Given: <span>f(x) = log3 (x + 1), look for f^-1 (2)
We are looking for the inverse of a function. The inverse of the function can be obtained by switching the variables and obtaining the values of the new function, before substituting f(2). Using a calculator:
</span><span>f^-1 (2) = 8</span>
Answer:
71.123 mph ≤ μ ≤ 77.277 mph
Step-by-step explanation:
Taking into account that the speed of all cars traveling on this highway have a normal distribution and we can only know the mean and the standard deviation of the sample, the confidence interval for the mean is calculated as:
≤ μ ≤ 
Where m is the mean of the sample, s is the standard deviation of the sample, n is the size of the sample, μ is the mean speed of all cars, and
is the number for t-student distribution where a/2 is the amount of area in one tail and n-1 are the degrees of freedom.
the mean and the standard deviation of the sample are equal to 74.2 and 5.3083 respectively, the size of the sample is 10, the distribution t- student has 9 degrees of freedom and the value of a is 10%.
So, if we replace m by 74.2, s by 5.3083, n by 10 and
by 1.8331, we get that the 90% confidence interval for the mean speed is:
≤ μ ≤ 
74.2 - 3.077 ≤ μ ≤ 74.2 + 3.077
71.123 ≤ μ ≤ 77.277
Answer:
As radius is perpendicular to tangent,
By pythagoras theorem :
x² = (x + 9)² - 15²
x² = x² + 18x + 81 - 225
18x = 207
x = 11.5
Answer:
1.2
Step-by-step explanation:
0.75 :x :: 5: 8
0.75 / x = 5 / 8
Cross multiply
5x = 0.75 * 8
x = 6/5
x = 1.2