Suppose you want to have $600,000 for retirement in 20 years. Your account earns 9% interest. How much would you need to deposit in the account each month?

Step-by-step explanation:

al nth term:

numerator:

[tex] = {n}^{2} [/tex]

denominator:

[tex] = n + 1[/tex]

so nth term :

[tex] = \frac{ {n}^{2} }{n + 1} [/tex]

b). 1; 11; 27; 49

first difference: 10; 16; 22

second difference :6

formula for 1st difference:3a+b

formula for 2nd difference:2a

Therefore:

2a=6

a=3

3a+b=10

sub in a

3(3)+b=10

9+b=10

b=1

sub into quadratic formula

[tex] {an}^{2} + bn + c[/tex]

[tex](3) {(1)}^{2} + (1)(1) + c = 1[/tex]

[tex]3(1) + 1 + c = 1[/tex]

[tex]3 + 1 + c = 1[/tex]

[tex]4 + c = 1[/tex]

[tex]c = - 3[/tex]

So Tn:

[tex]3 {n }^{2} + 1n - 3[/tex]

Step-by-step explanation:

a)

it is clearly a sequence of the square numbers over the numbers+1.

1/2 = 1²/(1+1)

4/3 = 2²/(2+1)

9/4 = 3²/(3+1)

16/5 = 4²/(4+1)

so, the nth term would be

n²/(n+1)

b)

an² + bn + c creates the sequence with increasing n (n = 1, 2, 3, 4, ...)

since for sequence the first starting value is often not generated by the general expression, we have to focus on n = 2, n = 3 and n = 4, and with that we get 3 equations with 3 variables (a, b, c) that we can solve :

n = 2

a×2² + b×2 + c = 11 = 4a + 2b + c

n = 3

a×3² + b×3 + c = 27 = 9a + 3b + c

n = 4

a×4² + b×4 + c = 49 = 16a + 4b + c

the first equation gives us

c = 11 - 4a - 2b

when we use this in the second equation, we get

27 = 9a + 3b + 11 - 4a - 2b = 5a + b + 11

b = 16 - 5a

now we use both of that in the third equation :

49 = 16a +4(16 - 5a) + 11 - 4a - 2(16 - 5a) =

= 16a + 64 - 20a + 11 - 4a - 32 + 10a =

= 2a + 43

2a = 6

a = 3

b = 16 - 5a = 16 - 5×3 = 16 - 15 = 1

c = 11 - 4a - 2b = 11 - 4×3 - 2×1 = 11 - 12 - 2 = -3

Answer: 49/30 or, 1 19/30

Multiply the total weight by the percentage

16 ounces x 0.03 = 0.48

0.48 ounces is fat

Answer:

-x² + 3x + 7

Step-by-step explanation:

• f(x) = 3x + 1

• g(x) = x² - 6

Then,

According to th' question :-

(f - g)(x) = f(x) - g(x)

= 3x + 1 - (x² - 6)

= 3x + 1 - x² + 6

= -x² + 3x + 7

Answer:

u=ABCDEF

Step-by-step explanation:

Answer:

27 20 13

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

It follows a pattern of -7 every time.

55,(-7) 48,(-7) 41, (-7)34

55-7=48

48-7=41

41-7=34

34-7=27

Hope this helps! Have a great day!

Answer: Long Division Calculator with Decimals

look this up see if it helps

Step-by-step explanation:

Answer: 1460720

To find volume just multiply them all-

4*19*31*10*62

1460720 ( i am not sure if those are the numbers you meant)

Answer:

  8x +12

Step-by-step explanation:

The outside factor is applied to each term inside parentheses:

  4(2x +3) = 4(2x) +4(3) = 8x +12

[tex]\huge\boxed{Hi\:there!}[/tex]

To simplify this expression, we should use the Distributive Property.

It states that

a(b+c)=ab+ac

Let's use it:

4(2x+3)

8x+12

That's the answer.

[tex]\huge\boxed{\boxed{\boxed{Hope\:it\:helps!}}}[/tex]

[tex]\huge\bold{Good\:luck!}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

Hello there, there are multiple ways of solving this problem, let me show you.

[tex]{\huge{\boxed{\mathbb{QUESTION}}}}}[/tex]

A Freight Train Travels 144 miles in 6 hours. How Far will it travel in 15 hours?

_________________

For this problem I will show you 2 methods.

[tex]{\huge{\boxed{\mathbb{METHOD\:ONE}}[/tex]

Cross multiplication, cross multiplication involves algebra to use.

Let x be our answer for this problem. Here is our it would look like

[tex]\frac{6}{144}=\frac{15}{x}[/tex], now we will cross multiply, here is what it'd look like now.

[tex]6x=2160[/tex], then do simple algebra and divide both sides by 6. and then we get [tex]x=360[/tex] miles in 15 hours.

_________________

[tex]{\huge{\boxed{\mathbb{METHOD\:TWO}}[/tex]

For method two we can look for the unit rate. Also known as our rate for one.

divide 144 by 6 and we get 24, then multiply it by 15 and we get 360.

_________________

[tex]{\huge{\boxed{\mathbb{EXACT\:ANSWER}}[/tex]

360 miles in 15 hours.

AnswerAnswers in explaination

Step-by-step explanation

PART A ANSWER: equation 1) y=1155x+982 and 2) y+100x+1000 both have x model the number of years and y model the investment they made.

PART B answer: The two equations I solved for above

Part C: if she goes with the first plan and invest for 20 years she'll get 24082 dollars and if she invest in the second one she'll get 3000 dollars. As you can see there is a huge difference between the two

Answer:

To calculate the ratio of an amount we divide the amount by the total number of parts in the ratio and then multiply this answer by the original ratio. We want to work out $20 shared in the ratio of 1:3. Step 1 is to work out the total number of parts in the ratio. 1 + 3 = 4, so the ratio 1:3 contains 4 parts in total.

Step-by-step explanation:

Step-by-step explanation:

hope it will help you a lot.......

Answer:

2 grams

Step-by-step explanation:

50 years is 5 half lives as 1 half life is 10 years.

64 divide 2 = 32-1 half life

32 divide 2 =16-2nd half life

16 divide 2 = 8-3rd half life

8 divide 2 = 4-4th half life

4 divide 2 = 2-5th half life

This means we will have 2 grams left of the radioactive substance after 50 years.

Answer:

23.5 feet per minute is the rate

Answer:

Step-by-step explanation:

The scale factor is the ratio between the man's actual height and the height of the drawing.

Scale = 64/4 = 16

Answer:

1/16

Step-by-step explanation:

the actual man is 16 times bigger than drawing.

[tex]\text{Given that,}\\\\s_1 = 5.95,\\\\s_2 = 5.42\\\\\\F= \dfrac{(s_1)^2}{(s_2)^2} = \dfrac{(5.95)^2}{(5.42)^2} = 1.21[/tex]

Answer:

i think the answe is A and B hope this helps

Step-by-step explanation:

Have a nice day!

Answer:

5.75 / 1.15 = 5

5 is an answer.

10/2 is also an answer.

25/5 is also also an answer.

100/20 is also also also an answer.

Answer:

let me check....

Step-by-step explanation:

(2,5) and (4,13)

y - y1 = y2 - y1

x - x1    x2 - x1

y - 5  = 13 - 5 = 8/2 = 4 x - 2     4 - 2

y - 5 = 4x - 8

y = 4x - 3

m = 4, c = -3

Answer:

A

Step-by-step explanation:

A has 11 boxes shaded in, whereas B only has 10. so A has more

Answer:

its 25.

Step-by-step explanation:because 50 divided by 2 is 25.

Answer:

40 units

Step-by-step explanation:

1) Find the side length of the square

Let the side be "s".

[tex]\rightarrow \frac{1}{2} \times s \times s = 50 \ \text{cm}^{2}[/tex]

[tex]\rightarrow s \times s = 50 \times 2[/tex]

[tex]\rightarrow s \times s = 100[/tex]

[tex]\rightarrow \sqrt{s \times s} = \sqrt{100}[/tex]

[tex]\rightarrow s = \±10[/tex]

[tex]\rightarrow s = 10 \ \text{units}[/tex]                                      (Side lengths can never be negative)

2) Find the perimeter of the square

[tex]\text{Perimeter of square = 4(s) = 4(10) = 40 units}[/tex]

Answer:

p = - [tex]\frac{2}{3}[/tex] , p = 2

Step-by-step explanation:

Using the discriminant to solve for p

Δ = b² - 4ac

The condition on the discriminant for 2 eeal and equal roots is

b² - 4ac = 0

Given

p²x² - (p + 2)x + 1 = 0

with a = p² , b = - (p + 2) , c = 1 , then

(- (p + 2) )² - 4p² = 0

(p + 2)² - 4p² = 0

p² + 4p + 4 - 4p² = 0

- 3p² + 4p + 4 = 0 ( multiply through by - 1 )

3p² - 4p - 4 = 0 ← in standard form

(3p + 2)(p - 2) = 0 ← in factored form

Equate each factor to zero and solve for p

3p + 2 = 0 ⇒ 3p = - 2 ⇒ p = - [tex]\frac{2}{3}[/tex]

p - 2 = 0 ⇒ p = 2

Answer:

some points that I found!

(0,-2), (-3,0), (-6, 2), keep it going from there, and then shade above the line

Answer:

y = 4x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x + 12 ← is in slope- intercept form

with slope m = 4

Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

To find c substitute (2, 3 ) into the partial equation

3 = 8 + c ⇒ c = 3 - 8 = - 5

y = 4x - 5 ← equation of parallel line