B
Here, x is the volume of the 10ml solution. Multiplying it by its concentration gives the amount of alcohol in it. 50 is the total volume of the 12% solution so (50 - x) gives the volume of the 15% solution. Multiplying this by the concentration gives the amount of alcohol in it. The sum of these amounts of alcohols is equivalent to the amount of alcohol in the 12% solution which is given by the product of its volume and concentration.
Answer:
Pr(X-Y ≤ 44.2) = 0.5593
Step-by-step explanation:
for a certain breed of terrier
Mean(μ) = 72cm
Standard deviation (σ) = 10cm
n = 64
For a certain breed of poodle
Mean(μ) = 28cm
Standard deviation (σ) = 5cm
n = 100
Let X be the random variable for the height of a certain breed of terrier
Let Y be the random variable for the height of a certain breed of poodle
μx - μy = 72 -28
= 44
σx - σy = √(σx^2/nx + σy^2/ny)
= √10^2/64 + 5^2/100
= √100/64 + 25/100
= √ 1.8125
= 1.346
Using normal distribution,
Z= (X-Y- μx-y) / σx-y
Z= (44.2 - 44) / 1.346
Z= 0.2/1.346
Z= 0.1486
From the Z table, Z = 0.149 = 0.0593
Φ(z) = 0 0593
The probability that the difference of the observed sample mean is at most 44.3 is Pr(Z ≤ 44.2)
Recall that if Z is positive,
Pr(Z≤a) = 0.5 + Φ(z)
Pr(Z ≤ 44.2) = 0.5 + 0.0593
= 0.5593
Therefore,
Pr(X-Y ≤ 44.2) = 0.5593
7 minutes is the time can you afford to walk
<em><u>Solution:</u></em>
Given that, train is leaving in 11 minutes and you are one mile from the station
Let "x" represent how much time can you afford to walk
Then, (11 - x) is the time you run
You can walk at 4mph and run at 8mph
<em><u>Convert to miles per minute</u></em>
1 hour = 60 minutes
We know that,
Given that, you are one mile from the station
Therefore,
1 mile = distance walk + distance run
Thus, 7 minutes is the time can you afford to walk
Gross pay is 1020.00
fed tax is 107.00
social security is 6.2% of gross pay......6.2% of 1020.00 =
0.062(1020) = 63.24
medicare is 1.45% of gross pay....1.45% of 1020.00 =
0.0145(1020) = 14.79
state tax is 19% of fed tax....19% of 107.00 =
0.19(107) = 20.33
therefore, her net pay is : 1020 - (107 + 63.24 + 14.79 + 20.33) =
1020 - 205.36 = 814.64
answer : the net pay is correct <==
