Answer:
105
Step-by-step explanation:
Answer:
84.13% of bottles will have volume greater than 994 mL
Step-by-step explanation:
Mean volume = u = 1000
Standard deviation =
= 6
We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.
x = 994
Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:
![z=\frac{x-u}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-u%7D%7B%5Csigma%7D)
Substituting the values, we get:
![z=\frac{994-1000}{6}=-1](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B994-1000%7D%7B6%7D%3D-1)
This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.
i.e. P(z > -1)
From the z-table this value comes out to be:
P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:
P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%
Answer:
116
Step-by-step explanation:
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The height of the kite above the ground is 36.8 ft
Let x be the height of the kite above Mamadou's hand.
Since the angle of elevation of the kite is 27° and the length of the kite's string is 75 ft long, the length of string, height of kite above Mamadou's hand and the horizontal distance between Mamadou and the kite form a right-angled triangle, with hypotenuse side, length of string of kite and opposite side, height of kite above Mamdou's hand, we have that
sin27° = x/75
Making x subject of the formula, we have
x = 75sin27
x = 75 × 0.4540
x = 34.05 ft
Since Mamadou's hand above the ground is y = 2.75 ft, the height of the kite above the ground, h = x + y
Substituting the values of the variables into the equation, we have
h = x + y
= 34.05 ft + 2.75 ft
= 36.8 ft
The height of the kite above the ground is 36.8 ft
Learn more about height of kite above ground:
brainly.com/question/16399072
Answer:
1 2/3 x 9/16
Step-by-step explanation: