What is the mean, median, mode, and range of this data set, 2,3,2,4,3,3,3,4,2,3,4,2,4,4,9,3,4,4
slava [35]
Answer:
Mean: 3.5
Median: 3
Mode: 4
Range: 7
Step-by-step explanation:
<h3>Answer: 6.95</h3>
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Explanation:
The reference angle is angle S = 41 degrees. The side opposite that (RT) is unknown and what we want to find. The adjacent side to the reference angle is TS which is 8 units long.
RT = x
TS = 8
The ratio of the opposite and adjacent side is equal to the tangent of the reference angle, so,
tan(angle) = opposite/adjacent
tan(41) = x/8
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We are given the value of tan(41) to be approximately 0.869, which means we will replace "tan(41)" with this decimal value and then isolate x by multiplying both sides by 8. This happens in the section below.
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tan(41) = x/8
0.869 = x/8
8*0.869 = 8*x/8
6.952 = x
x = 6.952
x = 6.95
RT = 6.95
Answer:
1000 m³
Step-by-step explanation:
The base of a cube is just a square.
The area of a square is
, where l is the length.
Since we know the area of the base (the square) we can find l easily.
![l^2 = 100\\\\l = \sqrt{100}\\\\l=10](https://tex.z-dn.net/?f=l%5E2%20%3D%20100%5C%5C%5C%5Cl%20%3D%20%5Csqrt%7B100%7D%5C%5C%5C%5Cl%3D10)
Now that we know the length of the sides, we have to take note that a cube has side lengths that are all congruent.
This means the height of the cube is also 10m.
Since the volume of a cube is represented as
, where l is the length, we can substitute 10 in as
to find it's total volume.
![10^3 = 1000](https://tex.z-dn.net/?f=10%5E3%20%3D%201000)
So the volume of this cube is 1000 m³.
Hope this helped!
Focus on the triangle PQN and triangle SQP, prove that they are similar:
PQ=PR, PN is the altitude, so QN=NR=9
PQ of ΔSQP:QN=15:9=5:3
PS:PN=20:12=5:3
∠PQN=∠SQP (they are the same angle, reflexive property)
therefore, according to the SAS similarity theorem, ΔPQN is similar to ΔSQP
∠PNQ=∠SPQ =90 degree
therefore, QPS is a right angle.
you may have to reword it depending on what your teacher requires, column proof or paragraph proof.