Sample space is the set of possible outcomes of an experiment.
1. <span>Tossing a coin three times
There are possible outcomes.
Tossing the coin for the first time it can be a haid (H) or a tail (T). So, we can have this outcomes:
HHH
HHT
HTH
THH
TTH
THT
TTT
total: 6 outcomes
2. </span><span>The order that the top 5 students will receive their diplomas.
Here we need to find the number of permutations: 5!=5*4*3*2*1=120
3. </span><span>Tossing a pair of dice
The possible outcomes are the following: (a,b), where a is the first dice and b is the second dice
</span>(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) , total 36 possible outcomes.
You can rewrite the differential equation as
This last expression looks like the one you describe. If you solve for A instead of t, you get
This is the same as your other answer.
Answer: It is proportional because 195/3 equals 65 and 325/5 equals 65 as well, so it is proportional.
Hope this helps! :)
Answer:
First question
a = 1 , h = 0 , k = 6 ⇒ third answer
Second question
y = 2x² + 4 ⇒ second answer
Third question
No of the choices correct ⇒ fourth answer
Step-by-step explanation:
First question
∵ f(x) = x² + 6
- It is a quadratic function with general form ax² + bx + c
- Its vertex is (h , k), where h = -b/2a and k = f(h)
∵ a = 1 , b = 0 , c = 6
∴ h = 0/2(1) = 0
∴ f(0) = 0² + 6 = 6
∴ a = 1 , h = 0 , k = 6 ⇒ third answer
Second question
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
∵ y = 2x²
∵ y is shifted 4 units up
∴ k = 4
∴ y + 4 = 2x² + 4
∴ y = 2x² + 4 ⇒ second answer
Third question
∵ y = -2x² + 3
- It is a quadratic equation with general form ax² + bx + c
- It represented graphically by parabola
- If a is positive the parabola opens upward
- If a is negative the parabola opens downward
∵ a = -2
∴ The parabola opens downward
∴ No of the choices correct ⇒ fourth answer
