Answer:
lol ty for the points
Step-by-step explanation:
Answer:
3 seconds
Step-by-step explanation:
You want to set h(t)=3, then take the root such that t≠0. You would have:
3=3+48t−16t^2
Let's solve your equation step-by-step.
3=3+48t−16t2
Step 1: Simplify both sides of the equation.
3=−16t2+48t+3
Step 2: Subtract -16t^2+48t+3 from both sides.
3−(−16t2+48t+3)=−16t2+48t+3−(−16t2+48t+3)
16t2−48t=0
Step 3: Factor left side of equation.
16t(t−3)=0
Step 4: Set factors equal to 0.
16t=0 or t−3=0
t=0 or t=3
3 makes more sense than 0 because the ball can't have been in the air for 0 seconds.
So the ball was in the air for 3 seconds.
Y = kx
when y= 12, x=3
12 = 3k
k = 12/3
k = 4
y = 4x
when x= 15
y = 4(15)
y = 60
Answer:
96 employees
Step-by-step explanation:
Given that the standard deviation = 22.8
The width in the question = 12
We solve for the margin of error E.
E = width / 2
= 12/2 = 6
At 99%
Alpha = 1-0.99
= 0.01
Alpha/2 = 0.01/2 = 0.005
Z0.005 = 2.576
Sample size n
= ((2.576x22.8)/2)²
= 95.8
= 96
The number of employees is 96
Thank you!
Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.
We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II
We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)
We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III
Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml
Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml
Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
