9514 1404 393
Answer:
∠A = 44°
Step-by-step explanation:
In order to find the measure of angle A, you need to know the value of the variable x. This means you need some relation that you can solve to find x.
Happily, that relation is "the sum of angles in a triangle is 180°." This means ...
84° +(x +59)° +(x +51)° = 180°
(2x + 194)° = 180° . . . collect terms
2x = -14 . . . . . . . . . . divide by °, and subtract 194
x = -7 . . . . . . . . . . . .divide by 2
Now, the measure of angle A is ...
∠A = (x +51)° = (-7 +51)°
∠A = 44°
First, let's calculate the mean and the mean absolute deviation of the first bowler.
FIRST BOWLER: <span>8,5,5,6,8,7,4,7,6
Mean = (Sum of all data)/(Number of data points) = (8+5+5+6+8+7+4+7+6)/9
<em>Mean = 6.222</em>
Mean absolute deviation or MAD = [</span>∑(|Data Point - Mean|]/Number of Data Points
MAD = [|8 - 6.222| + |5 - 6.222| + |5 - 6.222| + |6 - 6.222| + |8 - 6.222| + |7 - 6.222| + |4 - 6.222| + |7 - 6.222| + |6 - 6.222|]/9
<em>MAD = 1.136</em>
SECOND BOWLER: <span>10,6,8,8,5,5,6,8,9
</span>Mean = (Sum of all data)/(Number of data points) = (<span>10+6+8+8+5+5+6+8+9</span>)/9
<em>Mean = 7.222</em>
Mean absolute deviation or MAD = [∑(|Data Point - Mean|]/Number of Data Points
MAD = [|10 - 7.222| + |6 - 7.222| + |8 - 7.222| + |8 - 7.222| + |5 - 7.222| + |5 - 7.222| + |6 - 7.222| + |8 - 7.222| + |9 - 7.222|]/9
<em>MAD = 1.531
</em>
The mean absolute deviation represents the average distance of each data to the mean. Thus, the lesser the value of the MAD is, the more consistent is the data to the mean. <em>B</em><em>etween the two, the first bowler is more consistent.</em>
Anything to the power of 0 is just 1
The statements and reasons why the given statements are true are presented in the following two column proofs;
Question 1
Given: 9·(x + 6) - 41 = 75

Statement
Reason
S1. 9·(x + 6) - 41 = 75
R1. <u>Given</u>
S2. 9·(x + 6) = 116
R2. <u>Addition property</u>
S3. <u>9·x + 54 = 116 </u>
R3. Distributive property
S4. 9·x = 62
R4. <u>Subtraction property</u>
S5.
R5. <u>Division property of equality</u>
Question 2.
Statement
Reason
S1. m∠A + m∠B = m∠D
R1. Given
S2. ∠C and ∠D form a Linear Pair
R2. Definition of linear pair
S3. ∠C and ∠D are supplementary
R3. <u>Linear pair ∠s are supplementary</u>
S4. <u>∠C + ∠D = 180° </u>
R4. Definition of supplementary
S5. m∠C + m∠A + m∠B = 180°
R5. <u>Substitution property</u>
Question 3.
Statement
Reason
S1. ∠BDA ≅ ∠A
R1. Given
S2. ∠BDA ≅ ∠CDE
R2. <u>Vertical angle theorem</u>
S3. ∠CDE ≅ ∠A
R3. Transitive property of congruency
S4. m∠CDE = m∠A
R4. <u>Definition of congruency</u>
S5. <u>(13·x + 20)° = (14·x + 15)°</u>
R5. Substitution Property of Equality
S6. 14·x° = 13·x + 5°
R6. <u>Subtraction property</u>
S7. x = 5
R7. Subtraction property
Learn more here:
brainly.com/question/11331230
Answer:
461.8
Step-by-step explanation:
V=(1/3) πr^2h
V=(1/3)π(7^2)9
V=461.8
Sorry inputed wrong in calculator first time