If you throw exactly two heads in two tosses of a coin you win $36. If not, you pay me $16.

Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answers

Answer 1

Answer:

so the odds of getting a heads is 50 percent and the odds of doing it again is 25 percent so for example if you did this 4 times your would make -12 dollars

Related Questions

The area of a rectangular rug is 16 square feet. If the length of the rug measures 6 feet long, what is the width?

Answers

Answer:

6ft

Step-by-step explanation:

javahvpaiudbajbd;kjbzcuvbjkabr;kabga

Answer:

2 2/3 ft

Step-by-step explanation:

w = A/l

plug in the values

w = 16/6

solve.

2.6... = 2 2/3

therefore the width of the rug is 2 2/3 ft

What’s the complex number in polar form with argument theta between 0 and 2pie?
8+8i

Answers

9514 1404 393

Answer:

45. (8√2)∠π/4

46. (7√2)∠3π/4

Step-by-step explanation:

The polar form of a+bi is ...

a +bi ⇔ (√(a²+b²))∠arctan(b/a)

45. 8 +8i = (√(8² +8²))∠arctan(8/8) = (8√2)∠π/4

46. -7 +7i = (√((-7)² +7²))∠arctan(7/-7) = (7√2)∠3π/4

_____

Additional comment

The arctan function usually returns a value in the range -π/2 to π/2. The quadrant of the desired result can be determined by the signs of the components of the vector. For negative real parts, π needs to be added to the value that is usually returned by the arctan function.

Please assist, I'm really bad with word problems

Answers

Answer:

The surface area of the balloon is [tex]S(t) = \frac{100}{49} \pi t^8[/tex]

Step-by-step explanation:

Given;

S(r) = 4πr²

where;

S is the surface area of the balloon

r is the radius of the surface

The radius of the balloon at time "t" is given as;

[tex]r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0[/tex]

The surface area of the balloon as a function of time "t" is calculated as;

[tex]S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8[/tex]

STEM:

If you can rewrite a quadratic equation as a product of factors that equals zero, you
can solve the equation. To solve equations in this manner, you must use all your
factoring skills.

Example:

What are the solutions of the equation x2– x = 20?

First rewrite the equation so that one side equals zero.

x2– x = 20

x2 – x – 20 = 20 – 20

x2 – x – 20 = 0

Subtract 20 from each side.

Simplify.

Now, factor to rewrite the equation as a product of factors equal to zero. Find two
integers whose product is –20 and whose sum is –1. The product of 4 and –5 is
–20, and the sum of 4 and –5 is –1.

x + 4 = 0

x + 4 – 4 = 0 – 4

x = –4

x2 – x – 20 = 0

(x + 4)(x – 5) = 0

or

or

or

x – 5 = 0

x – 5 +5 = 0 +5

x = 5

The solutions are –4 and 5.

These "solutions" tell us where our quadratic function passess through the x-axis (ie this tells us the "roots" aka "x -intercepts" aka "zeros" aka "solutions" aka "zeros" are)

Question:

In the graph provided in the example, what do the coordinates (-4,0) and (5,0) represent?

A
The y- intercept of the function (ie where the function passes through the y-axis)

B
The x-intercept of the function (ie where the function passes through the x-axis)

C
The vertex of the function

D
none of the above

E
the zeros of the quadratic function

F
the roots of the quadratic function

Answers

9514 1404 393

Answer:

A, E, F

Step-by-step explanation:

Every point on the graph has coordinates (x, f(x)). This means a point such as (-4, 0) or (5, 0) is a point on the x-axis where f(x) = 0. It is all of ...

an x-intercepta root of the functiona zero of the function

These terms are used essentially interchangeably.

Rick's lumberyard has 360 yd of fencing with which to enclose a rectangular area. If the enclosed area is x yards long, express its area as a function of its length.

Answers

Answer:

180x - x²

Step-by-step explanation:

Since the yard has 360 yd. of fencing, hence the perimeter of Rick's lumberyard has 360 yd.

Given that the yard is x yards long. Let y represent the width of the yard. Hence:

Perimeter of the yard = 2(length + width) = 2(x + y)

Substituting:

360 = 2(x + y)

180 = x + y

y = 180 - x

Therefore the width of the yard is (180 - x) yard.

The area of the yard is the product of the length and the width, hence:

Area (A) = length * width

A = x * (180 - x)

A = 180x - x²

Expression for the area as a function of its length will be, Area = (180x - x²) square yards

It's given in the question,

Length of the fence with Rick's lumberyard = 360 yardsLength of the enclosed area = x yards

Since, length of the fence = Perimeter of the rectangular area

And Perimeter of the rectangular area = 2(length + width)

By substituting the values of area and the length in the expression,

360 = 2(x + width)

180 = x + width

Width = (180 - x) yards

Since, area of a rectangle is given by the expression,

Area = Length × Width

By substituting the values in the expression,

Area = x(180 - x)

= (180x - x²) square yards

Therefore, expression for the area in terms of its length will be, Area = (180x - x²) square yards.

Learn more,

https://brainly.com/question/2292262

Initially 100 milligrams of a radioactive substance was present. After 8 hours the mass had decreased by 2%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)

Answers

For initial 100 milligrams of a radioactive substance was if decreased by 2% in 8 hours, then half-life of the radioactive substance is 108.3 hours.

Rate of change is the change in one variable due to change in other.

Given the following:

Amount of a radioactive substance initially present=100mg

After 8 hours, mass decreased by 2%

Mass after 8 hours= 100-(2% of 100)

=100-(2*100/100)

=100-2

=98

The rate of decay is proportional to the amount of the substance present at time t.

Mathematically,

Let the amount of radioactive substance is A and at time t,

[tex]\dfrac d{dt}A\ \alpha\ A\\\\[/tex]

[tex]\dfrac d{dt}A= kA\\\\\\dA=kAdt[/tex]

On integrating both sides,

[tex]\int \frac {1}{kA}dA=\int dt\\\\[/tex]

[tex]\dfrac {ln A}{k}=t +ln \ c_1\\ln A =kt+k\ ln \ c_1\\[/tex]

On taking antilogarithm both sides,

[tex]e^{ln A} =e^{kt+k\ ln \ c_1\\A=e^{kt}e^{k\ ln \ c_1}\\A=e^{kt}e^{\ ln \ c_1^k}\\A=e^{kt}c_1^k \\[/tex]

Let, [tex]c_1^k=c[/tex]

[tex]A =e^{kt}c[/tex].................................1

At t=0, A=100

Substituting values in 1

[tex]100= e^0c\\c=100[/tex]

At t= 8, A=98

[tex]98=e^{k8}100\\0.98=e^{8k}\\8k=ln0.98[/tex]

k=-0.0064.

To determine the half time of the decay.

At half time A became A/2=50 mg

Substituting in 1.

[tex]50=e^{-0.0064t}100\\ln 0.5=-0.0064t\\t=\frac{ln 0.5}{-0.0064}\\t=108.3042\\t=108.3[/tex]....................................rounded to one decimal place.

Thus, The half-life of the radioactive substance is 108.3 hr.

Learn more about rate of change, here:

https://brainly.com/question/29044610

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What is an inscribed polygon is being constructed

Answers

Answer:

An inscribed polygon might refer to any

polygon which is inscribed in a shape,

especially: A cyclic polygon, which is

inscribed in a circle

Answer:

A square

Step-by-step explanation:

Which pair of angles are complementary?

Answers

Answer:

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees. Examples: 60° and 30° are complementary angles.

Answer:

Step-by-step explanation:

those two angles which gives 90 degree when added are complementary angles.

3. 72 in. ___ = ft help

Answers

Answer:

6 feet

Step-by-step explanation:

Answer:

72in is 6 feet

Step-by-step explanation:

linar system in variables
-x-3y-2z=8,
-x+y+6z=,
x-9y-2z=4

Answers

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system: