A new drug on the market is known to cure 24% of patients with colon cancer. If a group of 15 patients is randomly selected, what is the probability of observing, at most, two patients who will be cured of colon cancer? 15 choose 2(0.24)2(0.76)13 15 choose 0(0.76)15 + 15 choose 1(0.24)1(0.76)14 + 15 choose 2(0.24)2(0.76)13 1 − 15 choose 2(0.24)2(0.76)13 15 choose 0 (0.76)15 1 − 15 choose 0 (0.76)15

Answer:

a) [tex] P(t) =1600 +50t[/tex]

b) [tex] P(t) = 1600 (1.05)^t[/tex]

Step-by-step explanation:

Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."

Part a

For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:

[tex] P(t) = P_o + b t[/tex]

Where [tex] b =50[/tex] on this case since represent the increase per year of the slope for the linear model. And the initial amount is [tex] P_o = 1600[/tex], so then the model is:

[tex] P(t) =1600 +50t[/tex]

Part b

For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:

[tex] P(t) =P_o b^{t}[/tex]

Where [tex] P_o = 1600[/tex] represent the initial population and for this case b is the rate of increase [tex] b = 1+0.05 = 1.05[/tex] since each year we have an increase of 5% and t is the time. So then the model is given by:

[tex] P(t) = 1600 (1.05)^t[/tex]

The population of a town can be calculated through formulas for linear growth (P = P0 + rt) and exponential growth (P = P0 * e^(rt)), depending on whether the population grows by a fixed amount or percentage each year. To use these formulas, the specific growth rate of the town is needed.

The subject of the question is about writing formulas for population growth. Let's denote the initial population as P0, the rate of growth as r and the time in years as t. Here are two common formulas:

To use these formulas, you'd need to know the specific growth rate of the town. It's also important to remember that actual population changes can be more complex and may not follow these exact formulas.

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Answer:

a≈2.343

Step-by-step explanation:

View Image

Integrating an equation from boundary x₀ to x₁ gives you the area underneath that boundary.

So to find the boundary that split the equation into 2 equal areas, the boundary must lie somewhere between the 2 place to want to split up. In other word, a is the end boundaries of the first integral and the starting boundary of the second integral.

Since the two area must equal to each other, set the two integral equal to each other and solve for a.

The value of a for which x=a will divide the enclosed area into two equal areas will be 2.43.

Let us say x=a divides the region into two equal areas.

From the attached diagram,

Point D≡(a,8)

Point E≡(a, a)

The length of DE will be 8-a.

As we know that triangles ADE and ABO will be similar

So, [tex]\frac{areaADE}{areaABO} = (\frac{DE}{BO}) ^{2}[/tex]

[tex]\frac{1}{2} = (\frac{a-8}{8}) ^{2}[/tex]

[tex]a^2-16a+32 = 0[/tex]

a =13.66(Not Possible)

a= 2.34

Therefore, The value of a for which x=a will divide the enclosed area into two equal areas will be 2.43.

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The type of annuity in the question is known as a refunded annuity. It ensures that the entire contract value is utilized in case the annuitant dies prematurely. The payments would continue to a beneficiary until the total contract value has been paid.

The type of annuity described in the question, where payments continue to a beneficiary until the contract value is paid out if the annuitant dies prematurely, is referred to as a refunded annuity. Annuities are often used in retirement planning. This specific type of annuity gives protection to the annuitant's investment, ensuring that the whole amount of the contract value is utilized even if the annuitant dies before receiving the full value in payments. For instance, if an annuitant bought an annuity worth $200,000 and dies after receiving only $50,000, the beneficiary would continue to receive payments until the remaining $150,000 is paid out.

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A cash refund annuity is an annuity that promises to continue payments to a beneficiary until the contract value has been paid if the annuitant dies before that.

The type of annuity described in the question, where the payments continue to a beneficiary until an amount equal to the contract value has been paid if the annuitant dies before that, is called a cash refund annuity.

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Answer:

∼  : This symbol denotes similarity

∪ : This symbol means union

∩ : This symbol means Intersection

∅ : means an empty set

≠ : this symbol mean not equal to

! : This symbol means factorial

Step-by-step explanation:

Given symbols in the question:

∼  : This symbol denotes similarity

i.e the resemblance or likeness.

∪ : This symbol means union

i.e

A∪B element that belong to set A or set B

∩ : This symbol means Intersection

i.e

A∩B = Element that belong to set A and set B

∅ : means an empty set

For example

if A = { 1, 2, 3 }   B = { 4, 5, 6 }

Then,

A∩B = ∅

≠ : this symbol mean not equal to

i.e

LHS is not equal to RHS

! : This symbol means factorial

i.e

If we write 3!

we solve it as 3! = 3 × 2 × 1

The slope of the budget line for a consumer who has $100 to spend per day, with product A at $7/unit on the horizontal axis and product B at $15/unit on the vertical axis, is -0.47. More consumption of one good requires a sacrifice in the consumption of the other.

The subject of this question is the slope of the budget line in microeconomics, which represents the trade-off between two goods, product A and product B. It can be determined by dividing the price of the good on the horizontal axis (product A) by the price of the good on the vertical axis (product B). Hence, the slope of the budget line is $7/$15 = 0.47 (rounded to two decimal places). The slope is negative reflecting the fact that to obtain more of one good, a consumer needs to give up some of the other.

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The slope of the budget line is -7/15 or approximately -0.467.

       In this case, the slope = - (7 / 15).

After calculating, we get the slope as - 7/15 or approximately -0.467. This slope indicates the rate at which the consumer can trade product A for product B while staying within their budget.

Final answer:

The statement is true; the centroid of a triangle is the point that lies 2/3 of the way from each vertex to the midpoint of the opposite side. The centroid is the same point for all three vertices, which can be shown using vector operations that equate to (A+B+C)/3 for a triangle with vertices A, B, and C.

Explanation:

The statement that points lying 2/3 of the way from a vertex to the midpoint of the opposite side for any triangle in ℝ² (the real number plane) are all the same point, and this point is called the centroid of the triangle, is True. To prove this, consider a triangle ABC with vertices A, B, and C. If M is the midpoint of side BC, N is the midpoint of side AC, and O is the midpoint of side AB, then the points two-thirds of the way from the vertices A, B, and C to the midpoints of the opposite sides, respectively, can be represented by the vectors (2M+A)/3, (2N+B)/3, and (2O+C)/3.

Applying the midpoint formula and vector addition, we find that these points are equivalent to (B+C)/3, (A+C)/3, and (A+B)/3 respectively, which, when simplified, all yield to (A+B+C)/3, illustrating that the points coincide and thus prove the existence of a single centroid.

In a geometric context, the centroid is the point where the triangle’s medians intersect, and it also serves as the triangle's center of mass. The centroid divides each median in a 2:1 ratio, with the larger portion being closer to the vertex. This property is intrinsic to triangles and can be demonstrated using vector algebra or geometric arguments.

Answer:

b) 40 fishing lures and 20 duck decoys

c) 20 fishing lures and 24 duck decoys

Question:

Attached is the graph to be used to answer the questions.

Step-by-step explanation:

b) Any point above the straight line graph PPF is unobtainable, while points below or on the line graph are obtainable.

Finding each of the points on the graph and determine whether it is above, on or below the line graph.

- Only one point is above the graph (40 fishing lures and 20 duck decoys )

Therefore, 40 fishing lures and 20 duck decoys  is unobtainable.

c) for an efficient combination the points must be on the line of the graph (PPF).

The only point that falls on the line of the graph is (20 fishing lures and 24 duck decoys)

Therefore, 20 fishing lures and 24 duck decoys is an efficient combination.

Answer:

I would expect the standard error to decrease, because sample size increases.

Step-by-step explanation:

Standard error on the mean can be calculated using the equation:

[tex]\frac{s}{\sqrt{N}}[/tex]      where

Therefore, if the group makes several more measurements then the sample size increases, which makes the standard error on the mean smaller.  

The standard error is expected to decrease when more measurements are made and used to recalculate it.

The standard error of the mean is a measure of the variability of sample means. As you obtain more measurements and calculate the standard error again using all the measurements, you would expect the standard error to decrease. This is because the more measurements you have, the more precise your estimate of the true mean becomes.

When calculating the standard error, you divide the standard deviation by the square root of the sample size. The standard deviation measures the variability of the individual measurements, while the square root of the sample size represents the precision of the mean. As the sample size increases, the precision increases, resulting in a smaller standard error.

For example, let's say you initially had a small sample size of 10 and calculated a standard error of 2. If you then collect more measurements and increase the sample size to 20, you would expect the standard error to decrease, potentially to a value smaller than 2.

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Answer:

9x10^9

Step-by-step explanation:

2x4.5x10^9

just multiply by two.

Answer:

2,000,000,009

Step-by-step explanation:

2(4.5 x 10^9)

Distribute the 2

(2 x 4.5) +2(10^9)

= 9 + 2,000,000,000

Answer:

The exponential function is Y = 200 [1.07]ˣ

Step-by-step explanation:

Let Y represent the expected population

Let P represent the current population

Let r represent the population growth rate

let x represent the number of years or nth year.

The compound interest expression can used to derive the exponential function can be represented as follows

Y = P [1 + (r ÷ 100)]ˣ

Y = 200 [ 1 + (7 ÷ 100)]ˣ

Y = 200 [ 1 + (0.07)]ˣ

Y = 200 [1.07]ˣ

Final answer:

To model the population growth of deer in a national park, an exponential function P(t) = 200 * (1 + 0.07)^t is used. This reflects a starting number of 200 deer, with growth at a rate of 7% per year, allowing for future population predictions.

Explanation:

A wildlife biologist determines that there are approximately 200 deer in a region of a national park. The population grows at a rate of 7% per year. To model the expected population using an exponential function, we use the general formula for exponential growth P(t) = P0 * (1 + r)^t, where:

Given that the initial population (P0) is 200 deer and the annual growth rate (r) is 7% or 0.07, the exponential growth model to predict future population sizes can be written as P(t) = 200 * (1 + 0.07)^t.

This function can be used to calculate the expected number of deer in this region of the national park for any number of years into the future, allowing biologists and park management to make informed decisions regarding wildlife conservation and management.

Answer:Lilah's speed on the train is 60 mph and Mason's speed is 75 mph

Step-by-step explanation:

Let x represent the speed of Lilah.

Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train.

Distance = speed × time

Distance covered by Lilah in moving from Portland to Seattle would be

3 × x = 3x

It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train.

It means that Mason's speed is

x + 15

Distance covered by Mason would be

2.4(x + 15) = 2.4x + 36

Since the distance from Portland to Seattle is the same, then

3x = 2.4x + 36

3x - 2.4x = 36

0.6x = 36 x = 36/0.6 = 60 mph

Mason's speed would be 60 + 15 = 75 mph

Answer:approximately 50 years.

Step-by-step explanation:

Let $P represent the initial amount that she deposited. It means that principal,

P = $P

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 1.4%. So

r = 1.4/100 = 0.014

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. For the initial amount to double, it means that

A = 2P

Therefore

2P = P (1+0.014/1)^1×t

2P/P = (1.014)^t

2 = (1.014)^t

Taking log to base 10 of both sides, it becomes

Log 2 = log 1.014^t

Log 2 = tlog 1.014

0.301 = 0.006t

t = 0.301/0.006 = 50.2 years

Answer: 51.4 years

Step-by-step explanation:

There is what we call rule of 72 in Accounting to find the time  a sum of money will double if it is compounded annually at any given rate . The formula is given as :

t = [tex]\frac{72}{r}[/tex]

where t is the time and r is the rate.

t = ?

r = 1.4

Therefore :

t = 72/1.4

t = 51.4286

to the nearest tenth

t = 51. 4 years

Answer:

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Step-by-step explanation:

Let

x ----> the amount invested at 6%

30,000-x -----> the amount invested at 13%

we know that

The interest earned by the amount invested at 6% plus the interest earned by the amount at 13% must be equal to the interest earned by the total amount of $30,000 at 10%

Remember that

[tex]6\%=6\100=0.06[/tex]

[tex]13\%=13\100=0.13[/tex]

[tex]10\%=10\100=0.10[/tex]

so

The linear equation that represent this situation is

[tex]0.06x+(30,000-x)0.13=0.10(30,000)[/tex]

solve for x

[tex]0.06x+3,900-0.13x=3,000\\0.13x-0.06x=3,900-3,000\\0.07x=900\\x=\$12,857.14$[/tex]

[tex]x-\$30,000=\$17,142.86[/tex]

therefore

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Answer:

Option 2 -  [tex]x=\frac{7\pm3\sqrt{3}i}{2}[/tex]

Step-by-step explanation:

Given : Equation [tex](x-5)^2+3(x-5)+9=0[/tex]

To find : What is the solution of the equation ?

Solution :

Using substitution method,

Let y=x-5

[tex]y^2+3y+9=0[/tex]

Using quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, a=1, b=3 and c=9

[tex]y=\frac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}[/tex]

[tex]y=\frac{-3\pm\sqrt{-27}}{2}[/tex]

[tex]y=\frac{-3\pm3\sqrt{3}i}{2}[/tex]

Substitute back,

[tex]x=\frac{-3\pm3\sqrt{3}i}{2}+5[/tex]

[tex]x=\frac{-3\pm3\sqrt{3}i+10}{2}[/tex]

[tex]x=\frac{7\pm3\sqrt{3}i}{2}[/tex]

Therefore, option 2 is correct.

Answer:

Option 2

Step-by-step explanation:

I just took the test and got it right.

Answer:

Step-by-step explanation:

At a real estate​ agency, an agent sold a house for ​$392000.

The commission rate is 7.5​% for the real estate agency. This means that the amount of money that the real estate​ agency earn would be

7.5/100 = 392000 = 0.075 × 392000 = $29400

the commission rate for the agent is 20​% of the amount the real estate agency gets. This means that the amount that the agent would earn is 20/100 × 29400 = 0.2 × 29400 = $5880

Answer:

The answer to your question is below

Step-by-step explanation:

Functions

  f(x) = 12x           f⁻¹(x) = 2x

a)   f⁻¹(-2) = 2(-2)

     f⁻¹(-2) = -4

b) f(-4) = 12x

    f(-4) = 12(-4)

    f(-4) = -48

c) f(f⁻¹(-2)) =

   f(f⁻¹(x)) = 12(2x) = 24x

  f(f⁻¹(-2)) = 24(-2) = -48            

I think your functions are wrong they must be       f(x) = 1/2x    f⁻¹(x) = 2x        

a)  f⁻¹(-2) = 2(-2)

             = -4

b) f(-4) = 1/2(-4)

         = -2

c) f(f⁻¹(x)) = 1/2(2x)

              = x

  f(f⁻¹(-2)) = -2

Answer:

1)= -4

2)= -2

3)= -2

Step-by-step explanation:

Answer:

Option A) is correct.

Step-by-step explanation:

We need to use normalcdf command to find the probability that the variable would fall into a certain interval that we would supply.

As

and

And we have to determine the percent of students have scored more than 75 points.

So,

Mean = μ = 60

Standard Deviation = σ = 5

As we have to determine the percent of students have scored more than 75 points.

Hence,

normalcdf(75,100,60,5) = .0013

Converting on percentage → .0013 × 100 = 0.1

Therefore, option A) is correct as 0.1 percent of students have scored more than 75 points.

Keywords: distribution, mean, median

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Answer:

Perimeter= 12 feet   Area= 6 feet (squared)

Step-by-step explanation:

Perimeter= Adding all the sides together, that means it is 3+4+5= 12 feet

Area= Hight times base divided by 2. Because hight times base is area of a rectangle, and a right triangle (and all other triangles) is half of it. Because it is a right triangle, its hight must be 3 or 4, and base also 3 or 4. But no the same number twice, so 3*4=12, 12/2=6 feet (squared).

I hope that helped! =)

Answer:

Because order matters when performing subtraction or division.

Step-by-step explanation:

Consider the provided information.

We need to determine why there no commutative property for subtraction or division.

Commutative property states that although the numbers in an expression are interchanged, there is no change in result.

Let us understand with the help of an example

For addition: The commutative rule is a + b = b + a.

An example in numbers would be 5 + 2 = 2 + 5

Both give 7 as result.

For Subtraction:  4 – 2 = 2, but 2 – 4 = –2

So, in the case of subtraction, moving the numbers around produces a different answer.

For division: 4 ÷ 2 = 2,  2 ÷ 4 = [tex]\frac{1}{2}[/tex]

So, in the case of division, moving the numbers around produces a different answer.

Hence, order matters when performing subtraction or division.

Answer:

(-138) is the answer.

Step-by-step explanation:

Perfect square numbers between 15 and 25 inclusive are 16 and 25.

Sum of perfect square numbers 16 and 25 = 16 + 25 = 41

Sum of the remaining numbers between 15 and 25 inclusive means sum of the numbers from 17 to 24 plus 15.

Since sum of an arithmetic progression is defined by the expression

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

Where n = number of terms

a = first term of the sequence

d = common difference

[tex]S_{8}=\frac{8}{2} [2\times 17+(8-1)\times 1][/tex]

   = 4(34 + 7)

   = 164

Sum of 15 + [tex]S_{8}[/tex] = 15 + 164 = 179

Now the difference between 41 and sum of perfect squares between 15 and 25 inclusive = [tex]41-179[/tex]

= -138

Therefore, answer is (-138).

The sum of the perfect squares (16 and 25) between 15 and 25 is 41. The sum of all the other numbers between 15 and 25 is 179. So, when we subtract 179 from 41, we get -138.

To find the answer, we first need to identify which numbers between 15 and 25, inclusive, are perfect squares. A perfect square is a number which can be expressed as the product of an integer with itself. In this range, 16 and 25 are the perfect squares.

The sum of these perfect squares is 16 + 25 = 41.

Next, we need to find the sum of all the other numbers between 15 and 25, inclusive, that are not perfect squares. These numbers are 15, 17, 18, 19, 20, 21, 22, 23, and 24. Adding these numbers together gives a sum of 179.

Now subtract this second sum from the first to get the answer: 41 - 179 = -138

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Answer:

B on edu2020

Step-by-step explanation:

Answer:

700 children tickets, 950 adult tickets

Step-by-step explanation:

Let x and y be the number of tickets sold for children and adults, respectively. We know that the total number of tickets sold is 1650. So x + y = 1650, or x = 1650 - y

Also the total ticket revenue is $14200, at $12 per adult and $4 per child. We have:

4x + 12y = 14200

We can substitute x = 1650 - y

4(1650 - y) + 12y = 14200

6600 - 4y + 12y = 14200

6600 + 8y = 14200

8y = 14200 - 6600 = 7600

y = 7600 / 8 = 950 adult tickets

x = 1650 - 950 = 700 children tickets

Answer:

.75 is your answer

Step-by-step explanation:

Answer: 55 performances are needed to break even.

Step-by-step explanation:

Let x represent the number of musical performances that are made.

Producing a musical costs $88,000 plus $5900 per performance. This means that the total cost of x musical performances would be

88000 + 5900x

One sold-out performance earns $7500 in revenue. If every performance sells out, it means that the total revenue would be

7500 × x = 7500x

In order to break even, total cost would be equal to total revenue. Therefore,

7500x = 88000 + 5900x

7500x - 5900x = 88000

1600x = 88000

x = 88000/1600 = 55

Answer:

REALS. all real numbers are solution for the equation

Step-by-step explanation:

for the equation

x² = (x + 3)*(x − 3) + 9

distributing the terms in the parenthesis

x² = (x + 3)*(x − 3) + 9  = [x² - 3*x + 3*x - 3*3 ] + 9

x² = x² - 9 + 9

0 = 0

since this statement will be true regardless of the value of x , then the equation has solution for all real numbers .

Answer:

This is true.

Step-by-step explanation:

This would be known as the transitive property.

If A = B, and B = C, then A must equal C

Let me explain.

If A = 2, and B = 2, and A = C, C must also equal 2.

If something is equal then it's the same, so it makes sense for A = C if B is the same value as A and C.

A good way to recognize the property is if you see a number/letter appear twice, and they both equal different things. Then you see the two different letters are equal to each other. Hopefully this helped some.

The principle of independence is not transitive. If A and B are independent, and B and C are independent, it does not necessarily mean that A and C are independent. This can be proven through a counterexample involving coin tosses.

The statement 'If A is independent of B and B is independent of C, then A is independent of C' is not necessarily true. This is so because independence is not transitive.

Consider the following counterexample:

In this example, event A (getting head in first toss) is independent of B (getting tail in first toss), and B is independent of C (getting head in second toss). However, A is clearly not independent of C because both are 'getting head' on their respective tosses.

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Answer:

Step-by-step explanation:

The math club makes 35 bars of laundry soap a week and sells these at $20 each. This means that the total number of bars of laundry soap made in a 4 week month would be

4 × 35 = 140 bars

If the pupils found that 6 bars were destroyed by mice, the total number of bars of soap left would be

140 - 6 = 134 bars

Therefore, the total sale at the end of a four week month would be

134 × 20 = $2680

The total sales at the end of a 4-week month, given that 6 out of 35 soap bars were destroyed by mice every week and the price of each soap bar is $20, would be $2320.

The math club initially makes 35 bars of soap every week. However, due to the unforeseen mouse problem, 6 bars are rendered unsalable each week. Therefore, the club is effectively selling only 29 bars per week. Because the selling price of each bar is $20, each week's sales amount to 29 bars x $20/bar = $580.

Over 4 weeks, the total sales would then be $580/week x 4 weeks = $2320. So, the total amount of sales at the end of a 4-week month, after accounting for the mice damage, would be $2320.

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Answer: a. Number of visitors

b. average([tex]\mu[/tex]) amount spent per person by visitors to the park

c. Yes , we know  the average amount spent per person byvisitors to the park. It is $28 per person.

Step-by-step explanation:

For the given situation, A researcher wishes to estimate the average amount spent per person by visitors to a theme park.

Population by researcher's point of interest : "Number of visitors"

Parameter of interest : "average([tex]\mu[/tex]) amount spent per person by visitors to the park"

Since he takes a random sample of forty visitors and obtains an average of $28 per person.

Here , sample : forty visitors

And average amount spent per person by visitors to the park from sample :  

[tex]\overline{x}= [/tex] $28 per person.

The sample means is the best point-estimate for the population mean.

So , the best point-estimate for average amount spent per person by visitors to the park here is $28 per person.

The population of interest is:

The parameter of interest is:

Based on the sample, the way know the average amount spent per person by visitors to the park is:

This refers to the select sample which a researcher tries to draw conclusions from.

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Answer:

[tex] E(X) = 11 *\frac{4}{52} - 1*\frac{48}{52} = -\frac{1}{13}[/tex]

So we expect to lose approximately [tex] 1/13[/tex] for this game.

Step-by-step explanation:

For this case we can find the probability of win like this:

[tex] p_w = \frac{4}{52}[/tex]

Since we have 4 aces each time in a total of 52.

And the probability of loss is given by:

[tex] p_l = \frac{48}{52}[/tex]

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

And we can find the expected value with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]

Where X on this case represent the random variable "Amount of money win or loss in the game", for this case we can replace and we got:

[tex] E(X) = 11 *\frac{4}{52} - 1*\frac{48}{52} = -\frac{1}{13}[/tex]

So we expect to lose approximately [tex] 1/13[/tex] for this game.

The mean outcome of this wager is -$0.62, indicating an expected average loss of $0.62 per game.

To determine the mean outcome of this wager, we need to calculate the expected value. The probability of drawing an ace from the deck is 4/52, since there are 4 aces out of 52 cards. The payoff for drawing an ace is $11, while the payoff for not drawing an ace is -$1. The expected value is calculated by multiplying the probability of each outcome by its corresponding payoff and summing them up:

Expected value = (Probability of outcome 1 x Payoff for outcome 1) + (Probability of outcome 2 x Payoff for outcome 2)

Expected value = (4/52 x $11) + (48/52 x -$1)

Expected value = -$0.62

Therefore, if you play this game repeatedly, you would expect to lose $0.62 per game, on average. The expected value indicates an expected average loss, so it is not advisable to play this game to win money.

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The values of m and n are [tex]m=4[/tex] and [tex]n=1[/tex]

Explanation:

The two equations are [tex]m+n=5[/tex] and [tex]m-n=3[/tex]

From the equation [tex]m-n=3[/tex], we shall find the value of m such that

[tex]m=n+3[/tex]

Substituting the value of m in [tex]m+n=5[/tex], we get,

[tex]\begin{array}{r}{n+3+n=5} \\{2 n+3=5}\end{array}[/tex]

Subtracting both sides by 3,

[tex]2n=2[/tex]

Dividing both sides by 2, we get,

[tex]n=1[/tex]

Substituting [tex]n=1[/tex] in [tex]m-n=3[/tex]

[tex]\begin{array}{r}{m-1=3} \\{m=4}\end{array}[/tex]

Thus, the values of m and n are [tex]m=4[/tex] and [tex]n=1[/tex]