determine the polynomial equivalent to this expression.
x^2-9/x-3

A. x-3

B. -3x-9

C. x+3

D. x^2+3x​

Answer:

f^-1(x) = x + 5

Step-by-step explanation:

f(x) = x-5

y = x-5

Exchange x and y

x = y-5

Solve for y

x+5 = y-5+5

x+5 =y

The inverse is x+5

The answer is 3,240

Explanation:

To calculate the total income tax, it is necessary to calculate what is the 15% of 8000, and 17% for the remaining money, which is 12.000 (20,000 - 8,000= 12,000). Considering the statement specifies the 15% is paid for the first 8,000 and from this, the 17% is paid. Now to know the percentages you can use a simple rule of three, by considering 8000 and 12000 as the 100%. The process is shown below:

1. Write the values

[tex]8000 = 100[/tex]

[tex]x = 15[/tex] (the percentage you want to know)

2. Use cross multiplication

[tex]x =\frac{8000 x 15 }{100}[/tex]

[tex]x = 1200[/tex]

This means for the first 8000 the money Rafael needs to pay is 1,200

Now, let's repeat the process for the remaining money (12,000)

[tex]12000 = 100\\\\[/tex]

[tex]x = 17[/tex]

[tex]x = \frac{12000 x 17}{100}[/tex]

[tex]x = 2040[/tex]

Finally, add the two values [tex]1200 + 2040 = 3240[/tex]

Answer:

.15* house price = 28,500

house price = 28,500 / .15

house price =  190,000

Step-by-step explanation:

Answer: 190,000

Step-by-step explanation:

the equation looks like this - .15x=28,500. then you divide both sides by .15 and get x=190,000

Answer:

The answer is A.

Step-by-step explanation:

In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.

So for this question, m is 2/3 and b is 1.

Answer:

i believe it's 4.5

Step-by-step explanation:

Answer:

14 in. hope this helps!!:)

Step-by-step explanation:

You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.

Answer:

Total Area = [tex]104+16\,\sqrt{13}[/tex]

Step-by-step explanation:

If T.A. stands for Total Area, then we need to add the area of two equal right angle triangles of base 6' and height 4', which give : 2 * (6' * 4'/2) = 24 square feet. tothe area of three rectangles (the lateral faces of this triangular base prism):

[tex](8')*(4')+(8')*(6')+(8')*(\sqrt{6^2+4^2})= 32+48+8\,\sqrt{52} =80+8\,*\,2\,\sqrt{13}=80+16\,\sqrt{13}[/tex]

Therefore the total area of the prism is:

[tex]24+80+16\,\sqrt{13} =104+16\,\sqrt{13}[/tex]

Answer:

500 pounds

Step-by-step explanation:

Let the pressure applied to the leverage bar be represented by p

Let the distance from the object be represented by d.

The pressure applied to a leverage bar varies inversely as the distance from the object.

Written mathematically, we have:

[tex]p \propto \dfrac{1}{d}[/tex]

Introducing the constant of proportionality

[tex]p = \dfrac{k}{d}[/tex]

If 150 pounds is required for a distance of 10 inches from the object

[tex]150 = \dfrac{k}{10}\\\\k=1500[/tex]

Therefore, the relationship between p and d is:

[tex]p = \dfrac{1500}{d}[/tex]

When d=3 Inches

[tex]p = \dfrac{1500}{3}\\\implies p=500$ pounds[/tex]

The pressure applied when the distance is 3 inches is 500 pounds.

Step-by-step explanation:

In the fourth quadrant, the equation of the unit circle is:

y = -√(1 − x²), 0 ≤ x ≤ 1

The x and y coordinates of the centroid are:

cₓ = (∫ x dA) / A = (∫ xy dx) / A

cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A

For a quarter circle in the fourth quadrant, A = -π/4.

Solving each integral:

∫₀¹ xy dx

= ∫₀¹ -x √(1 − x²) dx

= ½ ∫₀¹ -2x √(1 − x²) dx

If u = 1 − x², then du = -2x dx.

When x = 0, u = 1.  When x = 1, u = 0.

= ½ ∫₁⁰ √u du

= ½ ∫₁⁰ u^½ du

= ½ (⅔ u^³/₂) |₁⁰

= (⅓ u√u) |₁⁰

= 0 − ⅓

= -⅓

∫₀¹ ½ y² dx

= ½ ∫₀¹ (1 − x²) dx

= ½ (x − ⅓ x³) |₀¹

= ½ [(1 − ⅓) − (0 − 0)]

= ⅓

Therefore, the x and y coordinates of the centroid are:

cₓ = (-⅓) / (-π/4) = 4/(3π)

cᵧ = (⅓) / (-π/4) = -4/(3π)

Answer:

The probability is  [tex]P(\= X > x ) = 0.78814[/tex]

Step-by-step explanation:

From the question we are given that

     The population  mean is  [tex]\mu = 149[/tex]

     The standard deviation is  [tex]\sigma = 14[/tex]

     The random number    [tex]x = 147.81[/tex]

      The sample  size is  [tex]n = 88[/tex]

The probability that  the sample mean would be greater than [tex]P(\= X > x ) = P( \frac{ \= x - \mu }{\sigma_{\= x} } > \frac{ x - \mu }{\sigma_{\= x} } )[/tex]

Generally the z- score of this normal distribution is mathematically represented as

       [tex]Z = \frac{ \= x - \mu }{\sigma_{\= x} }[/tex]

Now

        [tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x } = \frac{14 }{\sqrt{88} }[/tex]

         [tex]\sigma_{\= x } = 1.492[/tex]

Which implies that

         [tex]P(\= X > x ) = P( Z > \frac{ 147.81 - 149 }{ 1.492} )[/tex]

        [tex]P(\= X > x ) = P( Z > -0.80 )[/tex]

Now from the z-table  the  probability is  found to be

        [tex]P(\= X > x ) = 0.78814[/tex]

Answer:

The answer is

Step-by-step explanation:

x² + 2x - 3 - 2x² + x + 4

Group like terms

That's

x² - 2x² + 2x + x - 3 + 4

Simplify

- x² + 3x + 1

when x = 3

We have

(-3)² + 3(3) + 1

9 + 9 + 1

18 + 1

19

Hope this helps you

Answer:

$4800.25

Step-by-step explanation:

$42603 is a yearly salary.

There are 12 months in 1 year.

Monthly salary:

$42603/12 = $3550.25

Monthly travelling allowance: $1250

Total amount earned in 1 month:

$3550.25 + $1250 = $4800.25

Answer:

15%

Step-by-step explanation:

To calculate the margin of error, we can adopt this formula

Margin of error = critical value* (standard deviation/sqrt of sample size)

Where critical value is 2.33, sd is 0.78 and sample size is150.

Thus, we have:

Margin of error = 2.33*(0.78/√150)

Margin of error = 2.33*(0.78/12.2474)

Margin of error =2.33*0.06369

Margin of error = 0.1484 which is a 15% margin of error

Answer:

[tex]\boxed{135\°,315\°}[/tex]

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

[tex]\theta = 135+180n[/tex]

[tex]n[/tex] is any integer value.

The value of [tex]n[/tex] cannot exceed 1 or be less than 0, because the value of [tex]\theta[/tex] must be between 0 and 360 degrees.

[tex]\theta = 135+180(0)[/tex]

[tex]\theta = 135[/tex]

[tex]\theta = 135+180(1)[/tex]

[tex]\theta = 315[/tex]

Answer:

A. y ≤ 1/2x + 2

Step-by-step explanation:

Well look at the graph,

It is a solid line with it shaded down,

meaning it is y ≤,

So we can cross out B. and D.

So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.

now the slope can be found by seeing how far away each points are from each other,

Hence, the answer is A. y ≤ 1/2x + 2

Answer:

The upper confidence bound for population mean escape time is: 379.27

The upper prediction bound for the escape time of a single additional worker  is 413.64

Step-by-step explanation:

Given that :

sample size n = 26

sample mean [tex]\bar x[/tex] =  371.08

standard deviation [tex]\sigma[/tex] = 24.45

The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%

We need to determine the standard error of these given data first;

So,

Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]

Standard Error S.E = 4.7950

However;

Degree of freedom df= n - 1

Degree of freedom df= 26 - 1

Degree of freedom df= 25

At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

Similarly;

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 4.7950

The Margin of error = 8.18986

The upper confidence bound for population mean escape time is = Sample Mean + Margin   of  Error

The upper confidence bound for population mean escape time is =  371.08 +  8.18986

The upper confidence bound for population mean escape time is = 379.26986  [tex]\approx[/tex] 379.27

The upper confidence bound for population mean escape time is: 379.27

b.  Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.

The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]

The standard error of the mean = 24.91575614

Recall that : At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

∴

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 24.91575614

The Margin of error = 42.55611149

The upper prediction bound for the escape time of a single additional worker  is calculate by the addition of

Sample Mean + Margin of Error

= 371.08 + 42.55611149

= 413.6361115

[tex]\approx[/tex] 413.64

The upper prediction bound for the escape time of a single additional worker  is 413.64

Answer

Step-by-step explanation:

Given,

r = 10

Let's create an equation,

[tex]3r = 10 + 5s[/tex]

plugging the value of r

[tex]3 \times 10 = 10 + 5s[/tex]

Multiply the numbers

[tex]30 = 10 + 5s[/tex]

Move 5s to L.H.S and change its sign

Similarly, Move 30 to R.H.S and change its sign.

[tex] - 5s = 10 - 30[/tex]

Calculate

[tex] - 5s = - 20[/tex]

The difference sign ( - ) should be cancelled on both sides

[tex]5s = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5s}{2} = \frac{20}{5} [/tex]

Calculate

[tex]s = 4[/tex]

The value of s is 4.

Hope this helps..

Best regards!!

Answer:

A. 4 (on edgenuity)

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.

Answer:

26

Step-by-step explanation:

Given that:

At time, t=0, Billy puts 625 into an account paying 6% simple interest

At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.

If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.

In order to calculate n;

Let K constant to be the value of time for both accounts

At  time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:

[tex]K = 625 \times (1+ 0.06 K)[/tex]

[tex]K = 625 +37.5 K[/tex]

At year end 2; George  amount of 400 will grow at a force interest, then the value of  [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]

[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]

[tex]K =400 \times \dfrac{6+K}{8}[/tex]

[tex]K =50 \times ({6+K})[/tex]

[tex]K =300+50K[/tex]

Therefore:

If K = K

Then:

625 + 37.5 = 300 +50 K

625-300 = 50 K - 37.5 K

325 = 12.5K

K = 325/12.5

K = 26

the amounts in both accounts  at the end of year n = K = 26

Step-by-step explanation:

The formulae to find them are:

and mode= number of greatest frequency.

(note; f is frequency, N is number of data and x is x is the raw data)

hope it helps..

Answer:

20.8 hours

Step-by-step explanation:

2 3/5 = 2.6.The painter will take (2.6 × 8) = 20.8 hours to paint a wall.

Hope this helps and pls mark as brianliest :)

Answer:

20.8, 20 4/5, and 104/5

Answer:

y + 4 = 4/3(x - 6).

Step-by-step explanation:

The point-slope formula is shown below. We just need to find the slope.

(-4 - (-8)) / (6 - 3) = (-4 + 8) / 3 = 4 / 3

m = 4/3, y1 = -4, and x1 = 6.

y - (-4) = 4/3(x - 6)

y + 4 = 4/3(x - 6).

Hope this helps!

the answer is 36.36 but the closest to it is 37

Answer:

[0, infinity)

Step-by-step explanation:

clarence, I believe you meant y = |3x + 1|.  The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).

Step-by-step explanation:

It is given that,

Total length of a board is 65 inches

It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.

Let x is the length of other piece and y is the length of first piece such that,

y = 2x-7 ....(1)

Also,

x+y = 65 .....(2)

Put the value of y from equation (1) to equation (2) such that,

x+2x-7 = 65

3x=65+7

3x=72

x = 24 inches

Put the value of x in equation (1)

y = 2(24)-7

y = 41 inches

So, the length of first piece is 41 inches while the length of other piece is 24 inches.

Answer:

Largest possible length is 21 inches.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = [tex]l[/tex] inches and

Width = [tex]w[/tex] inches

As per given condition:

[tex]l = 2w+3[/tex] ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

[tex]P = 2 \times (Width + Length)[/tex]

Putting the given values and conditions as per equation (1):

[tex]60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch[/tex]

Putting in equation (1):

[tex]l = 2\times 9+3\\\Rightarrow l = 21\ inch[/tex]

So, the answer is:

Largest possible length is 21 inches.

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Hey there! I'm happy to help!

Let's set this up a system of equations where x represents the number of 10 dollar bills and y represents the number of 20 dollar bills.

10x+20y=440

x=y+2

We see that x has a value of y+2, so we can replace the x in the first equation with y+2 so we can solve for y.

10(y+2)+20y=440

We use distributive property to undo the parentheses.

10y+20+20y=440

We combine like terms.

30y+20=440

We subtract 20 from both sides.

30y=420

y=14

Since there are 2 more $10 bills, there would be 16 of those.

Therefore, there are 16 $10 bills and 14 $20 bills.

Have a wonderful day! :D

Answer:

23+15i

Step-by-step explanation:

(-3+2i) (-3-7i)

multiply -3 w (-3+2i) and multiply -7i w (-3+2i)

9-6i+21i-14i^2

combine like terms

9+15i-14i^2

i squared is equal to -1 so

9+15i-(14x-1)

9+14+15i

23+15i

hope this helps :)

Answer:

Number:3.75

Equation:7 x-9=3(x+2)

Step-by-step explanation:

Let the number be x.

According to the question,

7 x-9=3(x+2)

7 x-9= 3 x+ 6

7 x- 3 x= 9+6

4 x= 15

x=15/4

x=3.75

If you verify the answer you will get,

11.25=11.25

Thank you!