Answer: Std = 6.0
Step-by-step explanation:
Let us take a step by step process to solve this problem.
We have from the question that;
Population 1: 76 77 66 71 55 63 83 58
Population 2: 78 71 71 65 61 71 77 62
where n is no of occurrence = 8
taking the difference of P1 - P2 we have;
Difference (d) : -2 6 -5 6 -6 -8 6 -4
Total value of difference = -7
Difference squared (d₁ -d)² = 4 36 25 36 36 64 36 16
Total value of difference squared (d₁ -d)² = 253
The mean Σ = sum of values (d)/total value = -7/8 = -0.875
⇒ We are asked to find the value of the standard deviation of the paired difference.
Standard deviation is given as;
Std = √(Σ (Δd)² / n-1
Std = √[(253) / 8-1]
Std = √(253/7) = 6.0
Std = 6.0
cheers i hope this helped!!!!!!
The right angled triangle is missing, so i have attached it.
Answer:
Proved below
Step-by-step explanation:
From the attached image, we can see that QP is parallel to BC.
Now, looking at triangles AQP and ABC, we can see that;
∠ AQP = ∠ ABC
Also;
∠ APQ = ∠ ACB
This means that triangles ABC and AQP are similar.
We are told that P is the mid-point of AC.
Thus; AP = PC
We can now say that;
AP:AC = 1:2 and AQ:AB = 1:2
Since AQ:AB = 1:2, it means Q is the midpoint of AB.
Now, ∠ AQP = ∠ BQP
However, according to SAS congruence test, AQP is congruent to BQP.
Thus; AP = BP = CP
Since AP:AC = 1:2 as we saw earlier, then;
BP:AC = 1:2
Thus:
BP/AC = ½
BP = ½AC
Answer:
0.1
Step-by-step explanation:
2x*4 = 0.8
x = 0.1
Perimeter is the sum of all sides, thus 4 * 2x.
Answer:
3
Step-by-step explanation:
9514 1404 393
Answer:
- ∠PAO = 90°
- ∠APO = 30°
- ∠AOB = 120°
- PB ≈ 8.7
Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
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As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.