In the Tigers Football Club, there are 9 players to each coach, while in the Eagles Football Club, there are 17 players to every 2 coaches. If the total number of players and coaches in the two clubs is 232, how many players and coaches are in each club?

Answers

Answer 1

9514 1404 393

Answer:

Tigers: 8 coaches, 72 playersEagles: 16 coaches, 136 players

Step-by-step explanation:

We can define a "basic unit" of each team to be the minimum number of players and coaches that can have the given ratio. For the Tigers, that is 1 coach and 9 players, for a total of 10 team members. For the Eagles, that is 2 coaches and 17 players, for a total of 19 team members. If we have t basic units of Tigers and e basic units of Eagles, then we want ...

  10t +19e = 232 . . . . . the total of players and coaches in the two clubs

We want t and e to be integers, so this is a Diophantine equation. It can be solved any of several ways, including use of the Extended Euclidean Algorithm. Here, we'll make some observations based on "number sense."

The value of e must be an even number between 0 and 232/19 = 12. The product of e and 19 must be a number that ends in 2, because 10t will end in 0, and the sum with 19e must end in 2.

The only multiple of 9 that ends in 2 is 9×8 = 72, so the value of e must be a positive number less than 12 that ends in 8. We must have e=8.

Then t=(232 -8×19)/10 = 8. This tells us there are 8 "basic units" of each team.

The Tigers have 8 coaches and 72 players.

The Eagles have 16 coaches and 136 players.


Related Questions

You give up a full-time salary of $52,000 a year to go to school for 2 years. The total cost of going to school is $36,000. If you want to be able to recover your investment in 4 years or less, what is the minimum salary you would need to earn upon earning your degree?

Answers

Answer:

$9000

Step-by-step explanation:

36000:4=$9000

Which function below has the following domain and range?

Answers

Answer:

The first choice.

Step-by-step explanation:

Domain = x value (first value in a coordinate pair: (x,y))

Range = y value

A function cannot have a repeating Domain value.

This eliminates the last option since -4 is used twice.

The second option has 11 as a y value but it is not in the range.

The third option has 10 as an x value but it is not in the domain.

Please help me to solve this question​

Answers

Answer:

(p+5)(p-2)

Step-by-step explanation:

We are looking for two numbers that multiply to -10 (the rightmost number) and sum to 3 (the middle number)

These are 5 and -2

So we write

(p ____)(p ____)

and fill in the blanks

(p+5)(p-2)

Check by FOILing:

p^2 -2p + 5p -10

And combine the two middle terms.

p^2 + 3p - 10

PLZ HELP ME I NEED HELP PLZZZ!!!!!
Select all that apply.

Given the points (-6, 8) and (-3, 4), which of the following are true about the line passing through these points?

The line represents a direct variation function.
The line has a slope of -3/4 .
The point (9, -12) is also on the line.
The line has a slope of 3/4 .

Answers

Answer:

the point (9,-12) is also on the line

Step-by-step explanation:

by using the 2 points the equation is y=-4/3x

use x of 9

y = -12

it will also represent a direct variation function

so two of the 4 will be correct

Answer:

The point (9,-12) is also on the line

Step-by-step explanation:

Please give brainliest

Explain how you would go about factoring the following?

3x^2 +17x-28

Answers

Answer:

[tex](x + 7) \times (3x - 4)[/tex]

Step-by-step explanation:

[tex] {3}^{2} + 17x - 28[/tex]

[tex]3 {x}^{2} + 21x - 4x - 28[/tex]

[tex]3 \times x(x + 7) - 4x - 28[/tex]

[tex]3x \times ( x + 7) - 4(x + 7)[/tex]

[tex](x + 7) \times (3x - 4)[/tex]

what??? I need help urgent :( i didn’t focus in math

Answers

Answer: g(x) = (x+1)-3

Step-by-step explanation: Assuming you are moving from expression f to expression g, the plus one in the equation moves the vertex to the right one. subtracting three outside of the parenthesis moves the vertex down three, giving you a vertex of (1,-3). hope this helps!

Can someone plz solve the math problem i attached as a screenshot. Thx

Answers

Answer:

[tex]radius \: of \: first \: circle \: = \frac{3}{2} = 1.5cm \\ radius \: of \: \: second = \frac{4}{2} = 2cm \\ radius \: of \: third = \frac{6}{2} = 3cm \\ then \: ab \: length \\ = radius \: of \: first + diameter \: of \: second \: +r adius \: of \: third \\ = 1.5 + 4 + 3 \\ = 1.5 + 7 \\ = 8.5 cm\\ thank \: you[/tex]

for the food described, find what percent of total calories is from fat. if necessary round to the nearest tenth of a percent
*calories: 120
* calories from fat: 45

Answers

Answer:

37.5%
Explanation:

0.375

The percentage of 45 out of 120 is 38%  thus 38% calories from fat.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Given that,

Total calories = 120

Calories from fat = 45

Fraction of calories from fat = 45/120 = 0.38

Percentage of calories from fat out of total calories ⇒

(45/120) × 100 = 38%

Hence "The percentage of 45 out of 120 is 38%  thus 38% calories from fat".

For more about the percentage,

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Calculate the difference and enter it below.
-19-(-10)
Answer here

Answers

Answer:

+1 is the answer

Step-by-step explanation:

-19-(-10)

-19+10

+1

-19-(-10) first bracket open-19+10-9

<7 and <8 are complimentary angles. <5 = <8 and m<6 = 29. Find the measure of angle 7 and angle 5​

Answers

Step-by-step explanation:

since < 5 = < 8, so,

< 7 = < 6 = 29°

and < 5 = 90° - 29° = 61°

If y = -18 when x = 3, find x when y =30

Answers

Answer:

when x = 18. Putting x = 18 into the equation y = 6/x, we have y = 6/18. Simplifying the fraction gives us y = 1/3.

Step-by-step explanation:

I need help on this problem expand 2-x(x+6)

(This is distributive property)

Answers

Answer:

2-x^2-6x

Step-by-step explanation:

2-x(x+6)

2-x^2-6c

What is the slope of a line with the equation y-2=-3/4(x+5)?

Answers

Answer:

Gradient: m = -3/4

Step-by-step explanation:

Please view the PDF attached for full step by step explanation

Solve the problem please

Answers

Answer:

x = 9±sqrt(7)

Step-by-step explanation:

3(x-9)^2 =21

Divide each side by 3

3/3(x-9)^2 =21/3

(x-9)^2 =7

Take the square root of each side

sqrt((x-9)^2) =±sqrt(7)

x-9 =±sqrt(7)

Add 9 to each side

x = 9±sqrt(7)

2. If 3x - y = 4, what is the value of 27^x/3^y​

Answers

9514 1404 393

Answer:

  81

Step-by-step explanation:

Rewriting the expression as powers of 3, we get ...

  [tex]\dfrac{27^x}{3^y}=\dfrac{(3^3)^x}{3^y}=3^{3x-y}=3^4=\boxed{81}[/tex]

How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze? Use the six-step method.

Answers

Answer:

405 gallons

Step-by-step explanation:

Let it be that the amount of gallons of a 70% antifreeze solution  is x, when a mixture that is 60 percents of antifreeze is placed in y gallons

x+90=y - the equation of dependence between solutions

The amount of antifreeze in the first one is x/100*70= 0.7x (in gallons), in the second solution (15percents) antifreeze is 90/100*15=13.5 (in gallons).

In the mixture we should get there will be y/100*60=0.6y - gallons of antifreeze

0,7x+13.5=0.6y

We have two equations x+90=y and 0,7x+13.5= 0.6y

0.6x+54=0.6y

0.7x+13.5=0.6y

0.7x+13.5-0.6x-54= 0.6y-0.6y

0.1x-40.5=0

x=405- the answer

p.s. sorry, I don't know what the six-step method is. But the answer is right.

Irene has a checking account. On Monday she writes a $160 check for groceries. Then she deposits $125
into her account. Finally, she writes another check for $40. What was the total change in the amount of
money in Irene's account on Monday?

A. $85
B. - $85
C. $75
D. -$75
E. $325
F. - $325

Answers

Answer:

D. - $75

Step-by-step explanation:

We mark checks as negative and a deposit as positive:

- 160 + 125- 40

Add up to get the total change of:

-160 + 125 - 40 = - 75

Correct choice is D

Answer:

Answer :-

Here, Irene is having a checking account. First she write a check of $160. Then means it has an decrease money. (-160) Now, She deposit $125. This means Now, the balance is -160 + 125 = $-35. She again write a check of $40. (-40). Total change =>

-40 - 35

-75

Option D is correct mate!

Really need to someone to break this down so I can understand it
(a) Find the slope of the curve y= x^2 - 2x - 3 at the point ​P(2,​ -3​) by finding the limit of the secant slopes through point P.
(b) Find an equation of the tangent line to the curve at P(2, -3)

Answers

Answer:

Part A)

The slope is two.

Part B)

[tex]\displaystyle y = 2x - 7[/tex]

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

[tex]\displaystyle y = x^2 - 2x - 3[/tex]

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]

Since we want to find the slope of the curve at P(2, -3), x = 2.

Substitute:

[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]

Simplify. Note that f(2) = -3. Hence:

[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]

Substitute. m = 2. Therefore, our equation is:

[tex]\displaystyle y + 3 = 2(x-2)[/tex]

We can rewrite this into slope-intercept if desired:

[tex]\displaystyle y = 2x - 7[/tex]

We can verify this by graphing. This is shown below:

I also need an explanation please

Answers

(A)

Step-by-step explanation:

The meal cost $45.25 so 20% of this for tip is

($45.25)(0.20) = $9.05. Since the tip is split between 4 friends, divide this tip by 4 and each one paid ($9.05/4) = $2.26.

James had a peach that was 98 \text{ mm}98 mm98, start text, space, m, m, end text in diameter. One day he watered it with a magical solution, and it grew to 188{,}869 \text{ mm}188,869 mm188, comma, 869, start text, space, m, m, end text in diameter.
Approximately how many times as large did the diameter of the peach become after James watered it?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
2 \cdot10^32⋅10
3
2, dot, 10, cubed

(Choice B)
B
9 \cdot10^39⋅10
3
9, dot, 10, cubed

(Choice C)
C
2 \cdot10^42⋅10
4
2, dot, 10, start superscript, 4, end superscript

(Choice D)
D
9 \cdot10^49⋅10
4
9, dot, 10, start superscript, 4, end superscript

Answers

9514 1404 393

Answer:

  A.  2×10³

Step-by-step explanation:

The ratio of diameters is ...

  (189,869 mm)/(98 mm) ≈ 1927.3 ≈ 2000 = 2×10³

The diameter of the peach became about 2×10³ times as large.

Solve 1/3 (3x + 6) + 2x = 26

Answers

Answer: x = 8

Step-by-step explanation:

Given

(1/3) (3x + 6) + 2x = 26

Expand parentheses and apply the distributive property

(1/3) · 3x + (1/3) · 6 + 2x = 26

x + 2 + 2x = 26

Combine like terms

(x + 2x) + 2 = 26

3x + 2 = 26

Subtract 2 on both sides

3x + 2 - 2 = 26 - 2

3x = 24

Divide 3 on both sides

3x / 3 = 24 / 3

[tex]\boxed{x=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

URGENT. I NEED TO DO IT

Answers

Answer:

[tex]25x +10 \\ 25x \\ are \: the \: exprassion \\ thank \: you[/tex]

Answer:

2nd option and last option

Step-by-step explanation:

the first option is an equation: it has a solution.

the second option is an expression, and follows the criteria of an expression (can be made of co-effecients, symbols, operations, numbers, ect.), so it is one of our answers.

the third option is an equation since it has the equal sign, and thus, has a solution.

the fourth option is simply a number- a value. it does not fit as an equation (no solution) or an expression (can be made of co-effecients, symbols, operations, numbers, ect.)

lastly, our fith option is an expression. it is a coefficient (a multiplication problem between a known value and a variable). this is also one of our last answers.

using 3 discs complete the puzzle. what is the smallest number of moves you can find

Answers

The minimum number of moves is 7

PLS HELP! WILL GIVE BRAINLIEST

Answers

Answer:

csc x sec x

Step-by-step explanation:

csc = 1/sin

1/sin^2    /  cos/sin    =   1 / sin^2    *  sin/cos       =   1 / sin cos  = csc sec

QOX
7. A total of 2000 people attended a benefit
concert was held to raise money for a
children foundation. Student ticket cost $2
and an adult ticket cost $3. If the organizer
raises a total of $5050, how many students
attended the concert?
Let x = number of students
Let 2000 - x = number of adults



Need explanation

Answers

Answer: Student ticket cost $2 and an adult ticket cost $3.

257 kids total attended

Step-by-step explanation:

1.2 hours in hours and minutes​

Answers

Answer:

1 hour 12 minutes

Step-by-step explanation:

1.2 × 60 = 72 minutes

72-60 = 12 minutes

Add.

−5/6+(−2 5/8)

Enter your answer as a simplified fraction by filling in the boxes.

Answers

here’s your answer :)

Step-by-step explanation:

[tex] - \frac{5}{6} + ( - 2 \frac{5}{8} )[/tex]

[tex] = - \frac{5}{6} - \frac{21}{8} [/tex]

[tex] = \frac{ - 20 - 63}{24} [/tex]

[tex] = \frac{ - 83}{24} (ans)[/tex]

5,356+2,398
=(5,356+2)+ (2,398 + 2)
5,358+2400=7,758


is kElly's answer correct? what mistake did she make? ​

Answers

Answer:

No because she added 2 instead of 2398. She thought the 2 was separate because of the comma separating the 2 thousand. She also made a mistake by thinking she could add easily by adding 2 to 2398 to make 2400.

The addition of the given numbers is 7,758.

Use the concept of addition defined as:

In mathematics, addition is an arithmetic operation that combines two or more numbers to produce a sum.

It is a fundamental operation used to calculate the total or the result of combining quantities. When adding numbers, you start with the first number, and then incrementally add subsequent numbers to obtain a final sum. The order in which numbers are added does not affect the result, thanks to the commutative property of addition.

This fundamental concept of addition forms the basis for more advanced mathematical operations and problem-solving techniques.

The given numbers are:

5,356+2,398

Now simply add these numbers:

 5 3 5 6

+2 3 9 8  

 7 7 5 4  

Hence,

The addition of the given numbers is 7,758.

To learn more about the addition visit:

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2. The arithmetic mean of a distribution is 5. The second and the third moments about the mean are 20 and 140 respectively. Find the third moment of the distribution about 10.
Please explain the answer and workings. ​

Answers

Step-by-step explanation:

The arithmetic mean of a distribution is 5. The second and the third moments about the mean are 20 and 140 respectively. What is the third moment of the distribution about 10?

Call the random variable x.

Now, define a new variable y = x - 5. Note that x - 10 = y - 5.

So, it is clear that (x-10)^3 = (y-5)^3

Also, note that (y-5)^3 can be expanded as follows:

Expand (y-5)³

Result ; y³-15 y²+75 y - 125

Letting E denote expectation with respect to the random variable x, we see that

E[(y-5)^3 ] = E(y^3) -15 E(y^2) + 75 E(y) - 125

Again, recalling that y = x - 5, have

E(y^3) = 140

E(y^2) = 20

E(y) = E(x) - 5 = 5 - 5 = 0

Thus,

E[(y-5)^3 ] = 140 -15(20) + 75(0) -125 = -285

Finally, note that

E[(y-5)^3] = E[({x-5} -5)^3] = E[(x-10)^3]

So, we get E[(x-10)^3] = -285.

(4yz)-3(x)
Y=4, z=2, x=-3

Answers

Answer:

=288

Step-by-step explanation:

(4yz)-3(x)

(4(4)(2))-3(-3)

(4x8)x9

32x9

288

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