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mafiozo [28]
3 years ago
15

Completely factor the following expression t^2+4tv+4^2

Mathematics
1 answer:
VashaNatasha [74]3 years ago
4 0
Here is all I got for you. From the starting expression to the simplest one.
t^2 + 4tv + 4^2 =
t^2 + 4tv + 16 = 
t(t + 4v) + 16

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A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3.1g and
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Question 1

probability between 2.8 and 3.3

The graph of the normal distribution is shown in the diagram below. We first need to standardise the value of X=2.8 and value X=3.3. Standardising X is just another word for finding z-score

z-score for X = 2.8
z= \frac{2.8-3.1}{0.41} =-0.73 (the negative answer shows the position of X = 2.8 on the left of mean which has z-score of 0)

z-score for X = 3.3 
z= \frac{3.3-3.1}{0.41}=0.49

The probability of the value between z=-0.73 and z=0.49 is given by 
P(Z<0.49) - P(Z<-0.73)

P(Z<0.49) = 0.9879
P(Z< -0.73) = 0.2327 (if you only have z-table that read to the left of positive value z, read the value of Z<0.73 then subtract answer from one)

A screenshot of z-table that allows reading of negative value is shown on the second diagram

P(Z<0.49) - P(Z<-0.73) = 0.9879 - 0.2327 = 0.7552 = 75.52%

Question 2
Probability between X=2.11 and X=3.5

z-score for X=2.11
z= \frac{2.11-3.1}{0.41}=-2.41

z-score for X=3.5
z= \frac{3.5-3.1}{0.41} =0.98

the probability of P(Z<-2.41) < z < P(Z<0.98) is given by
P(Z<0.98) - P(Z<-2.41) = 0.8365 - 0.0080 = 0.8285 = 82.85%

Question 3
Probability less than X=2.96

z-score of X=2.96
z= \frac{2.96-3.1}{0.41}=-0.34
P(Z<-0.34) = 0.3669 = 36.69%

Question 4
Probability more than X=3.4
z= \frac{3.4-3.1}{0.41}=0.73
P(Z>0.73) = 1 - P(Z<0.73) = 1-0.7673=0.2327 = 23.27%



7 0
3 years ago
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