About 4.1 seconds. How long was the ball in the air? We are told that t represents time in seconds since the ball was thrown, so it started to be 'in the air' at t = 0 To answer the question, then, we need to know the time when it stopped being in the air. We are told that the ball hit the ground. So that's what happened when it stopped being airborne. We need to relate that event to the mathematics we're working with. What can we say about h , the height of the ball when the ball hits the ground? Answer: The height will be 0 when the ball stops being in the air. Now translate this back to the mathematics: The ball is in the air from t = 0 until the time t when h = 0 . Find the time t that makes h = 0 . That means: solve: − 5 t 2 + 20 t + 2 = 0 We can solve this by solving: 5 t 2 − 20 t − 2 = 0 (Either multiply both sides of the equation by − 1 , or add 5 x 2 − 20 x and − 2 to both sides and then re-write it the other way around) That's a quadratic equation, so try to factor first. But don't spend too much time trying to factor, because not every quadratic is easily factorable and that's OK, because we still have the quadratic formula if we need it. We do need it. t = − ( − 20 ) ± √ ( − 20 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) = 20 ± √ 440 10 = 20 ± √ 4 ( 110 ) 10 = 20 ± 2 √ 110 10 = 2 ( 10 ± √ 110 ) 2 ( 5 ) = 10 ± √ 110 5 We can see that 10 < √ 110 < 11 . In fact ( 10 + 1 2 ) 2 = 10 2 + 10 + 1 4 = 110.25 Using 10.25 as an approximation for √ 110 , we get : for the solution t = 10 − √ 110 5 we'll get a negative t . That doesn't make sense. The other solution gives t ≈ 10 + 10.25 5 = 20.5 5 = 4.1 seconds. So the ball was in the air from t = 0 until about t = 4.1 . The elapsed time is the difference, 4.1 seconds.
Answer:
a) About 48 of the shoppers, that is 
of the shoppers, received a free set of earbuds.
b) About 58 shoppers, that is 
received $5 off their first purchase.
Step-by-step explanation:
a. About how many shoppers received a free set of earbuds?
21% out of 230. So
About 48 of the shoppers, that is of the shoppers, received a free set of earbuds.
b. About how many shoppers received $5 off their first purchase?
25% out of 230, so:
About 58 shoppers, that is received $5 off their first purchase.
Answer: 0.82 miles per gallon
Step-by-step explanation:
Given : Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (x) (in miles per gallon) of her car.
The results are :45 44 43 44 45 44 43
The formula to find the standard deviation is given by :-
First we find mean of the given data ,
Now,
Now, standard deviation of the above results will be :-
Hence, the standard deviation of these results = 0.82 miles per gallon
Answer:
g(x) = 4^x + 1.
Step-by-step explanation:
The graph of f(x) = 4^x passes through the point (0, 1) because when x = 0, 4*0 = 1. Also when x = 1, 4^x= 4. So it passes through (1, 4).
For g(x) we have corresponding points (0, 2) and (1, 5).
So we see that g(x) is a similar graph but it has been translated up 1 unit.
Solution:
we are given that
A school director Must randomly select 6 teachers to participate in a training session there are 30 teachers at the schoo. The order of selection does not matter.
As we know
6 teacheras can be selected out of 30 teacher in 
ways.
Hence the required number of ways is 593775.
