Sketch the figure: Two different isosceles triangles with perimeter 4a + b
1 answer:
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Answer:
C. H0: µD = 0, HA: µD <0
Step-by-step explanation:
We assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. So for this case is better apply a paired t test.
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 for pretest , y = test value for posttest
x: 66, 94, 87, 84, 76, 88
y: 75, 100, 93, 85, 75, 90
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
Because the difference D is defined as Pretest-Postest. And we want to see if the postets score is higher than the pretest with th training.
The first step is calculate the difference and we obtain this:
d: -9, -6, -6, -1, 1, -2
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 :
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:
The p value is lower than the significance level assumed , so then we can conclude that we can reject the null hypothesis. So we can say that the differences between Pretest and Posttest
are less than 0.
To solve this problem, you must find the altitude, represented by a dashed line in this picture.
To do this, use the Pythagorean theorem: a^2 + b^2 = c^2
The hypotenuse (longest side in a triangle) is always the c value. So plug that into your equation for c.
This leaves you with:
a^2 + b^2 = 10^2
Next, plug in your one side length of the triangle that you have besides the hypotenuse, which is a 5. This will be your b value.
This leaves you with:
a^2 + 5^2 = 10^2
After that, square your number values to simplify the equation. To square a number, you multiply it by itself. In this case, 5 x 5 = 25 and 10 x 10 = 100.
So when you rewrite your equation you have:
a^2 + 25 = 100
To start to isolate your variable, subtract 25 on both sides of the equation to keep it balanced.
This results in:
a^2 = 75
To isolate your variable, square root the a variable and square root the other side to keep it balanced. A square root cancels out a square, so that’s how you know you can do this.
Since 75 isn’t a perfect square, find the highest perfect square that’s able to be multiplied to get 75. This is 25. 25 x 3 = 75 so put that under a radical sign.
After that, simplify the radical by taking the perfect square out of the “jail” (square root sign) this causes the perfect square to be square-rooted as it moves across to the other side of the sign. So, your final answer has a five on the outside of the radical sign with a 3 left inside.
So your final answer is:
5 radical sign 3.
(I apology for e lack of math symbols, I am on the road on vacation so I am on mobile.
I hope this still helps! :)
To do this, use the Pythagorean theorem: a^2 + b^2 = c^2
The hypotenuse (longest side in a triangle) is always the c value. So plug that into your equation for c.
This leaves you with:
a^2 + b^2 = 10^2
Next, plug in your one side length of the triangle that you have besides the hypotenuse, which is a 5. This will be your b value.
This leaves you with:
a^2 + 5^2 = 10^2
After that, square your number values to simplify the equation. To square a number, you multiply it by itself. In this case, 5 x 5 = 25 and 10 x 10 = 100.
So when you rewrite your equation you have:
a^2 + 25 = 100
To start to isolate your variable, subtract 25 on both sides of the equation to keep it balanced.
This results in:
a^2 = 75
To isolate your variable, square root the a variable and square root the other side to keep it balanced. A square root cancels out a square, so that’s how you know you can do this.
Since 75 isn’t a perfect square, find the highest perfect square that’s able to be multiplied to get 75. This is 25. 25 x 3 = 75 so put that under a radical sign.
After that, simplify the radical by taking the perfect square out of the “jail” (square root sign) this causes the perfect square to be square-rooted as it moves across to the other side of the sign. So, your final answer has a five on the outside of the radical sign with a 3 left inside.
So your final answer is:
5 radical sign 3.
(I apology for e lack of math symbols, I am on the road on vacation so I am on mobile.
I hope this still helps! :)