Suppose y = 48 + 3(2n - 1) is an explicit representation of an arithmetic sequence for integer values n ≥ 1. Find the xth partial sum of the series, as a quadratic function, where x represents the term number.

Answers

Answer 1

Answer:

Answer: 3x2 + 51x

Step-by-step explanation:

Answer 2

Answer: $a_n=48+3(2n-1)$

The formula of the sum of the arithmetic sequence:
$S_n=(a_1+a__n)/(2)\cdot n$
calculate:
$a_1=48+3(2\cdot1-1)=48+3=51$
substitute
$S_n=(51+48+3(2n-1))/(2)\cdot n=(99+6n-3)/(2)\cdot n=(96+6n)/(2)\cdot n=3n^2+48n$
Your answer is:
$\boxed{f(x)=3x^2+48x}$

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2) The Club Auto Parts Company has just recently been organized. It is expected to experience no growth for the next 2 years as it identifies its market and acquires its inventory. However, Club will grow at an annual rate of 5% in the third and fourth years and, beginning with the fifth year, should attain a 10% growth rate which it will sustain thereafter. The last dividend paid was $0.50 per share. Club has a cost of capital of 12%. What should be the present price per share of Club common stock?

Answers

Answer:

$20.84

Step-by-step explanation:

div 1 = $0.50

div 2 = $0.50

div 3 = $0.50 x 1.05 = $0.525

div 4 = $0.525 x 1.05 = $0.55125

years 5 and beyond we need to use the growing perpetuity formula:

stock price = [div 4 x (1 + g)] / (r - g) = ($0.55125 x 1.1) / (12% - 10%) = $30.32

now to determine the current value of the stocks we must calculate the present value of the future dividends and stock price:

stock price = $0.50/1.12 + $0.50/1.12² + $0.525/1.12³ + $0.55125/1.12⁴ + $30.32/1.12⁴ = $0.45 + $0.40 + $0.37 + $0.35 + $19.27 = $20.84

Plz help on question 15 through 17

Answers

I believe 17, is 4
Number 15 is 1

Which is the smallest decimal?
A. 0.04
B. 0.4
C. 0.39
D. 0.049

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

b has the least zeros so that's closer to the whole numbers

What is 8.170 in word form

Answers

Answer:

eight and seventeen hundredths

Step-by-step explanation:

Answer:

eight and seventeen hundredths

Ten weeks ago Jerry bought stock at 211/2
; today the stock is valued at 203
/8
. We could say the stock
is performing at which of the following?
A. On par
B. Par equality
C. Below par
D. Above par

Answers

Since 211/2 = 105.5 and 203/8 = 25.375, it is quite clear that Jerry has lost money on this stock. So the correct answer is C. Below par.

Answer:

(c) Below par

Step-by-step explanation:

Ratio at which stock is bought = 211/2

= 105.5

Therefore, the par value = 105.5

Recent ratio of stock = 203/8

= 25.375

Value of stock today = 25.375

Since the ratio is decreased Hence, the value of stock is below par value.

At a concert 2/5 of the people were men, there were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert.

Answers

Final answer:

In solving the question, we establish two equations based on the condition provided, including the ratios among men, women, and children. Solving the equation, we find out that there were 270 people at the concert.

Explanation:

This question relates to the mathematical concept of ratio and proportion as well as fraction.

According to the question, 2/5 of the attendees at the concert were men and men outnumbered children by 45. First, let's make the number of children, x. So, the number of men will be x + 45. Because 2/5 of the total attendees were men, set up the equation: 2/5 * Total = x + 45.

There were 3 times as many women as children, thus the number of women will be 3x. So, the total number of people in the concert is the sum of the men, women, and children, which is (x + 45) + 3x + x. Simplifying this, we get 5x + 45 = Total. Therefore, if we substitute (x + 45) for 2/5 of the total in our original equation, we have 2/5 * (5x + 45) = x + 45. Solving this equation, we get x = 45.

So, if we substitute x=45 into our total equation, we get Total = 5(45) + 45 = 270. Therefore, there were 270 people at the concert.

Learn more about Ratio and Proportion here:

brainly.com/question/26974513

#SPJ12

This involves creating some equations.

First, these are what the letters I used stand for:

c = children

w = women

m = men

x = total population

Then, we must make an equation for each statement.

2/5x = m (2/5 of the people are men)

3c = w (there are 3 times as many women than children)

45+c = m (there are 45 more men than children)

Now, let's start plugging in our numbers:

x = all the men, women, and children

2/5(m+w+c) = m

2/5 (45+c +3c + c) = m [Now simplify]

2/5 (45 + 5x) = m [Now Distribute]

2/5(45) + (2/5)(5x) = m

2c + 18 = m [Above we stated that there were the same amount as men as c +45]

2c + 18 = 45 +c [Now set equal to c]

2c (-c) +18 = 45 +c (-c)

c+18 (-18) = 45 (-18)

c = 27

Now that we know that there was 27 children, we can plug 27 in for c in the other equations.

MEN = 27 + 45

WOMEN = 3(27)

CHILDREN = 27

Now add those three answers to find your total!

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