Answer:
2 x^2 - 3 x + 6
Step-by-step explanation:
Simplify the following:
-(3 x^2 + 4 x - 17) + 5 x^2 + x - 11
-(3 x^2 + 4 x - 17) = -3 x^2 - 4 x + 17:
-3 x^2 - 4 x + 17 + 5 x^2 + x - 11
Grouping like terms, 5 x^2 - 3 x^2 + x - 4 x - 11 + 17 = (5 x^2 - 3 x^2) + (x - 4 x) + (-11 + 17):
(5 x^2 - 3 x^2) + (x - 4 x) + (-11 + 17)
5 x^2 - 3 x^2 = 2 x^2:
2 x^2 + (x - 4 x) + (-11 + 17)
x - 4 x = -3 x:
2 x^2 + -3 x + (-11 + 17)
17 - 11 = 6:
Answer: 2 x^2 - 3 x + 6
Answer:
Step-by-step explanation:
The correct answer is the last number line because with an inequality, the "equal to" sign below the "<" or ">" means the circle should be filled in. The line is traveling in a negative direction because the inequality says that n is less than -1.
Answer:
a

b

Step-by-step explanation:
From the question we are told that
The number of students in the class is N = 20 (This is the population )
The number of student that will cheat is k = 3
The number of students that he is focused on is n = 4
Generally the probability distribution that defines this question is the Hyper geometrically distributed because four students are focused on without replacing them in the class (i.e in the generally population) and population contains exactly three student that will cheat.
Generally probability mass function is mathematically represented as

Here C stands for combination , hence we will be making use of the combination functionality in our calculators
Generally the that he finds at least one of the students cheating when he focus his attention on four randomly chosen students during the exam is mathematically represented as

Here




Hence


Generally the that he finds at least one of the students cheating when he focus his attention on six randomly chosen students during the exam is mathematically represented as

![P(X \ge 1) =1- [ \frac{^{k}C_x * ^{N-k}C_{n-x}}{^{N}C_n}]](https://tex.z-dn.net/?f=P%28X%20%20%5Cge%201%29%20%3D1-%20%5B%20%20%5Cfrac%7B%5E%7Bk%7DC_x%20%2A%20%5E%7BN-k%7DC_%7Bn-x%7D%7D%7B%5E%7BN%7DC_n%7D%5D%20)
Here n = 6
So
![P(X \ge 1) =1- [ \frac{^{3}C_0 * ^{20 -3}C_{6-0}}{^{20}C_6}]](https://tex.z-dn.net/?f=P%28X%20%20%5Cge%201%29%20%3D1-%20%5B%20%20%5Cfrac%7B%5E%7B3%7DC_0%20%2A%20%5E%7B20%20-3%7DC_%7B6-0%7D%7D%7B%5E%7B20%7DC_6%7D%5D%20)
![P(X \ge 1) =1- [ \frac{^{3}C_0 * ^{17}C_{6}}{^{20}C_6}]](https://tex.z-dn.net/?f=P%28X%20%20%5Cge%201%29%20%3D1-%20%5B%20%20%5Cfrac%7B%5E%7B3%7DC_0%20%2A%20%5E%7B17%7DC_%7B6%7D%7D%7B%5E%7B20%7DC_6%7D%5D%20)
![P(X \ge 1) =1- [ \frac{1 * 12376}{38760}]](https://tex.z-dn.net/?f=P%28X%20%20%5Cge%201%29%20%3D1-%20%5B%20%20%5Cfrac%7B1%20%20%2A%20%2012376%7D%7B38760%7D%5D%20)


Answer: Draw a line through the two points (0,2) and (3,3). See the attached image below.
How did I get these two points? The first point comes from the fact that "at the start, the height is 2 inches" meaning that x = 0 hours and y = 2 inches pair up together. This is show as point A. This is the y intercept as this is the location where the blue graph crosses the vertical y axis.
Point B is found by moving 1 unit up from point A and 3 units to the right to land on (3,3). So we have x = 3 hours and y = 3 inches pair up together.
Note: the slope is rise/run = 1/3 helping us determine the unit rate or speed in which the water is rising (ie the water is rising one-third of an inch per hour)