Answers and Step-by-step explanation:
Hypotheses are:
H o=19.8
H 1 ≠19.8
Here we have following information:
s=2.45, X bar=20.1, n=50
So test statistics will be
t=20.1-19.8/(2.45/
=0.87
Degree of freedom : d f = n - 1 = 50 - 1 =49
Test is two tailed so critical value of the test is -1.30 and 1.30.
Rejection region:
if t < -1.30 and t > 1.30, reject H o
Since test statistics lie in the rejection region so we fail to reject the null hypothesis.
(b)
The observed significance of the test is
P value =0.3885
(c)
Since p value is greater than 0.20 so we fail to reject the null hypothesis.
Answer:
2980
Step-by-step explanation:
2.98*10^3 = 2980
Answer: 1.) √121= 11
Step-by-step explanation:
11•11=121
The problem above uses the concept of ratio and proportion. The ratio between the cost and amount of the organic milk should always be equal. The proportion between two cases is shown below,
($2.52 / 0.5 gallon) = (x / 4 gallons)
Solving for x gives x = 20.16. Therefore, 4 gallons of organic milk costs $20.16.
For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
