Solve the Equation p - 15 = 30.

Answer: The Middle Ages lasted approximately from  the 5th to the late 15th century. It began with the fall of the Western Roman Empire and merged into the Renaissance and the Age of Discovery.

Answer:

x = 3

Step-by-step explanation:

Given the equation :

6x + 5=9x - 4

Collect like terms :

6x - 9x = - 4 - 5

-3x = - 9

Divide both sides by - 3

-3x / - 3 = - 9 / - 3

x = 3

Hence, x = 3

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

3.20 gallons

Step-by-step explanation:

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

Answer:

p ( x > 2746 ) = p ( z > - 1.4552 )

                      = 1 - 0.072806

                      = 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Step-by-step explanation:

Given data:

51% of male voters preferred a Republican candidate

sample size = 5490

To win the vote one needs ≈ 2746 votes

In order to advice Gallup appropriately lets consider this as a binomial distribution

n = 5490

p = 0.51

q = 1 - 0.51 = 0.49

Hence \(n_{p}\) > 5  while \(n_{q}\)  < 5

we will consider it as a normal distribution

From the question :

number of male voters who prefer republican candidate  ( mean ) ( u )

= 0.51 * 5490 = 2799.9

std = \(\sqrt{npq}\) = \(\sqrt{5490 * 0.51 *0.49}\) = 37.0399  ---- ( 1 )

determine the Z-score = (x - u ) / std  ---- ( 2 )

x = 2746 , u = 2799.9 , std = 37.0399

hence Z - score = - 1.4552

hence

p ( x > 2746 ) = p ( z > - 1.4552 )

                      = 1 - 0.072806

                      = 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Answer:

8.90

Step-by-step explanation:

178 * 5% = 8.90

Answer:

\(x = 120 \times \cos(45) - 0 = 120 \times 0.7 = 84 \\ y = 120 \times \sin(45) - 150 = 84 - 150 = 64\)

Answer:

She will have 7 extra bags.

Step-by-step explanation:

[13(7+6)]/9

(13 * 13)/9

169/9

18.8

9 * 18 = 162

169 - 162 = 7

She will have 7 extra bags.

Answer:

It will take 2 1/2 years

Step-by-step explanation:

Using simple interest, it is found that it will take 2.5 years for the account to reach $713.

The amount of money after t years in simple interest is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

For this problem, the parameters are: \(A(t) = 713, A(0) = 620, r = 0.06\).

Then:

\(A(t) = A(0)(1 + rt)\)

\(713 = 620(1 + 0.06t)\)

\(1 + 0.06t = \frac{713}{620}\)

\(0.06t = 1.15 - 1\)

\(0.06t = 0.15\)

\(t = \frac{0.15}{0.06}\)

\(t = 2.5\)

It will take 2.5 years for the account to reach $713.

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Answer:

7(4q+5)..................

Answer:

5.353

Step-by-step explanation:

hope this helps!

Answer:

5.353

Step-by-step explanation:

There are many numbers that satisfy this condition and 5.353 is one of them

Answer:

x= 50°

w= 130°

y°= 110°

z°=30°

Step-by-step explanation:

x°= 180° - 60°- 70° ( angle sum of triangle)

= 50°

w°= 180° - 50° ( adjacent angles on a straight line)

= 130°

y°= 180° - 70° ( adjacent angles on a straight line)

= 110°

z°= 180 - 40° - 110° ( angle sum of triangle)

= 30°

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

Here, we have,

the conditions for mapping the strip transformation pattern onto itself:

The strip pattern can be mapped onto itself in two different ways.

The first way is to translate the strip pattern horizontally and then rotate it by 180° degrees.

The second way is to reflect the strip pattern across a vertical line.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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complete question:

Which transformations map the strip pattern onto itself?

a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°

a horizontal translation only

a horizontal translation, a reflection across a horizontal line, and a glide reflection only

a horizontal translation and a 180° rotation only

Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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Answer: the volume of the body is1590.4m^3

This body is composed of a cillinder and two hemisferes. The two hemispheres forms an entire sphere, so we can calculate the volume of the cillinder and the volume of the sphere and add them up

Volume of the cillinder:

Volume of sphere:

diameter=2*r so the radius is half the lenght of the diameter

now we add them up

Answer:

Step-by-step explanation:

15% of 20 is 3

Answer:

y=3x+0

Step-by-step explanation:

Answer:

y = 3x

Step-by-step explanation:

formula = y = mx + b

m = slope

b = y-intercept (but we dont see it here, it goes through the point 0)

To find slope do rise over run ( y/x)

r/r = 3/1 = 3

The slope is 3

y = 3x or y = 3x + 0 (same thing)

Hope this helped!

Have a supercalifragilisticexpialidocious day!

9514 1404 393

Answer:

  (c)  f(t)=21,000(0.85)^t

Step-by-step explanation:

Each year, the value is multiplied by 1-15% = 85% = 0.85. This is correctly shown in the function ...

  f(t)=21,000(0.85)^t

Answer:

Step-by-step explanation:

36/9

Answer:

The experimental probability depends on how many times you're spinning it and theoretical probability is stating what "would" happen if you're only spinning it once. After you get the theoretical probability, you would multiply that percentage by 25 to get the experimental probability percentage.

Step-by-step explanation:

The experimental probability depends on the number of times the experiment is conducted. The result from a theoretical probability is what would happen if the experiment is done once.

Probability determines how likely a stated event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0. Experimental probability is based on the result of an experiment that has been carried out multiples times

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Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

The correct option B. Path B: since velocity v is tangent to a circular path.

Any linear component of an object's motion that travels a circular path is called tangential velocity.

Thus, the rock will follow path B since velocity v is tangent towards the circular path.

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The complete question is

A girl attaches a rock to a string, which she then swings counter-clockwise in a horizontal circle. The string breaks at point P in the figure, which shows a bird's-eye view (as seen from above). Which path (A-E) will the rock follow?

A. Path A

B. Path B

C. Path C

D. Path D

E. Path E

I think first one is the answer

mark me as branlist and follow me

Answer:

\(\frac{1}{n^{18}} = (n^{-3})^6\)

Step-by-step explanation:

Given

\(\frac{1}{n^{18}}\)

Required

Determine its equivalent

\(\frac{1}{n^{18}}\)

Express 18 as 3 * 6

\(\frac{1}{n^{18}} = \frac{1}{(n^{3})^6}\)

This can be rewritten as:

\(\frac{1}{n^{18}} = (\frac{1}{n^{3}})^6\)

Apply the following law of indices:'

\(\frac{1}{a^b} = a^{-b}\)

\(\frac{1}{n^{18}} = (n^{-3})^6\)

Hence;

(d) is correct

Answer:D

Step-by-step explanation: cause im big brain

Answer:

-433

Step-by-step explanation:

Step 1: Define

-5(4 + 9s) - 7(4q - 6)

s = 7

q = 5

Step 2: Simplify expression

Distribute: -20 - 45s - 28q + 42

Combine like terms: -45s - 28q + 22

Step 3: Substitute

-45(7) - 28(5) + 22

Step 4: Evaluate

-315 - 140 + 22

-445 + 22

-433

The side lengths for the triangle are given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Then the length AC is given as follows:

\(AC = \sqrt{(5 - (-7))^2 + (0 - 3)^2}\)

AC = 12.4.

The length AB is given as follows:

\(AB = \sqrt{(-3 - (-7))^2 + (6 - 3)^2}\)

AB = 5.

The length BC is given as follows:

\(BC = \sqrt{(5 - (-3))^2 + (6 - 0)^2}\)

BC = 10.

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The z-score for the given normally distributed data of typing test is 3.33 and its left and right p -value is equal to 0.9996 and 0.00043 respectively.

As given in the question,

Mean of the typing test 'μ' = 60 words per minutes

Standard deviation of the typing test 'σ' = 6 word per minutes

Number of words per minutes 'X' = 80

z- score = ( X - μ ) / σ

             = ( 80 - 60 ) / 6

             = 20 /6

             = 3.33

z-score graph for the given data indicates the left tailed p -value .

Using table:

left tailed p -value = 0.9996

Right tailed p - value = 0.00043

two tailed p- value = 0.00086

Two tailed confidence level is given by 0.9991

Therefore , the z-score of the given mean and standard deviation is equal to 3.33 and left and right p -value is 0.9996 and 0.00043 respectively.

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