Answer:
<em>Maximum: (-1,9)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic function</u>
If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:
Where a is the leading coefficient.
We are given the following function:
To find the vertex, we need to complete squares. First, factor -2 on the first two terms:
The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:
Taking out the -1:
Factoring the trinomial and operating:
Comparing with the vertex form we have
Vertex (-1,9)
Leading coefficient: -2
Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.
Maximum: (-1,9)
Complete question :
Suppose someone gives you 8 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $8 if you succeed and you lose $2 if you fail. What is the expected value of this game to you? What can you expect if you play 100 times.
Answer:
$0.5 ; win $50 with 100 rolls
Step-by-step explanation:
From a roll of two fair dice; probability of obtaining an even number :
Even numbers = (2, 4, 6) = 3
P = 3 /6 = 1 /2
For 2 fair dice ; probability of rolling two even numbers : independent event.
1/2 * 1/2 = 1/4
Hence, p(success) = 1/4 ; P(failure) = 1 - 1/4 = 3/4
Probability table
Winning = $8 or loss = - $2
X : ____ 8 ______ - 2
P(x) __ 1/4 ______ 3/4
Expected value : E(x) = ΣX*P(x)
E(x) = (8 * 1/4) + (-2 * 3/4)
E(x) = 2 - 1.5
E(x) = $0.5
Since expected value is positive, the expect to win
If played 100 times;
Expected value = 100 * $0.5 = $50
Step-by-step explanation:
345x19=467 that's it good luck
Answer:
B. 333 in.2
Step-by-step explanation:
The area of the base is 81^2
lateral is 45 x 4 = 180^2 (9x5x4)
180^2 add the 72 pyramid = 252^2 + base of 81^2 = 333^2
Composite figueres i do like this as shown to you a few seconds ago.
The triangle shows us just the height
4 inches
We can see that height is smaller central isosceles height across the center base point.
We also can remember to use the length 9inches but divide by 2 and get each triangle area this way.
4 x 1/2 base = 4x 1/2 4.5 = 4 x 2.25 = 9^2 each right side triangle
9 x 8 = 72^2
we add the areas 72+ 81+lateral 180 = 333 inches^2
Total slices=4*6=24. Take away 3 slices leaving 21=18+3=3 pizzas and ½ a pizza, 3½.
