Answer:
1) Is the pattern an arithmetic sequence?
Yes it is
2)Identify a and d.
a = First term = 2
d = Common difference = 2
3) Write the 50th term of the sequence.
50th term = 100
4) Find the total number of logs in the first 10 rows.
= 1010 logs
Step-by-step explanation:
Is the pattern an arithmetic sequence?
Yes it is
2) Identify a and d.
A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on,
The formula for arithmetic sequence =
an = a+ (n - 1)d
a = First term
d = Common difference
For the above question:
a = 2
d = Second term - First term
= 4 - 2
d = 2
3) Write the 50th term of the sequence.
Using the formula for arithmetic sequence
an = a+ (n - 1)d
a = 2
n = 50
d = 2
a50 = 2 + (50 - 1)2
= 2 + (49)2
= 2 + 98
= 100
The 50th term = 100
4)Find the total number of logs in the first 10 rows.
Sum of first n terms = n/2(a + l)
n = 10
a = first term = 2
We are told that there are 200 logs in the bottom row, hence:
l = last term = 200 logs
Hence,
Sn = 10/2×[ (2 + 200
= 5(202)
= 1010 logs
Answer:
Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.
Step-by-step explanation:
We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.
<u><em>Let </em></u>
<u><em> = sample mean comprehensive strength</em></u>
The z-score probability distribution for sample mean is given by;
Z = 
~ N(0,1)
where, 
= population mean comprehensive strength = 5500 psi
= standard deviation = 100 psi
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P( > 4985 psi)
P( > 4985 psi) = P( > 
) = P(Z > -15.45) = P(Z < 15.45)
= <u>0.99999</u>
<em>Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.</em>
Please note that pi has just one value. The only difference stems from round-off error when you don't use all of the digits following "3.14159 ... " to represent the value of pi. The formula for circumference is C = 2 pi r, or C = pi d,
where r=radius and d=diameter.
Circle A: Diameter 9 inches and Circumference of 28.26 inches
If the diameter is 9 inches, then C = 28.26 inches = pi (9 inches). Divide 28.26 inches by 9 inches. Note that you MUST round off the ratio (pi) that you obtain, since 28.26 has 4 significant figures and 9 has just one.
28.26
------- = 3.14, but because 9 has just one significant figure, you must round
9 this 3.14 to just 3.
Answer:
isn't it 28
Step-by-step explanation:
