Answer: 0.3061.
Step-by-step explanation:
Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean , the actual temperature of the medium, and standard deviation .
Let X be the random variable that represents the reading of the thermometer.
Confidence level :
We know that the z-value for 95% confidence interval is 1.96.
Then, we have
But all readings are within 0.6° of .
So,
Hence, the required standard deviation will be
1. The counterclockwise rotation by 90° about the origin has rule:
(x,y)→(-y,x).
Then
(-3,-1)→(1,-3).
2. Translation 4 units up has rule:
(x,y)→(x,y+4).
Then
(1,-3)→(1,1).
Answer: after composition of transformations the image point has coordinates (1,1).
Part A
The number of members in the equal-size groups will be the Greatest Common Divisor of the numbers 20 and 25. That number is 5. There are several ways to find this number. One way is to look at the prime factors of 20 and 25:
20 = 2*2*5
25 = 5*5
The largest factor common to both is 5.
There will be 5 students in each group.
Part B
The number of groups is the number of students divided by the size of the group.
There will be 20/5 = 4 groups of sixth graders.
There will be 25/5 = 5 groups of seventh graders.