Answer:
vertex = (- 2, - 36)
Step-by-step explanation:
Given a parabola in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
f(x) = 5x² + 20x - 16 is in standard form
with a = 5, b = 20 and c = - 16
= -
= - 2
Substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = 5(- 2)² +20(- 2) - 16 = 20 - 40 - 16 = - 36
vertex = (- 2, - 36)
Answer:
The probability is 0.0775
The expected value is 4.75 clubs
The standard deviation is 1.8875 clubs
Step-by-step explanation:
The variable X follows a binomial distribution, because we have n identical and independent events (19 cards) with a probability p of success and 1-p of fail (there is a probability of 1/4 to be club and 3/4 to be diamond, heart or spade). Then, the probability that x of the n cards are club is:
So, the probability P of drawing at least 8 clubs is:
P = P(8) + P(9) + P(10) + ... + P(18) + P(19)
Replacing, the values of x, from 8 to 19, on the equation above, we get:
P = 0.0775
Additionally, the expected value E(x) and standard deviationS(x) for this distribution is given by:
E(x)=np = 19(0.25) = 4.75
Using the given information and what we know about linear equations, we will find the sketch below.
<h3>How to sketch a graph?</h3>Here we need to analyze each part separately.
In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:
First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.
Then he stops for 20 minutes, this is represented with a horizontal line.
Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.
So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation
The sketch can be seen below.
If you want to learn more about linear equations, you can read:
