The price C, in dollars per share, of a high-tech stock has fluctuated over a twelve-year period according to the equation C= 14 +12x – x2, where x is in years. The price C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = 2x + 30. For what values are the two stock prices the same?

The 7th term of the geometric sequence with the first term being 5 and a common ratio of 2 is calculated using the formula Tn = [tex]a * r^{n-1}[/tex]. The 7th term is found to be 320.

The question asks us to determine the 7th term in a geometric sequence where the first term is 5 and the common ratio is 2. The formula for the nth term of a geometric sequence is given by
Tn = [tex]a * r^{n-1}[/tex], where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number. Substituting the given values into the formula, we can find the 7th term as follows:
T7 = [tex]5 * 2^{(7-1)}[/tex] = 5 * 2⁶ = 5 * 64 = 320. Hence, the 7th term of the geometric sequence is 320.

We have factorized the expression 'r2 - 6r - 9s2 + 9' into (r - 3)^2 - (3s)^2 and then used the difference of squares formula to find the factorization as (r - 3 + 3s)(r - 3 - 3s). So the correct answer is option A)

The question asked for the complete factorization of the expression r2 - 6r - 9s2 + 9. To factorize this, we can rewrite it into the formula form of a perfect square, which is a^2 - 2ab + b^2 = (a - b)^2.

Our expression fits this form when a = r and b = 3s. Following this, we can rewrite the expression as (r - 3)^2 - (3s)^2 = (r - 3 + 3s)(r - 3 - 3s). Therefore, the correct answer is option A) (r - 3 + 3s)(r - 3 - 3s)

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Express 0.41 as a fraction in the simplest form will be 41/100.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The number is 0.41.

Then express 0.41 as a fraction in the simplest form will be

⇒ 0.41

Multiply and divide by 100. Then we have

⇒ 0.41 x 100 / 100

⇒ 41 / 100

More about the fraction number link is given below.

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The function's formula that represents the number of pages Naoya has left to read at time t would be P(t) = 570 - 55t.

From the information given we know that Naoya reads at a rate of 55 pages per hour. After 4 hours of reading, he still has 350 pages left to read. This means that before he started reading, he had (55 pages/hour * 4 hours + 350 pages) = 570 pages in total. Since he reads at constant rate, the function that describes the remaining pages to read would be P(t) = 570 - 55t, where t represents the time in hours and P(t) is the number of pages left to read.

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The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.

The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.

The area of the new, larger office is 968 ft².

Answer:

Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

Step-by-step explanation:

Given : diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters.

To find : volume of the roll of pennies.

Solution : We have given that

Diameter of a penny =  19.05 millimeters.

Width of each penny = 1.52 millimeters.

Volume of cylindrical roll of penny = pi * r² * h

Where, r = radius , h =height

Radius = [tex]\frac{Diameter}{2}[/tex]

Radius=   [tex]\frac{19.05}{2}[/tex].

Radius = 9.525 mm

Plugging the values of r , h and pi = 1.14.

Volume of cylindrical roll of penny = pi * r² * h

Volume of cylindrical roll of penny =3.14 * (9.525)² * 1.52

Volume of cylindrical roll of penny = 433.02 mm³

Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

Therefore, Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

Answer:

[tex]y=\frac{3}{2}(x+4)[/tex]

Step-by-step explanation:

We are given

[tex]\frac{2}{3}y-4=x[/tex]

Since, we have to solve for y

so, we will isolate y on anyone side

Firstly, we add both sides by 4

[tex]\frac{2}{3}y-4+4=x+4[/tex]

[tex]\frac{2}{3}y=x+4[/tex]

Multiply both sides by 3

[tex]3\times \frac{2}{3}y=3\times(x+4)[/tex]

[tex]2y=3\times(x+4)[/tex]

now, we can divide both sides by 2

and we get

[tex]y=\frac{3}{2}(x+4)[/tex]

Let the age of the Jane be [tex] x [/tex]

So age of Helen =  [tex] x [/tex] + 8

Twenty years ago,

Age of Jane = [tex] x [/tex] - 20

And age of Helen = [tex] x [/tex] + 8 - 20 = [tex] x [/tex] - 12

Helen was three times as old as Jane

[tex] x [/tex] - 12 = 3 ([tex] x [/tex] - 20)

[tex] x [/tex] - 12 = 3 [tex] x [/tex] - 60

Add - 3[tex] x [/tex] on both sides,

[tex] x [/tex] - 3 [tex] x [/tex] - 12 = 3 [tex] x [/tex] - 3 [tex] x [/tex] - 60

-2[tex] x [/tex] - 12 = - 60

Add  12 on both sides

-2[tex] x [/tex] - 12  + 12 = - 60 + 12

-2[tex] x [/tex] = - 48

Divide both side by -2

[tex] \frac{-2x}{-2}=\frac{-48}{-2} [/tex]

[tex] x [/tex] = 24

Age of Jane = 24 yrs

Age of Helen = 32 yrs

The quotient of the expression (x - 1)/(7x² - 3x - 9) cannot be determined

How to determine the quotient of the expression

From the question, we have the following parameters that can be used in our computation:

(x - 1)/(7x² - 3x - 9)

From the above, we have

degree of the numerator = 1

degree of the denominator = 2

The degree of the numerator is less than the degree of the denominator

This implies that the quotient of the expression cannot be determined

B.pay as much as possible

Step-by-step explanation:

Debts are unpaid money that a person owes to its lenders. The lender can be any bank or any other financial institution or any person.

Long accumulated debts on banks, if not paid, can result in a person filing for bankruptcy. So, it is always good if you pay your debts on time.

Paying minimum or slightly more than minimum amount will result in paying more in the near future. It is possible that if you always pay minimum amount, you will not be able to clear debts anytime soon.

So, its best that if you have money, always pay as much as possible to get rid of your debt.  

Answer:

Step-by-step explanation:

Given:

1) Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years.

Published data - Already recorded data used

2)  Mia asked 20 random students at her school how many hours they spend on the computer each day.

Survey by Random sampling -- since a small size of whole population selected at random

3) Beatriz recorded the number of customers entering a store for each hour interval.

This is observational data because data was collected after really observing and recording the number of customers entering a store for each hour interval.

The coordinates are

A(-4,-3) →A'(-1, -1)

B(-1, 1) → B'(2, 3)

C(3, 5) → C'(6, 7)

D(2,-5) → D'(5,-3)

Step-by-step explanation:

Given the graph of figure whose coordinates are

A(-4, -3), B(-1, 1), C(3, 5), D(2, -5)

We have to find the coordinates of the image after a translation using T(x, y) → (x + 3, y + 2).

Coordinates after translation are

A(-4,-3) → A'(-4+3, -3+2)=A'(-1, -1)

B(-1, 1) → B'(-1+3, 1+2)=B'(2, 3)

C(3, 5) → C'(3+3, 5+2)=C'(6, 7)

D(2,-5) → D'(2+3, -5+2)=D'(5,-3)

which are required coordinates of the image after a translation of the figure below using (x, y) → (x + 3, y + 2).

hope this helps :)