<span>v = 4/3*pi*r^3
derivating both sides with respect to t
dv/dt = 4*pi*r^2*dr/dt
when d = 1.7, r = 0.85, and dv/dt = 2:
2 = 4*pi*(0.85)^2*dr/dt
thus
dr/dt = 1/(2pi*(0.85)^2)
=1/(2*3.14*0.85^2)
=0.22</span><span />
Answer:
H0 : μ = 0.75
H1 : μ > 0.75
Step-by-step explanation:
Given :
Sample size, n = 125
x = 99
Phat = x / n = 99 / 125 = 0.792
Population proportion, P = 0.75
The hypothesis :
Null hypothesis :
H0 : μ = 0.75
Alternative hypothesis ;
Egates the null hypothesis ; since the sample proportion is greater than the the population proportion or claim "; then we use the greater than sign.
H1 : μ > 0.75
Answer:

Step-by-step explanation:
To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:
![A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%262%262%5C%5C-7%26-3%265%26-8%5C%5C4%261%261%261%5C%5C3%267%26-1%261%5Cend%7Barray%7D%5Cright%5D)
And the vector B is formed with the solution of each equation of the system:![b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-3%5C%5C6%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called
.
![A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]](https://tex.z-dn.net/?f=A_%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%263%262%262%5C%5C-7%26-3%265%26-8%5C%5C4%266%261%261%5C%5C3%261%26-1%261%5Cend%7Barray%7D%5Cright%5D)
The value of y using Cramer's rule is:

Find the value of the determinant of each matrix, and divide:


Answer:
Step-by-step explanation:
In the past, mean of age of employees
i.e. 
Recently sample was taken
n = sample size = 60
Mean of sample = 45
Std dev of sample s = 16

(Right tailed test)
Since only population std deviation is known we can use t test only
Std error = 
Mean difference = 45-40 =5
Test statistic t=
df = 60
p value =0.008739
Since p < 0.05 we reject null hypothesis
The mean age has increased.
No problem 72 cubic squares