Answer:
The Answer is: Josh hit 47 balls.
Step-by-step explanation:
Let j = Josh number of hits and c = Caiden number of hits:
j = c/2 + 9
Total:
j + c = 123.
Substitute:
(c/2 + 9) + c = 123
c/2 + c = 123 - 9
c/2 + c = 114
1/2c + 2/2c = 114
3/2c = 144
c = 144 (2/3) = 76, Number of hits for Caiden
Solve for j:
j = 76/2 + 9
j = 38 + 9 = 47, number of hits for Josh
Proof:
j + c = 123
47 + 76 = 123
123 = 123
Hope this helps! Have an Awesome Day!! :-)
Both Rhianna and Christopher were correct as they took different reference angles.
Step-by-step explanation:
Step 1:
The value of the tan of a reference angle is calculated using the above formula.
The hypotenuse is the longest side of the triangle is always opposite the right angle of the triangle.
In this triangle, the hypotenuse is the side measuring 5 units.
Step 2:
When the reference angle is A, the opposite side measures 3 units and the adjacent side measures 4 units.
So 
When the reference angle is C, the opposite side measures 4 units and the adjacent side measures 3 units.
So 
So both Rhianna and Christopher were right as they took different reference angles i.e. A and C.
The only correct answer would be A because of the following reasons
1. Sin is defined as opposite/hypotenuse
2. Cos is defined as adjacent/hypotenuse
Answer:
Part 1. 0.9259 % per year
Part 2. P = 281.4e^(0.009 259t); 338.6 million
Step-by-step explanation:
Data:
P₀ = 281.4 million
P = 308.7 million
Part 1. Growth rate
t = 2010 - 2000 = 10 yr
P = P₀e^(rt)
308.7 = 281.4e^(10r)
e^(10r) = 1.0970
10r = ln1.0970
r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259
r = 0.9259 % per year
The 10-year continuous growth rate is 0.9259 % per year.
Part 2. Population model
The population model is
P = 281.4e^(0.009 259t)
where P is in millions and t is the number of years since 2000.
By 2020,
P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203
P = 338.6 million
The estimated population in 2020 is 338.6 million.
