Answer:0.09 < 0.6 < 0.7 < 0.8 < 0.99 < 1
Step-by-step explanation:
Answer:
Option B
Step-by-step explanation:
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
By substituting the values in the given expression,
7² = x² + 2²
49 = x² + 4
x² = 49 - 4
x² = 45
x = √45
x = 3√5
x = 6.7 ft
Option B will be the correct option.
Answer:
a) P(X ≤ 2) = 0.87
b) P(X ≥ 5) = 0.01
c) P(1 ≤ X ≤ 4) = 0.71
d) P ( X = 0 ) = 0.28
e) σ(X) = 1.09 , E(X) = 1.25
Step-by-step explanation:
Given:
- Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.05)
Where, n = 25 and p = 0.05
Find:
(a) Determine P(X ≤ 2).(b) Determine P(X ≥ 5).(c) Determine P(1 ≤ X ≤ 4).(d) What is the probability that none of the 25 boards is defective?(e) Calculate the expected value and standard deviation of X.
Solution:
- The probability mass function for a binomial distribution is given by:
P ( X = x ) = nCr * (p)^r * ( 1 - p )^(n-r)
a) P(X ≤ 2):
P(X ≤ 2) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 )
= (0.95)^25 + 25*0.05*0.95^24 + 25C2*0.05^2*0.95^23
= 0.87
b) P(X ≥ 5):
P(X ≥ 5) = 1 - [P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)
= 1 - [ 0.87 + 25C3*0.05^3*0.95^22 + 25C4*0.05^4*0.95^21]
= 1 - 0.98994
= 0.01
c) P(1 ≤ X ≤ 4):
P(1 ≤ X ≤ 4) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)
= ( 0.87 - 0.95^25) + 0.11994
= 0.71
d) P( X = 0 )
P ( X = 0 ) = 0.95^25 = 0.28
e) E(X) & σ(X):
E(X) = n*p
E(X) = 25*0.05 = 1.25
σ(X) = sqrt ( Var (X) )
σ(X) = sqrt ( n*p*(1-p) ) = sqrt ( 25*0.05*0.95 )
σ(X) = 1.09
I got u!
Okay,
B is initial amount of followers, which is 100.
R is the growth rate which would be 1% every 12 hours. For the sake of this problem, it uses days as a time marker so I will bump it up to 2% since there are 24 hours in the day.
T is time.
Here is our equation based on the given facts:
F(x)= 100(1+0.02)^t (2% here is 0.02 in decimal form) (^t is the exponent)
Now the first question:
Plug in 5 for t (time) since it’s asking abt 5 days. Here’s the equation filled out:
F(x)=100(1+0.02)^5
Now you would solve for f(x).
You get 110.4. (If you need me to go into detail here of how I got 110.4 just let me know and I’d be happy to expand on it!)
1) 110.4 followers
Now number 2; she wants 1 million followers eventually. Looking back out our equation, we can keep everything the same, but since she eventually wants 1 mil, we need to plug in 1 mil for f(x). Since we aren’t sure how many days it will take, we need to keep t. Here it is:
1,000,000=100(1+0.02)^t
We need to solve for t to find out how many days it will take her. (Again, I can go into detail if you need) 465.1 days.
2) it will take Taylor 465 days to get 1 million followers
3) the chart; ( I’m rounding up to the nearest whole number here.)
0 = 0
10 = 122
20 = 149
50 = 269
100 = 724
300 = 38,023
500 = 1,995,657
4) the amount of followers are increasing so fast, because in exponential equations, the rate is increasing. For example here, the exponential number (t) is days. Every day this number will go up causing the rate of her followers to skyrocket.
5) just plot those points I gave you above. :)
Answer: the value of y is - 2
Step-by-step explanation:
