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2 months ago

The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting

Mathematics

1 answer:

Svet_ta [12.7K]2 months ago

5 0

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is: $a_n=6(3)^{n-1}$

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

$a_n=a(r)^{n-1}$

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

$a_n=a(r)^{n-1}\\a_5=6(3)^{5-1}\\a_5=6(3)^4\\a_5=6*81\\a_5=486$

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

$a_n=6(3)^{n-1}$

Here n=20

Calculating the 20th week

$a_n=6(3)^{n-1}\\a_{20}=6(3)^{20-1}\\a_(20)=6(3)^{19}\\a_{20}=6973568802$

15.9

Detailed explanation:

$\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9$

5 0

1 month ago

Igor recently immigrated to the UK. He was an experienced surgeon in his country but had to re-do his medical training in order

AnnZ [12381]

Answer:

a) The outlier is the point located at the bottom right of the graph

b) The plotted points resemble a line that has a positive gradient

c) By conducting correlation analysis, we can determine the strength of the correlation

Step-by-step explanation:

a) The problem presents a scenario where Igor, who has recently moved, is experienced but needs to retrain medically to practice in the UK

Thus, he corresponds to the outlier situated nearest to the graph's bottom right

b) According to the scatter graph, there's a direct relationship showing that as a doctor's age increases, their annual salary tends to climb as well

Referencing the graph:

Age Salary

22 £28000

26 £30000

34 £44000

38 £42000

42 £30000

42 £46000

50 £55000

The data points follow a line demonstrating the proportional increase of salary with age.

c) To reinforce this conclusion's reliability, correlation analysis should be conducted to ascertain the relationship between age and annual incomes.

4 0

1 month ago

Roxanne likes to fish. She estimates that 30% of the fish she catches are trout, 20% are bass, and 10% are perch. She designs a

lawyer [12517]

Response:

Detailed explanation:

3 0

13 days ago

Read 2 more answers

Question Number 12 You are a landscaper working on the design of a parking lot in a new shopping center. You are measuring the l

babunello [11817]

Answer:

$Length\: of\: D=37\frac{3}{16} \:feet$

Step-by-step explanation:

Here are the details provided:

The handicapped space measures $10\frac{1}{16}$ feet next to the curb.
The other three spaces each are $8\frac{3}{8}$ feet wide.
There are four lines separating the spaces, each line being $\frac{1}{2}$ foot long.

The Median D will be calculated as follows:

Width of the handicapped spot
3 times the width of the other spaces
4 times the width of the lines

$= 10\frac{1}{16} + (3 X 8\frac{3}{8})+(4 X\frac{1}{2})\\=\frac{161}{16} + \frac{3 X 67}{8}+\frac{4}{2}\\=\frac{161}{16} + \frac{201}{8}+\frac{4}{2}\\=\frac{161+402+32}{16}\\=\frac{595}{16}\\Length\: of\: D=37\frac{3}{16} \:feet$

7 0

1 month ago

Mrs Atkins is going to choose two students from her class to take part in a competition.

babunello [11817]

Given:
Total girls in class = 16.
Total boys in class = 14.
To determine:
The various combinations for selecting one girl and one boy.
Solution:
We have,
Total girls = 16
Total boys = 14
Thus,
The total combinations for selecting one girl from 16 girls = 16.
The total combinations for selecting one boy from 14 boys = 14.
Now, the various ways to select one girl and one boy amount to:
Therefore, the total number of combinations is 224.

6 0

1 month ago