What is the first term of the geometric sequence presented in the table below? n 4 9 an 243 59,049

Answers

Answer 1

Answer: Reminder: the formula for a geom. seq. is

a(n) = a(1)*r^(n-1), where a(1) is the first term, n is the counter and r is the common ratio.

I first noted that 243 is a power of 3; specifically, 243=3^5, or 243=3(3)^4, or 243=(3^2)(3)^(4-1). Notice that I'm trying here to rewrite 243=3^5 in the form a(n) = a(1)*r^(n-1): a(4) = a(1)(3)^(4-1), or a(4) = a(1)(3)^3 = 243. Then by division we find that a(1) = 243/27 = 9. Is it possible that a(1)=9?

Let's try out our formula a(n)=9(3)^(n-1). Steal n=9 and see whether this formula gives u s 59049:

n(9) = 59049 = 9(3)^(9-1), or 9(3)^8. True or false? 3^8= 6561, and 9(3)^8 = 59049.

YES! That's correct.

Therefore, the desired formula is

a(n) = 9(3)^(n-1). The first term, a(1) is 9(3)^(1-1) = 9(3)^0 = 9*1 = 9.

Answer 2

Answer:

Final answer:

The first term of the geometric sequence is 3. Calculation is done using the formula for the nth term of a geometric sequence and substituting the given values.

Explanation:

To find the first term of the geometric sequence, one can use the formula for the nth term of a geometric sequence, which is a = arn-1. Here, 'a' is the first term, 'r' is the common ratio and 'n' is the term position. As provided in the table, when n=4, an=243 and when n=9, an=59049. We can setup the equation 243 = a*r3 and 59049 = a*r8. Dividing the second equation by the first we get r5 = 243, leading to r=3. Substitute r=3 into the first equation to find 'a' and we get a= 3.

Learn more about geometric sequence here:

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Use the given data to construct a confidence interval for the population standard deviation, σσ. Assume that the population has a normal distribution: The football coach randomly selected the following players and timed how long each player took to perform a certain drill. The times (in minutes) were:[10,10,15,10,11,7,5,5]

Find a 95.0 confidence interval for the population standard deviation σ

A) 2.6194049<σ<6.43192582.6194049<σ<6.4319258
B) 2.2194049<σ<6.83192582.2194049<σ<6.8319258
C) 2.6194049<σ<7.43192582.6194049<σ<7.4319258
D) None of These

Answers

Answer:

The confidence interval for the population standard deviation would be:

C) 2.6194049<σ<7.4319258

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

$\bar x$ represent the sample mean

n=8 the sample size

Confidence=95% or 0.95

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates.

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$((n-1)s^2)/(\chi^2_(\alpha/2)) \leq \sigma \leq ((n-1)s^2)/(\chi^2_(1-\alpha/2))$

On this case we need to find the sample standard deviation with the following formula:

$s=\sqrt{(\sum_(i=1)^8 (x_i -\bar x)^2)/(n-1)}$

And in order to find the sample mean we just need to use this formula:

$\bar x =(\sum_(i=1)^n x_i)/(n)$

The sample mean obtained on this case is $\bar x= 9.125$ and the deviation s=3.357

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=8-1=7$

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 values.

The excel commands would be: "=CHISQ.INV(0.025,7)" "=CHISQ.INV(0.975,7)". so for this case the critical values are:

$\chi^2_(\alpha/2)=16.012$

$\chi^2_(1- \alpha/2)=1.690$

And replacing into the formula for the interval we got:

$((7)(3.357)^2)/(16.012) \leq \sigma ((7)(3.357)^2)/(1.690)$

$4.927 \leq \sigma^2 \leq 46.678$

Now we just take square root on both sides of the interval and we got:

$2.2194049 \leq \sigma \leq 6.8319258$

So the best option would be:

C) 2.6194049<σ<7.4319258

Please Explain This Function out for me :)
f(s) =10 (s-65)+75

Answers

most of the time it saids that s= a number.

f(s) = 10(s - 65) + 75
f(s) = 10(s) - 10(65) + 75
f(s) = 10s - 650 + 75
f(s) = 10s - 575

Which image shows the triangle's incenter? Appreciate the help!

Answers

It's the last image. The one with D

A building blueprint has a scale of 2 inches equal to 25 feet. on the blueprint, the 10 story building has a height of 12 inches what is the actual height of 1 story

Answers

Answer:

The actual height of 1 story is 15 feet.

Step-by-step explanation:

The given scale is

$2 \ inches = 25 \ feet$

We know the 10 story building has a height of 12 inches, but we need the actual height of 1, that is, the height of 1 story in feet.

Let's divide to find the number of inches per story

$(12)/(10)=1.2$

There are 1.2 inches per story.

Now, we know $2 \ inches = 25 \ feet$ , let's use the rule of three

$x=1.2in(25ft)/(2in)= 15ft$

Therefore, the actual height of 1 story is 15 feet.

2 inches: 25 feet.

1 inch: 25/2 feet

1 inch = 12.5 feet.

12 inches = 12.5 * 12 feet

= 150 feet.

The 12 inches height has an actual height of 150 feet.

Can someone help me please

Answers

Answer:

46.5

Step-by-step explanation:

Solution

A=a+b

2h=5.3+13.3

2·5=46.5

If a semi circle has a diameter of 5 m what is the area?

Answers

Answer:

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

Step-by-step explanation:

Semi circle formula: 1/2 * 4/3 * pi * r^3

r = 2.5

1/2 * 4/3 * pi * 2.5^3

2/3 * pi * 2.5^3

2/3 * pi * 15.625

10.416..... * pi

Exact answer = 10.417pi

We can estimate pi as 3.14

So, 10.417 * 3.14 = 32.70938

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

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A student randomly draws a card from a standard deck and checks to see if it is his favorite suit. He then returns the card to the deck, shuffles, and repeats the experiment. He performs the experiments 30 times. Can the probability of drawing his favorite suit be found by using the binomial probability formula? Why or why not?Yes. The events are dependent; however, the 5% guideline can be applied to this situation. No. The trials are fixed, but the probability of success changes for every trial. No. The probability of success remains the same for every trial, but the trials are not fixed. Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.