For a sporting event 6,000 tickets were sold, and the proceeds were $78,000. Tickets for children 16 and younger, were $8, adults were $16, and seniors 60 and older were $12. There were 2 times more adults than children at the sporting event.

What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the sporting event?

Responses
c+a+s=6,000
8c+12a+16s=78,000
2a=c

c+a+s=6,000
8c+16a+12s=78,000
a=2c

c+a+s=6,000
8c+12a+16s=78,000
a=2c


c+a+s=6,000
8c+16a+12s=78,000
2a=c

Answer:

s = 2 1/3 + 1/2

t = 2/3 + 3/2

We have to find the sum of both s and t.

2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6

2/3 + 3/2 = 4/6 +  9/6 = 13/6 = 2 1/6

If we look at the number lines, we can see that c matches with both points.

Answer:

6[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Another way to write 5 2/3 is to change this into an improper fractions.  Another names for 1 is 3/3.  I am going to add 5, 3/3 to 2/3

3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 2/3 = 17/3

We want to add this to 11/12, but to do that we need a common denominator.  I need to make an equivalent fraction of 17/3 where 12 is the denominator

[tex]\frac{17}{3}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{68}{12}[/tex]  Now we can add the two fractions together.

[tex]\frac{68}{12}[/tex] + [tex]\frac{11}{12}[/tex] = [tex]\frac{79}{12}[/tex] = 6[tex]\frac{3}{4}[/tex]

The number of hours that the the pool been draining if currently there are 8,840 gallons in the pool is 6.25 hours.

Let the time taken be represented by h.

Therefore, the appropriate expression will be:

14340 - 880h= 8840

Collect like terms

880h = 14340 - 8840

880h = 5500

h = 5500/880

h = 6.25 hours

The number of hours is 6.25 hours.

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Answer:

h * $15 - $20

Step-by-step explanation:

h - number of hours per day

$15 - earnings per hour

$20 cost per day

h * $15 - gross earnings per day

h * $15 - $20 - net earnings per day

Answer:

21

Step-by-step explanation:

If A 45 translates to be 35, then x can be given by (35×27)÷45 =21

Answer:

7x+2/x² +x +2

that's my answer

Answer:

The correct answer is B, I took the test :)

You just turn the percentages into decimals

The probability distribution table is formed clearly in the answer part.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The probability for all the elements in the sample space can be shown in one table known as distribution table.

Suppose X be the event of choosing a major.

Then, its probability can be given as P(X).

Here, the percent value of a given event is equivalent to their probability.

It can be represented in the form of table as,

X (Major chosen by student)                              P(X) (Probability)

    Math                                                                    3% = 0.03

   Nursing                                                                22% = 0.22

  Psychology                                                           16% = 0.16

 Criminal justice                                                      11% = 0.11

   Business                                                              48% = 0.48

This table is known as the probability distribution table.

Hence, the probability distribution table is formed by calculating the probability for each of the events.

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If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.

As per the question statement, 31 horses are competing in a show.

We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.

To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.

That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.

To solve this question, we just need to know the formula of permutation which goes as [tex][(nPr)=\frac{n!}{(n-r)!} ][/tex],  i.e., we are to select an ordered set or "r" from a set of "n".

As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get

[tex](31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.[/tex]

That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.

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Answer:

false

Step-by-step explanation:

Answer:

The figure A is translated from the third quadrant to the second quadrant thus the formula used is P(x,y) = T(a,b) = Image of P(x+a, y+b). The object A and its image B are congruent and the direction and magnitude of the displacements are given by the direction and magnitude of translation vector t = ( a,b ). Where, a is the horizontal displacement ( along x-axis ) and b is the vertical displacement ( along y-axis ).

I'd say its A because:

5x#of pies + the money the principal pitched in (75) is less than or equal to 386 dollars (their goal for the field trip).

The inequality equation is given by 5p + 75 ≤ 386 , where p is the number of pies the class sells

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality relation be represented as A

Let the number of pies the class sells be p

Now , the equation will be

The total amount for the field trip = $ 386

The amount given to the students = $ 75

The cost of 1 pie = $ 5

So , the cost of p pies = 5p

Now , the total amount with the students = cost of p pies + amount given to the students

Substituting the values in the equation , we get

5p + 75 ≤ 386

Therefore , the value of A is 5p + 75 ≤ 386

Hence , the inequality relation is 5p + 75 ≤ 386

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Answer:

2

Step-by-step explanation:

Y = 5

x = 4

Substitute

5 + 1 - 4

6 - 4

2

Answer:

Given that x = 4 and y = 5,

[tex]\sf 5 + 1 - 4\\(5 + 1) - 4\\5 + 1\\= 6\\= 6 - 4\\= 2[/tex]

Therefore, the answer is 2.

Answer:

x would equal -1.03(1 DP)

"-26x - 12 = 15, solve for x."

Step-by-step explanation:

Start with adding 12 to both sides of the expression. Sides were switched purposely.

[tex]15 + 12 = -26x - 12 + 12[/tex]

Next, simplify your addition process. You do this by using a specific rule.

[tex](-a) = a\:\:\mathrm{if\:a\neq 0}\\-26x = 26x\\26 + (x)\\= 26 + 1\\= 27\\= -26x=27[/tex]

Lastly, we are going to divide both sides by -26(x was cancelled).

[tex]\frac{-26x}{-26}=\frac{27}{-26}[/tex]

Thus,

[tex]x= -1.03[/tex]

➲ Hope this helps, address any concerns if needed.

Answer:

x = -1.038

Step-by-step explanation:

- 26x - 12 = 15

- 26x = 15 + 12

- 26x = 27

x = - 27/26

x = - 1.038

__________

hope this helps!

The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).

In this problem we have the coordinates of a original point and a translation vector, the coordinates of the image is obtained by using the following formula:

Y'(x, y) = Y(x, y) + T(x, y)

Where:

To learn more on Y(x, y) = (- 4, - 9) and T(x, y) = (- 6, 2), then the coordinates of the resulting point are:

Y'(x, y) = (- 4, - 9) + (- 6, 2)

Y'(x, y) = (- 10, - 7)

The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).

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The cost of a dozen of eggs is $3.

Given two dozen eggs and a loaf of bread cost K4.94 and

Half a dozen of bread cost K2.32

Cost of a dozen of eggs = ?

we know that, 24E ₊ B = 8.50 and

6E ₊ 2B = 6.50

multiply the first equation by 2 and substract

48E ₊ 2B = 17

6E ₊ 2B = 6.50

after solving both equations we get:

42E = 10.50

we are searching for the value of a dozen eggs, which is 12E

multiply 42E = 10.50 by 12/42 = 6/21

and you get

12E = 10.50 × (6/21) \\ 10.50 = 21/2

12E = (21×6)/(2×21)

12E = 3

so a dozen eggs cost 3 dollars.

Hence we get the cost of a dozen of eggs as $3

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Answer:

33915

Step-by-step explanation:

87% is the average, so you have to find 87% of 4500.

Answer: i do not know

Step-by-step explanation:

cause i do not know

Given difference quotient is f(x) = -x²+2x+5.

Simplified version is (f(x + h) - f(x))/h = 1.

If f(x) = x - 5, then

f(h) = h - 5

f(x + h) = (x + h) - 5

(f(x + h) - f(x))/h = (((x + h) - 5) - (x - 5))/h

(f(x + h) - f(x))/h = (x + h - 5 - x + 5)/h

(f(x + h) - f(x))/h = h/h

(f(x + h) - f(x))/h = 1

since h ≠ 0.

The average rate of change of the function over an interval is measured by the difference quotient (in this case, an interval of length h). The instantaneous rate of change is hence the limit of the difference quotient (i.e., the derivative).

The slope of secant lines can be calculated using the difference quotient. Almost identical to a tangent line, a secant line traverses at least two points on a function.

That equation is known as a difference quotient because both the numerator and denominator are differences.

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Answer:

Step-by-step explanation:

Jess had the faster speed than Eli.

We have the relation connecting Distance travelled, Time taken to travel and the speed given by,

Distance Travelled = Speed x Time taken

Here, we need to find the speed of Eli and Jess to find out who was faster.

So we use the formula, Speed = Distance travelled / Time taken

Distance travelled by Eli = 3 miles

Time taken by Eli = 2/5 hour

Speed of Eli = Distance / Time taken

                    = 3/(2/5)

                    = 15/2 = 7.5 miles per hour

Distance travelled by Jess = 4/5 mile

Time taken by Jess = 1/10 hour

Speed of Jess = Distance / Time taken

                        = (4/5)/(1/10)

                        = 8 miles per hour

Comparing the speeds of Eli and Jess, Jess had the faster speed of 8 miles per hour.

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The kinetic energy T units of a motion body (of constant mass) varies as the square of its speed v m/s. If kinetic energy T = 800 units when speed v= 20m/s: Calculate V when T= 1800.​

If T=1800 then V=30m/s.

kinetic energy is nothing but The energy an object has as a result of motion is known as kinetic energy.

Given that,

If T = 800 units when v= 20m/s

Kinetic energy formula is

[tex]T=\frac{1}{2}mv^{2}[/tex]

Here, T is kinetic energy , m is mass and v is speed

Now,

[tex]800=\frac{1}{2}m(20)^{2} \\800\times2=m(400)\\\frac{1600}{400}=m\\ m=4[/tex]

We got mass m as 4

Now, when T= 1800 find v=?

[tex]1800=\frac{1}{2}\times4\times v^{2} \\1800\times2= v^{2} \\ v^{2} =900\\v=30[/tex]

Therefore, we got speed v=30m/s when the kinetic energy T=1800.

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From the situation described, we have that:

a) The linear function is: f(s) = 120 - 12s.

b) She can take 10 sips before she needs to refill.

c) The graph is given at the end of the answer.

d) The domain is: 0 ≤ s ≤ 10.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the parameters are given as follows:

m = -12, b = 120.

Hence the function is:

f(s) = 120 - 12s.

She can take sips until f(s) = 0, hence:

120 - 12s = 0

12s = 120

s = 10.

She can take 10 sips before she needs to refill, and hence the domain(set that contains the input values for the function) is 0 ≤ s ≤ 10.

The graph is given at the end of the answer.

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Answer:

Step-by-step explanation:

The least Andrew's average could possibly be when he goes up to bat the tenth time of the series is 0.399.

Here, we are given that,

Andrew's batting average = 0.400

Number of career hits for 0.400 batting average = 2000

Previous bat times for 0.400 batting average = 5,000

Now,

For the least possible average, he must have zero career hits in every match he bats.

Before the tenth time of the series, he will bat in 9 times

He must have 0 career hits in these 9 matches he bats in

therefore,

The total number of career hits = 2000

Total number of bat times = 5,000 + 9 = 5,009

Hence,

Average = (Total career hits) ÷ (Total number of times he bats)

= 2000 ÷ 5,009

= 0.399

Thus, the least his average could possibly be when he goes up to bat the tenth time of the series is 0.399.

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