Compute successive differences of the terms.
If they are all the same, the sequence is arithmetic and the common difference is the difference you have found.
If successive pairs of differences have the same ratio, the sequence is geometric and the common ratio is the ratio you have determined.
Example of arithmetic sequence:
1, 3, 5, 7
Successive differences are 3-1 = 2, 5-3 = 2, 7-5 = 2. All the differences are 2, which is the common difference of the sequence.
Example of geometric sequence:
1, -3, 9, -27
Successive differences are -3-1 = -4, 9-(-3) = 12, -27-9 = -36. These are not the same, so the sequence is not arithmetic. Ratios of successive pairs of differences are 12/-4 = -3, -36/12 = -3. These are the same, so the sequence is geometric with common ratio -3.
According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.
The answer is 5.35, 275, 336, and 535
''Two one-step equationsx + 7 = 10x = 7-7 = 10 - 7x = 3
y + 47 = 20y = 47 - 47 = 20 - 47y = 27
Two equations that contains fractions + 2 + 3 = 55/5 = or 1
+ 12 + 7 = 1919/20 =
Distributive property2x - 4(+4) = 10(+4)2x - 16 = 402x - 16 + 16 = 40 + 162x = 5656 ÷ 2 = 28x = 28
Decimalsx = 1.2 + 7.8 ÷ 3(5)1.2 + 7.8 = 99 ÷ 3 = 33 x 5 = 1515.0
One real-world problem that is solved by an equationJohnny deposits $2,000 into a bank account. If the interest rate is 5% per month how much will he have gained in interest in 6 years?5% of 2,000 is 100100 x 12 = 1,2001,200 x 6 = 7,200Johnny would gain $7,200 in 6 years''
hope this helps
Answer:
a. P(x = 0 | λ = 1.2) = 0.301
b. P(x ≥ 8 | λ = 1.2) = 0.000
c. P(x > 5 | λ = 1.2) = 0.002
Step-by-step explanation:
If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:
a. What is the probability of selecting a carton and finding no defective pens?
This happens for k=0, so the probability is:
b. What is the probability of finding eight or more defective pens in a carton?
This can be calculated as one minus the probablity of having 7 or less defective pens.
c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?
We can calculate this as we did the previous question, but for k=5.
