the time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list, along with the five-number summary. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

It depends on the sign of [tex]x-4[/tex].

Recall the absolute value function's definition:

[tex]|x| = \begin{cases}x & \text{if } x \ge 0 \\ -x & \text{if } x < 0\end{cases}[/tex]

Now, if [tex]x-4\ge0[/tex], then

[tex](x-4)|x-4| = (x-4)(x-4) = x^2 - 8x + 16[/tex]

On the other hand, if [tex]x-4<0[/tex], then

[tex](x-4)|x-4| = -(x-4)(x-4) = -(x-4)^2 = -x^2 + 8x - 16[/tex]

What you first suggested is incorrect. We have

[tex]x^2 - 16 = (x - 4) (x + 4)[/tex]

but [tex]|x-4| \neq x + 4[/tex].

We can show this using the definition again. If [tex]x-4\ge0[/tex], then

[tex]x-4 = x+4 \implies -4=4[/tex]

which is a contradiction; on the other hand, if [tex]x-4<0[/tex], then

[tex]-x+4 = x+4 \implies 2x = 0 \implies x =0[/tex]

holds for only one value of [tex]x[/tex].

Answer:

(3,0)

Step-by-step explanation:
I think this is right.

Answer:

c

Step-by-step explanation:

Distance can be defined as the amount of ground covered or walked by a physical object, regardless of its direction, starting or ending point.

In order to determine the total distance walked by this person, we would simply add each of the distances recorded together as follows:

Total distance = 3 + 7 + 4 + 5 + 4

Total distance = 23 miles.

In order to determine the total displacement vector, we would add all of the vectors together as follows:

3 miles East = <5, 0>

7 miles Southeast = <7/√2, -7/√2> or <7cos45°, -7sin45°>

4 miles South = <0, -4>

5 miles Southwest = <-5/√2, -5/√2> or <-5cos45°, -5sin45°>

4 miles East = <4, 0>

Total displacement vector = <5 + 7/√2 + 0 - 5/√2 + 4, 0 - 7/√2 - 4 - 5/√2 + 0>

Total displacement vector = <9 + 2/√2, -4 - 12/√2>

Total displacement vector = <9 + 1.41, -4 - 8.49>

Total displacement vector = 10.41i - 12.49.

If this person walked straight home, the total distance walked is giving by  the resultant of the above displacement vector:

Total distance = √[10.41² + (-12.49)²]

Total distance = √[108.37 + 156.00]

Total distance = √264.37

Total distance = 16.26 miles.

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Complete Question:

A person starts walking from home and walks: 3 miles East 7 miles Southeast 4 miles South 5 miles Southwest 4 miles East.

a. This person has walked a total of _____ miles.

b. Find the total displacement vector for this walk:

c. If this person walked straight home, they'd have to walk

The number of ways in which the word detail can be arranged in such a way that the vowels occupy only the odd positions is 36.

We will find the number of permutations in which the word DETAIL can be arranged such that the vowels occupy odd positions.

The vowels are E, A and I. They can occupy 1st, 3rd and 5th position in any order. Hence, the number of ways to do that is 3! = 6.

Now, the consonants D, T and L can occupy 2nd, 4th and 6th position in any order. Hence, the number of ways to do that is 3! = 6.

Hence,

Total number of ways = 3! * 3! = 6*6 = 36.

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Answer:

40

Step-by-step explanation:

Add ratio 2+5=7

Divide 140 by 7 = 20

Multiply 20 by the ratio Jayden has which is 2

20x2=$40

-10 minus -4 = -6

Solving the equation

-10 minus -4

= -10 - (-4)

= -10 + 4

= -6

-10 minus -4 = -6

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Answer:

6x^2+6x

Step-by-step explanation:

2x(3x^2+5x-2)

6x^2+10x-4x

6x^2+6x

Answer:

B. (x − 4) and (x + 8)

Step-by-step explanation:

ok nice :0

The value of A - B is - 12

It is given that A + B = 0 .......... ( Eq . 1 )

⇒ A = - B ............ ( i )

Another equation which is given is :

AB  = - 36 ........... ( Eq . 2 )

Using (i) in Eq . 2

- B ( B ) = -  36

- B ² = - 36

B ² = 36

B  = √ 36

B = 6 .......( ii )

Using B = 6 in ( i ) ,

A B = - 36

A ( 6 ) = - 36

A = -6

This implies,  A = - 6 and B = 6

Now to find the value of A - B , we need to put the values

A - B = - 6 - 6

=  - 12

Hence, the value of A - B is - 12 .

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Answer:

i think ur saying that j=4 so the answer is 13

just 4+9

Step-by-step explanation:

Answers:

1.) Plot the numbers on the y-axis (vertical line) and the countries on the x-axis (horizontal). Then, put "Cars (billions)" to label the y-axis and put "Country" to label the x-axis. There is an example attached.

2.) Do the same thing as #1 but label the y-axis with "People (hundreds)" and the x-axis as "Colonies".

3.) Japan because 8 is the greatest amount comparing to the other countries.

4.) Japan made 6 million more cars than Spain since 8 - 2 = 6. (We are counting the cars in millions)

The other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

The general equation of a straight line is -

y = mx + c

Given in the question is a equation that describes the one side of a rectangular patio. From the question, we can write -

Equation representing a side of Patio - y = 2/3x + 5/3

If we compare the equation representing a side of Patio with the general equation of line, we get -

y = 2/3 x + 5/3      

[y] = [m] x + [c]

From this we can conclude that -

m = 2/3 = slope of line

c = 5/3 = y - intercept

The patio is in the shape of a rectangle. Therefore, the side opposite to the line of slope → 2/3 will be equal in length and parallel to it. We know, that the slope of two parallel lines are same. So, the slope of line parallel to  y = 2/3x + 5/3  will be 2/3.

The remaining two sides are perpendicular to both the side of slope → 2/3. The remaining sides are also parallel to each other, indicating they both have same slope. The slope of a line perpendicular to a given line (L) is given by -

m [p] x m [L] = -1

m [p] = - 1 / m [L]

m [p] = - 3/2

Therefore, the remaining two sides will have slope of  -3/2.

Therefore, the other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

[Refer to the graph attached]

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Let [tex]x=t[/tex]. Then

[tex]x+z = 0 \implies z = -x = -t[/tex]

[tex]x + y + z = 6 \implies y = 6 - x - z = 6 - t - (-t) = 6[/tex]

so our parametric equations for the line are

[tex]\begin{cases}x(t) = t \\ y(t) = 6 \\ z(t) = -t\end{cases}[/tex]

where [tex]t\in\Bbb R[/tex].

Answer:

Question 4x-8/2=10       Answer X=7

Step-by-step explanation:

          [tex]\frac{2\left(4x-8\right)}{2}=10\cdot \:2[/tex]

        4x-8=20

        4x-8+8=20+8

        4x=28

          [tex]\frac{4x}{4}=\frac{28}{4}[/tex]

                       X= 7                                

Hope this helps

Pls mark brainliest

Final answer:

The odds against exactly 5 cars passing over the bridge in that time is calculated as 4:21

A probability must be between 0 and 1 (nothing can happen with a greater than 100% likelihood). The chances are not as limited. Odds can be any positive number; for example, a chance of 2/3 is equivalent to odds of 2/1. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

By dividing the odds in the first group by the odds in the second group, the odds ratio is calculated. For many clinicians, odds and odds ratios are difficult to comprehend. Odds are calculated by dividing the likelihood of an event happening by the probability that it won't.

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The area left to be tiled on Wednesday is 1/6

Let the total area to tile be 60 sq feet

We have taken 60 sq feet as the LCM of 2 and 3 is 6. So taking up 60 makes our calculation part easy.

Area tiled on Monday = 1/3*60 = 20 sq feet

Area tiled on Tuesday = 1/2*60 = 30 sq feet

Area remaining to be tiled = 10 sq feet

So, a fraction of the area left to be tiled = Area left to be tiled/Total area to be tiled

= 10/60 = 1/6

Hence, 1/6 of the area is left to be tiled

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Answer:1/6

Step-by-step explanation:

The cost of each drink purchased at the AMC theaters is $6.09

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the cost of one drink. After using the coupon, their total cost before tax was $29.18. Hence:

2(11) + 2(x) - 5 = 29.18

x = 6.09

The cost of each drink purchased at the AMC theaters is $6.09

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According to the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.

An outlier is a value that is significantly different from the other values in a random sampling of a population. In some ways, this definition leaves it up towards the analyst (or a consensus process) to determine what is abnormal.

Identifying potential outliers is critical for such following reasons. An outlier could imply faulty data. For example, the data could have been wrongly coded, or an experiment could have been done erroneously.

An outlier is defined as an observation that is less than or more than Q3 times IQR.

We need to look for place variances in Q1 and Q3.

When we utilize the IQR approach to discover outliers outside of Q1 and Q3, we create a "fence." Outliers are any values that fall outside of the defined boundary.

To construct this fence, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3.

IQR = (1.5 - Q1)

IQR = (1.5 + Q3)

This provides us with the minimum and maximum fence posts to which we can compare every observation.

the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.

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The given statement is True.

"It is not always helpful to rewrite an equation in standard form as a first step in solving it."

In standard form, the right side of an equation should be 0 and every component on the left side should be 1. For example, x2 = 4; to express this in standard form, move the number 4 to the left side of the equation, resulting in x2 - 4 = 0.

If you are asked to find x in this circumstance, there is no need to write the equation in standard form; simply take this same real number of both of the equation's sides to find x.

Ax+By=C is the common structure for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to find both intercepted communications when an equation is stated in this way (x and y). This form is indeed useful for solving two-linear equation systems.

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I understand that the question you are looking for is:

It is not always helpful to rewrite an equation in standard form as a first step in solving it.

True/False

Using proportions, the San Gabriel Mountains grow 0.00000000114 km/h.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we have that:

Hence the speed is:

0.00001/8760 = 0.00000000114 km/h.

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The system of equations involving 1/3x - 3y = -4 and x - 9y = -12 has infinite number of solutions.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

1/3x - 3y = -4     (equation 1)

x - 9y = -12     (equation 2)

Using the second equation, find the value of one variable, lets say x, in terms of the other.

x - 9y = -12     (equation 2)

x = 9y - 12

Substitute the equation of x to the first equation.

1/3x - 3y = -4     (equation 1)

1/3(9y - 12) -3y = -4

3y - 4 - 3y = -4

Combining the all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

3y - 3y = -4 + 4

0 = 0

Since we did not get unique values for x and y, check if one of the equations is a simplified form of the other. Multiply the first equation with 3.

1/3x - 3y = -4     (equation 1)

3(1/3x - 3y) = 3(-4)

x - 9y = -12

Since this new equation is the same with the second equation, this means that the lines of the two equations are the same(overlapping). Hence, the system of equations has infinite number of solutions.

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We want to do a change of units of a rate, from words per minute to words per hour.

We will find that the answer is 22,200 words per hour.

The rate that we need to modify is:

370 words/minute

So the time is in the denominator.

Also, remember that:

1 hour  = 60 minutes.

Then:

1 minute = (1/60) hours.

Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:

370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour

                               22,200 words/hour.

Then the rate is 22,200 words per hour.

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Answer:

We want to do a change of units of a rate, from words per minute to words per hour.

We will find that the answer is 22,200 words per hour.

The rate that we need to modify is:

370 words/minute

So the time is in the denominator.

Also, remember that:

1 hour  = 60 minutes.

Then:

1 minute = (1/60) hours.

Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:

370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour

                              22,200 words/hour.

Then the rate is 22,200 words per hour.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Ok so I know I prolly didn't work this out the way they want you to, but this is how i have always done it and got the correct answer.

So, there are 180 degrees in a triangle right? Well, we know 2 angles, 65 and 51. So add them together and you get 116. Simply subtract 116 from 180 to find the missing angle.

65 + 51 = 116

180 - 116 = 64

m<PST = 64 degrees

Answer:

Inequality:

8in > x - 5in

Solution:

x < 13in

Step-by-step explanation:

If the length 8in is is bigger than the width (x - 5in) then we just need to write it:

8in > x - 5in

To solve for x, we need to move everything but x to the other side

8in > x - 5in

13in > x

Answer:

Well that depends

Step-by-step explanation:

During this time, Helen Barnes from tri-state realty called for information about a stone listing. The assistant should give Helen the information she is asking for.

An unlicensed assistant broker does a number of responsibilities. Nonetheless, it is vital that every broker understands what an unlicensed broker is legally allowed to do when compared to a licensed assistant broker, in order to avoid getting into trouble.

Therefore, we conclude that in this question, the assistant should give Helen the information she is asking for.

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Complete question is; all of the licensees at stone realty are attending an off site conference for the afternoon. the broker’s unlicensed assistant remained at the office to answer the telephone. during this time, helen barnes from tri-state realty called for information about a stone listing. what should the assistant do?

The "3g" in the numerator of the expression represents the total cost of gas.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Now,

given expression: [tex]\frac{3g}{4}[/tex], Where the value of g is determined by:

From the expression, we can conclude that:

Hence, The "3g" in the numerator of the expression represents the total cost of gas, before the money is split amongst the friends.

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Answer:27 and 13

Step-by-step explanation: 27 + 13= 40

27 x 13= 351