A group of seven kids line up in a random order. Each ordering of the kids is equally likely. There are three girls and four boy
1 answer:
Using the arrangements formula, it is found that there is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.
<h3>What is the arrangements formula?</h3>The number of possible arrangements of n elements is the factorial of n, that is:
.
The total number of outcomes is the arrangement of 7 elements, hence:
T = 7! = 5040.
The desired number of outcomes is all girls(3!), then all boys(4!), hence:
D = 3! x 4! = 6 x 24 = 144.
Hence, the probability is:
p = D/T = 144/5040 = 0.0286.
There is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.
More can be learned about the arrangements formula at brainly.com/question/24648661
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Answer:
Step-by-step explanation:
The standard form of a quadratic equation is
The vertex form of a quadratic equation is
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
In this case, our quadratic equation is . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
⇒
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is
⇒
⇒
⇒
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is:
a: 1
h: 3
k: -25
Hope this helps!