Need help with a problem. For some reason I can not seem to get it correct. Thinking my formula is wrong. Here's the problem:Assume that there are approximately 140x10^9 stars in our galaxy.
Our galaxy is 50,000 light years from the center to the edge, but just 1,000 light years thick. It's shaped like a thin disk or cylinder. If the stars were distributed equally throughout the galaxy, how many stars would you expect to find in one cubic light year?

I thought it would be Pir^2l. Then divide that by the number of stars. What am I doing wrong? Thanks, been 20 years since I had to do math like this!

Answers

Answer 1

Answer: $r=50,000\text{ ly}=5\cdot10^4\text{ ly}\nh=1,000 \text{ ly}=10^(3)\text{ ly}\n V=\pi r^2h\n\n V=\pi \cdot(5\cdot10^4)^2\cdot10^3\nV=\pi \cdot25 \cdot10^8 \cdot10^3\n V=2.5\pi\cdot10^(12) \text{ ly}^3\n\n(140\cdot10^9)/(2.5\pi\cdot10^(12))=\n(1.4\cdot10^(11))/(2.5\pi\cdot10^(12))=\n0.56\pi\cdot10^(-1)=\n5.6\pi\cdot10^(-2)\approx1.76\cdot10^(-1)$

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Which measurement is the best estimate for the length of a bean?A : 13 mm

B : 13 cm

C : 13 m

D : 13 km

Answers

The best estimate for the length of a bean would be B: 13 cm

Answer:

13mm

Step-by-step explanation:

Which expression is equivalent to (7x - 5 ) - ( 3x - 2)?

Answers

$(7x - 5 ) - ( 3x - 2)$

$7x-5-3x+2$

$(7x-3x)-5+2$ $\ Gather \ like \ terms$

$4x-5+2$

$4x-3$

Distribute the minus sign into the second parenthesis to get 7x-5-3x+2.
Then combine like terms to get 4x-3

1) point R has coordinates of (1,0) point S is symmetric to point R with respect to the line y=-2, what are the coordinates of point S2)point N has coordinates of (-1,2) point M is symmetric to point N with respect to the line y=X, what are the coordinates of point M

3) x^2=36
A. 9sqrt. 2 - 9sqrt. 2
B. 6 - 6
C. 4sqrt. 3 - 4sqrt. 3
D. 18 - 18

4) x^2=90
A. 10 sqrt. 3 - 10 sqrt. 3
B. 3 sqrt. 10 -3 sqrt. 10
C. 3 sqrt. 15- 3 sqrt. 15
D. 45 - 45

Answers

The right answer for the question that is being asked and shown above is that: "C. 4sqrt. 3 - 4sqrt. 3."

The right answer for the question that is being asked and shown above is that: "B. 3 sqrt. 10 -3 sqrt. 10."

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.