Factor the following:
3 n^4 + 21 n^3 + 27 n^2
Factor 3 n^2 out of 3 n^4 + 21 n^3 + 27 n^2:
Answer: 3 n^2 (n^2 + 7 n + 9)
Answer:
34
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [ 1, 6 ], thus
f(b) = f(6) = 6³ - 9(6) = 216 - 54 = 162
f(a) = f(1) = 1³ - 9(1) = 1 - 9 = - 8
average rate of change = 
= 
= 34
Answer:
Well I can't make a table but I can explain the answer.
Step-by-step explanation:
So you have $1,800 on a payment plan. In three months, the balance is 1,350. So 1,800-1,350=450. This means he paid $450 in three months. 450/3 is 150. He pays $150 a month. Then 2 months later, (5 months after purchase) he has balance is $1,050. 1,350-1,050=300. 300/2=150. Further evidence of the fact that he pays 150 dollars a month. This means that the 6th month, he will have $900 dollars left on the payment. 7th month... $850, 8th month... $600, 9th month... $450, 10th month... 300 dollars, 11th month... 150, and 12 month he will have paid off all of his computer. Hope it helps, sorry it is so long. Have a great day! :D
Answer:
A company produces electric insulators. The strength of the insulators is important since a broken insulator may cause a short circuit. Unfortunately, the strength varies significantly due to the material. Because of the expense, only a limited number of insulators could be tested. The engineers sampled 25 insulators (From a production run of 200), and conducted a destructive test to determine the force that was required to break the insulators. The mean value of this force was 1723 lbf with a sample standard deviation of 90 lbf. You may approximate the population standard deviation with the sample standard deviation for the following questions. a. Determine if the population is large enough or if a finite population correction (FPC) factor is needed. If so, what is the FPC factor? b. For 95% confidence, determine the margin of error (+ lbf) c. For these conditions, estimate the range of the probable population mean. Provide lower and upper values. For 95% confidence, determine the margin of error ( Assume the same mean and sample standard deviation. What is one advantage and one disadvantage of using 50 insulators instead of 25 insulators? d. lbf) if 50 insulators were tested.
Step-by-step explanation:
Answer:
The volume of the sphere is 1436 in³
The equation is
V = ⁴⁄₃ * 3.14 * (7ft)³
Step-by-step explanation:
radius = half of diameter
d = 14ft
r = 14ft / 2 = 7ft
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 7ft
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (7ft)³
V = 4.187 * 343 in³
V = 1436 in³
The volume of the sphere is 1436 in³
