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ycow [4]
3 years ago
7

The formula S=16t^2 is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds. The heig

ht of a building is 1221 feet . How long would it take for an object to fall from the top

Mathematics
2 answers:
astraxan [27]3 years ago
7 0
H(t)=-16t^2+1221 is the function for the height as a function of time.  It will hit the ground when h=0 so:

-16t^2+1221=0

16t^2-1221=0

16t^2=1221

t^2=1221/16

t=√(1221/16) seconds

t≈8.74 seconds  (to nearest hundredth of a second)
FinnZ [79.3K]3 years ago
4 0
S=16t^2
1221=16t^2
1221/16=t^2
square root of 76.3=t
t=8.7

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What is the smallest positive integer divisible by 6 and 2 you can write using at least one 2 and one 6?
Elodia [21]

Answer:

26, not divisible by 6

62, not divisible by 6

126, is divisible by 6 and 2. Is the smallest

8 0
3 years ago
A ski gondola carries skiers to the top of a mountain. assume that weights of skiers are normally distributed with a mean of 199
Allushta [10]
A) maximum mean weight of passengers = <span>load limit ÷ number of passengers
</span><span>
maximum mean weight of passengers = 3750 </span>÷ 25 = <span>150lb

</span>B)  First, find the z-score:
z = (value - mean) / stdev
   = (150 - 199) / 41
   = -1.20

We need to find P(z > -1.20) = 1 - P(z < -1.20)

Now, look at a standard normal table to find <span>P(z < -1.20) = 0.11507, therefore:
</span>P(z > -1.20) = 1 - <span>0.11507 = 0.8849

Hence, <span>the probability that the mean weight of 25 randomly selected skiers exceeds 150lb is about 88.5%</span> </span>

C) With only 20 passengers, the new maximum mean weight of passengers = 3750 ÷ 20 = <span>187.5lb

Let's repeat the steps of point B)

z = (187.5 - 199) / 41
   = -0.29

P(z > -0.29) = 1 - P(z < -0.29) = 1 - 0.3859 = 0.6141

</span>Hence, <span>the probability that the mean weight of 20 randomly selected skiers exceeds 187.5lb is about 61.4%

D) The mean weight of skiers is 199lb, therefore:
number</span> of passengers = <span>load limit ÷ <span>mean weight of passengers
                                     = 3750 </span></span><span>÷ 199
                                     = 18.8
The new capacity of 20 skiers is safer than 25 skiers, but we cannot consider it safe enough, since the maximum capacity should be of 18 skiers.</span>
4 0
3 years ago
We have two fair three-sided dice, indexed by i = 1, 2. Each die has sides labeled 1, 2, and 3. We roll the two dice independent
Nikitich [7]

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 : Result on 1st die.

- Random Variable X_2: Result on 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

 

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                 ( X = -2 ):  { X_2 = 1 , X_1 = 3 }  

                P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )  

                                :  ( 1 / 3 ) * ( 1 / 3 )  

                                : ( 1 / 9 )    

                ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )        

 ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

               P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )

                                :  3*( 1 / 3 ) * ( 1 / 3 )

                                : ( 3 / 9 ) = ( 1 / 3 )        

                  ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

               P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )

                                : 2* ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )

                  ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                 P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )  

                                   :  ( 1 / 3 ) * ( 1 / 3 )  

                                   : ( 1 / 9 )                  

- The distribution Y = X_2,

                         P(Y=0) = 0

                         P(Y=1) =  1/3

                         P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

8 0
3 years ago
Death Valley is the location of the lowest land elevation in the USA which is 282 feet below sea level.The location with the hig
il63 [147K]

Answer:

20,038

Step-by-step explanation:

20,320 - 282

7 0
3 years ago
Mark bought 12 boxes of paper clips and 10 packages of index cards for a
Nata [24]

Answer:

paper clips = $1.85

index cards = $3.95

Step-by-step explanation:

Mark

12 paper clips = x

10 index cards = y

$61.70 total

Janice

15 paper clips = x

7 index cards = y

$55.40 total

12x + 10y = 61.70

15x + 7y   = 55.40

*** you want to cancel out one of the letters

(12x + 10y = 61.70) * -7

(15x + 7y   = 55.40) * 10

-84x -70y = -431.9

150x + 70y = 554.0

150x + 70y = 554.0

-84x -70y = -431.9

66x + 0 = 122.1

66x = 122.1

x = 122.1 ÷ 66

x = 1.85

plug it back in

15(1.85) + 7y   = 55.40

27.75 + 7y   = 55.40

7y   = 55.40 - 27.75

7y = 27.65

y = 27.65 ÷ 7

y = 3.95

8 0
3 years ago
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