John is 4 years older than becky, and john’s and becky’s combined ages is 58. how old are becky and john?

What is the recursive formula of the geometric sequence? 1/2, 3/4, 9/8, 27/16,...

o-na [289]

Answer: Recursive formula of the given geometric sequence is $a_{n}=a_{1}r^{n-1}$ .

Step-by-step explanation:

All geometric sequences have a first term a and common ratio r .

Now, in the given question

The first term is $a=\frac{1}{2}$

The common ratio $r=\frac{3}{2}$

Now, fifth term is $a_{5}=a_{1}r^{5-1}=a_{1}r^{4}$

$=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{4}=\frac{1}{2}\times \frac{81}{16}=\frac{81}{32}$

Sixth term $a_{6}=a_{1}r^{6-1}=a_{1}r^{5}$

$=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{5}=\frac{1}{2}\times \frac{243}{32}=\frac{243}{64}$

.

nth term is $a_{n}=a_{1}r^{n-1}$ .

7 0

1 year ago

Neptune is 2,798,842,000 miles from the sun. How many hours does it take lightto travel from the sun to Neptune?

Mrrafil [7]

9514 1404 393

Answer:

4.17 hours

Step-by-step explanation:

The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...

(2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h

It takes about 4.17 hours for light to travel from the sun to Neptune.

4 0

2 years ago

Which of the following represents 2x - 5y + 15 = 0 written in slope-intercept form? y = -x + 3 y = x - 3 y = x + 3

Llana [10]

Y=2/5x+3 is the answer
Hope it helped!

4 0

1 year ago

Read 2 more answers

Suppose that a company claims that its chocolate bars weigh 1.6 ounces on average. It took many large samples, and each time the

Nuetrik [128]

Answer:

The company's chocolate bars weigh 1.6 ounces on average.

Step-by-step explanation:

We are given that a company claims that its chocolate bars weigh 1.6 ounces on average.

It took many large samples, and each time the mean weight of the sample was within the 95% confidence interval.

95% confidence level means a range of values that you can be 95% certain contains the true mean of the population.

Thus by definition we can say that The company's chocolate bars weigh 1.6 ounces on average.

Hence Option B is correct.

4 0

2 years ago

Read 2 more answers

Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 10

son4ous [18]

There is a relationship between confidence interval and standard deviation:
$\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}$
Where $\overline{x}$ is the mean, $\sigma$ is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
$\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}$
When we do all the calculations we find that:
$\overline{x}=123.8\\ \sigma=11.84$
Now we can find confidence intervals:
$($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\$
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing

6 0

2 years ago