Original price $60 markup 15%

Robert is already 50 miles from his home on his way to the game he is driving 55 miles per an hour

ASHA 777 [7]

i would need more details!

what is the answer?

3 0

3 years ago

Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.

Fantom [35]

Part 1: You can simplify $a_n$ to

$\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}$

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

$|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}$

(b) And because both fractions in $a_n$ converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

$|a_n| \ge \boxed{0}$

(c) Finally, $a_n$ is bounded above and below, so it is a bounded sequence.

Part 2: Yes, $a_n$ is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since $a_n$ is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

$\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10$

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

$\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty$

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

5 0

3 years ago

Political party affiliation is believed to be a very strong indicator of how voters will vote in Presidential Elections. You are

Norma-Jean [14]

Answer:

The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

7 0

3 years ago

Which graph is an example of a function?

Artist 52 [7]

Answer:

the graph that represents a function is B

Step-by-step explanation:

if you look at B it is facing from-to +, which means that question B is a function

4 0

3 years ago

Find all real numbers z for which the equation (z-5)x^2-zx+5=0 only has one real solution. If you find more than one, then list

Nataliya [291]

Step-by-step explanation:

For the quadratic equation to have 1 repeated real solution, the discriminant b² - 4ac must be zero.

=> (-z)² - 4(z - 5)(5) = 0

=> z² - 20(z - 5) = 0

=> z² - 20z + 100 = 0

=> (z - 10)² = 0

Therefore z = 10.

7 0

3 years ago