A) There are 36 possible outcomes.
b) The probability of a sum of 6 is 5/36.
c) She should roll a sum of 7 45 times.
d) She should roll a sum of 10 45 times.
Explanation
a) There are 6 outcomes for the first die and 6 outcomes for the second one. By the fundamental counting principle, there are 6*6 = 36 outcomes for both dice together.
b) The ways to get a sum of 6 are:
1&5; 2&4; 3&3; 4&2; 5&1. There are 5 possibilities out of a total of 36, or 5/36.
c) The ways to get a sum of 7 are:
1&6; 2&5; 3&4; 4&3; 5&2; 6&1. There are 6 out of 36, or 6/36=1/6. Since she is rolling the dice 150 times, she should get a sum of 6
1/6(150) = 150/6 = 45 times.
d) The ways to get a sum of 10 or more are:
4&6; 5&5; 6&4; 5&6; 6&5; 6&6
There are 6 ways out of 36, or 6/36 = 1/6. Since she is rolling the dice 150 times, she should get a sum of 10 or more
1/6(150) = 150/6 = 45 times.
Answer: 8
Step-by-step explanation:
The degree of freedom for t-distribution of testing the differnce between the two population mean is given by :-
, where 
= Size of first sample.
= Size of second sample.
As per given ,
Veterinarian selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths.
i.e. 
and 
Now , If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are
Hence, the correct answer is 8.
Answer:
Explained below.
Step-by-step explanation:
The regression equation to predict amount of precipitation (in inches) in July from the average high temperatures (in degrees Fahrenheit) in July is as follows:
PRECIP = 2.0481 + 0.0067 HIGH
(1)
The value of the slope of the regression line is, 0.0067.
(2)
The predictor variable in this context is the average high temperatures (in degrees Fahrenheit) in July.
(3)
The response variable in this context is the amount of precipitation (in inches) in July.
(4)
The slope of a regression line is average rate of change in the dependent variable with one unit change in the independent variable.
The slope here is 0.0067.
This value implies that the average rate of change in the amount of precipitation (in inches) in July increases by 0.0067 inches with every 1°F increase in the average high temperatures.
(5)
Compute the mount of precipitation for a city that has an average high temperature in July of 87.31°F as follows:
PRECIP = 2.0481 + 0.0067 HIGH
= 2.0481 + 0.0067 × 87.31°F
= 2.633077
≈ 2.63 inches.
Newton's Law of Cooling states that the change
of the temperature of an object is proportional to the difference between its
own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent
to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the
temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
