Please help me and thank you.
2 answers:
Answer:
Step-by-step explanation:
The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.
Area of the rectangle:
Area of the triangle:
Thus, the area of the figure is
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Answer:
<u>Triangle ABC and triangle MNO</u> are congruent. A <u>Rotation</u> is a single rigid transformation that maps the two congruent triangles.
Step-by-step explanation:
ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).
- length of AB = √[(12-4)² + (8-8)²] = 8
- length of AC = √[(12-4)² + (8-14)²] = 10
- length of CB = √[(4-4)² + (8-14)²] = 6
ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).
- length of MN = √[(4-4)² + (16-8)²] = 8
- length of MO = √[(4+2)² + (16-8)²] = 10
- length of NO = √[(4+2)² + (8-8)²] = 6
Therefore:
- AB ≅ MN
- AC ≅ MO
- CB ≅ NO
and ΔABC ≅ ΔMNO by SSS postulate.
In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.
Answer:
The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution should be 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 = 28 - 1 = 27
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.314
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 34.6 - 0.646 = $33.954
The upper end of the interval is the sample mean added to M. So it is 34.6 + 0.646 = $35.246
The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.