Answer:
the solution of the system is:
x = 1 and y = 2.
Step-by-step explanation:
I suppose that we want to solve the equation:
-6*x + 6*y = 6
6*x + 3*y = 12
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate y in the first equation:
6*y = 6 + 6*x
y = (6 + 6*x)/6
y = 6/6 + (6*x)/6
y = 1 + x
Now we can replace this in the other equation:
6*x + 3*(1 + x) = 12
6*x + 3 + 3*x = 12
9*x + 3 = 12
9*x = 12 - 3 = 9
x = 9/9 = 1
Now that we know that x = 1, we can replace this in the equation "y = 1 + x" to find the value of y.
y = 1 + (1) = 2
Then the solution of the system is:
x = 1 and y = 2.
Answer:
(A) There should have been 5 outcomes of HT
(B) The experimental probability is greater than the theoretical probability of HT.
Step-by-step explanation:
Given
-- Sample Space
--- Sample Size
Solving (a); theoretical outcome of HT in 20 tosses
First, calculate the theoretical probability of HT
![P(HT) = \frac{n(HT)}{n(S)}](https://tex.z-dn.net/?f=P%28HT%29%20%3D%20%5Cfrac%7Bn%28HT%29%7D%7Bn%28S%29%7D)
![P(HT) = \frac{1}{4}](https://tex.z-dn.net/?f=P%28HT%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
Multiply this by the number of tosses
![P(HT) * n= \frac{1}{4} * 20](https://tex.z-dn.net/?f=P%28HT%29%20%2A%20n%3D%20%5Cfrac%7B1%7D%7B4%7D%20%2A%2020)
![P(HT) * n= 5](https://tex.z-dn.net/?f=P%28HT%29%20%2A%20n%3D%205)
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Solving (b); experimental probability of HT
Here, we make use of the table
![P(HT) = \frac{n(HT)}{n(S)}](https://tex.z-dn.net/?f=P%28HT%29%20%3D%20%5Cfrac%7Bn%28HT%29%7D%7Bn%28S%29%7D)
![P(HT) = \frac{6}{20}](https://tex.z-dn.net/?f=P%28HT%29%20%3D%20%5Cfrac%7B6%7D%7B20%7D)
---- Experimental Probability
In (a), the theoretical probability is:
![P(HT) = \frac{1}{4}](https://tex.z-dn.net/?f=P%28HT%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
---- Experimental Probability
By comparison;
![0.30 > 0.25](https://tex.z-dn.net/?f=0.30%20%3E%200.25)
ok so for the 2 ft pillows the perimeter would be 8 ft and for the 1 ft pillows the perimeter would be 3 ft. So you would need 8(2)+3(3)=16+9=25 so she needs 25 feet of trimming.
Answer:
The proof is given below.
Step-by-step explanation:
Given m∠AEB = 45° and ∠AEC is a right angle. we have to prove that EB divides ∠AEC into two congruent angles, it is the angle bisector.
Given ∠AEC=90° (Given)
∠AEC=∠AEB+∠BEC
⇒ 90° = 45° +∠BEC (Substitution Property)
By subtraction property of equality
⇒ ∠BEC = 90° - 45° = 45°
Hence, both angles becomes equal gives ∠AEB≅∠BEC
Since EB divides ∠AEC into two congruent angles, ∴ EB is the angle bisector.