Answer:
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value with right arm , y = test value with left arm
The system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
The first step is calculate the difference 
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The 4 step is calculate the statistic given by :
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
We know that
step 1
find the volume of a cylinder
volume of a cylinder=pi*r²*h
where
h=13 cm
r=1 cm
volume of a cylinder=pi*1²*13----> 13*pi cm³
step 2
find the volume of a cone
volume of a cone=(1/3)*pi*r²*h
where
r=1 cm
h=3 cm
volume of a cone=(1/3)*pi*1²*3-----> pi cm³
step 3
find the volume of the laser pointer
volume of the laser pointer=volume of a cylinder+volume of a cone
volume of the laser pointer=13*pi+pi-----> 14*pi cm³
the answer is
volume of the laser pointer is 14*pi cm³
Answer:
P(t) = 27000 * (1/9)^(t/4)
Step-by-step explanation:
This problem can me modelled with an exponencial formula:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.
In this problem, we have that the inicial population/value is 27000, the rate is -8/9 (negative because the population decays), and the time t is in months, so as the rate is for every 4 months, we use the value (t/4) in the exponencial.
So, our function will be:
P(t) = 27000 * (1-8/9)^(t/4)
P(t) = 27000 * (1/9)^(t/4)
Answer:
8 teams
5 girls and 4 boys
Step-by-step explanation:
To determine how many teams we can have , we need to determine the greatest common factor.
girls:40 = 5*8
boys:32 = 4*8
The greatest common factor is 8
So we will have 8 teams
There will be 5 girls and 4 boys on each team
Remember, rise/run is the easiest way to determine slope
y=mx+b is form
mx is slope, whilst b is y int
so, answer? y=-3x-2
Or A.
