State the domain and range of the following function.

The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.

The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.

The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:

20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35

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Answer:

p = 0.11 (rounded to 2 DP)

p = 0.111 (rounded to 3DP)

Step-by-step explanation:

p = 0.48³

p = 0.110592

Rounded to 2 DP

p = 0.11

Rounded to 3DP

p = 0.111

Answer:

Step-by-step explanation:

(49/72)-(13/14)

-125/504

Answer: 163/60

Step-by-step explanation:

when adding fractions you have to get to a common denomenator and then add your fractions together

Answer:

50%

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

Looking at the problem, we can take 25, and divide 50 by it.

25 ÷ 50 = 0.5

0.5 is equal to 5/10, which is also equal to 50%, meaning that 50% of 50 is 25.

Answer:

congruent

Step-by-step explanation:

Answer: 5/14

Step-by-step explanation:

5 white / 8 total

4 white / 7 total

5/8 * 4/7 = 20/56 = 5/14

Step-by-step explanation:

I said it I knew it I did it I submit for you so I'm the one that is if if you know me.

Answer:

y= root 2 kilometers

Step-by-step explanation:

[tex] \frac{2 \sqrt{2} }{2} = \sqrt{2} [/tex]

Step-by-step explanation:

I'm pretty sure it's 19200? or maybe im writing is wrong

Answer:

After 24 years population of the city will be 27000.

exponential function.

Step-by-step explanation:

in picture

Answer:

91.675% decrease

Step-by-step explanation:

Answer:

1.)E₁  =  4,03

2) E₂ = 3,85

3) σ₁²  =  1,23

4)σ₂²  = 1,14

5)σ₁  = 1,11

6)σ₂   = 1,07

5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median  0,18 and difference in standard deviation 0,04

Step-by-step explanation:

1.-Expected value of the job satisfaction score for senior executive

E₁, variance σ₁ and standard deviation  σ₁   and expected value  of the job satisfaction score for  Middle Manager E₂  variance σ₂ and standard deviation  σ₂

E(X)  =  ∑ ( xi *f(xi)

JSS      IS senior executive                   IS Middle Managers

1                      0,05                                             0,04

2                     0,09                                              0,1

3                      0,03                                             0,12

4                      0,44                                             0,45

5                      0,39                                             0,29    

∑ xi*f(xi)  =  1*0,05 +  2 *0,09 + 3*0,03 + 4 * 0,44 + 5 * 0,39

E₁  =  0,05 + 0,18  + 0,09 + 1,76  + 1,95

1.)E₁  =  4,03

2.) ∑ xi*f(xi)

E₂ = 1* 0,04  + 2 * 0,1 + 3*0,12 + 4*0,45 +5*0,29

E₂  = 0,04  +  0,2  +  0,36 + 1,8 + 1,45

E₂ = 3,85

2 ) E₂ = 3,85

3) Variance of job satisfaction scores for senior executives.

x²       f(x)                  x²* f(x)

1          0,05                0,05

4         0,09                 0,36

9         0,03                 0,27    

16        0,44                 7,04

25       0,39                 9,75

σ₁²  = [ ∑ x²*f(x) ] - μ²           ∑ x²*f(x)  = 17,47

In this case    μ = E       μ²   =  ( 4,03)²   =  16,24

For senior executives:   σ₁²  = 17,47  - 16,24   = 1,23

σ₁²  =  1,23

And  standard deviation σ₁  = 1,11

For Middle managers

x²       f(x)                  x²* f(x)

1          0,04                0,04

4         0,1                      0,4

9         0,12                  1,08      

16        0,45                 7,2

25        0,29                7,25

                ∑ x²*f(x)  =  15,97

σ₂²  =  15,97  -  (3,85)²  =  15,97  -  14,82

σ₂²  = 1,14

σ₂   = √1,14   =  1,07

5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median  0,18 and difference in standard deviation 0,04

Answer:

158,808 !

Step-by-step explanation:

13,234 × m (months)

13,234 × 12

= 158,808

The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.

To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.

5 + 5 = 10

(5 + 10) = 15

(10 + 15) = 25

(15 + 25) = 40

(25 + 40) = 65

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Answer:

The answer is C.

I did the practice.

9514 1404 393

Answer:

Step-by-step explanation:

Angle 5 is the third angle of the triangle whose other two angles are 45° and 55°. So, its measure is ...

  ∠5 = 180° -45° -55°

  ∠5 = 80°

__

This figure cannot be solved for angle 4 unless we assume the horizontal lines are parallel. Using the angle numbers as vertex designators, angle 245 and the one marked 45° are alternate interior angles, so are congruent. Angle 4 is vertical with the angle that is the sum of angle 245 and 75°, so we have ...

  ∠4 = 75° +45°

  ∠4 = 120°

Answer:

[tex]\huge\mathfrak\red{Answer} \\ \\ 7 + 9x > 73 \\ \\ x = 7 \: \: \: \: \: \: given \\ \\ 7 + (9 \times 7) > 73 \\ \\ 7 + 63 > 73 \\ \\ 70 > 73 \\ \\ but \: 70 \: is \: not \: grater \: \: than73 \\ \\ so \: this \: equation \: is \: not \: true \\ \\ \huge\mathfrak\purple{Answer = no} \\ \\ \small\mathfrak\red{hope \: it \: helps...}[/tex]

9514 1404 393

Answer:

  year 2066

Step-by-step explanation:

In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.

Then we can write equations for men's and women's wages as follows:

Using the 2-point form of the equation for a line, we have ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Men's wages

  y = (42800 -38907)/(2010-1960)(x -1960) +38907

  y = 77.86(x -1960) +38907

  y = 77.86x -113,698.6 . . . . . where x is the year

Women's wages

  y = (34700 -23606)/(2010 -1960)(x -1960) +23606

  y = 221.88x -411,278

These values are equal when ...

  77.86x -113,698.6 = 221.88x -411,278

  297,580.2 = 144.02x . . . . . . . add 411278 -77.86x

  2066.2 = x . . . . . . . divide by the coefficient of x

Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.

_____

Alternate solution

In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.

The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.

_____

Additional comment

The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.

Answer:

yes

Step-by-step explanation:

Answer:

[tex]y=\frac{3}{2} x-6[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

[tex]3x = 2y[/tex]

Switch the sides

[tex]2y=3x[/tex]

Divide both sides by 2 to isolate y

[tex]\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x[/tex]

Now that this equation is in slope-intercept form, we can easily identify that [tex]\frac{3}{2}[/tex] is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope [tex]\frac{3}{2}[/tex] . Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{3}{2} x+b[/tex]

2) Determine the y-intercept

[tex]y=\frac{3}{2} x+b[/tex]

Plug in the given point, (4,0)

[tex]0=\frac{3}{2} (4)+b\\0=6+b[/tex]

Subtract both sides by 6

[tex]0-6=6+b-6\\-6=b[/tex]

Therefore, -6 is the y-intercept of the line. Plug this into [tex]y=\frac{3}{2} x+b[/tex] as b:

[tex]y=\frac{3}{2} x-6[/tex]

I hope this helps!

Answer:

0.23 is the answer

I wish you luck in your assignments.

Answer:

square root of 819 or 28.6

Step-by-step explanation:

Answer:

x=0.69897009

Step-by-step explanation:

expand by logarithms

10^x=5

=log(10^x)=log(5)

=x log(10)=log (5)

log base 10 of 10 is 1

x.l =log(5)

multiple bothside by 1

x=log(5)

x=0.6989709

Answer:

[tex]\neq \neq \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \geq x^{2} x^{2} \sqrt{x} \frac{x}{y} x_{123} x_{123}[/tex]

Step-by-step explanation:

yeah