Answer:
B. Generate 5 random integers from 1 to 10 and see how many times the numbers 1 to 8 are generated.
Step-by-step explanation:
William wants to simulate 5 shots with an 80% chance each shot. Let's see what is each option simulate
A.
This option is wrong. Since you generate 8 different possibilities(1-8), the chance for each is 1/8= 12.5%. The chance for either 3 and 5 is 25% and it's far from 80%
B.
This option is true. You generate 5 numbers which represent the 5 shots. Since you generate 10 different possibilities(1-10), the chance for each is 1/10= 10%. The chance for 1 to 8 is 80% .
C.
There is no information about the chance for the dart score, so this option won't simulate the situation accurately.
D.
This option is wrong. You generate 3 numbers which represent the 3 shots instead of 5.
To factor 3x + 9 you should know that 3 is a common factor of both 3 and 9, so you can factor 3 out in both numbers like this.
3x + 9
3(x + 3)
When you factor out 3 on both numbers you should know that 3 X 3 = 9 and since you factored out 3 there would be another 3 left so you would have the answer: 3(x + 3)
Here is another equation that might help:
24x + 36
Since 12 is a common factor of both numbers, factor 12 out of the equation:
12 (2x + 3)
You know that 12 x 2 = 24 and that 12 x 3 = 36
And since you can't factor out anymore numbers because 2 and 3 doesn't have any common factors with each other you get the answer:
12 (2x + 3)
Answer:
(30,35,0)
Step-by-step explanation:
We are given that
The velocity of particle,
Substitute 
The tangent line at t=3 is given by
Now, substitute t=4
Hence, the position of particle at 
=(30,35,0)
Answer:
Step-by-step explanation:
<u>Given quadratic function:</u>
<u>Points on the graph:</u>
- (-2,-35), (1,-5), (3,- 15)
<u>Substitute values of x and y and solve the system of equations:</u>
- -35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
- -5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
- -15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3
<u>Subtract eq 2 from eq 1:</u>
- -35 - (-5) = 4a - 2b + c - a - b - c
- -30 = 3a - 3b
- b = a + 10 ⇔ eq 4
<u>Subtract eq 2 from eq 3:</u>
- -15 - (-5) = 9a + 3b + c - a - b - c
- -10 = 8a + 2b
- b = -4a - 5 ⇔ eq 5
<u>Compare eq 4 and eq 5, solve for a:</u>
- a + 10 = -4a - 5
- a + 4a = -5 - 10
- 5a = -15
- a = -3
<u>Find the value of b using eq 4:</u>
<u>Find the value of c using eq 2:</u>
- -5 = -3 + 7 + c
- c = -5 - 4
- c = -9
<u>We now have a, b and c:, the function is:</u>
