Perform the indicated operation. Be sure the answer is reduced.

You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."

optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.

Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:

1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)

2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1

[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]

[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]

maximizing E w.r.t. x,

dE/dx = 0

2x^2 - 400x + 19600 = 0

x = ( 400+/- sqrt(160000-4*2*19600) ) / 4

Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4

x = 85.85786

We just have to calculate E(x=85) and E(x=86) and compare.

E((x=86) = 87.35 and E(x=85) = 87.33

so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

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Answer:

59

Step-by-step explanation:

So, lets look at our numbers in the sequence. So it goes 5 to 8, 8 to 11, 11 to 14, and 14 to 17. This seems like a change in three. So the every 1 term changes the orginal 5 value by 3.

So wouldnt this mean we can multiply the change in terms by the amount of terms? Which is 19*3? Well, sort of. This is the right way of doig this, but we must remember that we already know the first term, 5. So this means we will be doing 18*3.

This gets you 54. Now just add the amount of the 18 terms onto the first term:

54+5

=

59

So your answer is 59.

Hope this helps!

The radius of the sphere is 9 cm.

It is a three-dimensional figure where the volume is given as:

The volume of a sphere is 4/3πr³.

We have,

The surface area of a sphere = 324π cm²

4πr² = 324π

r² = 324/4

r² = 81

r = √81

r = ±9

r = -9 cm (rejected)

r = 9 cm

Thus,

The radius is 9 cm.

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Answer:

in step 2, 60 should be multiplied by the quantity 8-15, not by 8

Step-by-step explanation:

i looked at the image they provided and figured this out, and solved it on my own account but the image wont load

Answer:

4+

5+4+2

+2+4+9+3

+3.5+3.5

=99cm

Answer:

I think the answer is A

Sorry if i am wrong

Step-by-step explanation:

Answer: It is a straight line

Step-by-step explanation:

Answer:

15degrees

Step-by-step explanation:

From the given diagram

<1+<2 + <DCB = 180

<1+<2+120 = 180

<1+<2 = 180 - 120

<1+<2 = 60

<2 = 60 - <1

<2 = 60 - 45

<2 = 15degrees

Hence the measure <2 is 15degree

Answer:

A

Step-by-step explanation:

Given

[tex]\frac{x}{\sqrt{2} }[/tex]

Multiply numerator/ denominator by [tex]\sqrt{2}[/tex] to rationalise the denominator

= [tex]\frac{x\sqrt{2} }{\sqrt{2}(\sqrt{2}) }[/tex]

= [tex]\frac{x\sqrt{2} }{2}[/tex] → A

Answer:

1           3           5         6        11

__ +  ____ =   ___ + ___ = ___ simplified: 1 1/10

2          5           10        10      10

Step-by-step explanation:

Find a common denominator which is 10.

1 1/10 is your answer.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]

Answer:

k\

Step-by-step explanation:

j

Answer:

y=1.5x+2

Step-by-step explanation:

Mark me brainliest pls

2 is the y intercept so a+ 2 is already part of the equation

slope = y2-y1/x2-x1

6-4.5/2-1 = 1.5

y=1.5x + 2

Answer:

（1）：

angle1/2/3/4=90

angle6=51

angle7=40

angle8=89

angle9=51

angle10=40

angle12=50

angle13=130

angle14=50

Step-by-step explanation:

Q1：

angle1 2 3 4 divided 360 into four equal parts

so 360/4=90

angle11=110degree

so angle12 is 180-130=50 degree

because angle 12 3 10 are in triangle

their sum is 180

so angle 10=180-90（angle3）-50（angle12）=40

because angle 10 5 6 sum is 180

so angle 6 is=180-89（angle5）-40（angle10）=51

because angle 5 6 7 sum is 180

angle7=180-51（angle6）-89（angle5）=40

angle8=angle5=89

angle9=angle6=51

angle12 &13sum is 180

so angle13=180-50=130

angle14=angle12=50

Answer:

probably 21

Step-by-step explanation:

Answer:

KL ≈ 16.6 ft

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos25° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MK}{KL}[/tex] = [tex]\frac{15}{KL}[/tex] ( multiply both sides by KL )

KL × cos25° = 15 ( divide both sides by cos25° )

KL = [tex]\frac{15}{cos25}[/tex] ≈ 16.6 ft ( to the nearest tenth )

By taking derivative, slope of the logarithmic function can be found.

The slope of a logarithmic function can be found by taking the derivative of the function with respect to x using the rules of logarithmic differentiation. The general form of the derivative of a logarithmic function is:

d/dx(log(f(x))) = (1/f(x))*(df/dx)

The slope means change in Y with respect to change in X. The slope is the ratio of the rise to run and it shows the steepness of the plane.

The slope is denoted by m.

Example:

Find the slope of y = log(x^2+1)

d/dx(log(x^2+1)) = (1/(x^2+1))*(2x) = 2x/(x^2+1)

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Answer: 3, 6, 15, 17, 21

Step-by-step explanation:

Answer:

Trinomial

Step-by-step explanation:

If there is 1 term, monomial

2 term - binomial

3 term- trinomial

Answer: She has to interpret who has a job not who doesn't.

Step-by-step explanation:

Answer:

x = 17, MN = 11

Step-by-step explanation:

Given 2 secants from an external point to a circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

(5)

7(7 + x) = 8(8 + 13) = 8 × 21 = 168 ( divide both sides by 7 )

7 + x = 24 ( subtract 7 from both sides )

x = 17

(6)

9(9 + 2x - 7) = 10(10 + 8)

9(2x + 2) = 10 × 18 = 180 ( divide both sides by 9 )

2x + 2 = 20 ( subtract 2 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

MN = 2x - 7 = 2(9) - 7 = 18 - 7 = 11

Answer:

a)2.33

b) 2.83

Step-by-step explanation:

What is the mean absolute deviation and population standard deviation of this data set? 1, 4, 6, 7, 9, 9

Step 1

Find the Mean

n = 6

Mean = Sum of values/Number of value

= 1 +4 + 6 +7 + 9+ 9/6

= 36/6

= 6

a) Mean Absolute Deviation

Formula

= |x - Mean|/n

= | (1 - 6)+(4 - 6) + (6 - 6)+(7 - 6)+ (9 - 6) + (9 - 6)|/6

= 5 + 2 + 0 + 1 + 3 + 3/6

= 14/6

= 2.3333333333333

Approximately = 2.33

b) Population Standard deviation

Formula

=√(x - Mean)²/n

= √ (1 - 6)²+(4 - 6)² + (6 - 6)² +(7 - 6)² + (9 - 6)² + (9 - 6)²/6

= √25+ 4+0+ 1+ 9+9/6

= √48/6

= √8

= 2.828427125

Approximately = 2.83

The answers for Center of the circle is (-4,3) and radius is 2√10 units.

(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.

Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

Examples of  Algebraic Expressions

2x2+3xy+4x+7

Given,

[tex]x^2+y^2+8x-6y-15=0[/tex]

⇒ x².+8x+16–16+y²-6x+.9–9–15=.0

(x+4)²+(y-3)²-16–9–15=0

I.e. (x+4)²+(y-3)²=40

(x+4)²+(y-3)²={2√10}²

Hence center is (-4,3) and radius is 2√10 units.

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Answer:

Thjs is hard mat

Step-by-step explanation:

I just need points mateeeee

Answer:

C

Step-by-step explanation:

Put in the form y/x and you should have equivalent fraction

12/4 = 3

15/5 = 3

18/6 = 3

When the fractions are simplified, they all equal 3.

Answer:

The surface area of a sphere is given by the formula:

surface area = 4 * pi * r^2

Where r is the radius of the sphere.

Using this formula, the surface area of an orange with a radius of 3.5 cm is:

surface area = 4 * pi * (3.5 cm)^2

= 4 * pi * 12.25 cm^2

= 49.0307 cm^2

The volume of a sphere is given by the formula:

volume = (4/3) * pi * r^3

Where r is the radius of the sphere.

Using this formula, the volume of an orange with a radius of 3.5 cm is:

volume = (4/3) * pi * (3.5 cm)^3

= (4/3) * pi * 42.875 cm^3

= 113.097 cm^3

Step-by-step explanation:

Given ,

To Find : The Surface Area and the volume of a spherical orange

In order to find the surface area of a spherical orange we use the formula,

[tex]SA = 4\pi r^{2}[/tex]

[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]

[tex]SA =[/tex] [tex]154cm^{2}[/tex]

And now to find the volume of a sphere

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]

[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]

Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]

Step-by-step explanation:

x² - 32 = 4x

x² - 4x - 32 = 0

with a little bit experience we see immediately that this is

(x - 8)(x + 4) = 0

the positive x for this to be true is x = 8.

formally, the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =

= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =

= (4 ± 12)/2 = 2 ± 6

x1 = 2 + 6 = 8

x2 = 2 - 6 = -4

we were right at the beginning.

the positive solution is x = 8.

The triangles can be proved congruent by SAS theorem.

Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.

To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.

Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;

Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.

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Answer:

[tex] {8}^{3n} = {8}^{6} \\ 3n = 6 \\ n = 2[/tex]

Answer:

[tex]n = 2[/tex]

Step-by-step explanation:

[tex]( {8}^{n} )^{3} = {8}^{6} [/tex]

[tex] {8}^{n \times 3} = {8}^{6} [/tex]

[tex]n \times 3 = 6[/tex]

[tex]n = \frac{6}{3} [/tex]

[tex]n = 2[/tex]

In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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