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2 years ago

What is the explicit formula for the sequence 10, 15, 22.5, 33.75, …?

Mathematics

1 answer:

Flura [38]2 years ago

8 0

Answer:

Step-by-step explanation:

Since there's no one one number you can add to one number in the sequence to get to the next number, this is not arithmetic. It must be geometric. We need then to find the common ratio. Let's start with the first 2 numbers, find a ratio, and then use it to test for accuracy.

10x = 15 and

x = $\frac{15}{10}=\frac{3}{2}$ If this is in fact a geometric sequence witha common ratio of 3/2, we should be able to multiply 15 by 3/2 to get to the next number in the sequence. Let's try it out:

$15(\frac{3}{2})= \frac{45}{2}=22.5$ Good. So the common ratio is 3/2. The formula for an explicit geometric formula is

$A_n=a_1(r)^{n-1$ where a1 is the first number in the sequence and r is the common ratio. Filling in:

$A_n=10(\frac{3}{2})^{n-1$

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What’s the percent increase in 5 and 12

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A lot

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The equation of a graph is 4x - 3y = 5. What is the x-intercept?

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Which Of the following pairs of functions are inverse of each other?

damaskus [11]

One way is to solve for the inverse of the first function

remember, to solve, replace f(x) or g(x) with y, switch x and y, solve for y and replace it with $f^{-1} (x)$

$f(x)=x/2+8\\y=x/2+8\\x=y/2+8\\x-8=y/2$

$2x-16=y$

$f^{-1}=2x-16$

nope, not A

<h3>What is the inverse function?</h3>

The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by $f^{-1}.$

$f(x)=3x^3+16\\y=3x^3+16x=3y^3+16\\x-16=3y^3\\(x-16)/3=y^3$

$f^{-1}(x)=\sqrt[3]{((x-16)/3)}$

nope, not the same

not B

$f(x)=18/x-9\\y=18/x-9\\x=18/y-9\\x+9=18/y\\y(x+9)=18\\y=18/(x+9)\\f^{-1}(x)=18/(x+9)$

The correct, answer is C.

To learn more about the inverse function visit:

brainly.com/question/2972832

#SPJ1

5 0

1 year ago

Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

And replacing we got:

$ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392$

Now we have everything in order to replace into formula (1):

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

7 0

2 years ago