Answer:
A) sample mean = $1.36 million
B) standard deviation = $0.9189 million
C) confidence interval = ($1.93 million , $0.79 million)
*since the sample size is very small, the confidence interval is not valid.
Step-by-step explanation:
samples:
- $2.7 million
- $2.4 million
- $2.2 million
- $2 million
- $1.5 million
- $1.5 million
- $0.5 million
- $0.5 million
- $0.2 million
- $0.1 million
sample mean = $1.36 million
the standard deviation:
- $2.7 million - $1.36 million = 1.34² = 1.7956
- $2.4 million - $1.36 million = 1.04² = 1.0816
- $2.2 million - $1.36 million = 0.84² = 0.7056
- $2 million - $1.36 million = 0.64² = 0.4096
- $1.5 million - $1.36 million = 0.14² = 0.0196
- $1.5 million - $1.36 million = 0.14² = 0.0196
- $0.5 million - $1.36 million = -0.86² = 0.7396
- $0.5 million - $1.36 million = -0.86² = 0.7396
- $0.2 million - $1.36 million = -1.16² = 1.3456
- $0.1 million - $1.36 million = -1.26² = 1.5876
- total $8.444 million / 10 = $0.8444 million
standard deviation = √0.8444 = 0.9189
95% confidence interval = mean +/- 1.96 standard deviations/√n:
$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million
$1.36 million - $0.57 million = $0.79 million
Okay, just break it up so you're not overwhelming yourself or anything :)
So here, do it in steps-
Let's do 5(3 + t) first:
Distribute the 5, or in non-mathematical terms, just multiply 5 by 3 and t. This will give you 15 + 5t.
Now onto -3(t + 1):
Again, just multiply -3 by t and 1. This will come out to: -3t - 3.
*Note: the 3 is negative because it's "MINUS 3" in the original equation and remember that any number times a negative, if it isn't negative itself, will turn out to be negative.... (aka "-" x "-" = "+" | "+" x "+" = "+" | "-" x "+" = "-")*
ANYWAY
Now just put both answer together and you get:
15 + 5t -3t - 3. You can only add and minus the LIKETERMS (which are the things that are the same) - in this case, the liketerms are 15 and -3 ,,,, AND 5t and -3t.
15 - 3 = 12
5t - 3t = 2t
12 + 2t is your final answer. Hope that helps! :)
x=3, you can find this by using finding common bases for equation b because 243=3^5. Because of that you can get rid of three on both sides to get the equation 2x-1=5 and then just solve for x to get x=3. For the first equation 5^3=625 so that also proves x=3.
Sorry if my explanation is a little disorganized if you need more help feel free to ask
X+3 or x-8
These answers will both work!
