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A sequence has an initial value (I) of -17 and its fourth term (a4) is 35. What is its general equation? Its 14th term?

aleksley [76]

Answer:

The sequence is an Arthemtic Progression

An=A1+(n-1)d

A1 is first term, An is nth term, n is number of term, and d is common difference

therefore

A4=35, A1= -17

A4=A1+(4-1)d

35= -17+3d

35+17=3d

52=3d

52/3=3d/3

14=d

common diffrence(d)=14

The general solution is given by

An= -17+(n-1)14

An= -17+14n-14

An= -31+14n

An= 14n-31

A14 term, means n=14

From An=A1+(n-1)d

A14= -17+(14-1)14

= -17+(13×14)

= -17+182

= 165.

Therfore, the 14th term is 165.

2. A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?

solution

common ratio(r)=4/5

eighth term(G8)=393216/3125

From Gn= G1r^(n-1)

G8 means n=8

G8=G1r^(n-1)

393216/3125=G1(4/5)^(8-1)

393216/3125=G1(4/5)^7

G1=(393216/3125)/(4/5)^7

G1=600

The first term is given by G1=600

Therefore

The General equation is given by

The General equation is given by Gn= 600(4/5)^(n-1)

3rd term (G3)

G3= G1(4/5)^(3-1) where n=3,

=600(4/5)^2

=600(16/25)

=384

Therefore, the 3rd term is given by G3= 384.

I have made some Corrections i messed up somewhere.

7 0

3 years ago

Since 201020102010, the town of Fall River has been experiencing a growth in population. The relationship between the elapsed ti

barxatty [35]

Answer:

48,558

Step-by-step explanation:

The function which models the relationship between the elapsed time, t in years, since 2010 and the town's population, P(t), is given as:

$P(t)=36800\cdot2^{^\dfrac{t}{25}}$

Now, 2020-2010=10 Years

Therefore we are required to calculate the population of the town 10 years after.

To do this, we simply substitute t=10 in the function.

$P(10)=36800\cdot2^{^\dfrac{10}{25}}}\\=48557.9\\\approx 48558$

According to the model, the population in Fall River will be 48,558 in the Year 2020.

7 0

4 years ago

Distinguish between an axoim and a theorem

Anton [14]

Answer:

An axiom is often a statement assumed to be true for the sake of expressing a logical sequence. ... These statements, which are derived from axioms, are called theorems. A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.

Step-by-step explanation:

I think this is right, but don't quote me on this.

7 0

3 years ago

A private ship carries two types of cargo: large crates and extra-large crates. Each type of crate weighs a specific amount.

Arisa [49]

Answer:

G. 32

Step-by-step explanation:

32 x 335 = 10720

16,100 - 10720 = 5380/190 = 28.3157894737

275 x 32 = 8800

18,800 - 8800 = 10,000/400 = 25 (This is the closer).

30 x 335 = 10,050

16,100 - 10,050 = 6050/190 = 31.8421052632

30 x 275 = 8250

18,800 - 8250 = 10550/400 = 26.375 (Same reason why it does't work)

25 x 335 = 8375

16,100 - 8375 = 7725/190 = 40.6578947368

25 x 275 = 6875

18,800 - 6875 = 11925/400 = 29.8125

24 x 335 = 8040

16,100 - 8040 = 8060/190 = 42.4210526316

24 x 275 = 6600

18,800 - 6600 = 12200/400 = 30.5

8 0

3 years ago

A professor has kept records on grades that students have earned in his class. If he wants to examine the percentage of students

AleksandrR [38]

Answer:

Pie chart

Step-by-step explanation:

Given that a professor has kept records on grades that students have earned in his class

He wants to examine the percentage of students earning the grades A, B, C, D, and F during the most recent term,

We have to find which kind of plot could he make

Box plot gives comparison for interval of scores this is to some extent helpful to find out the percentage of students getting a range of scores

Timeplot is irrelevant here. Dot plot will not be of much use.

Histogram is to some extent useful as box plot

But the best one is pie chart giving easy visual comparison for various grades A, B,C,D,E and F

8 0

3 years ago