PLEASE HELP<br> <br> <br> How do you simplify a fraction that involves variables

Margaret [11]

Answer:

Step-by-step explanation:

Since there is no single number we can add to one number in the sequence to get to the next one, this is not arithmetic. That means it's geometric, if it's a sequence at all. To get from 2 to 6 we multiply by 3. To get from 6 to 18 we multiply by 3. To get from 18 to 54 we multiply by 3. Therefore, this is in fact geometric and the common ratio is 3. The standard form of a geometric explicit formula is

$A_n=a_1(r)^{n-1$ where n is the position of a number in the sequence, a1 is the first number in the sequence, and r is the common ratio. We have then

a1 = 2 and r = 3. Therefore, the explicit formula is

$A_n=2(3)^{n-1$ and you can use this to find the value of any number in the sequence. Very handy; much more so than the recursive formula, which requires that all the numbers in a sequence be found in order in order to get to a desired value.

6 0

3 years ago

The staff at the arcola country club prepares tables for a wedding reception they are able to prepare 6 tables in 45 minutes how

Nezavi [6.7K]

4 hours=240 minutes
240 minutes=5 1/3 45 min. intervals
5 1/3 x 6 = 16/3 x 6 = 32

The staff can prepare 32 tables in 4 hours

8 0

4 years ago

#14, what is this answer ?

trapecia [35]

Answer:

option 3

Step-by-step explanation:

5 0

3 years ago

Three solid shapes A,B and C The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of

dmitriy555 [2]

Answer:

9:20

Step-by-step explanation:

Given:

Surface area of shape A = 9 cm²

Surface Area of shape B = 16 cm²

Ratio of volume of shape A to B = 27:125

Required:

Find the ratio of the height of shape A to the height of shape C.

Ratio of surface area (A:B)² = ratio of linear measures (A:B)

Thus,

(A:B)² = (A:B)

(A/B)² = (A/B)

$(\frac{A}{B})^2= (\frac{9}{16})$

Take the square root of both sides:

$(\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}})$

$\frac{A}{B} = \frac{3}{4}$

Ratio of volume of shape B to C = 27:125

Thus,

(B:C)³ = 27:125

$(\frac{B}{C})^3= (\frac{27}{125})$

Take the cube root of both sides:

$(3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})$

$\frac{B}{C} = \frac{3}{5}$

Therefore, ratio of lengths A:B:C =

3:4:C

A:3:5

To make them equivalent, we have:

9:12:C

A:4:20

Therefore, the ratio of the height of shape A to the height of shape C =

9:20

6 0

4 years ago

A cereal company is putting 1 11 of 3 33 prizes in each box of cereal. The prizes are evenly distributed so the probability of w

Black_prince [1.1K]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A cereal company is putting 1 of 3 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1/3. Adam wonders how many boxes he should expect to buy to get all 3 prizes. He carried out 32 trials of a simulation and his results are shown below.

3 12

4 4

5 5

6 5

7 0

8 0

9 2

10 2

11 0

12 2

Use his results to estimate the probability that it takes 9 or more boxes to get all 3 prizes. Give your answer as either a fraction or a decimal. P ( 9 or more boxes ) =

Answer:

P(x ≥ 9) = 18.75%

Step-by-step explanation:

A cereal company is putting 1 of 3 prizes in each box of cereal.

Adam is trying to find out how many boxes he should buy to get all 3 prizes.

He carried out 32 trials and got the following results.

We want to estimate the probability that it takes 9 or more boxes to get all 3 prizes.

No. of Boxes | frequency

3 | 12

4 | 4

5 | 5

6 | 5

7 | 0

8 | 0

9 | 2

10 | 2

11 | 0

12 | 2

9 or more boxes means equal to 9 boxes or greater than 9 boxes.

P(x ≥ 9) = No. of boxes equal or greater than 9/total no. of boxes

The total no. of boxes is 32

From the above data, count the number of boxes equal to or greater than 9. (6 times)

P(x ≥ 9) = 6/32

P(x ≥ 9) = 3/16

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

Therefore, there is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.

3 0

3 years ago

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PLEASE HELP How do you simplify a fraction that involves variables