días se producen 3000 ruedas.

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The expected value of betting 32 is -$0.053, making the 4th option the right choice.

In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.

The probability distribution can be shown as:

 x       $35       -$1

p(x)    1/38      37/38

as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.

Thus, the expected value can be calculated as E(x) = ∑x.p(x).

Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.

Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.

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Answer:

Step-by-step explanation:

eq. of line is 2x-3y=-3

its slope=(-co-efficient of x/co-efficient of y)=-2/-3=2/3

slope of line perpendicular to given line=-3/2

eq. of line through (-3,0) is

y-0=-3/2 (x+3)

2y=-3x-9

3x+2y=-9

or

any eq. perpendicular to given line is

3x+2y=c where c is a constant.

it passes through (-3,0)

3(-3)+2(0)=c

c=-9

reqd. eq. is

3x+2y=-9

Using equivalent angles, the solutions to the equation are given as follows:

[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

[tex]\sin{\theta} = -0.966[/tex]

Applying the inverse relation:

[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]

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The inverse of the given function [tex]f(x)=\sqrt[5]{x^3}[/tex] is [tex]f^{-1}(x)=x^{\frac{5}{3}}[/tex]

The given function is:

[tex]f(x)=\sqrt[5]{x^3}[/tex]

This function can be written in exponent form as:

[tex]f(x)=x^\frac{3}{5}[/tex]

Make x the subject of the formula:

[tex]x=[f(x)]^\frac{5}{3}[/tex]

Let x be replaced by [tex]f^{-1}(x)[/tex] and f(x) be replaced by x

The inverse function therefore becomes:

[tex]f^{-1}(x)=x^{\frac{5}{3}}\\\\ f^{-1}(x)=\sqrt[3]{5}[/tex]

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Option B. The estimate that would most likey come from the small sample is going to be B. 59 % (+-21%).

The sample space can be gotten rom the margin of error. A smaller sample space would be gotten by dividing with a larger number.

This would give a margin of error that is large. In the second option, we can see that the largest margin of error is ± 21%.

Hence this is the answer to the question.

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