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2 years ago

16, 13, 10 is this sequence arithmetic or geometric and determine the common difference/ ratio in simplest form

Mathematics

2 answers:

Yuliya22 [10]2 years ago

7 0

Hii!

_________________________________________________________

$\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}$

1. This sequence is arithmetic

2. The common ratio is 3.

$\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation.}}}\circ\leftharpoonup$

$\bullet$ Difference between arithmetic and geometric sequences

$\twoheadrightarrow\sf Arithmetic\quad sequences$ - In arithmetic sequences, we add the same amount to obtain the next term.

$\twoheadrightarrow\sf Geometric\quad sequences$ - In geometric sequences we multiply times the same amount to obtain the next term.

$\bullet$ Since we add the same amount to get the next term, the given sequence is arithmetic

$\twoheadrightarrow\sf Common\;difference:-3$

$\bullet$ In the given sequence we add -3, or subtract 3, to obtain the next term

Hope that this helped! Best wishes.

$\stackrel\ast{\textsl{Reach far. Aim high. Dream big.}}$

lina2011 [118]2 years ago

4 0

Answer:

It is arithmetic progression

Step-by-step explanation:

If wwe see, the numbers are going down by 3 each time, therfore the common difference is 3

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Penelope invested 60% of her retirement account in stocks and 40% in gold. Penelope believes that the return to stocks over the

hjlf

Answer:

1) mean = 21, standard deviation σ = 21.9317

2) the probability that Penelope's portfolio will earn at least 12% in the next 12 months is 0.6591

Step-by-step explanation:

Given the data in the question;

1. According to Penelope's beliefs, what are the mean rate of return and the standard deviation of return of her portfolio?

Mean μ = Return = ( 60% × 15) + ( 40% × 30 ) = 9 + 12 = 21

mean = 21

standard deviation σ = √( (0.6² × 25²) + ( 0.4² × 40² ) )

standard deviation σ = √( (0.36 × 625) + ( 0.16 × 1600 ) )

standard deviation σ = √( 225 + 256 )

standard deviation σ = √481

standard deviation σ = 21.9317

2) What is the probability that Penelope's portfolio will earn at least 12% in the next 12 months

so we are to find P( X > 12 )

converting into standard normal variable;

⇒ P( Z > X-μ / σ )

= P( Z > ( 12-21 / 21.9317 ) )

= P( Z > ( -9 / 21.9317 ) )

= P( Z > -0.41 )

FROM z-score table; P( Z > -0.41 ) is 0.3409

P( X > 12 ) = 1 - 0.3409

P( X > 12 ) = 0.6591

Therefore, the probability that Penelope's portfolio will earn at least 12% in the next 12 months is 0.6591

3 0

3 years ago

Write x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers.

Mariulka [41]

X² − 6x + 7 = 0

Let's complete the square [x²-6x+(??)²] -(??)² +7 = 0

As you noticed we have added the unknown square & also subtract the same so that not to change the equation

The question now is to calculate this square (??)²

We know that the middle term (6x) is twice the square root of the 1st times the square root of the 2nd, That is 6x=2x (multiply) √(??)²

6x = 2x?? & ??=6x/2x===> ?? =3 & (??)² =9

Hence plug (??)² into the equation above:

x² - 6x + 9 - 9 +7 =0

(x²-6x+9) -9 + 7 =0

(x-3)² -2 =0 ====> (x-3)² = 2 (that is B)

7 0

4 years ago

Read 2 more answers

AREA, PERIMETER & VOLUME QUESTION

MrRissso [65]

Answer:

1. Case B

2. 9 cm³

3. 20 cm.

4. 4.5 m³

Step-by-step explanation:

Question 1: We are required to fit a drum having volume 14,000 cm³.

We know that the volume of cylinder = πr²h, where r is the radius and h is the height. So, according to the cases:

A. Here, r = 100 mm = 10 cm, h = 300 mm = 30 cm.

So, volume of the drum = πr²h = $\pi \times 10^{2} \times 30$ = 9424.78 cm³.

We cannot put the given drum inside this drum.

B. Here, r = 200 mm = 20 cm, h = 30 cm.

So, volume of the drum = πr²h = $\pi \times 20^{2} \times 30$ = 37699.11 cm³.

C. Here, r = 32 cm, h = 250 mm = 25 cm.

So, volume of the drum = πr²h = $\pi \times 32^{2} \times 25$ = 80424.77 cm³.

Out of options B and C, the smallest volume is in CASE B i.e. 37699.11 cm³.

So, Case B is the correct option.

Question 2: We have the dimensions of the speaker as,

Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m

Now, Volume of a cuboid = L×W×H

Thus, volume of the speaker = 0.45 × 0.4 × 0.5 = 0.09 m³ = 9 cm³.

Question 3: We have that the volume of the speaker is 30,000 cm³.

Also, Length = 30 cm = 0.45 m, Height = 500 mm = 50 cm.

So, volume of the speaker = L×W×H

i.e. 30,000 = 30 × W × 50

i.e. W = $\frac{30,000}{1500}$

i.e. W = 20 cm.

Hence, the width of the speaker is 20 cm.

Question 4: We have the dimensions as,

Base= 2 m, Length = 3 m, Height = 1.5 m

So, the volume of prism = $\frac{base\times height}{2} \times length$

i.e. Volume = $\frac{2\times 1.5}{2} \times 3$

i.e. Volume = 4.5

Thus, volume of the sand needed to be filled is 4.5 m³.

7 0

4 years ago

The greatest of four consecutive even integers is 14 less than twice the smallest integer. What are the integers

kakasveta [241]

20,22,24,26 is the answer

7 0

3 years ago

Kali and Ryan are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and apple cheesecake

valentina_108 [34]

Answer:

New York style cheesecake: $6 Apple cheese cake: $7

Step-by-step explanation:

Ryan and Kali sold the same amount of apple cheesecakes which means the New York cheesecakes differed in amount. Ryan sold 2 more than Kali so the difference in amount would be the cost of 2 New York cheese cakes.

Ryan made $91 and Kali made $79. Since they sold the same amount of apple cheesecakes, we can use their difference in money made to find the cost of 2 New York cheesecakes. So take away 79 from 91 and you get 12. $12 is the price of 2 New York cheesecakes. So take the 12 and divide it by 2. You get 6. $6 is the price of one New York cheesecake.

To find the amount of one apple cheesecake, you just need to multiply the amount of New York cheesecakes Kali sold by the price of 1 New York cheesecake. So 6 multiplied by 12 is equal to 72. Take the money Kali made and take away 72 from it. You get 7. 7 is the cost for one apple cheesecake. $7 for 1 cheesecake.

I hope this helps!

8 0

3 years ago