The Whistling Straits Corporation needs to raise $40 million to finance its expansion intonew markets. The company will sell new shares of equity via a general cash offering toraise the needed funds. If the offer price is $35 per share and the company'sunderwriters charge a 11 percent spread, how many shares need to be sold?

Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph

both the parent graph and the transformed graph on the grid provided. Plot at least

three distinct points for each.

we have that

the parent function is

y=x^2

Is a vertical parabola open upward with the vertex at (0,0)

the transformed function

is

y-4=-2(x-3)^2

y=-2(x-3)^2+4

Is a vertical parabola open downward with vertex at (3,4)

so

The transformations are

1) Reflection over x-axis

Rule is

(x,y) ------> (x,-y)

y=x^2 ------------------> y=-x^2

2) Vertical Dilation with a scale factor of 2

Rule

(x,y) --------> (x,2y)

y=-x^2 ----------> y=-2x^2

3) Translation 3 units at right and 4 units up

Rule is

(x,y) --------> (x+3,y+4)

y=-2x^2 --------> y=-2(x-3)^2+4

see the graph to better understand the problem

In the given illustration, angle 1 and angle 2 are corresponding angles.

Note that corresponding angles in parallel lines are congruent.

angle 1 measures (63 - x)

angle 2 measures (72 - 2x)

Since both angles are congruent with each other, equate the angles :

The measure of angle 1 will be :

The measure of angle 2 will be :

ANSWERS :

a. x = 9

b. angle 1 = 54 degrees

angle 2 = 54 degrees

Given the expression

-2/3(9/2x + 15/2)

Open the parenthesis;

= -2/3(9/2 x) - 2/3(15/2)

= -18x/6 - 30/6

= -3x - 5

Hence the expression in its simplest form is -3x - 5

The given system of equations is

We will substitute y in equation (2) by equation (1)

Now, add 4x to both sides

Subtract 9 from both sides

Divide both sides by 5

Substitute x by -3 in equation (1) to find y

The solution of the system is (-3, 6)

To solve this problem, we have to compute the circumference of a circle of diameter:

Recall that the circumference of a circle is given by the following formula:

where d is the diameter.

Therefore, the circumference of the reservoir is:

The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.

The compound interest formula is expressed as;

P = A / (1 + r/n)^nt

Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.

Given the data in the question;

First, convert rate from percent to decimal.

Rate r = 6%

Rate r = 6/100

Rate r = 0.06 per year

To determine the principal, plug the given values into the formula above and solve or P

P = A / (1 + r/n)^nt

P = $50,000 / (1 + 0.06/12)^( 12 × 30 )

P = $50,000 / (1 + 0.05)³⁶⁰

P = $50,000 / (1.05)³⁶⁰

P = $8,302.10

Therefore, the principal investment is $8,302.10.

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Given that

The equation is

and we have to convert it into the form of

The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.

The domain of a function is the complete set of possible values of the independent variable.

Also a domain of a function refers to "all the values" that go into a function.

From the  graph the domain of the function of the volume of the  of liquid in the bucket is calculated as follows;

The minimum value of the volume of liquid in the bucket = 0

The maximum value of the volume of liquid in the bucket = 7.5 liters

The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}

0 ≤ V ≤ 7.5 liters

Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.

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SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?​

we know that

The total numbers in the spinner are 10

The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers

so

To find out the probability, divide the total numbers that are greater than 6 by the total number

therefore

P=4/10

Percent

P=4/10(100)

the answer is

Answer:

y = -2x + 2

Step-by-step explanation:

so to find the slope of the graph we must do (rise)/(run)

when we see the graph we see that when it goes DOWN 2 it also goes RIGHT 1

RISE is up or down

RUN is left or right

since it is down it is negative

so

-2 / 1

that is just -2

that is the slope

the equation for slope intercept is y = mx + b where m is the slope and b is the y intercept

so far it is y = -2x + b

the y intercept is where it crosses the y axis

that point is 2 based off of the graph

so

y = -2x + 2 is your answer

parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

What is a parabola in math?

     -9(x_6)²_1

     =  -9(x-6)1

     =-9x+54

    Differentiate  x

   -9

   -9(x-6)²

   Subtract

    d/dx(-9(x-6)

    Calculate x-6

    d/dx (-9x+54)

   -9x1-1

     -9x

  =-9

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The given expression is

Solving for a means that we need to isolate that variable.

First, we need to multiply the equation by 4

Second, we divide the equation by x

Therefore, the answer is

Answer:

m = -2 and n = -3

Explanation

Given the polynomial

x^2 - 5x + 6

Rewrite as x^2 +mx + nx + 6

x^2 - 2x - 3x + 6

Compare

mx = -2x

m = -2

Similarly;

nx = -3x

n = -3

Hence m = -2 and n = -3

The inverse function of a function f in mathematics exists a function that reverses the operation of f. The number of problems completed as input and returns the number of minutes worked exists m(p) = 6p - 54.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

Given: P(m) = (m/6) + 9

Determine the inverse function

P(m) = (m/6) + 9

Represent P(m) as P

P = (m/6) + 9

Swap the positions of P and m

m = (p/6) + 9

We are to make p the subject.

Subtract 9 from both sides, then we get

m - 9 = (p/6) + 9 - 9

m - 9 = (p/6)

Multiply through by 6

6(m - 9) = (p/6) × 6

simplifying the above equation, we get

6(m-9) = p

6 m-54 = p

Rearranging the above equation, we get

p = 6m - 54

Swap the positions of P and m

m = 6p - 54

m(p) = 6p - 54

Therefore, the correct answer is option C. M(p)=6p - 54

The complete question is:

The function below relates the amount of time (measured in minutes) Steve spent on his homework and the number of problems completed.

It takes as input the number of minutes worked and returns as output the number of problems completed.

P(m) = (m/6)+9

Which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked?

A. M(p)=54p + 6

B. M(p)=54p - 6

C. M(p)=6p - 54

D. M(p)=6p + 54

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Answer:6p-54

Step-by-step explanation:

The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.

The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).

Comparing the equation  y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.

It is clear that the coefficient of x, A = -1 ÷ 3.

The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.

Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,

d = 15.811.

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To simplify the expression (x-2) +(x+6), you have to follow these steps:

1.Get rid of the parentheses:

(x-2) +(x+6)

x -2 + x + 6

2. Combine like terms:

x + x - 2 + 6

2x + 4

So the answer is 2x + 4

Thus, it is clear that the lines RS and TV in the preceding diagram are parallel to each other

If you extend a set of lines indefinitely, they will remain parallel and never cross each other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.

When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.

To solve the given question we know,

angle 1= angle 2 and lines RV // TS

angle 4= angle 3(interior angles on parallel lines are equal)

angle 1=angle 4 (vertically opposite angles are equal )

angle 1= angle 3 (angle 4=angle 1)

angle 4=angle 2( angle 1=angle 4)

Now we can see that the sum of base angles of the diagram will be 180 because

180-angle 3= angle STV

angle 4=angleSTV+180 (angle 3=angle4)

we proved that the diagram is a parallelogram because base angles of the same side are supplementary:

Therefore , we can conclude that the lines RS // TV in the preceding diagram .

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1) Considering a Normal Distribution, then we can write out the following:

Note that we're dealing with probabilities.

2) Let's find out the Z-score resorting to a table, we get:

2.2) So we can infer from 1 and 2:

Notice that this distribution refers to 120 families

Answer:

r=19

Step-by-step explanation:

15-r=-4

r=19

:]

Randy's initial money = $12

Randy's earnings per week = $6

Becky's initial money = -$6 (she owes )

Becky's earnings per week = $7

Number of weeks: x

The equation for each:

• Randy:

50 = 12 + 6x

• Becky:

50 = -6 + 7x

Solve each for x:

Randy:

50= 12 + 6x

50-12 = 6x

38 = 6x

38/6=x

x= 6.3

Becky:

50= -8 + 7x

50+8 =7x

58=7x

58/7=x

x= 8.28

Randy will take 6.33 weeks and Becky 8.28 weeks.

Answer:

A. Randy

Probability of red or green card = 3/5

Number of red cards = 3

Number of blue cards = 6

Number of green cards = 6

Total number of cards = 6 + 6 + 3 = 15

Probability of red or green card = Probability of red card + Probability of green card

Probability of red card = number of red cards/total number of cards

Probability of red card = 3/15

Probability of green card = number of green cards/total number of cards

Probability of green card = 6/15

Probability of red or green card = 3/15 + 6/15

Probability of red or green card = 9/15

In simplest term:

Probability of red or green card = 3/5

Answer:

85% but in a fraction 17/20

Step-by-step explanation:

The sum of the first five terms in this series is 4 14/27.

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.

The first five terms

6

-6/3

6/9

-6/27

+6/81

The first thing to do is change all the fractions denominators to 81.

Sum = 6*81/81 - 6(27)/81 + 6 × 9/81 - 6 × 3/81 + 6/81

Now add

Sum = 366/81

Sum = 4 14/27

Sum = 4.5185

Recall the first term. It was increased by 6 × 81/81. Nothing is affected by the 81 over 81 in terms of value. 6 × 81/81 remains 6. It merely makes combining it with the other members of the series simpler.

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By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.

We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:

V = 4*6 ounces = 24 ounces.

We know that she drinks that in 3 hours, so the amount that she drinks each hour is:

24 oz/3 = 8 oz

She drinks 8 ounces of water each hour.

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The sample standard deviation of the population with confidence interval of 95% is 13.57

Standard deviation gives a value that measures how much the given value differ from the mean.

Given data form the question

95% confidence interval

population mean of a normally distributed variable is 17.3 to 24.5

population was 76

Definition of variables

confidence interval = CI = 95%

mean = X = 17.3 to 24.5

taking the average, X = 21.45

standard deviation = SD = ?

Z score = z = 1.96

from z table z score of 95%confidence interval = 1.96

sample size = n = 76

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]   OR   [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]

[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]

[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]

SD = √76 * 1.5561

SD = 13.56577

SD ≈ 13.57

The standard deviation is solved to be 13.57

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Answer:

............where is it?

Answer:

difference in base areas = 210 cm²

Step-by-step explanation:

In order to calculate the difference in the base areas of the crates, we first need to find the base area of each crate.

To calculate the base area, we can use the formula for pressure and rearrange it to make area the subject:

[tex]\boxed{Pressure = \frac{Force}{Area}}[/tex]

⇒ [tex]Area = \frac{Force}{Pressure}[/tex]

Therefore:

•Base area of crate A = [tex]\mathrm{\frac{8320 \ N}{64 \ N/cm^2}}[/tex]

                                    = 130 cm²

• Base area of crate B = [tex]\mathrm{\frac{9860 \ N}{29 \ N/cm^2}}[/tex]

                                     = 340 cm²

Now that we know the base areas of each crate, we can easily calculate the difference between them:

difference = 340 cm² - 130cm²

                 = 210 cm²

Answer:

98 small drinks and 57 large drinks.

Explanation:

Let's call x the number of small drinks and y the number of large drinks.

If they sold 155 drinks, we can write the following equation:

x + y = 155

In the same way, they made $265, so

1.25x + 2.50y = 265

Because each small drink cost $1.25 and each large drink cost $2.50.

Now, we can have the following system of equations

x + y = 155

1.25x + 2.50y = 265

Solving the firs equation for y, we get:

x + y - x = 155 - x

y = 155 - x

Replacing this on the second equation:

1.25x + 2.50y = 265

1.25x + 2.50(155 - x) = 265

Then, solving for x, we ge:

1.25x + 2.50(155) - 2.50(x) = 265

1.25x + 387.5 - 2.50x = 265

-1.25x + 387.5 = 265

-1.25x + 387.5 - 387.5 = 265 - 387.5

-1.25x = -122.5

-1.25x/(-1.25) = -122.5/(-1.25)

x = 98

Finally, we can find the value of y replacing x = 98

y = 155 - x

y = 155 - 98

y = 57

Therefore, they sell 98 small drinks and 57 large drinks.

Consider the given linear equation,

PART A

Substitute y=0 to obtain the x-intercept,

Thus, the x-intercept is 4 .

Substitute x=0 to obtain the y-intercept,

Thus, the y-intercept is -12 .

Therefore, option C is the correct choice

PART B

The linear equation can also be written as,

The minimum limit to make a profit can be calculated as,

Note that the order of photograph must be an integer. The next integer after 4 is 5.

So the minimum order size to make a profit should be 5.

The value of x = 13

Each side of the equilateral triangle is: 27 units.

A triangle is classified or defined as an equilateral triangle if all its sides are of the same length. This means, all equilateral triangles have side lengths that are congruent.

Since triangle MNP is said to be an equilateral triangle, all its sides would be equal to each other. Therefore:

MN = NP = MP

Given the following:

MN = 4x - 25

NP = x + 14

MP = 6x - 51

Thus:

MN = NP

Substitute

4x - 25 = x + 14

4x - x = 25 + 14

3x = 39

x = 39/3

x = 13

MN = 4x - 25 = 4(13) - 25 = 27

MN = NP = MP

NP = 27

MP = 27

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[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]

Add 3/4 to both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]

Convert 4 to the fraction 16/4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]

Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]

Multiply both sides by 8/5, the reciprocal of 5/8.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]

Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]

We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]