A 12-ft-by-15-ft rectangular swimming pool has a 3-ft-wide no-slip surface around it. What is the outer perimeter of the no-slip surface?.

The result provides convincing evidence that the tsa officers did not carrry out a truly random sample.

A simple random sample is a subset of a statistical population in which each member has an equal chance of being selected.

In statistics, a simple random sample is a subset of individuals picked at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.

In this case, it's important to note that the fact that all the people chosen were first class members means that it was bias and not a random sampling.

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Answer:

The first option is correct :)

Step-by-step explanation:

x=-6, x=-2

|x+4|=2

x+4=2, x=-2

x+4=-2, x=-6

:] (Tell me if this is incorrect!)

(brainliest would help a lot)

Answer: the first one (-2,-6)

Step-by-step explanation:

|x+4| = 2

subtract 4 from both sides and you get -2

|x+4| = -2

subtract 4 from both sides and you get -6

If you want to check your answers, plug it into the original equation

THE DOMAIN & RANGE OF THE FUNCTION g(x)=|x + 4| is

This is further explained below.

Generally, The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

[tex](-\infty, \infty)[/tex]

Set-Builder Notation:

[tex]$\{x \mid x \in \mathbb{R}\}$[/tex]

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

[tex]$[0, \infty)$[/tex]

Set-Builder Notation:

[tex]$\{y \mid y \geq 0\}$[/tex]

Determine the domain and range.

Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]

Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]

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The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.

From the question, we have the following;

Hypotenuse=17 foot

Height(y)=13 feet

Base(x)=(17^2-13^2)^1/2

        =120^1/2 or sqrt(120)

The ladder against the wall is a right angle triangle, so we have:

x^2+y^2=17^2

x^2+y^2=289

Top slips down at 2ft/s

dy/dt=-2 ft/s, where height (y)=13ft

The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt

Now, we take the derivative with respect to time:

=x^2+y^2=17^2

=2x(dx/dt)+2y(dy/dt)=0

Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s

2(sqrt(120))(dx/dt)+2(13)(-2)=0

2(sqrt(120))(dx/dt)-52=0

We solve for dx/dt:

dx/dt=52/(2sqrt(120))

dx/dt=52/21.9089

dx/dt=2.373 ft/s

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When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph.  Allison arrived, Austin still had 24 miles to go.

Let t be the time they drove.

Then you have this "distance" equation

58t = 46t + 24

saying that both parts of the equation represent the same distance.  Then

58t - 46t = 24

12t = 24

t = 2  hours.

Hence the distance is, 2 x 58 = 116 mph.

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Answer:

The selling price is:  [tex]\$77,520[/tex]

Step-by-step explanation:

Step 1: Identify the profit made

A profit of 14% is made on the article.

This means that the article was sold at a price that had 14% of its original price added to it.

The 14% of the original price is:

[tex]14\% \times 68000\\=\frac{14}{100}\times 68000\\\\\text{Calculate the value}\\\frac{14}{100}\times 68000\\=9520[/tex]

So, a profit of $9520 was made

Step 2: Calculate the selling price

The selling price will be the sum of the original price and the profit.

The selling price is:

[tex]68000+9520\\=77520[/tex]

Graph the cubic using its end behaviour and a few selected points.

The leading coefficient test requires one variable only

Answer:

87

Step-by-step explanation:

Answer:87

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

The Question was:
7x + 14 = 28

Subtract 14 from both sides.

7x = 28 − 14

Subtract 14 from 28 to get 14.

7x = 14

Divide both sides by 7.

x = 14/7

​

Divide 14 by 7 to get 2.

x = 2

Answer:

x=2

Step-by-step explanation:

To solve a question like that, we have to isolate the variable.

What is the variable? A variable is a letter partaking in an equation that is in place of a number or solution that makes the equation true.

In this case, the variable is x.

To isolate the variable, we must do the opposite action that is being done to the number.

For example, if a number was added to one side by 28, we can subtract both sides by 28 so it negates the addition and does not alter the original equation.

7x+14=28                We can subtract the 14 on both sides to negate the                                -14  -14                     addition.

7x=14                      Divide each side by 7 to isolate x.

x=2

The solutions are x = -1,  y = 1 and z = 5  

In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z  or a, b, c .. etc.  

According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method

Here, we have three linear equations with 3 and 2 variables

4x - 2y + 3z = 9 ----(1)

x - 2y = -3 -----(2)

2x + 3y = 1​ -----(3)

Here, to find x, y and z we will use Elimination method

First of all solve (2) and (3) as given below

2 × (2) ⇒  2x - 4y = - 6 -----(4)

1 × (3) ⇒  2x + 3y = 1​  

Now subtract (3) from (4)

(4) - (3) ⇒ 2x - 4y -2x - 3y  = - 6 - 1

⇒ - 7y = -7

⇒   y = 1

Substitute y = 1 in (2)

(2) ⇒ x - 2(1) = -3

x - 2 = -3

x = -1    

Now substitute x = -1 and y = 1 in (1)

(1) ⇒ 4(-1) - 2(1) + 3z = 9  

- 6 + 3z = 9

3z = 15

z = 5

From above calculations

The values of x = -1,  y = 1 and  z = 5

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Answer:

a. 5.6

b. 38.4

c. 8.25

d. 24

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-7 is the greatest because it is closer to 0 on the number line.

Answer:

(a)Vertex

(c)3 seconds

Explanation:

Part A

The maximum point on a parabola is called the Vertex.

Part C

To find out how much the plain was in the air, find the values of t at which the height, h=0.

Next, subtract the second value of t from the first value.

First, set h=0:

Factorize:

Therefore, the plane hits the ground after 3 seconds.

Answer:

15

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

10 x 7 = 70

7 x 4 = 28

Since it's $4 to make 10 copies, it'll be $2 to make 5

28 + 2 = 30

$30 for 75 copies (a bad deal honestly)

Please mark Brainliest!!

Answer:

$30 dollars for 75 copies

Step-by-step explanation:

What we know:

$4 for every 10 copies.

How to figure out:

Divide 4/10 = .4    .4 is the cost per copy.

We do this because if it is 4 dollars per 10 copies, then we have to figure out the cost per copy. So we have to do how many dollars goes into each copy.

Now we know the cost of one copy we can multiply the amount of copies we need by the price of one.

75 x 0.4 = 30     30 is the price of 75 copies.

Answer:

y = -x + 4

Step-by-step explanation:

(-1, 5), (2. 2)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁        2 - 5          -3           -3

m = ----------- = ----------- = --------- = ------- = -1

        x₂ - x₁        2 - (-1)       2 + 1        3

y - y₁ = m(x - x₁)

y - 5 = -1(x - (-1))

y - 5 = -1(x + 1)

y - 5 = -x - 1

  +5        +5

----------------------

y = -x + 4

I hope this helps!

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = 8, - 4) and (x₂, y₂ ) = (- 1, 5) ← 2 ordered pairs from the table

m = [tex]\frac{5-(-4)}{-1-8}[/tex] = [tex]\frac{5+4}{-9}[/tex] = [tex]\frac{9}{-9}[/tex] = - 1 , then

y = - x + c

to find c use any ordered pair from the table

using (2, 2 ) , then

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = - x + 4 ← in slope- intercept form

with y- intercept c = 4

The length of the side SU will be equal to 4√2.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

The formula for the Pythagorean theorem will be given as:-

H² = P² + B²

Here,

H = Hypotenuse

P = perpendicular

B= Base

The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.

Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.

H² = P² + B²

sx² = xv² + sv²

sx = √ ( 2² + 2² )

sx = √8

sx = √ ( 2 x 2 x 2 )

sx = 2√2

SU = 2 sx

SU = 2 x 2√2

SU = 4√2

Therefore, the length of the side SU will be equal to 4√2.

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Answer:

6x^9

Step-by-step explanation:

Hello!

Multiply the like terms:

The correct answer is the 3rd option, 6x^9.

Associative property of the sum states that the order the operations are done doesn't matter as long as the sequence of operands also doesn't change. This property is given by:

Therefore, the equation that illustrates the associative property is:

Answer:

+ 9

Step-by-step explanation:

x²+ 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 6x + 9

= (x + 3)² ← a perfect square

Answer:

(5, 20)

Step-by-step explanation:

(5, 20) is the only ordered pair which falls on the line

A complex number z is given in the form:

z = (x.y) = (realpart) x + imaginary part (iy)

In this case:

z1 = -7i

z2 = 3+3i

To write in trigonometric form:

Multiplication in trigonometric form:

Multiplication in standard form:

The length in feet of the pole is 13 ft.

The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.

Use the Pythagorean relationship:

c²= a² + b²

= 5²  +  12²

= 25 + 144

= 169

c = 13

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The average change in sales income per month is $ 3 million.

What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.

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Answer:

Step-by-step explanation:

it 10

The scale factor which takes circle m to circle n as depicted in the attached image is; 3.

It follows from the task content that the scale factor which takes circle m and transforms it to circle n is to be determined.

Hence, since both circles have the same center, the center can be taken as a point of reference.

Therefore, the distances between the center of the circles m and n to any point on their circumferences are; 3 units and 9 units respectively.

On this note, since circle n is; 9/3 = 3 times as large as circle m, it follows that the required scale factor is; 3.

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Answer:

The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100

Percentage of red pins = (21÷70)×100

= 30%

The ratio House blend/Organic Free Trade blend is the same and must remain the same.

So, the proportion is:

Where x is the unknown amount of the Organic Free Trade blend.

So, from the proportion, we have:

Answer: 156 pounds of Organic Free Trade blend

a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.

b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.

c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.

The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set  B or including more sets

For the first problem, the sets  contain:

n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0

So,  n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

               = 10 +15+25-0-0-0-0-0

              =  50

For the second  problem, since no student can have  more than one major.

So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)

As  we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17

So ,  (A∪B∪C∪D∪E∪F∪G) =  31+88+19+11+41+22+17= 229

For the third problem,  we have

n(A)=5

n(B)=3

n(C)=2

n(D)=7

n(E)=6

So, the number of elements will be (A∪B∪C∪D∪E) =  5+3+2+7+6 =23

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The equation using x to represent the number of guests at your party is 300 + 9x = 534

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let x represent the number of guests at your party.

Here, renting a roller rink for your birthday costs $300 plus $9 per person. This will be:

300 + 9x = 534

Collect like terms

9x = 534 - 300

9x = 234

Divide

x = 234 / 9

x = 26

The number of guest is 26.

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