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frez [133]
3 years ago
5

Given a sequence is defined by the explicit definition t_n= n^2+nt n = n 2 + n, find the 4th term of the sequence. (i.e. t_4t 4)

Mathematics
2 answers:
Ne4ueva [31]3 years ago
7 0

<em>*100% CORRECT ANSWERS</em>

kykrilka [37]3 years ago
5 0

Answer:

Question 1:  20

Question 2: 27

Step-by-step explanation:

Question 1:  

Given a sequence is defined by the explicit definition t_{n} = n^{2} + n

Therefore, the 4th term i.e. t_{4} = 4^{2} + 4 = 20 (Answer)

So, the third option is correct.

Question 2:  

Given a sequence is defined by the explicit definition t_{n} = 2^{n} - n

Therefore, the 5th term i.e. t_{5} = 2^{5} - 5 = 27 (Answer)

So, the third option is correct.

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(3 marks) A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year. The battery live
Ksenya-84 [330]

Answer:

0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year

This means that \mu = 3, \sigma = 0.5

What is the probability that a given battery will last between 2.3 and 3.6 years?

This is the p-value of Z when X = 3.6 subtracted by the p-value of Z when X = 2.3. So

X = 3.6

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.6 - 3}{0.5}

Z = 1.2

Z = 1.2 has a p-value of 0.8849

X = 2.3

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.3 - 3}{0.5}

Z = -1.4

Z = -1.4 has a p-value of 0.0808

0.8849 - 0.0808 = 0.8041

0.8041 = 80.41% probability that a given battery will last between 2.3 and 3.6 years

4 0
2 years ago
I need help with this​
Natali [406]

Answer: 1,004.8 cubic meters (choice D)

Work Shown:

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*8^2*15

V = 1,004.8

8 0
2 years ago
Read 2 more answers
What is the distance between the two points (5, -2) and (-3, 8)?
galben [10]

Answer:

  2√41 ≈ 12.81 units

Step-by-step explanation:

The distance between two points is conveniently found using the distance formula:

  d = √((x2 -x2)^2 +(y2 -y1)^2)

  d = √((-3-5)^2 +(8-(-2))^2) = √(64 +100) = 2√41 ≈ 12.81 . . . units

6 0
3 years ago
What is 8/9-1/2 in simplest form
xenn [34]
First, we must find common denominators in order to subtract the terms. we can multiply 8/9 by 2/2 and 1/2 by 9/9.
we get:
16/18-9/18
16-9= 7 and we keep the same denominators, so our final simplified answer is:
7/18
hope this helped!! xx
6 0
2 years ago
What is the length of the pillow
Allushta [10]

Answer:

It would be nice to have the equation and/or picture, however I am giving a list of common pillow sizes for reference.

Step-by-step explanation:

Pillow size: Metric Measurements (cm) Imperial Measurements

Standard                     (51 x 66 cm)          20" x 26"

Queen                     (51 x 76 cm)            20" x 30"

King                     (51 x 92 cm)            20" x 36"

European square      (66 x 66 cm)            26" x 26"

3 0
3 years ago
Read 2 more answers
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