Answer:
John should use:
4 grams of the 30% solution and 16 grams of the 60% solution
Step-by-step explanation:
Let the number of grams of the 30% solution = x
Let the number of grams of the 60% solution = y
John needs 20 grams of 54% acid solution for his science project.
Hence,
x + y = 20 grams..... Equation 1
x = 20 - y
His school's science lab has bottles of 30% solution and bottles of 60% solution.
30% × x + 60% × y = 54% × 20
0.3x + 0.6y = 10.8......Equation 2
We substitute 20 - y for x in Equation 2
0.3(20 - y) + 0.6y = 10.8
6 - 0.3y + 0.6y = 10.8
- 0.3y + 0.6y = 10.8 - 6
0.3y = 4.8
y = 4.8/3
y = 16 grams
x = 20 - y
x = 20 - 16
x = 4 grams
Therefore, John should use:
4 grams of the 30% solution and 16 grams of the 60% solution
Answer:
t₁ = 2,75 sec
Step-by-step explanation:
The ball will get h maximum when dh/dt ( its vertical component of the speed is equal to 0. At this moment the ball has flown half of the total flight time
Then
h(t) = - 4t * ( 4*t - 11 )
h(t) = - 16*t² + 44*t
Taking derivatives on both sides of the equation we get:
dh/dt = - 32*t + 44
dh/dt = 0 ⇒ -32*t + 44 = 0
t = 44/32 ⇒ t = 1,375 s
So twice this time
2*t = 2 * 1.375
Total time t₁ = 2,75 sec
A Z-score helps us to understand how far is the data from the mean. The number of phones who have battery life in the range of 11.4 to 13 range is 1145.
<h3>What is Z-score?</h3>
A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
The percentage of phones who have battery life in the range of 11.4 to 13 range is,
= 0.50 - 0.0228
= 0.4772
Now, the number of phones who have battery life in the range of 11.4 to 13 range is,
Number of phones = 0.4772 × 2400 = 1145.28 ≈ 1145
Hence, the number of phones who have battery life in the range of 11.4 to 13 range is 1145.
Learn more about Z-score:
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a. 
has an average value on [5, 11] of
b. The mean value theorem guarantees the existence of 
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