Remove the radical by raising each side to the index of the radical. a = √ 3 , − √ 3 a=3,-3 a ≈ 1.73205080 , − 1.73205080
Answer:
7.38×10^3
Step-by-step explanation:
The usual rules of exponents apply.
(20.5×10^7)(3.6×10^-5) = (2.05)(3.6)(10^(8-5)) = 7.38×10^3
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<em>Additional comment</em>
You can have your scientific or graphing calculator or your spreadsheet compute this product for you and display the result in scientific notation. You can enter the numbers in scientific notation or in standard form in any calculator or spreadsheet. (For a spreadsheet, the first number would be entered 20.5e7 or 2.05e8.)
The applicable rule of exponents is ...
(10^a)(10^b) = 10^(a+b)
Just as the place values increase by factors of 10 going to the left of the decimal point, so they decrease by factors of 10 to the right. The number 3 in 0.000036 is in the 5th place to the right of the decimal point, so has a place value of 10^-5.
Answer:
Null hypothesis:
Alternative hypothesis:
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.
Step-by-step explanation:
Information provided
represent the sample mean for the MPG of the cars
represent the population standard deviation
sample size of cars
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test
Hypothesis
We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation the statistic is given by:
(1)
Calculate the statistic
Replacing we have this:
Decision
Since is a two tailed test the p value would be:
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.
an = a1r^(n-1)
a5 = a1 r^(5-1)
-6 =a1 r^4
a2 = a1 r^(2-1)
-48 = a1 r
divide
-6 =a1 r^4
---------------- yields 1/8 = r^3 take the cube root or each side
-48 = a1 r 1/2 = r
an = a1r^(n-1)
an = a1 (1/2)^ (n-1)
-48 = a1 (1/2) ^1
divide by 1/2
-96 = a1
an = -96 (1/2)^ (n-1)
the sum
Sn = a1[(r^n - 1/(r - 1)]
S18 = -96 [( (1/2) ^17 -1/ (1/2 -1)]
=-96 [ (1/2) ^ 17 -1 /-1/2]
= 192 * [-131071/131072]
approximately -192
