What is an equation of the vertical line that passes through (-2,-9)

Determine whether the sequence converges or diverges. If it converges, give the limit.

vaieri [72.5K]

Answer:

The given series converges and $\lim_{n \to \infty} a_n =0$

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

<u>Since each next term is less than its preceding term, so it is decreasing.</u>

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>

Hence, the given series converges.

Now limit will be: $\lim_{n \to \infty} a_n$

$\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0$

Hence, $\lim_{n \to \infty} a_n =0$

7 0

3 years ago

A 100 mL vial of 25% solution is available in stock. An order is recieved for 6 g to be added to 250 mL of fluid for an iv infus

Ne4ueva [31]

9514 1404 393

Answer:

274 mL

Step-by-step explanation:

Often medical solutions expressed as a percentage are not really a percentage as such. A percentage is the ratio of two quantities with the same units.

Here, the context given by the problem suggests the "25%" solution is really (25 g)/(100 mL). That is, the units are grams and milliliters--different units.

With that assumption, we want to find the volume (v) of solution needed to deliver 6 g of medicine. An appropriate proportion* is ...

v/(6 g) = (100 mL)/(25 g)

v = (6 g)(100 mL)/(25 g) = 24 mL

So, the total volume of the infusion is ...

250 mL +24 mL = 274 mL

_____

* The concentration is given in terms of g/mL, but we have used a proportion that is mL/g. The reason for that is we want the variable to be in the numerator of the ratio. The variable here represents volume, so we have written the proportion with volumes in the numerators.

Having the variable in the numerator means the equation can be solved in one step--by multiplying by its denominator.

3 0

3 years ago

Solve for x. |x| – 5 = 7

musickatia [10]

Answer:

x=12 or x= -12 (answer A)

Step-by-step explanation:

|x| – 5 = 7

|x| = 12

x=12 or x= -12 (answer A)

6 0

3 years ago

Suppose 52% of the population has a college degree. If a random sample of size 563563 is selected, what is the probability that

amm1812

Answer:

The value is $P(| \^ p - p| < 0.05 ) = 0.9822$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.52$

The sample size is n = 563

Generally the population mean of the sampling distribution is mathematically represented as

$\mu_{x} = p = 0.52$

Generally the standard deviation of the sampling distribution is mathematically evaluated as

$\sigma = \sqrt{\frac{ p(1- p)}{n} }$

=> $\sigma = \sqrt{\frac{ 0.52 (1- 0.52 )}{563} }$

=> $\sigma = 0.02106$

Generally the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

$P(| \^ p - p| < 0.05 ) = P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 ))$

Here $\^ p$ is the sample proportion of persons with a college degree.

So

$P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P(\frac{[[0.05 -0.52]]- 0.52}{0.02106} < \frac{[\^p - p] - p}{\sigma } < \frac{[[0.05 -0.52]] + 0.52}{0.02106} )$