To calculate the distance between 2 points we will use the following equation:
![D=\sqrt[]{(x_2-x_1)^2-(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%5B%5D%7B%28x_2-x_1%29%5E2-%28y_2-y_1%29%5E2%7D)
For this exercise we have the following data:
We plug the values into the distance equation and solve for the unknown Y
Answer:
x = 1/7(k+12)
Step-by-step explanation:
7x - 12 = k
Add 12 to each side
7x - 12+12 = k+12
7x = k+12
Divide each side by 7
7x/7 = (k+12)/7
x = 1/7(k+12)
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ = 15.7
H1 : μ < 15.7
This is a one sample t test :
Test statistic = (xbar - μ) ÷ (s/√(n))
n = sample size = 33
Using calculator :
The sample mean, xbar = 15.41
The sample standard deviation, s = 0.419
Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))
Test statistic = - 3.976
Using the Pvalue calculator :
Degree of freedom, df = n - 1 ; 33 - 1 = 32
Pvalue(-3.976, 32) = 0.000187
Decison region :
Reject H0 if Pvalue < α
Since Pvalue < α ; we reject H0
There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.
Answer:
Step-by-step explanation:
drain empties 1/10 of the desired amount per minute
pump fills 1/14 of the desired amount per minute
when both are active, the net drain is 1/10-1/14 = 1/35 of the desired amount per minute
It takes 35 minutes to reach the cut-off level.
1/2y^2=1/2x^2+8. The curve's slope at (x,y) is x/y, so dy/dx=x/y. To solve this differential equation, rearrange it to: y*dy=x*dx, and by integrating both sides, we get 1/2y^2=1/2x^2+C (some constant). Plug in (0,4) into this equation, 8=0+C, so C=8. The curve's equation is 1/2y^2=1/2x^2+8.
