Tickets for admission to a high school football game cost $3 for students and $5 for adults. During 1 game, $2995 was collected from the sale of 729 tickets. Write & solve a system of equations to find the number of student tickets, x, and number of adult tickets, y, sold.

Answer:

1.900 2(i)1260 (ii)9 3.20 4.80 5.36 6(i)540 (ii)100

Step-by-step explanation:

1.(7-2)*180

=5*180

=900

2(a)(i) (9-2)*180

          =7*180

          =1260

     (ii) 9

3 360/x=18

          x=20

4 (5-2)*180

=3*180

=540

2y+y+y+110+110=540

                     4y=320

                       y=80

5 360/x=30

          x=36

6(i) (5-2)*180

=3*180

=540

  (ii)x+95+115+115+115=540

                                 x=100

Simplifying it down:

(10/6)*4

40/24

Answer:

sales equal $15,000

Step-by-step explanation:

x = amount of sales

f(x) = 500 + 1/6x

3000 = 500 = x/6

2500 = x/6

x = 15,000

The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

The initial node represents the decision whether to invest in the development of the microbiological product.

The two possible outcomes are a successful development or failure after 2 years.

(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.

Starting from the end nodes and working backwards, we have:

For large-scale production with high sales:

Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m

For large-scale production with low sales:

Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m

For small-scale production with high sales:

Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m

For small-scale production with low sales:

Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m

At the 2-year node, the expected value for a successful development is:

For large-scale production:

Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m

For small-scale production:

Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m

Finally, at the initial node, the expected value for investing in the development is:

Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m

Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.

(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:

Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp

Setting this equal to zero and solving for p, we get:

p = 1

Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.

(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.

The utilities are increasing and concave, indicating diminishing marginal utility of money.

This means that the new owner is risk-averse.

The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.

To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.

If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.

If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.

If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.

If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.

If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.

Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

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The equation for the line that passes through point (-5, 2) that is parallel  and perpendicular to y = 2/3x + 1

For the equation of the line parallel to the line the  y = 2/3x + 1 slope must be equal, hence m = 2/3

equation passing through point (-5, 2)

(y - y₁) = m  (x - x₁)

y - (-5) = 2/3(x - 2)

y + 5 = 2/3 x - 4/3

y = 2/3 x - 19/3

For the line perpendicular to the line y = 2/3x + 1 the slope is negative reciprocal of the slope in the line.

m = 2/3

perpendicular m' = -3/2

equation passing through point (-5, 2)

(y - y₁) = m'  (x - x₁)

y - (-5) = -3/2(x - 2)

y + 5 = -3/2 x + 3

y = -3/2 x + 3 - 5

y = -3/2 x - 2

the perpendicular line is y = -3/2 x - 2

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Moving the vertices does not affect the relationship between the diagonals. They bisect each other in all cases.

Answer:

Despite changing the vertices, the opposite sides and opposite interior angles of the parallelogram remain equal.

Step-by-step explanation:

PLATO AWNSER

490

472 <490<500

it fits the criteria

Answer:

The area between the curves is 4 square units.

Step-by-step explanation:

We want to find the area bounded by:

y = x

x = 0

in the interval x = 1, x = 3

This is simply equal to the integral of the function f(x) = x between x = 1 and x = 3

Written as:

\(\int\limits^3_1 {x} \, dx\)

And the integral of x is equal to x^2/2

Then:

\(\int\limits^3_1 {x} \, dx = (\frac{3^2}{2} - \frac{1^2}{2}) = (\frac{9}{2} - \frac{1}{2} ) = \frac{8}{2} = 4\)

The area between the curves is 4 square units.

Answer:

3.02 is the answer for this question if the answer is correct plz mark me as brainliest

Answer:

3.02

Step-by-step explanation:

51.34 ÷ 17 = 3.02

Answer:

(a + b)(p - 2)

Step-by-step explanation:

ap + bp - 2a - 2b ( factor first/second and third/fourth terms )

= p(a + b) - 2 (a + b) ← factor out (a + b) from each term )

= (a + b)(p - 2)

Answer:

Third option is the right choice.

Step-by-step explanation:

\(y=a(b)^x\)   where "b", is the common ratio.

The common ratio for third table is constant for all the terms.

Best Regards!

Answer:

The average heart beats 80 - 90 timers per minute. In 1 second it beats 1.33 1.5 times

Step-by-step explanation:

Quora

False. To calculate a percent increase, the portion is not the missing element. The portion refers to the initial or original value, while the missing element is the final or increased value.

The formula for calculating a percent increase is:

Percent Increase = (Final Value - Initial Value) / Initial Value * 100

In this formula, the initial value is the portion that represents the starting or original value. The final value is the missing element, as it represents the increased or final value after the increase.

By subtracting the initial value from the final value, we obtain the difference between the two. Dividing this difference by the initial value gives us the relative increase as a decimal or fraction. Multiplying by 100 converts it into a percentage, representing the percent increase.

Therefore, the portion in calculating a percent increase is the known value or initial value, while the missing element is the final value that we are trying to determine or find.

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Answer:6y+30

Step-by-step explanation:

simplify the expression :)<3

Answer:

6y + 30

Explanation:

10(y + 3) - 4y

Expand 10(y + 3): 10y + 30

10y + 30 - 4y

Simplify

= 6y + 30

- PNW

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

Answer:P= 16 + 2\|65 units; A= 56 units2

Step-by-step explanation:

Answer: 29

It is very simple, just substitute.

x = 9, y = 10

Replace the x and y in the expression to that.

You get: 9 + 10 + 10. Just add and you will get 29.

Answer:

9+10+10=29

Step-by-step explanation:

We know that x=9, so where ever we see x we know it is 9. We also know that y=10, so where ever we see y we know it is 10. So then we just replace the variables with our numbers then just add them.  That is I got 9+10+10=29

Hope this helps!

The graph of the equation is plotted and attached

Red = (x + 6)² - 1

blue =  -(x + 3)² + 1

green = x² - 1

orange  = -(x - 3)² + 1

purple = (x - 6)² - 1

The parabolic equation is a quadratic equation of the form y = ax^2 + bx + c,

where

a, b, and c are constants and a is not equal to zero.

This equation represents a parabola, which is a U-shaped curve.

The equations of the graphs is gotten using the idea of transformation

The parent function usually have equation of y = x²

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer:

Step-by-step explanation:

12x²-15x

I am really very sorry I tried to help you but I can't and I couldn't delete it

sorry

The amount you need to Deposit each year is approximately $17,191.66.

To calculate the amount you need to deposit each year to have $55,000 in your savings account in 3 years, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value of the annuity (desired amount of $55,000)

P = Annual deposit

r = Annual interest rate (6.5% or 0.065)

n = Number of years (3)

We need to solve for P, so let's rearrange the formula:

P = FV * (r / ((1 + r)^n - 1))

Substituting the given values into the formula:

P = 55000 * (0.065 / ((1 + 0.065)^3 - 1))

P ≈ $17,191.66

Therefore, the amount you need to deposit each year is approximately $17,191.66.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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8 inches :) (im pretty sure)

Answer:

B

Step-by-step explanation:

A door isn't about the size of my foot

Not the size height of my house

Not the size of my street

Sooooooo...

Given that a future value annuity of 8,000 is accrued at 9% compounded annually, the present value of the annuity is evaluated as

Thus,

Substitute the above value into equation 1, to solve for PV

Hence, the sum to be invested is 31117.21

The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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To complete the conditional relative frequency table, we need to determine the values of the letters A and B in the table.  In this case, A = 0.88 and B = 0

To determine the values of A and B in the conditional relative frequency table, we need to analyze the totals in each column.

Looking at the "total" column, we see that the sum of the entries is 1.0. This means that the entries in each row must add up to 1.0 as well.

In the first row, the entry before 10 p.m. is missing, so we can solve for A by subtracting the other two entries from 1.0:

A = 1.0 - (0.9 + a)

In the second row, the entry for 17 years old is missing, so we can solve for B:

B = 1.0 - (0.15 + 0.12)

From the fourth column, we know that the total of the 17 years old entries is 0.12, so we substitute this value in the equation for B:

B = 1.0 - (0.15 + 0.12) = 0.73

Now, we substitute the value of B into the equation for A:A = 1.0 - (0.9 + a) = 0.88

Simplifying the equation for A:

0.9 + a = 0.12

a = 0.12 - 0.9

a = -0.78

Since it doesn't make sense for a probability to be negative, we assume there was an error in the data or calculations. Therefore, the value of A is 0.88, and B is 0.12.

Thus, A = 0.88 and B = 0.12 to complete the conditional relative frequency table.

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Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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The mathematical method that cannot be used to solve a linear equation is the factoring method.

A linear equation is an equation that depicts the straight-line relationship between the dependent variable and the independent variable.

There are six common methods for solving a linear equation, namely:

Factoring involves the even division of an algebraic expression by another expression.

Thus, we can conclude that factoring is not a method for solving a linear equation.

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