Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point 
in the plane is 
, but we know that 
and 
share the same critical points, so we need only worry about minimizing 
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that 
is a critical point. The Hessian for the target function is
which is positive definite for all 
, so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is 
.
Answer:
n + 1 = 24 million x 1.15
Step-by-step explanation:
The sales is increased 15 percent, so every year 24million is multiplyed with 1.15 to get the result... so yea
Answer:
Check Explanation
Step-by-step explanation:
A) The null hypothesis would be that the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white & there is no significant evidence that the company's hiring practices are discriminatory.
Mathematically,
H₀: μ₀ = 0.53
And the alternative hypothesis would be that there is a significant difference between the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white. More specifically, that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white & there is significant evidence that the company's hiring practices are indeed discriminatory.
Mathematically,
Hₐ: μ₀ < 0.53
B) The two errors that can come up in this hypothesis testing include -
Type I error: We reject the null hypothesis because we obtain that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white and conclude that there is indeed significant evidence that the company's hiring practices are discriminatory when in reality, there is no significant difference and hence, no discrimination.
Type II error: We accept the null hypothesis (fail to reject the null hypothesis) because we obtained that there is no significant difference between the proportion of newly hired candidates that are not white & th proportion of applicants that are not white and conclude that there is no discrimination in the company's hiring practices when in reality, there is significant difference in the stated proportions above and significant evidence that there is indeed significant evidence that the company's hiring practices are discriminatory.
C) The power of the test increases as the significance level reduces. This is because t-statistic increases as significance level reduces.
D) The standard error of the mean used in computing the t-score is given as
σₓ = (σ/√n)
It is evident that as the value of n increases, the standard error reduces and this widens the effect of the test, hence, the power of the test increases.
Hope this Helps!!!
Answer:3.9
Step-by-step explanation:
you have to add the decimal to the exponent
<span>12x = 7y-10y
12x = -3y
-4x= y
y = -4x</span>
