1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andreyandreev [35.5K]
3 years ago
13

A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase

of 4% per year beginning in the second year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.
Mathematics
1 answer:
FrozenT [24]3 years ago
6 0

Answer: the athlete's salary for year 7 of the contract is $3795957

Step-by-step explanation:

The player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4%. This means that the amount he gets each year is 1.04 times of the previous year's amount. The rate at which his salary increases is in geometric progression. The nth term of a geometric progression is expressed as

Tn = ar^n-1

Where

Tn is the salary for the nth year

a is the salary for the first year

r is the rate at which the salary is increasing. So

a = 3,000,000

n = 7

r = 1.04

We want to determine T7. It becomes

T7 = 3000000 × 1.04^(7-1)

T7 = 3000000 × 1.04^6

Tn = $3795957

You might be interested in
Missing value in the equivalent fraction 2/5 = ?/15
Schach [20]
The missing value is 6 so 2/5 = 6/15
8 0
2 years ago
Read 2 more answers
The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr
-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the <em>y-intercept (s-intercept) in this case is 6</em>. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is <em>no x-intercept (t-intercept)</em>. It means that there is <em>not</em> a single year when the number of shirts sold is 0.


(PART B): As you can see in the graph (attached with the question) that the <em>f(t)</em> is increasing (exponentially) with the increase in <em>t. </em>Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."


(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = \frac{y_2 - y_1}{x_2 - x_1} --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = \frac{22-12.5}{7-5} = 4.75

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).


(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in <em>hundreds. </em>It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

g(t) = f(t) + 10 --- (Y)

Why did I add f(t)? Because in the question, the word "<em>and</em>" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15

Hence, g(t) is (1.5)^t + 15

8 0
3 years ago
Read 2 more answers
If f={(0,2),(2,6),(3,5),(4,9)} what is f^(-1)(9)
tangare [24]

Answer is 9 f-^1

I hope this correct :D

7 0
3 years ago
If A = 3x2 + 3x - 6 and B = -2x2 - 6x + 7, thenA - B equals1) -5r- 11x + 132) 5r2 + 11x – 133) -5x2-x+14) 5x2 -*+1
Grace [21]
3x^2-(-2x^2)+5x-(-6x)-6-(7)=5x^2+11x\text{ - 13}

Therefore, the correct answer is:

2)5x^2+11x\text{ - 13}

5 0
1 year ago
Can someone explain this? :)
Alchen [17]

I'll do part (a) to get you started.

The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.

We also see that b = 123 as well since a = b (they are vertical angles).

Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.

c+123 = 180

c = 180-123

c = 57

-------------------------

To summarize, we have these three angles

a = 123

b = 123

c = 57

6 0
3 years ago
Read 2 more answers
Other questions:
  • Someone help me with this one?
    5·2 answers
  • Use determinants to find out if the matrix is invertible.[Start 3 By 3 Matrix 1st Row 1st Column 20 2nd Column 5 3rd Column 3 2n
    7·1 answer
  • What is the value of x
    9·1 answer
  • Can someone help me ?
    12·1 answer
  • NEED HELP QUCKILY PLZ HURRY
    9·2 answers
  • Complete the following chart to summarize the different ways to prove triangles are congruent
    14·1 answer
  • What are the domain and Range of f(x)=Log(x+6)-4
    6·1 answer
  • A website-hosting service charges a one-time setup fee of $20 plus d dollars for each month. A business owner paid $70 for the f
    14·1 answer
  • Please help me need ASAPp
    11·1 answer
  • If m 1 = (x + 60° and m 2= (5x - 64)°, what is m 3?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!