Answer:
The minimum score a person must have to qualify for the society is 162.05
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Test scores are normally distributed with a mean of 140 and a standard deviation of 15. This means that 
.
What is the minimum score a person must have to qualify for the society?
Since the person must score in the upper 7% of the population, this is the X when Z has a pvalue of 0.93.
This is 
.
So
The minimum score a person must have to qualify for the society is 162.05
Given:
From 1:00 pm to 3:30 pm the room temperature had dropped from 82F to 72F.
To find:
The average rate of change of temperature in this room over the period.
Solution:
Time between 1:00 pm to 3:30 pm is 2 hr 30 minutes, i.e., 2.5 hours.
So, change in time is 2.5 hours.
Room temperature had dropped from 82F to 72F.
Change in temperature = 72 F - 82 F
= -10 F
We know that, average rate of change of temperature in this room over the period is
Therefore, the average rate of change of temperature in this room over the period is -4. It means the temperature is decreasing 4 F per hour.
Answer:
240/30= 8
144/3= 48
135/45= 3
108/9= 12
Step-by-step explanation: these are it simplified aka divided
Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze EQUATION 1: x + y = 150 (total of 150 gallons mixed) EQUATION 2: .45x + .75y = .55(x + y) Simplify and solve the system of equations Multiply second equation by 100 on both sides to remove the decimals 45x + 75y = 55(x + y) Combine like terms 45x + 75y = 55x + 55y 45x - 55x + 75y - 55y = 0 -10x + 20y = 0 Now we have the following system of equations: x + y = 150 -10x + 20y = 0 Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x 10x + 10y = 1500 -10x + 20y = 0 ------------------------------ 30y = 1500 Solve for y 30y = 1500 y = 50 Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze
