To calculate approximately the amount or value of something is called _________.
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A formal power series over R is a formal infinite sum f = X[infinity] n=0 anxn, where the coefficients an ∈ R. We add power series term-by-term, and two power series are the same if all their coefficients are the same. (We don’t plug numbers in for x, because we don’t want to worry about issues with convergence of the sum.) There is a vector space V whose elements are the formal power series over R. There is a derivative operator D ∈ L(V ) defined by taking the derivative term-by-term: D X[infinity] n=0 anxn ! = X[infinity] n=0 (n + 1)an+1xn What are the eigenvalues of D? For each eigenvalue λ, give a basis of the eigenspace E(D, λ). (Hint: construct eigenvectors by solving the equation Df = λf term-by-term.)
If a² + b² = c², then which of the following are also true? Select all that apply.Optionsa² - b² = c²b² + a² = c²c² + a² = b²c² - a² = b²c² - b² = a²
Which situation is best represented by the following equation? 45w + 123.95 = 753.95 A. Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes? B. Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes? C. Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes? D. Erica paid $753.95 for dance classes. She paid $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?
Scarlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
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Answer:
65.7 grams.
Step-by-step explanation:
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Answer:
1) h = -1/2t^2 +10t
2) h = -1/2(t -10)^2 +72
3) domain: [0, 20]; range: [0, 50]
Step-by-step explanation:
1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...
h = a(t -10)^2 +50
To find the value of "a", we must use another point on the graph. (0, 0) works nicely:
0 = a(0 -10)^2 +50
-100a = 50 . . . . . . subtract 100a
a = -1/2 . . . . . . . . . divide by -100
Then the standard-form equation is ...
h = (-1/2)(t^2 -20t +100) +50
h = -1/2t^2 +10t
__
2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.
h = -1/2(t -10)^2 +72
__
3.) The horizontal extent of the graph for Firework 1 is ...
domain: 0 ≤ t ≤ 20
The vertical extent of the graph for Firework 1 is ...
range: 0 ≤ h ≤ 50
abc14
determine whether each expression is a monomial
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Answer:
15
Step-by-step explanation:
abcdefghijknobeughriuwekhjtwu4igrjsnbei
Which of the following are true?
1. {a,c} ⊆ Z
2. a ∈ Z
3. {c} ⊆ Z
4. {c} ∈ Z
5. b ∈ Z
6. {a,b} ∈ Z
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(treat
as one element of
)
The power set of is
1. is true because both
and
.
2. is true.
3. is true (same reason as part 1).
4. is false because
does not contain the set
, rather just the element
itself.
5. is false because the element
on its own simply is not in
. That
does not mean
, but that
belongs to a subset of
.
6. is true.
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Answer:
(a) 0.0178 <= p <= 0.0622
(b) p <= 0.0586
Step-by-step explanation:
We have that the sample proportion is:
p = 12/300 = 0.04
(to)
For 95% confidence interval alpha = 0.05, so critical value of z will be 1.96
Therefore, we have that the interval would be:
p + - z * (p * (1-p) / n) ^ (1/2)
replacing we have:
0.04 + - 1.96 * (0.04 * (1-0.04) / 300) ^ (1/2)
0.04 + - 0.022
Therefore the interval would be:
0.04 - 0.022 <= p <= 0.04 + 0.022
0.0178 <= p <= 0.0622
(b)
For upper bounf z-critical value for 95% confidence interval is 1.645, so upper bound is:
p + z * (p * (1-p) / n) ^ (1/2)
replacing:
0.04 + 1.645 * (0.04 * (1-0.04) / 300) ^ (1/2)
0.04 + 0.0186 = 0.0586
p <= 0.0586
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Answer:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.
See explanation below.
Step-by-step explanation:
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:
(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Let's assume that the calculated statistic is
Since is a right tailed test test the p value would be:
And we know that the p value is 0.225. If we select a significance level for example 0.05 or 0.1 we see that
And on this case we have enough evidence to FAIl to reject the null hypothesis that the means are equal. So then the best conclusion would be:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.