Answer:
So the p value is higher the significance level given 0.1, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before score is equal 0. So then we don't have enough evidence to say that the score for the second exam is different than the score for the first exam.
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 before (first exam) , y = test value after (second exam)
The system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
The first step is calculate the difference 
The statistic given by :
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a left tailed test the p value is given by:
So the p value is higher the significance level given 0.1, so then we can conclude that we FAIL to reject the null hypothesis that the difference mean between after and before score is equal 0. So then we don't have enough evidence to say that the score for the second exam is different than the score for the first exam.
Answer:
(x - 3)(x + 7)
Step-by-step explanation:
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You have the equations set up correctly. I will use r and b as the variables to make it easier to follow.
12r + 8b = 70
20r + 12b = 110
First let's solve one of the equations for one of the variables.
12r = 70 - 8b
Now plug that in for r in the second equation.
Simplify
b = 5 grams
Now plug 5 in for b in one of the original equations to find r.
12r + 8(5) = 70
12r = 30
r = 2.5 grams
So the red marbles weigh 2.5 grams, and the blue marbles weigh 5 grams.
Answer:
146
Step-by-step explanation:
Hey there to find the area of this shape we will divide it into 2 shapes first one is a trapezoid and the second one is a triangle. first, we find the area of a trapezoid. to find the area of a trapezoid we use the formula:
A = 
in this situation
a = 4
b = 14
h = 10
Now we plug it into the formula which will look like:
A = 
if we solve it:
4+14 = 18
18/2 = 9
9*10 = 90
so the area of the trapezoid is 90
Now we find the area of triangle. to find the area of a triangle we use the formula:
A = 
in this situation
b = 14
h = 8 ( because the height of the trapezoid was 10 and the height of both shapes combined is 18 so we do 18 - 10 = 8 )
Now we put the numbers into the formula which will look like:
A = 
if we solve it :
14*8 = 112
= 56
so the area of the triangle is 56
Now we add the area of both shapes:
56 + 90 = 146
area of the big shape = 146
Have a wonderful day
