Round your answer to the nearest hundredth
2 answers:
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Answer: The area of the triangle is: " 8.5 cm² " ;
or, write as: " 8
cm² " .
_______________________________________________________
Explanation:
_________________________________________________________
The formula {"equation"} for the area of a triangle is:
A = () * b * h ;
in which: A = area;
b = base;
h = [perpendicular] height;
___________________________________
{also, can be written as: " A = (b * h) / 2 " .}.
______________________________________
Solve for the area, "A" ; by plugging in the known values shown in the figure (image attached):
______________________________________
base, "b" = 13 cm ;
[perpendicular] height, "h" = 5 cm ;
______________________________________
A = (b * h) / 2 ;
= (13 cm * 5 cm) / 2 ;
= [ (13 * 5) cm²] / 2 ;
= 65 cm² / 2 ;
A = " 8.5 cm² " ; or, write as: " 8 cm² " .
_________________________________________________________
Answer: " 8.5 cm² " ; or, write as: " 8 cm² " .
_________________________________________________________
The area of the triangle is: " 8.5 cm² " ;
or, write as: " 8 cm² " .
_________________________________________________________
or, write as: " 8
_______________________________________________________
Explanation:
_________________________________________________________
The formula {"equation"} for the area of a triangle is:
A = (
in which: A = area;
b = base;
h = [perpendicular] height;
___________________________________
{also, can be written as: " A = (b * h) / 2 " .}.
______________________________________
Solve for the area, "A" ; by plugging in the known values shown in the figure (image attached):
______________________________________
base, "b" = 13 cm ;
[perpendicular] height, "h" = 5 cm ;
______________________________________
A = (b * h) / 2 ;
= (13 cm * 5 cm) / 2 ;
= [ (13 * 5) cm²] / 2 ;
= 65 cm² / 2 ;
A = " 8.5 cm² " ; or, write as: " 8
_________________________________________________________
Answer: " 8.5 cm² " ; or, write as: " 8
_________________________________________________________
The area of the triangle is: " 8.5 cm² " ;
or, write as: " 8
_________________________________________________________
Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
==================================================
Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
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We have the two equations x+y = 180 and y+z = 180 to form this system of equations
Which is really the same as this system
The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.
"<span>Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find 
, 
, the t-test statistic, and the critical values to test the claim that 
"
You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.
For the example, please refer to the attached picture.
A) Find </span><span>
You are asked to find the mean difference between the two variables, which is given by the formula:
These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)
In our example:
</span><span>
</span>
B) Find <span>
</span><span>You are asked to find the standard deviation, which is given by the formula:
</span>
These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1
In our example:
= √14.5
= 3.81
C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
where SE = standard error is given by the formula:
These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract
6) divide by the standard error
In our example:
SE = 3.81 / √8
= 1.346
The problem gives us <span>, therefore:
t = [(9.75 - 9) - 0] / 1.346</span>
= 0.56
D) Find
You are asked to find what is the t-value for a 0.05 significance level.
In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).
We find <span>
</span>
Since our t-value is less than <span>
</span> we can reject our null hypothesis!!
You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.
For the example, please refer to the attached picture.
A) Find </span><span>
You are asked to find the mean difference between the two variables, which is given by the formula:
These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)
In our example:
</span><span>
B) Find <span>
</span><span>You are asked to find the standard deviation, which is given by the formula:
</span>
These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1
In our example:
= √14.5
= 3.81
C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
where SE = standard error is given by the formula:
These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract
6) divide by the standard error
In our example:
SE = 3.81 / √8
= 1.346
The problem gives us <span>
t = [(9.75 - 9) - 0] / 1.346</span>
= 0.56
D) Find
You are asked to find what is the t-value for a 0.05 significance level.
In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).
We find <span>
Since our t-value is less than <span>