the student council is organizing a trip to a rock concert. all proceeds from ticket sales will be donated to a charity. tickets to the concert cost $31.25 per person if a minimum of 104 people attend. for every 8 extra people that attend, the price will decrease by $1.25 per person.a). how many tickets need to be sold to maximize the donation to charity?b). what is the price of each ticket that maximizes the donation?c). what is the maximum donation?

Answers

Answer 1

Answer: I got the maximum donation $152

Answer 2

Answer:

Final answer:

To maximize the donation to charity, a total of 117 tickets need to be sold. The price per ticket that maximizes the donation is $29.0625. The maximum donation is $3,400.3125.

Explanation:

To maximize the donation to charity, we need to determine the number of tickets that need to be sold and the price per ticket that will result in the maximum donation.

a) To find the number of tickets, we can start with the minimum attendance requirement of 104 people. For every 8 extra people that attend, the price decreases by $1.25. So the number of extra people is calculated by dividing the total increase in price ($31.25 - $30) by the decrease per person ($1.25), which is 8. Therefore, the number of extra people is 13. To find the total number of tickets, we add the minimum attendance of 104 people and the number of extra people of 13. So the total number of tickets that need to be sold to maximize the donation to charity is 117.

b) To find the price per ticket, we start with the price of $31.25 and take into account the decrease of $1.25 for every 8 extra people. We can calculate the price decrease per person by dividing $1.25 by 8, which is $0.15625. To find the price per ticket, we subtract the decrease per person from the initial price, multiplied by the number of extra people. So the price per ticket that maximizes the donation is $31.25 - ($0.15625 × 13) = $29.0625.

c) To find the maximum donation, we multiply the price per ticket by the total number of tickets sold. So the maximum donation is $29.0625 × 117 = $3,400.3125.

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#3 AB and AD are tangent to the circle centered at point C. Find the value of x. *show your work plz i need help

Answers

Answer: x=4

Step-by-step explanation:

tangent lines from the same point to a circle are congruent in length, so we can say that

5x+8 = 8x-4

5x -5x +8 = 8x - 5x -4

8 = 3x - 4

8+4 = 3x -4 + 4

3x = 12

3x/3 = 12/3

x=4

What is tangent in trigonometry?

Tangent Meaning in Trigonometry

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal zero.

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Answer:

x=4

Step-by-step explanation:

tangent lines from the same point to a circle are congruent in length, so we can say that

5x+8 = 8x-4

5x -5x +8 = 8x - 5x -4

8 = 3x - 4

8+4 = 3x -4 + 4

3x = 12

3x/3 = 12/3

x=4

How do you write 245%as a fraction, mixed number, or whole number in simplest form?

Answers

245 over 100 as a fraction

2 with 45 over 100 as a mixed number

2 with 9 over 20 as a mixed number simplest form

49 over 20 as a non mixed fraction in simplest form (improper fraction)

Solve the following system of equations for all three variables. 2x+y+6z=2 // −2x+8y−3z= 4 //−2x+8y−9z= −8what is x, y, and z?

Answers

can you add a picture ??

Sofia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 566 glasses. There are currently 371 glasses. If each set on sale contains 18 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Sofia should buy?

Answers

Answer:

371 + 18x ≥ 566

Step-by-step explanation:

We know:

current # of glasses= 371

glasses per set= 18

glasses needed= 566

# of sets= x

At least means she can also have more than 566 glasses, so we will use the ≥ ("greater than or equal to") symbol:

glasses per set⋅# of sets+current # of glasses≥glasses needed

18x+371 ≥ 566

or, by the commutative property of addition,

371+18x ≥ 566

Inequality #2

We could also switch the two sides of the inequality, but we have to be careful which symbol we use. At least means the number of glasses needed should always be less than or equal to the glasses the restaurant has, including the glasses they already had, plus the sets Sofia bought.

Inequality #3

566 ≤ 18x+371

566≤ 371+18x

Inequality #4

Final answer:

To determine the minimum number of sets of glasses Sofia should buy, an inequality can be used. Subtract the current number of glasses from the desired number of glasses and divide by the number of glasses in each set to find the minimum number of sets needed.

Explanation:

To determine the minimum number of sets of glasses Sofia should buy, we need to find the difference between the desired number of glasses and the current number of glasses. The desired number of glasses is given as at least 566 and the current number of glasses is 371. So the inequality we can use is: 566 - 371 ≥ 18x, where x is the number of sets of glasses Sofia should buy.

We subtract 371 from 566 to get 195 and then divide by 18 to find the minimum number of sets of glasses Sofia should buy. Therefore, the minimum number of sets of glasses = 195 ÷ 18 = 10.83. Since we can't have a fraction of a set, Sofia should buy at least 11 sets of glasses.

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Which of the following is a cubic binomial with a positive leading coefficient?A. 8−27x3

B. 1+2√x3

C. 3x3−x2+12

D. x4−16

Answers

The cubic binomial expression with a positive leading coefficient is 1+2x^3

How to determine the cubic binomial expression?

A cubic binomial expression has the following properties:

It has 2 terms
One of its variable term has a power of 3

This means that a cubic binomial expression is represented as:

ax^3 + b or b + ax^3

From the question, we understand that it has a positive leading coefficient.

This means that:

a > 0

From the list of options, we have:

1+2x^3

Hence, the cubic binomial expression with a positive leading coefficient is 1+2x^3

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the answer is C

C. 3x^3-x^2+12

Use the elimination method1) 3x+y=-1 5x-y=9
2) 4x+6y=24 4x-y=10
3)2x-y=-3 x+3y=16
4) 2x+3y=7 3x+4y=10

Answers

1) 3x+y=-1 5x-y=9
First of all we have add both equation but to be sure that the value we want to eliminate are both in a way that would make it possible t be deleted.
  3x+y=-1
  5x-y= 9
8x = 8
x= 1
In this case we are able to eliminate y becuase if we add +y-y we get that our answer is 0. and 3x + 5x would be 8x and -1+9 would be equal to 8 and to find x we needed to divided giving us that the answer for x is 1 becuase 8/8 is 1.
Then to find y we substitude the value of x in any of the formulas.
3(1)+y= -1
3+y= -1
y= -1-3
y=-4
When we have our y value we can determine if it is correct by replace the values.
5(1)--4= 9
5+4= 9
9=9
Up until now we are fine. So we do the same with the other equation.
3(1)+-4=-1
3+-4=-1
-1=-1
So by this we can now detemine that.
x= 1
y= -4

2) 4x+6y=24 4x-y=10
4x+ 6y =24
4x-y=10 (*-1)
4x+6y=24
-4x+y=-10
7y= 14
y= 14/7
y= 2
In this case we are not able to delete any of the variables so we multiplied by -1 to be able to eliminate x.
Then to find x we substitute the value of y in any of the formulas.
4x-2=10
4x= 10+2
x= 12/4
  x= 3
So we now know our variables so we substituted them to see if they are correct.
  4(3)+6(2)=24
12+12=24
24=24
We do the same with the other equation.
  4(3)-2=10
12-2 =10
   10= 10
So we can assume that.
x= 3
y= 2

3)2x-y=-3 x+3y=16
(3*)2x- y= -3
x+ 3y = 16
6x -3y = -9
x+3y =16
7x= 7
x= 1
In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y.
Then to find y we substitute the value of x in any of the formulas.
1+ 3y = 16
3y= 16-1
y= 15/3
y= 5
So we now know our variables so we substituted them to see if they are correct.
2(1)- 5 =-3
2-5= -3
-3= -3
We do the same with the other equation.
1+3(5)= 16
1+15=16
16=16
So we now are sure that
x= 1
y= 5

4) 2x+3y=7 3x+4y=10
2x+3y =7 ( * - 4)
3x+4y =10 ( * 3)
-8x -12y = -28
9x +12y = 30
x= 2
In this case we are not able to delete any of the variables so we multiplied one of teh quations by - 4 to be able to subtract in our sum and the other by 3 to have the same number on y to be able to eliminate y.
Then to find y we substitute the value of x in any of the formulas.
2(2)+3y= 7
4+3y=7
3y= 7-4
y= 3/3
y= 1
So we now know our variables so we substituted them to see if they are correct.
3(2)+4(1)= 10
6+4=10
10=10
We do the same for the other
2(2)+3(1)=7
4+3= 7
7=7
So with that we can say that.
x= 2
y= 1

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