Answer:
Step-by-step explanation:
1) Let the random time variable, X = 45min; mean, ∪ = 30min; standard deviation, α = 15min
By comparing P(0 ≤ Z ≤ 30)
P(Z ≤ X - ∪/α) = P(Z ≤ 45 - 30/15) = P( Z ≤ 1)
Using Table
P(0 ≤ Z ≤ 1) = 0.3413
P(Z > 1) = (0.5 - 0.3413) = 0.1537
∴ P(Z > 45) = 0.1537
2) By compering (0 ≤ Z ≤ 15) ( that is 4:15pm)
P(Z ≤ 15 - 30/15) = P(Z ≤ -1)
Using Table
P(-1 ≤ Z ≤ 0) = 0.3413
P(Z < 1) = (0.5 - 0.3413) = 0.1587
∴ P(Z < 15) = 0.1587
3) By comparing P(0 ≤ Z ≤ 60) (that is for 5:00pm)
P(Z ≤ 60 - 30/15) = P(Z ≤ 2)
Using Table
P(0 ≤ Z ≤ 1) = 0.4772
P(Z > 1) = (0.5 - 0.4772) = 0.0228
∴ P(Z > 60) = 0.0228
Answer:
1.) 16/20
2.) 15/35
3.) 12/9
4.) 52/60
5.) 9 inches
6.) 24 centimeters
7.) 16 logs
8.) $15.40
9.) 10 miles
10.) 1.5 inches
I hope this is good enough:
Given:
Length of rectangle = (x+10) cm
Width of the rectangle = x cm
Perimeter = 32 cm
To find:
The length of the rectangle.
Solution:
We know that,

Where, l is length and w is width.
Substituting the values, we get



Subtract 20 from both sides.


Divide both sides by

So, the length is

Therefore, the length of the rectangle is 13 cm.
Answer:
The estimate is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is 
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as



Next we obtain the critical value of
from the normal distribution table, the value is

Generally the margin of error can be mathematically represented as

=> 
=> 
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is

substituting values
