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LenKa [72]
3 years ago
7

A baseball team consists of 2 stars, 13 starters, and 10 substitutes. For tax purposes, the team owner must value the players. T

he value of each player is defined to be the total value of the salary he will earn until retirement. At the beginning of each season, the players are classified into one of four categories: Category 1 Star (earns $1 million per year) Category 2 Starter (earns $400,000 per year) Category 3 Substitute (earns $100,000 per year) Category 4 Retired (earns no more salary) Given that a player is a star, starter, or substituteDetermine the value of team's players.
Mathematics
1 answer:
inessss [21]3 years ago
4 0

Answer:

The total value of the team=$8.2 million

Step-by-step explanation:

Step 1

Determine the total value of the team as follows;

V=(S×s)+(T×t)+(B×b)

where;

V=total value of the team

S=total value per star player

s=number of stars in the team

T=total value per starter

t=number of starters in the team

B=total value per substitute

b=number of substitutes in the team

In our case;

S=1 million per year

s=2 stars

T=400,000

t=13

B=100,000

b=10

replacing;

V=(1,000,000×2)+(400,000×13)+(100,000×10)

V=(2,000,000+5,200,000+1,000,000)

V=8,200,000=8.2 million

The total value of the team=$8.2 million

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Answer: 1. Route ABC is a right triangle.

2. Route CDE ia not a right triangle.

3. Distance HJ= 23.32miles

4. Distance GE = 17

5. Missing length= 35

6. The sides 16, 60, 62 do NOT belong to a right triangle.

Step-by-step explanation:

Going by Pythagoras theorem, for triangle to be proven to be a right triangle, the condition below must be satisfied.

Hypotenuse² = Opposite² + Adjacent²

For question 1,

Hyp =13, opp = 5, Adj is 12

Going by Pythagoras rule.

Since 13²= 5² + 12²

Then triangle ABC is a right triangle.

For question 2,

Using the same Pythagoras theorem to prove,

In triangle CDE,

Hyp= 22, opp= 18, Adj = 14

Since 22² is not = 18² + 14²

then CDE is not a right triangle.

For question 3,

For triangle HIJ, since it is confirmed to be a right triangle, then we use the Pythagoras theorem to calculate the missing side.

Longest side if the triangle= IJ = hypotenuse = 25

HI = 9.

IJ² = HI² + HJ²

HJ²= IJ² - HI²

HJ² = 25² - 9²

HJ² = 625 - 81

HJ= √544

HJ = 23.32miles

For question 4,

FGE is also shown to be a right triangle and the missing side GE is the longest side which is also the hypotenuse.

FG= 8, FE =15

Using the Pythagoras theorem,

Hyp² = FG² + FE²

GE² = 8² + 15²

GE² = 289

GE = √289

GE = 17.

For question 5,

The hypotenuse is given as 37, one side is given as 12, let's call the missing side x

Going by Pythagoras theorem,

37² = 12²+ x²

x²= 37² - 12²

x²= 1225

x=√1225

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The missing side is 35inches.

For number 6,

The numbers given are 16, 60, 62

To know if three sides belong to a right angle, we simply put them to test using Pythagoras theorem.

It is worthy of note that the longest side is the hypotenuse.

This brings us to the equation to check below that since:

62² Is not = 60² + 16²

Then the side lengths 16, 60, 62 do not belong to a right angle.

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