Answer:
(h,k) = (32,-4)
r = 32
Step-by-step explanation:
The general equation for a circle is given by:
(1)
where (h,k) is the center of the circle and r is the radius.
You have the following equation:
(2)
You first need to complete squares in order to obtain an equation of the form (1). Thus, you have that the second term must be in a perfect square trinomial:
2b = 64
b = 32
Then, you have to sum 32^2 and also subtract the same number in the expression (2):
you compare the last result with expression (1) and obtain that the raiuds of the circle is r = 32
Furthermore, the center of the circle is (h,k) = (32,-4)
Answer:
Third option i.e. A. 
and B. About 4,323 people
Step-by-step explanation:
We are given that,
Initial population of the town = 2,700
The rate of growth = 4% = 0.04
Part A: Since, the equation for the growth is given by,
Population growth = 
, where P is the initial population, r is the rate of growth and x is the time period of growth.
We have, according to the question,
Population growth = 
i.e. Population growth =
Thus, the equation for the population growth is .
Part B: Now, it is required to find the population after 12 years i.e. x= 12.
So, we have,
Population =
i.e. Population = 
i.e. Population = 
i.e. Population = 4,323
Hence, the population after 12 years is 4,323 people.
Thus, the third option is correct.
Answer:
Step-by-step explanation:
The amount of money that Jason earns is dependent on the amount of time, t in hours that he works
The function f(x) = 15t represents the money he earns for working t hours. Therefore, the dependent variable is f(x) and the independent variable is t
Jason works at least 5 hours but not more than 10. This means that The minimum amount that he can earn is 15×5 = $75
The maximum amount that he can earn is 15×10 = $150
The practical domain is all possible values for t. It becomes
5 lesser than or equal to t lesser than or equal to 10
The practical range is all possible values for f(x). It becomes
75 lesser than or equal to f(x) lesser than or equal to 150
Answer:
y=5x+1
Step-by-step explanation:
If you look closely at each side, you will see that the x increases by one and the y increases by five.
To get to zero (0) from one (1), you need to substract one.
Every time one is subtracted for x, 5 is subtracted from y.
6-5=1
<u>Hope this helps :-)</u>
Answer:
a. Mean = 6
Variance = 2.4
Standard Deviation = 1.55
b. P(X=16) = 0.124
Step-by-step explanation:
Given
n = Total shots = 10
p = Probability of success = 60%
p = 60/100
p= 0.6
q = Probability of failure
q = 1-p
q = 1 - 0.6
q = 0.4
a.
Mean = np
Mean = 10 * 0.6
Mean = 6
Variance = npq
Variance = 10 * 0.6 * 0.4
Variance = 2.4
Standard Deviation = √Variance
Standard Deviation = √2.4
Standard Deviation = 1.549193338482966
Standard Deviation = 1.55 --------- approximated
b.
We have X = 16
x = 10
Assume that the events "success" on the various throws are independent.
The 10th success came on the 16th attempt
So, the player had exactly 10 successes and 6 failures on 16th trial
So Probability = nCr 0.6^10 * 0.4^6
Where n = 15 and r = 9 (number of attempts and success before the 16th trial)
15C9 * 0.6^10 * 0.4^6
= 5005 * 0.0060466176 * 0.004096
= 0.123958563176448
= 0.124 ------ Approximated
