Answer:
11 over 24 = 0.458
Step-by-step explanation:
Answer:
(3b + c)(a - 2b)
Step-by-step explanation:
Given
3ab - 6b² - 2bc + ac ← Rearranging
= 3ab + ac - 6b² - 2bc (factor the first/second and third/fourth terms )
= a(3b + c) - 2b(3b + c) ← factor out (3b + c) from each term
= (3b + c)(a - 2b)
Answer:
A triangle with angles:
"45°, 45°, 90°"
Is a triangle rectangle, with two catheti of equal length.
Now, there is a lot of problems that you can solve with this:
"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"
Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)
And because the catheti are equal, then the angles are 45°, 45° and 90°.
Answer:
a

b

c
Option A is correct
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
The probability of success is 
The number of success we are considering is r = 10
Now the probability of failure is mathematically evaluated as

substituting value


Now using the binomial distribution to find the probability of exactly 10 successes we have that
![P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}](https://tex.z-dn.net/?f=P%28X%20%3D%20%20r%20%29%20%3D%20%20%5B%5Cleft%20n%20%7D%20%5Catop%20%7Br%7D%7D%20%5Cright.%20%5D%20%2A%20p%5Er%20%2A%20%20q%5E%7Bn-%20r%7D)
substituting values
![P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}](https://tex.z-dn.net/?f=P%28X%20%3D%20%2010%20%29%20%3D%20%20%5B%5Cleft%2015%20%7D%20%5Catop%20%7B10%7D%7D%20%5Cright.%20%5D%20%2A%20p%5E%7B10%7D%2A%20%20q%5E%7B15-%2010%7D)
Where
mean 15 combination 10 which is evaluated with a calculator to obtain
![[\left 15 } \atop {10}} \right. ] = 3003](https://tex.z-dn.net/?f=%5B%5Cleft%2015%20%7D%20%5Catop%20%7B10%7D%7D%20%5Cright.%20%5D%20%20%3D%203003)
So


Now using the normal distribution to approximate the probability of exactly 10 successes, we have that

Applying continuity correction

substituting values


Standardizing

The where
is the mean which is mathematically represented as

substituting values


The standard deviation is evaluated as

substituting values


Thus



From the normal distribution table we obtain the
as

And the 

There value can also be obtained from a probability of z calculator at (Calculator dot net website)
So


Looking at the calculated values for question a and b we see that the values are fairly different.
The bus fare is x, and the ferry fare is y.
x + y = 8
The bus fare will increase by 10% and the ferry fare will increase by 25%.
1.1x + 1.25y = 9.25
Multiply the first equation by -1.1:
-1.1x - 1.1y = -8.8
Add this to the original second equation.
0.15y = 0.45
y = 3
x + y = 8
x + 3 = 8
x = 5
The bus fare is $5, and ferry fare is $3.