Answer:
<h2>A.</h2>
Step-by-step explanation:
The given table is
Days Bees
0 10,000
10 7,500
20 5,600
30 4,200
40 3,200
50 2,400
Where 
represents days and 
represents bees.
The exponential function that models this problem must be like
, which represenst an exponential decary, because in this case, the number of bees decays.
We nned to use one points, to find the rate of decay. We know that 
, because it starts with 10,000 bees.
Let's use the points (10, 7500)
Solving for 
, we have
Using logarithms, we have
Replacing all values in the model, we have
Therefore, the right answer is the first choice, that's the best approximation to this situation.
Answer:
1. 0
2. 18 th term
3. 209
4. 670
Step-by-step explanation:
1. n^th term of an A.P = a + (n - 1)d , where n is the term
6 = a + (5 - 1)d ... (i)
5 = a + (6 - 1)d ... (ii)
a + 4d = 6 ... (i)
a + 5d = 5 ... (ii)
Subtracting (ii) - (i) we get;
0 + d = -1 , d = -1
So the common difference (d) = -1
And first term (a);
a + 4(-1) = 6
a = 6 + 4 = 10
11^th term will be;
= 10 + -1(11 - 1) = 10 - 10 = 0
2. The A.P is;
1, 4, 7, 10, 14, ....
The first term (a) = 1
The common difference (d) = 3
= a + (n - 1)d
52 = 1 + (n - 1)3
3n - 3 + 1 = 52
3n = 52 + 2 = 54
n = 54/3 = 18 th term
3. The A.P is;
4, 9, 14, ... , 254
The first term (a) = 4
The common difference (d) = 5
= a + (n - 1)d
To find what term number 254 is;
254 = 4 + (n - 1)5
5n - 5 + 4 = 254
5n = 254 + 1 = 255
n = 255/5 = 51
The 10^th term from the end of the AP is the 42^nd term.
= 4 + (42 - 1)5 = 4 + 205 = 209
4. The A.P is;
5, 8, 11, 14, ...
The first term (a) = 5
The common difference (d) = 3
Sum of n terms in an A.P is given by;
= 
(2a + (n - 1)d)
= 
(10 + 19(3) = 10(10 +57) = 670
Step-by-step explanation:
According to the U.S. Census Bureau, about 63% of Americans are adults (18 and over). Use the U.S. population estimate of 308 million people to calculate the number of American adults in 2010. Round to the nearest hundred thousand adults
Answer:
Step-by-step explanation:
Factor the Polynomial.
3
x
4
(
x
+
5
)
2
Answer:
Option (4)
Step-by-step explanation:
By the property of exterior angle of a triangle,
"Exterior angle of a triangle is equal to the sum of two opposite interior angles."
In the triangle ABC,
∠ACD is an exterior angle and ∠BAC and ∠ABC are the opposite interior angles.
m∠ACD = m∠BAC + m∠ABC
95° = m∠BAC + m∠ABC
Therefore, Option (4) will be the correct option.
