write the polynomial in standard form.Then name the polynomial based on its degree and number of terms.6 – 2x3 – 3x + 6x3
2 answers:
Answer:
Standard form
Name the polynomial based on its degree is cubic polynomial
Name the polynomial based on number of terms is trinomial.
Step-by-step explanation:
Consider the given polynomial
We have to write the polynomial in standard form and Then name the polynomial based on its degree and number of terms.
Consider the given polynomial
We first simplify the given polynomial by adding like terms,
LIKE TERMS are term having same variable with same power.
Here, are like terms,
Thus adding both we get,
Thus, polynomial becomes,
In standard form, terms are arranged in decreasing order of power of variables.
can be written as
Thus, the given polynomial has highest power of 3 so its a cubic polynomial on the basis of degree.
and Since, it consist of three terms so it is a trinomial on the basis of number of terms.
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Answer:
a)
b)
c) n=62
d) n=138
Step-by-step explanation:
Note: "Each chip contains n transistors"
a) A chip needs all n transistor working to function correctly. If p is the probability that a transistor is working ok, then:
b) The memory module works with when even one of the chips is defective. It means it works either if 8 chips or 9 chips are ok. The probability of the chips failing is independent of each other.
We can calculate this as a binomial distribution problem, with n=9 and k≥8:
c)
This equation was solved graphically and the result is that the maximum number of chips to have a reliability of the memory module equal or bigger than 0.9 is 62 transistors per chip. See picture attached.
d) If the memoty module tolerates 2 defective chips:
We again calculate numerically and graphically and determine that the maximum number of transistor per chip in this conditions is n=138. See graph attached.
Answer:
Step-by-step explanation:
Hello!
You have the hypothesis that the average weight loss for rubber after an abrasion test is less than 3.5 mg. To test this a large sample of pieces of rubber were sampled and subjected to the abrasion test.
With the given information you must test whether the researcher's hypothesis is sustained or not.
The study variable is,
X: Weight loss of rubber cured in a certain way after being subjected to the abrasion test. (mg)
There is no information about the variable distribution, but since it is said that the sample is a "large number" I'll take it as if it is bigger than 30 and apply the Central Limit Theorem to use the approximation of the sample mean to normal. This way I can use the Z-statistic for the test.
Symbolically the statistic hypothesis is:
H₀: μ ≥ 3.5
H₁: μ < 3.5
α: 0.05 (since is not listed, I'll choose one of the most common signification levels)
You have a one-tailed critical region, this means the p-value will also be one-tailed to the left of the distribution (i.e. →-∞)
The formula of the statistic is:
Z= <u> X[bar] - μ </u> ≈ N(0;1)
δ/√n
To calculate the statistic you have to use the information given.
The sample mean X[bar]= 3.4 mg
Upper bond of 95% CI= 3.45 mg
The basic structure of a CI for the mean is
"estimator" ± "margin of error"
Upper bound is "estimator" + "margin of error"
Using the formula:
Ub= X[bar] + d ⇒ 3.45= 3.4 + d
⇒ d= 3.45 - 3.4 = 0.05
Where d is the margin of error
d= * (δ/√n)
d= * (δ/√n)
d/= (δ/√n)
(δ/√n)= 0.05/ 1.96 = 0.0255
(δ/√n) is the denominator in the formula, corresponds to the standard deviation of the distribution.
Now you have all values and can calculate the statistic under the null hypothesis:
Z= <u> 3.4 - 3.5 </u> = -3.92
0.0255
And the p-value:
P(Z ≤ -3.92) = 0.000044 ⇒ My Z- table goes up to P(Z ≤ -3.00) = 0.001, so using strictly the table I can say that the probability is less than 0.001.
To calculate the exact probability I've used a statistic program.
p-value < 0.001
I hope it helps!