Which of the following is a polynomial function in factored form with zeros at –6, –2, and 3?


f(x) = (x – 6)(x – 2)(x + 3)


f(x) = (x + 6)(x + 2)(x – 3)


f(x) = x3 + 5x2 – 12x – 36


f(x) = x3 – 5x2 – 12x + 36

Answer:

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909) =  0.0287

Step-by-step explanation:

step(i):-

Mean of the Population = 292.5 yards

Standard deviation of the Population = 14.2 yards

sample size 'n' =60 drives

               N = 4244 drives

Step(ii):-

Let X⁻ be random sample average

[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

Let  X⁻ = 289

[tex]Z = \frac{289 -292.5}{\frac{14,2}{\sqrt{60} } }[/tex]

Z  = - 1.909

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909)

                = 0.5 -A(1.909)

                = 0.5 -0.4713

               = 0.0287

Conclusion:-

The Probability that the sample average was 289 yards or less = 0.0287

Answer:

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range [tex]R = U\sqrt{\frac{H}{g} }[/tex]

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

[tex]60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}[/tex]

Squaring both sides we have;

[tex](\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet[/tex]

The arrow will hit the target 1.84feet below the bullseye.

Answer:

8.7

Step-by-step explanation:

on edge . You're welcome

Answer:

  7 and 8

Step-by-step explanation:

  54 is between 7^2 = 49 and 8^2 = 64.

The square roots have the same relationship.

  49 < 54 < 64

  √49 < √54 < √64

  7 < √54 < 8

Answer: 30 for addition and 2376 for multipaction

Step-by-step explanation: Depending on how what algebraic expression.

Answer: The area of circle V is 196π ft² (196Pi feet squared)

Step-by-step explanation:

From the equation for area of a circle,

A = πr²

Where A is the area of the circle

r is the radius of the circle

In Circle V, the radius, r of the circle is 14 feet

That is,

r = 14ft

Hence, Area is

A = π × (14ft)²

A = π × 14ft × 14ft

A = 196π ft²

Hence, the area of circle V is 196π ft² (196Pi feet squared)

Answer:

The answer is D on Edge 2020

Step-by-step explanation:

I did the Quiz

Answer:

Option C.

Step-by-step explanation:

Let a point (x, y) has a sequence of transformations,

Option A).

Reflects across x-axis then the coordinates will be,

(x, y) → (x, -y)

Then reflects across the y-axis,

(x, -y) → (-x, -y)

Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.

Option B).

(x, y) rotate 90° counter clockwise about the origin.

(x, y) → (-y, x)

Then reflect across x-axis,

(-y, x) → (y, x)

Since coordinates of the image and the actual are not same therefore, image doesn't map itself.

Option C).

(x, y) when reflected across x-axis,

(x, y) → (x, -y)

Then reflected over the x-axis,

(x, -y) → (x, y)

In this option point (x, y) maps onto itself after these transformations.

Option D).

(x, y) rotated 90°counterclockwise about the origin

(x, y) → (-y, x)

Then translated up by 2 units.

(-y, x) → (-y, x+2)

Therefore, (x, y) gets changed after these transformations and doesn't maps itself.

Option (C) will be the answer.

Answer:

you have it correct the answer is option c

Step-by-step explanation:

Answer:

left, if looking from person's point of view

Step-by-step explanation:

Answer:

It would be A

Step-by-step explanation:

If you cut off the overlapping cubes, you get the image on A.

Answer:

Step-by-step explanation:

Surface Area is the combined area of all two-dimensional surfaces of a shape. Just like ordinary area, the units are the squares of the units of length (that is, if a shape's sides are measured in meters, then the shape's area is measured in square meters

Answer:

T = £85.87

the cost of the petrol the car used in November is £85.87

Step-by-step explanation:

Given;

In November Hillary drove 580 miles in her car;

Distance travelled d = 580 miles

the car travelled 33.5 miles for each gallon of petrol used;

Fuel consumption rate r = 33.5 miles per gallon

Number of gallons N consumed by the car is;

N = distance travelled/fuel consumption rate

N = d/r = 580/33.5 = 17.3134 gallons

Given that;

Petrol cost £1.09 per litre

Cost per litre c = £1.09

1 gallon = 4.55 litres

Converting the amount of fuel used to litres;

N = 17.3134 gallons × 4.55 litres per gallon

N = 78.77612 litres

The total cost T = amount of fuel consumption N × fuel cost per litre c

T = N × c

T = 78.77612 litres × £1.09 per litre

T = £85.87

the cost of the petrol the car used in November is £85.87

Answer:

200.96 units

Step-by-step explanation:

Use the formula for the volume of a cone [tex]V=\pi r^{2} \frac{h}{3}[/tex]

Plug in the values ([tex]\pi[/tex]=3.14) and multiply them all out

Answer:

≈ 201

Step-by-step explanation:

V= πr²h/3

V= 3.14*4²*12/3= 200.96 ≈ 201

Answer:

1.8

Step-by-step explanation:

Answer:

y = - 3x + 9    or     (y - 6) = - 3(x - 1)

Step-by-step explanation:

I'm assuming you are looking for the equation of the line.

First, let's find the slope of the line, which we use equation (y1-y2) / (x1-x2)

x1: 1      x2: 2

y1: 6     y2: 3

(6-3) / (1-2) = 3 / -1 = -3

The slope of the line is -3.

The equation for slope-intercept form is y = mx + b, where m is slope and b is the y - intercept.

y = -3x+b

Now substitute a set of points in (any coordinates work). I'll use (1, 6)

6 = -3(1)+b

6 = - 3 + b

b = 9

So our equation in slope intercept form is y = - 3x + 9

You can also write this in point slope form,   (y-y1) = m (x-x1)     m is still slope

(y - 6) = - 3(x - 1)

Answer:

2/1

Step-by-step explanation:

So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)

and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE

it is 2

then you just count over to point B from that spot where you counted up. RUN TO IT

1

so it is 2/1 or just 2

((point (0,1) would have worked too))

Answer:

X=-2or,-3

Step-by-step explanation:

X^2+5x+6=0

or,x^2+(2+3)x+6=0

or,x^2+2x+3x+6=0

or,x(x+2)+3(x+2)=0

or,(x+3) (x+2)=0

Either,

x+3=0 x+2=0

or,x=-3 or,x=-2

Therefore,the value if x is -2 or -3 .

I HOPE IT WILL HELP YOU

Answer:

i think it's c.)3.5 i may be wrong

Step-by-step explanation:

Answer:

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

Answer:

(a) See below

(b) r = 0.9879  

(c) y = -12.629 + 0.0654x

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is  

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

   x            y             xy                      x²             y²    

   36       0.22              7.92               1296           0.05

   67        0.62            42.21              4489           0.40

   93         1.00            93.00           20164           3.46

 433        11.8          5699.4          233289        139.24

 887      29.3         25989.1          786769       858.49

1785      82.0        146370          3186225      6724

2797     163.0         455911         7823209    26569

3675   248.0         911400        13505625   61504        

9965   537.81     1545776.75  25569715   95799.63

(ii) Calculate the correlation coefficient

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]

(c) Regression line

The equation for the regression line is

y = a + bx where

[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

   x            y       Estimated   Residual

    36        0.22        -10                 10

    67        0.62          -8                  9

    93        1.00           -7                  8

   142        1.86           -3                  5

  433       11.8             19               -  7

  887     29.3             45               -16  

 1785     82.0            104              -22

2797    163.0            170               -  7

3675   248.0            228               20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

Answer:

x = pi/6

x = 11pi/6  

x = 5pi/6  

x =7pi/6

Step-by-step explanation:

2 sec^2 (x) + tan ^2 (x) -3 =0

We know tan^2(x) = sec^2 (x) -1

2 sec^2 (x) +sec^2(x) -1 -3 =0

Combine like terms

3 sec^2(x) -4 = 0

Add 4 to each side

3 sec^2 (x) = 4

Divide by 3

sec^2 (x) = 4/3

Take the square root of each side

sqrt(sec^2 (x)) = ±sqrt(4/3)

sec(x) = ±sqrt(4)/sqrt(3)

sec(x) = ±2 /sqrt(3)

Take the inverse sec on each side

sec^-1 sec(x) = sec^-1(±2 /sqrt(3))

x = pi/6 + 2 pi n    where n is an integer

x = 11pi/6 + 2 pi n  

x = 5pi/6 + 2 pi n  

x =7pi/6 + 2 pi n  

We only want the solutions between 0 and 2pi

Answer:

To compute the probabilities, just divide the number of times a number was landed by the total amount of outcomes.

Spinning 2: 30/120 = 0.25  

Spinning 3: 19/120  = 0.16

Spinning 4:  25/120  = 0.21

Spinning 5:  29/120  = 0.24

Spinning 6:  17/120  = 0.14

Stacy would spin a 6 approximately 0.14*50 = 7 times in 50 tries.

Answer:

1/52

Step-by-step explanation:

Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189  ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple  choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

The number of allowances that Robert has claimed is four. Option d is correct.

A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).

From the given information:

The tax allowance = Gross income - savings amount

The tax allowance = $951 - $762

The tax allowance = $189

From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:

0  → $259

1   →  $242

2   → $224

3   → $207

4  → $189

5   → $173

6  →  $162

7   → $151

8  →  $140

Therefore, we can conclude that the number of allowances that Robert has claimed is four.

Learn more about tax withholding here:

https://brainly.com/question/25927192

Answer:

The coordinates of point A after both transformations becomes (0, 3)

Step-by-step explanation:

Translation 4 units down is equivalent to -4 units in the y direction, therefore, we have;

A(-3, 4), B(6, 4), and C(2, -3) becomes

A(-3, 4 - 4), B(6, 4 - 4), and C(2, -3 - 4) which is A(-3, 0), B(6, 0), and C(2, -7)

Rule on operation on coordinates due to rotation of a triangle 90° clockwise is as follows;

For vertex coordinate, (x, y), we change it to (y, -x)

Therefore, we have the coordinates of the point A(-3, 0) after a rotation of 90° clockwise becomes A(0, 3).

Answer:

26

Step-by-step explanation:

Answer:

32/25 walls per gallon.

Step-by-step explanation:

Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall

Hence 1 gallon would be 4/5÷5/8=

4/5 × 8/5= 32/25 walls per gallon.

Answer:

  B.  g(x)

Step-by-step explanation:

g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.

f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.

g(x) has the smallest minimum value

Answer: d) all of the above

Step-by-step explanation:

A Hamiltonian circuit is where you follow the path of the circuit touching EVERY VERTEX only ONE time.

Notice that each path given allows every vertex to be touched and each vertex is touched only once.

Therefore, all the options given are valid paths for a Hamiltonian circuit.

Answer:

Down below

Step-by-step explanation:

   a. Net income= $100,000 (as given in the question)

   b. Return on equity= (net income)/(shareholder’s equity)

Shareholder’s equity= $400,000

Thus return on equity= 100000/400000 = 0.25  or 25%

   a. Net income= $100000 + 50000 –  12800 (debt interest 8% of     $160000)

= $137,200

b. Return on equity= (net income)/(shareholder’s equity)

= 137200/400000

=0.343  or 34.3%

a. Net Income= $100000 + 50000

= $150000

b. Return on equity= (net income)/(shareholder’s equity)

= 150000/(400000 + 160000)

Where ($560,000) 400000 + 160000 is shareholder’s equity

= 0.27 or 27%

Answer:

a) The third quartile Q₃ = 56.45

b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Step-by-step explanation:

Given that :

[tex]Q_1[/tex]  =  30.8

Median [tex]Q_2[/tex] =  48.5

Mean  = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]

[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]

[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]

[tex]1.38Q_3 = 77.904[/tex]

Divide both sides by 1.38

[tex]Q_3 = 56.45[/tex]

b) The objective here is to determine the approximate value of the variance;

Using the relation

[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]

[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]

[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]

[tex]-0.38* \sigma = {(-19.5) }{}[/tex]

[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]

[tex]\sigma =51.32[/tex]

Variance =  [tex]\sigma^2 =51.32^2[/tex]

[tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Answer:

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly​ selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that both will be hopelessly romantic is

                   [tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            = [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Answer:

  the sum shown is (20/21)a -(1/7)

Step-by-step explanation:

As written, the sum is ...

  [tex]a-\dfrac{\frac{3}{7}}{3}-\dfrac{a}{21}=\boxed{\dfrac{20}{21}a-\dfrac{1}{7}}[/tex]

__

We wonder if you mean the quotient ...

  ((a-3)/7)/((3-a)/21)

  [tex]\dfrac{\left(\dfrac{a-3}{7}\right)}{\left(\dfrac{3-a}{21}\right)}=\dfrac{a-3}{7}\cdot\dfrac{21}{3-a}=\dfrac{-21(3-a)}{7(3-a)}=\boxed{-3}[/tex]

_____

Comment on the problem presentation

Parentheses are required when plain text is used to represent fractions. The symbols ÷, /, and "over" all mean the same thing: "divided by." The denominator is the next item in the expression. If arithmetic of any kind is involved in the denominator, parentheses are needed. This is the interpretation required by the Order of Operations.

When the expression is typeset, fraction bars and text formatting (superscript) serve to group items that require parentheses in plain text.

__

Please note that some authors make a distinction between the various forms of division symbol. Some use ÷ to mean ...

  (everything to the left)/(everything to the right)

and they reserve / solely for use in fractions. Using this interpretation, your expression would be ...

  (a -(3/7))/(3 -(a/21)) = (21a -9)/(63 -a)

That distinction is not supported by the Order of Operations.