Answer:
a). Area = 54 square units
b). Perimeter = 33.7 units
Step-by-step explanation:
Vertices of the triangle ABC are A(-4, -2), B(1, 7) and C(8, -2).
(a). Area of the triangle ABC =
(Absolute value)
By substituting the values from the given vertices,
Area = ![\frac{1}{2}[(-4)(7+2)+(1)(-2+2)+8(-2-7)]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%28-4%29%287%2B2%29%2B%281%29%28-2%2B2%29%2B8%28-2-7%29%5D)
= ![\frac{1}{2}[-36+0-72]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B-36%2B0-72%5D)
= 
= (-54) unit²
Therefore, absolute value of the area = 54 square units
(b). Distance between two vertices (a, b) and (c, d)
d = 
AB = 
= 
= 10.295 units
BC = 
= 
= 11.402 units
AC = 
= 12 units
Perimeter of the triangle = AB + BC + AC = 10.295 + 11.402 + 12
= 33.697
≈ 33.7 units
Answer:
Step-by-step explanation:
i dont the answer dude
Answer:
The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 27 - 1 = 26
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.7787.
The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 4.9 - 3.7 = 1.2.
The upper end of the interval is the sample mean added to M. So it is 4.9 + 3.7 = 8.6.
The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).
Answer:
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Step-by-step explanation:
<em>blue</em><em> </em><em>pens</em><em>=</em><em>720×40%</em>
<em>blue</em><em> </em><em>pens</em><em>=</em><em>720×40/100</em>
<em>blue pens</em><u>=</u><u>288</u>