What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, –0.04,

Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .? A. f(1) = 4, f(n + 1) = –2f(n) for n ≥ 1 B. f(

AlekseyPX

Answer: D. $f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n)$

Step-by-step explanation:

The given sequence: $4, -2,1,\dfrac{-1}{2},\dfrac14,....$

Here, first term: $f(1)=4$

Second term: $f(2)=-2$

Third term : $f(3)=\dfrac{-1}{2}$

It can be observed that it is neither increasing nor decreasing sequence but having the common ratio.

Common ratio: $r=\dfrac{f(2)}{f(1)}=\dfrac{-2}{4}=\dfrac{-1}{2}$

So, $f(n+1)=\dfrac{-1}{2}f(n)$ [as in G.P. nth term= $a_{n+1}=ar^n$ ]

Hence, correct option is D. $f(1) = 4,\ \ f(n+1)=\dfrac{-1}{2}f(n)$

5 0

2 years ago

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fis

maks197457 [2]

Answer:

p = 0.293

Conclusion:

"There is insufficient evidence to state that the distribution of fish in Green Valley Lake is not the same as the distribution of fish in Echo Lake."

Step-by-step explanation:

------------R/trout--O/trout---bass--catfish---total

GVL - - - 105 - - - 27 - - - - - 35--- 24 - - - 191

EL - - - - 135------- 48-------- 67 - - 43 - - - 293

Total - - 240 - - - 75 - - - - - 102--- 67 - - - 484

Note : GVL = GREEN VALLEY LAKE ; EL = ECHO LAKE.

H0: The distribution of fish caught in green valley is the same as that caught in Echo lake.

H1: The distribution of fish caught in Green Valley lake is different from that caught in Echo valley lake.

Using the chi-squared test statistic calculator ;

χ2 = 3.7269

p-value = 0.2925.

p-value = 0.293

Conclusion:

"There is insufficient evidence to state that the distribution of fish in Green Valley Lake is not the same as the distribution of fish in Echo Lake."

5 0

2 years ago

Write the equation of a line that is parallel to {y=-0.75x}y=−0.75xy, equals, minus, 0, point, 75, x and that passes through the

andrew-mc [135]

A straight line parallel to another is one that has the same slope. The generic equation of a line can be written as y-yo = m (x-xo). If we look for a parallel line that passes through the point (8.0). We should look for a line with the values m = -0.75, xo = 8, yo = 0. Substituting in the generic equation, we have that the line sought is y = -0.75 (x-8)

7 0

2 years ago

Which expressions can you use to find 75% of 56? Check all that apply.

alisha [4.7K]

Your answer would be B and C

7 0

2 years ago

Read 2 more answers

A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running a

Artemon [7]

The speed of the fox should be greater than the rabbit's speed in other to catch up, Hence, the speed of the fox must be 35/t + 40

The distance between the rabbit and fox, d = 35 feets

The rabbit's speed = 40 feets per second

Fox's speed = F

In other to obtain a specific speed for the fox, the time at which the fox is required to catch up with the rabbit should be given.

Let the time = t

Recall :

Speed = distance / time

Distance = speed × time

Rabbit's distance from fox after time t will be :

35 + (40 × t) = 35+40t

Fox's distance after time, t = fox speed × t = F × t

In other to catch up ; both fox and rabbit must be at the same distance ;

Rabbit's distance at time t = Fox's distance at time t

35+40t = Ft

To solve for F which is the fox's speed:

Divide both sides by t

(35+40t) / t = Ft/t

35/t + 40 = F

Hence, the fox' s speed must be : 35/t + 40

To obtain the exact speed of the fox, we must be given a specific time value.

Learn more : brainly.com/question/18112348

4 0

2 years ago

What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, –0.04, –0.14,