Which is the first step in simplifying 4(3x-2)+6x(2-1)

Answer and Step-by-step explanation:

The computation of dividends per share on each class of stock for each of the four years is shown below:-

Particulars                1st year     2nd-year     3rd-year     4th year

Preferred dividend

paid a                         $34,000   $38,000    $36,000    $36,000

Number of preferred

stock b                       60,000     60,000       60,000       60,000

Dividend per share

(a ÷ b)                         $0.57       $0.63          $0.60             $0.60

Dividend paid to common

stockholders c               $0             $38,000    $44,000     $64,000

Number of common stock

shares d                       410,000     410,000     410,000     410,000

Dividend per share

on common stock        $0             $0.093        $0.11          $0.16

(c ÷ d)

Working note:

Preferred dividend = Number of preferred stock shares × Par value per share × Percentage of dividend

= 60,000 × $20 × 3%

= $36,000

Preferred stock

For 1st year

= $34,000

For 2nd-year

Dividend in year 2+ Dividend balance in year 1

= $36,000 + ($36,000 - $34,000)

= $38,000

For 3rd-year

= $36,000

For 4th year

= $36,000

Common stock dividend

Particulars                      1 year        2 year       3 year       4 year

Total dividend paid       $34,000  $76,000   $80,000     $100,000

Less:

Preferred stock

dividend                      $34,000      $38,000  $36,000     $36,000

Dividend paid to common

stockholders                 $0             $38,000    $44,000     $64,000

Answer:

3/20s

Step-by-step explanation:

Answer:

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.

Step-by-step explanation:

Data given and notation  

[tex]n_1 = 24 [/tex] represent the sampe size 1

[tex]n_2 =16[/tex] represent the sample size 2

[tex]s^2_1 = 32[/tex] represent the sample variance for 1

[tex]s^2_2 = 38[/tex] represent the sample variance for 2

The statistic for this case is given by:

[tex]F=\frac{s^2_1}{s^2_2}[/tex]

Hypothesis to verify

We want to test if the true deviations are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.

Answer:

308.67 cm ^ 3 / week

Step-by-step explanation:

A cantaloupe is approximately a sphere, therefore its approximate volume would be:

V = (4/3) * pi * (r ^ 3)

They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm

if we derive the formula from the volume we are left with:

dV / dt = (4/3) * pi * d / dr [(r ^ 3)]

dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt

dV / dt = 4 * pi * (r ^ 2) * dr / dt

we replace all the values and we are left with:

dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6

dV / dt = 308.67

Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:

First Derivative

[tex]h'(t) = -32\cdot t +128[/tex]

Second Derivative

[tex]h''(t) = -32[/tex]

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

[tex]-32\cdot t +128 = 0[/tex]

[tex]t = \frac{128}{32}\,s[/tex]

[tex]t = 4\,s[/tex] (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]

[tex]h(4\,s) = 576\,ft[/tex]

The highest altitude that the object reaches is 576 feet.

Answer:

The work will be "1909212.015 J". The further explanation is given below.

Step-by-step explanation:

The given values are:

Liquid's density

= 760 kg/m³

Height

= 3 meters

Gravity

g = 3.8 m/s²

Value of y is:

y = 5 log (x-2)

y = 0

y = 4

As we know,

⇒  [tex]\Delta V=\pi r^2 \Delta y[/tex]

⇒  [tex]y =5log(x-2)[/tex]

⇒  [tex]\frac{y}{5} =log (x-2)[/tex]

⇒  [tex]e^{\frac{y}{5}}=(x-2)[/tex]

⇒  [tex]x=e^{\frac{y}{5}}+2[/tex]

Now,

[tex]\Delta F=ma[/tex]

      [tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]

So that,

⇒  [tex]\Delta W = \Delta F.distance[/tex]

            [tex]=\Delta F(4-y)[/tex]

The required work will be:

⇒  [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]

         [tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]

         [tex]=760\times 9.8 \pi[81.455][/tex]

         [tex]=1909212.015 \ J[/tex]

Answer:

-18 < -x-4 < -8

Step-by-step explanation:

We start with the initial range as:

4 < x < 14

we multiplicate the inequation by -1, as:

-4 > -x > -14

if we multiply by a negative number, we need to change the symbols < to >.

Then, we sum the number -4, as:

-4-4> -x-4 > -14-4

-8 > -x-4 > -18

Finally, the range for -x-4 is:

-18 < -x-4 < -8

Answer:

never intersect

Step-by-step explanation

parallel lines do not intersect and neither do parallel planes

Hey there! :)

Answer:

3(d + 1)²

Step-by-step explanation:

Given 3d² + 6d + 3:

Begin by factoring out '3' from each term:

3(d² + 2d + 1)

Factor terms inside of the parenthesis:

3(d + 1)(d + 1) or 3(d + 1)².

Answer:

x= -14

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

(4+1)/(8-2)= 5/6

y + 1 = 5/6(x - 2)

y + 1 = 5/6x - 5/3

y + 3/3 = 5/6x - 5/3

y = 5/6x - 8/3

6(y = 5/6x - 8/3)

6y = 5x - 16

-5x + 6y = -16

Answer:

Thirty-one million, six hundred and twenty-four

Four billion, six million, eighty-five thousand, and twelve

six million five hundred thousad

twenty-five million, four hundred and thirty thousand and seven hundred and fifty-six

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

It's the first one. The angles are supplementary not complementary.

Answer:

I would have to say A

Step-by-step explanation:

Answer:

      Lateral surface area is

≈

502.65cm²

      Base area is

=

πr^2

Answer:

13, 21

Step-by-step explanation:

Fibonacci sequence-

Each number is added to the number before it.

1+1=2

2+1=3

3+2=5

5+3=8

Answer:

The missing numbers are 13, and 21.

The pattern given is the Fibonacci Sequence, where each number is the sum of the two numbers before it, starting with 0 and 1. (i.e. 5 is 2+3)

Answer:

xy + 8x - y - 8

Step-by-step explanation:

We can use the FOIL method to expand these two binomials. FOIL stands for First, Outer, Inner, Last.

F: The First means that we multiply the first terms of each binomial together. In this case, that would be x · y = xy.

O: The Outer means that we multiply the outer terms, or the first term of the first binomial and the second term of the last binomial, together. In this case, that would be x · 8 = 8x.

I: The Inner means that we multiply the inner terms, or the second term of the first binomial and the first term of the second binomial, together. In this case, that would be (-1) · y = -y.

L: The Last means that we multiply the last terms of each binomial together. In this case, that would be (-1) · 8 = -8.

Adding all of these together, we get xy + 8x - y - 8 as our final answer.

Hope this helps!

Answer:

[tex]xy+8x-y-8[/tex]

Step-by-step explanation:

=> (x-1)(y+8)

Using FOIL

=> [tex]xy+8x-y-8[/tex]

Answer:

Step-by-step explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

  P = A(1+r)(1 -(1 +r)^-n)/r

  P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

  20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

  $1,200,000 -636,215.95 = $563,784.05

Answer:

1 3 4 5

Step-by-step explanation:

The rotation does not change the angle measure, the side lengths and the shape of the shape that is being rotated.

An angle measure the size, the shape, and the position of center of rotation do not change after rotation.

If one thing is rotated then it will not change the angle measures, the side lengths and shape of the body. The rotation does not change the center of object.

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Answer:

June Financial Reports

a) Cost of goods available for sale = $5,250

b) Moving-Average unit cost for:

i) June 1:  = $5

ii)        12:  = $4.75

iii)       15: = $4.75

iv)      23:  = $5.75

v)       27:  = $5.25

Step-by-step explanation:

a) Calculations:

Date     Explanation   Units     Unit Cost    Total Cost   Moving Average Cost

June 1 Inventory          150        $4                $600         $4.000

      12 Purchase         450          5               2,250            4.750

      15 Sale                 500          7                      3,500     4.750

     23 Purchase         400          6               2,400            5.750

     27 Sale                 420          8                      3,360     5.250

     30 Inventory           80

Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)

b) Moving-Average unit cost for:

i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)

ii)        12: Cost  of goods available/Units of goods available = $4.75 ($600 + 2,250/600)

iii)       15: Cost  of goods available/Units of goods available = $4.75 ($475/100)

iv)      23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500

v)       27: Cost of goods available/Units of goods available = $5.25 ($420/80)

The question is incomplete. Here is the complete question.

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:

Question #1: I prefer outdoor activities, rather than indoor activities.

Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.

Question #3: I prefer texting, rather than talking on the phone.

Question #4: I prefer living in a small town, rather than in a big city.

Here are the results for the questionaire, with a group of 5 participants:

                        Question1     Question2   Question3       Question4

participant A           1                      1                   -1                      -1

participant B           -1                     1                    1                       1

participant C           -1                    -1                    1                       1

participant D           1                     -1                   -1                      -1

participant E            1                    -1                    1                       1

Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".

(a) Which pairs of paricipants are compatible?

(b) Which pairs of participants are incompatible?

(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only

allowing  "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?

Answer: (a) Participants A and D; B and C; C and E.

(b) Participants A and B; A and C; A and E; B and D; C and D;

Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.

Vectors form angles between themselves and can be found by the following formula:

cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]

which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.

For the compatibility test, find the angle between vectors:

1) The vectors magnitude:

Magnitude of a vector is given by:

||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]

Since all the vectors have value 1, they have the same magnitude:

||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2

||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2

2) The dot product of vectors:

A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]

The angle that has cosine equal -1/2 is 120°, so incompatible

A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4

cos [tex]\alpha _{2}[/tex] = -1

Angle = 180° --------> incompatible

A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2

cos [tex]\alpha _{3}[/tex] = 1/2

Angle = 60° ---------> COMPATIBLE

A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2

cos [tex]\alpha_{4}[/tex] = -1/2

Angle = 120° --------> incompatible

B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha _{5}[/tex] = 1/2

Angle = 60° -------------> COMPATIBLE

B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4

cos[tex]\alpha_{6}[/tex] = -1

Angle = 180° -----------> incompatible

B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0

cos[tex]\alpha _{7}[/tex] = 0

Angle = 90° -------------> may or may not

C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2

cos[tex]\alpha_{8} =[/tex] -1/2

Angle = 120° ---------------> Incompatible

C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2

cos [tex]\alpha_{9}[/tex] = 1/2

Angle = 60° ---------------> COMPATIBLE

D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0

cos [tex]\alpha_{10}[/tex] = 0

Angle = 90° -----------------> may or may not

(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.

Answer:

The Pythagorean Triplet that has 5 is 3-4-5

Step-by-step explanation:

We can prove this using Pythagorean Theorem: a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

======================================================

Work Shown:

1 hour = 60 minutes

2 hours = 120 minutes (multiply both sides by 2)

1/4 hour = 15 minutes (divide both sides of the first equation by 4)

2 & 1/4 hours = 2 hours + 1/4 hour

2 & 1/4 hours = 120 minutes + 15 minutes

2 & 1/4 hours = 135 minutes

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

1 minute = 60 seconds

135 minutes = 8100 seconds (multiply both sides by 135)

2 & 1/4 hours = 8100 seconds

Answer:

Options A, C and D are true.

- The average daily revenue for days when the Red Sox do not play away is $1,768.32.

- The average daily revenue for days when the Red Sox play away is $2,264.57.

- On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

Step-by-step explanation:

The complete Question is presented in the attached image to this solution.

Analyzing the options at a time

A) The average daily revenue for days when the Red Sox do not play away is $1,768.32.

This option is true as 1768.32 is the intercept which is the average daily revenue when the Red Sox=0, that is, 0=no, when red sox do not play away.

B) The average daily revenue for days when the Red Sox play away is $1,768.32.

This is false because when the Red Sox play away, the value is 1 and the average revenue = 1768.32 + 496.25 = $2,264.57

C) The average daily revenue for days when the Red Sox play away is $2,264.57.

This is true. I just gave the explanation under option B.

D) The average daily revenue for days when the Red Sox do not play away is $1,272.07.

This is false. The explanation is under option A.

E) On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

This is true. It is evident from the table that the 0 and 1 coefficient is 496.25. This expresses the difference in average daily revenue when the Red Sox games are played away and when they are not.

Hope this Helps!!!

Answer:

See below for the table.

Step-by-step explanation:

The results for the thirty cases are listed below:

U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U

The table summarizing the frequency distribution of the primary causes leading to student dropout is:

[tex]\left|\begin{array}{c|c}$Cause&$Frequency\\----------&----\\\\$Unexcused absences (U)&9\\$Illness (I)&9\\$Family problems (F)&7\\$Other causes (O)&5\\-----------&---\\$Total&30\end{array}\right|[/tex]

Answer:

AB=4

Step-by-step explanation:

The transitive property states if A=B and B+C than A+C  Next substitute

AB=x and x=4 so AB=4

Hope this helps, if it did, please give me brainliest, it helps me a lot. :)

Have a good day!

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The probability P(A) that an event A will occur is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question,

=>The event A is selecting a king the second time from a 52-card deck.

=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,

number-of-possible-outcomes-of-event-A = 4

=> Since there are 52 cards in total,

total-number-of-sample-space = 52

Substitute these values into equation above;

P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

Answer:

Step-by-step explanation:

Cos θ = u*v    

             IuI *IvI

u * v = 7*(-1) + (-2)*2

       = -7 - 4

      = -11

IuI = [tex]\sqrt{7^{2}+(-2)^{2}}\\[/tex]

    = [tex]\sqrt{49+4}\\\\[/tex]

    = [tex]\sqrt{53}[/tex]

I vI = [tex]\sqrt{(-1)^{2}+2^{2}}\\[/tex]

     = [tex]\sqrt{1+4}\\\\[/tex]

      = [tex]\sqrt{5}\\[/tex]

Cos θ = [tex]\frac{-11}{\sqrt{53}*\sqrt{5} } \\\\[/tex]

          = [tex]\frac{-11}{16.28}\\\\[/tex]

   Cos θ = -0.68

θ = 132.5°

Answer:

9,000 inches^3

Step-by-step explanation:

The first part is 20 x 20 x 20, which equals 8,000

The second part is 10 x 10 x 10, which is 1,000

1,000 + 8,000 = 9,000

Answer:

The z–score corresponding to 45 is z=2.

Step-by-step explanation:

We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.

The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.

The z-score for X=45 can be calculated as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2[/tex]

The z–score corresponding to 45 is z=2.

Answer:

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."

From the given diagram

We can see that every term is made up with a square which side is n and three small square side is 1.

So,

1st term is 1 × 1 + 3 = 4

2nd term is 2 × 2 + 3 = 4

3rd term is  3 × 3 + 3 = 12

4th term is 4 × 4 + 3 = 19

So, nth term is [tex]n^{2} +3[/tex]

Hence, The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

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