The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5 and each adult ticket sells for $10. The auditorium can hold a maximum of 110 people. The drama club must make a minimum of $700 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.​

Answer:

(- 4, 169 ) , (- 9, 414 )

Step-by-step explanation:

y = - 49x - 27 → (1)

y = x² - 36x + 9 → (2)

substitute y = x² - 36x +9 into (1)

x² - 36x + 9 = - 49x - 27 ( add 49x to both sides )

x² + 13x + 9 = - 27 ( add 27 to both sides )

x² + 13x + 36 = 0 ← in standard form

(x + 4)(x + 9) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 9 = 0 ⇒ x = - 9

substitute these values into (1) for corresponding values of y

x = - 4 : y = - 49(- 4) - 27 = 196 - 27 = 169 ⇒ (- 4, 169 )

x = - 9 : y = - 49(- 9) - 27 = 441 - 27 = 414 ⇒ (- 9, 414 )

Answer:

15

Step-by-step explanation:

5x3 =15

Answer:

15

Step-by-step explanation:

We can round the two numbers so then we can multiply by the rounded numbers to get a close answer.

4.9 rounded to the nearest whole number is 5.

3.1 rounded to the nearest whole number is 3.

Now, we can multiply by the two numbers we got here.

5 × 3 = 15, so the answer to the question is 15.

The probability is \(\frac{11}{30}\) .

What is the probability?

 Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, Probability has been introduced in mathematics.

F= The probability that the dice land on different numbers.

F=(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)

F = \(\frac{30}{36}= \frac{5}{6}\)

E= The event that at least one lands on 6.

E=(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)

E= \(\frac{11}{36}\)

What is the probability of E, when given that F has occurred?

P= \(\frac{P(EF)}{P(F)}\) = \(\frac{1-P(EF)}{P(F)}\)

=> P = \(\frac{\frac{11}{36} }{\frac{5}{6} }\) = \(\frac{11}{30}\)

Hence the Probability is \(\frac{11}{30}\) .

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Answer:

Its D

square root of 37 = 6.0

Step-by-step explanation:

Answer:

(2x+7)(x+7)

Step-by-step explanation:

Answer:

242 sq. cm.

Step-by-step explanation:

Surface Area

The probability of failure on trial 9 is 0.74.

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The probability of failure on a trial is equal to 1 - the probability of success on that trial. Therefore, the probability of failure on trial 9 is 1 - 0.26 = 0.74.

Hence, the probability of failure on trial 9 is 0.74.

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Answer:

The frame should be 36 + 2b + 16 + 2b

Step-by-step explanation:

To solve this question, let assign 36 in x 16 in as the dimension of the painting.

276 in^2 is the area of the framing material to be used.

Let the width of the frame around the frame be "b", thus; the dimension of the frame is 36 + 2b + 16 + 2b

The expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

The management of First American Bank faces a decision regarding the installation of an emergency power generator to mitigate potential losses from physical catastrophes such as power failures or fires.

To evaluate this decision, we can use decision tree analysis.

Without the generator, there is a 10% chance of a power outage. In the event of an outage, there is a 0.05 probability of very large losses ($80 million) and a 0.95 probability of slight losses ($1 million). To calculate the expected loss from not installing the generator, we can use the following formula:

Expected loss = (probability of outage) x [(probability of large loss x large loss amount) + (probability of slight loss x slight loss amount)]

Expected loss = 0.1 x [(0.05 x $80 million) + (0.95 x $1 million)]
Expected loss = 0.1 x [$4 million + $950,000]
Expected loss = 0.1 x $4.95 million
Expected loss = $495,000

Now let's compare this expected loss to the cost of installing the emergency power generator, which is $800,000. Since the expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

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Answer:

76.9

Step-by-step explanation:

5= d/t = 1000m/135 =76.9

Answer:

x > -10/7

Step-by-step explanation:

divide both sides by -7 and it will be x= -10/7

Explanation

Imagine we had 6 light switches. They represent 'a' through 'f'.

Light switch number 1 being flipped on means we include 'a', and it turned off means we exclude 'a'. The same idea applies to the other switches.

Each switch has 2 choices, so there are (2*2*2)*(2*2*2) = 2^6 = 64 different combos of on/off. That's the number of subsets of {a,b,c,d,e,f}.

The general rule is that if we had n elements in the set, then there are 2^n different subsets. This includes the set itself and the empty set.

Note: The power set is the set of all subsets of a given set.

x²+2x-15=(x+5)(x-3) there is nothing to factoriz

Answer:

1.)  1 ,2, 31, 62

2.)  1, 3, 5, 9

3.) 540

Step-by-step explanation:

1.)  1x62= 62

2x31= 62

31x2= 62

62x1=62

Each of these number are a multiple of 62.

2.) 1x45=45

3x15=45

5x9= 45

9x5= 45

3.) 420÷2= 210

420÷3= 140

420÷5= 84

420÷6= 70

420÷9= 46.667 This number is not a multiple of 420 because the answer is in decimals which means 9 is not divisible by 420

540÷2= 270

540÷3= 180

540÷5= 108

540÷6= 90

540÷9= 60

540÷10= 54

2, 3, 5, 6, 9 and 10 is divisible by all of these numbers

Answer:

1)  1 ,2, 31, 62

2)  1, 3, 5, 9

3.) 540

Step-by-step explanation:

1)  62 would be divisible by 2 because its an even number, and if you split 62 in half, you would get 31.

2) 4+5 = 9. 3 and 9 are both divisible by 9, and 5 is divisible by 5.

3) All of the numbers are divisible by 10, 5, and 2 in the list. 250 is not divisible by 3, so we can take it off the list.  The rest of the numbers are all divisible by 6. All we have left is 9. Both 420 and 510 add their values up to 6, which is not divisible by 9. That leaves us with 540 as our answer.

-kiniwih426

Answer:

A. (x,y)-(-x,y)

Step-by-step explanation:

1. Look at the first FG, It is Positive X and Positive Y

2. A reflection is simply flipping something to the opposite side, So now look at which part the 2nd FG is.

3. Now as we notice the G is in the Negative X, So that would be -X, But then when we look at the Y, It is in the positives!

Answer:

5.2

Step-by-step explanation:

adding all the numbers together and dividing it by 10.

Answer:

mean = 5.2

Step-by-step explanation:

The mean (or average) of a group of numbers is defined as the value calculated by adding all the given numbers together and then dividing the result by the number of numbers given.

Therefore,

\(\boxed{\mathrm{mean = \frac{sum \ of \ the \ numbers}{number \ of \ numbers}}}\).

In the question, the numbers given are: 3, 7, 2, 4, 7, 5, 7, 1, 8, and 8.

Therefore,

sum = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8

       = 52

There are 10 numbers given in the question. Therefore, using the formula given above, we can calculate the mean:

\(\mathrm{mean = \frac{52}{10}}\)

            \(= \bf 5.2\)

Hence, the mean of the given numbers is 5.2.

Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

Answer:

m > $380

Step-by-step explanation:

First, the math:

$500-$120= $380.

She still needs $380.

Her $380 still needed is less than m, which gives us the last answer the most logical.

I hope this helped! Have a nice day.

Answer:

El número es el 47

Step-by-step explanation: Con los dígitos de los siguientes números se obtiene que su suma es 11

47        4  +  7  =  11

38         3  +  8 =  11

29         2   + 9  = 11

Si se cambia el orden de los dígitos:

47       se convierte en    74        74 - 47  =  27

38                  "    "             83        83 - 38 =  45

29                  "    "             92        92 - 29 = 63

Entonces el número solicitado es el 47

The sine function y = 3sin(θ) has one complete cycle in the interval from 0 to 2π. The amplitude of the function is 3, and the period is 2π.

The general form of the sine function is y = A × sin(Bθ + C), where A represents the amplitude, B represents the frequency (or 1/period), and C represents a phase shift.

In the given function y = 3sin(θ), the coefficient in front of the sine function, 3, represents the amplitude. The amplitude determines the maximum distance from the midpoint of the sine wave. In this case, the amplitude is 3, indicating that the graph oscillates between -3 and 3.

To determine the number of cycles in the interval from 0 to 2π, we need to examine the period of the function. The period of the sine function is the distance required for one complete cycle. In this case, since there is no coefficient affecting θ, the period is 2π.

Since the function has a period of 2π and there is one complete cycle in the interval from 0 to 2π, we can conclude that the function has one cycle in that interval.

Therefore, the sine function y = 3sin(θ) has one complete cycle in the interval from 0 to 2π. The amplitude of the function is 3, indicating the maximum distance from the midpoint, and the period is 2π, representing the length of one complete cycle.

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Answer:

Sources of electrical current

Step-by-step explanation:

Based on the information given the reason why

He/ She places a compass at different positions on a wall until the compass needle change to a direction was because the construction worker

was most likely using the compass to find the Sources of an ELECTRICAL CURRENT or where the ELECTRICAL CURRENT originated from reason been that ELECTRICAL CURRENT is the movement of electric charge from cathode to anode .

Answer:

D. Sources of electrical current

Step-by-step explanation:

I just took the test

Answer:

Step-by-step explanation:

To find the standard deviation of the population, we first need to find the mean of the population.

Mean = (28 + 28 + 29 + 31 + 28 + 24) / 6 = 28

Next, we need to find the variance of the population.

Variance = [(28 - 28)^2 + (28 - 28)^2 + (29 - 28)^2 + (31 - 28)^2 + (28 - 28)^2 + (24 - 28)^2] / 6

Variance = (0 + 0 + 1 + 9 + 0 + 16) / 6 = 2.67

Finally, we can find the standard deviation of the population by taking the square root of the variance.

Standard deviation = sqrt(2.67) ≈ 1.63

Therefore, the standard deviation of the population is approximately 1.63 seconds.

Answer:

the answer is A

Step-by-step explanation:

Answer:

A. - ∞ < x < ∞

Step-by-step explanation:

Answer:

9-7= 2

8 / 2 = 4

4 X 9 = 36

4 X 7 = 28

36 students in math class

Answer:

36 students in the math class

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

B and D are the middle angle in both triangles.

Answer:

∠B ≅ ∠D this is the correct answer

Applying the inscribed angle theorem, m∠CED = 34°.

According to the inscribed angle theorem, measure of inscribed angle DCE = 1/2(measure of intercepted arc ED).

m(ED) = 180 - 112 [semicircle]

m(ED) = 68°

m∠CED = 1/2(68°) [inscribed angle theorem]

m∠CED = 34°

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