In a board game, you roll a die to win or lose points, depending on the outcome. The outcomes follow this probability distribution.


If a player can only win by accumulating 20 points, which of the following best describes the fairness of the game?

Answer:

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Step-by-step explanation:

[tex]\sin(\theta)+1=\cos(2\theta)[/tex]

Applying double angle identity:

[tex]\cos(2\theta)=1-2\sin^2(\theta)[/tex]

Doing so would give:

[tex]\sin(\theta)+1=1-2\sin^2(\theta)[/tex]

We need to get everything to one side so we have 0 on one side.

Subtract 1 on both sides:

[tex]\sin(\theta)=-2\sin^2(\theta)[/tex]

Add [tex]2\sin^2(theta)[/tex] on both sides:

[tex]\sin(\theta)+2\sin^2(\theta)=0[/tex]

Let's factor the left-hand side.

The two terms on the left-hand side have a common factor of [tex]\sin(\theta)[/tex].

[tex]\sin(\theta)[1+2\sin(\theta)]=0[/tex].

This implies we have:

[tex]\sin(\theta)=0 \text{ or } 1+2\sin(\theta)=0[/tex].

We need to solve both equations.

You are asking they be solved in the interval [tex][0,2\pi)[/tex].

[tex]\sin(\theta)=0[/tex]

This means look at your unit circle and find when you have your y-coordinates is 0.

You this at 0 and [tex]\pi[/tex]. (I didn't include [tex]2\pi[/tex] because you don't have a equal sign at the endpoint of [tex]2\pi[/tex].

Now let's solve [tex]1+2\sin(\theta)=0[/tex]

Subtract 1 on both sides:

[tex]2\sin(\theta)=-1[/tex]

Divide both sides by 2:

[tex]\sin(\theta)=\frac{-1}{2}[/tex]

Now we are going to go and look for when the y-coordinates are -1/2.

This happens at [tex]\frac{7\pi}{6}[/tex] and [tex]\frac{11\pi}{6}[/tex].

The solution set given the restrictions is

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Answer:

True

Step-by-step explanation:

The binomial distribution that has a probability of success equal to .20, would be left skewed for sample size of 20.

The given statement "The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20" is false.

The statement is incorrect. The binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would not necessarily be left-skewed. The shape of the binomial distribution depends on the values of the probability of success and the sample size.

In general, for a binomial distribution with a small probability of success (such as 0.20) and a large sample size (such as 20), the distribution tends to approximate a normal distribution. As the sample size increases, the binomial distribution becomes more symmetric and bell-shaped.

Therefore, it is not accurate to claim that the binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would be left-skewed.

To know more about binomial distribution:

https://brainly.com/question/33656163

#SPJ2

Answer:

△ABC ~ △DEF

Step-by-step explanation:

the AA (angle angle) postulate is a postulate that says two triangles can be similar if they have two congruent angles. using this postulate with how each triangle has a 90° angle and ∠F is congruent to ∠C, we can determine that △ABC ~ △DEF.

The correct answer is C. OBC DE because of the definition of similarity in terms of similarity transformations.

A similarity transformation is a transformation that maps a figure onto a similar figure. A similar figure is a figure that has the same shape as the original figure, but may be a different size and orientation.

A rigid transformation is a transformation that maps a figure onto a congruent figure. A congruent figure is a figure that has the same size and shape as the original figure.

Since a series of rigid transformations maps F onto C where F is congruent to C, then the rigid transformations must have preserved the shape and size of F. This means that the rigid transformations must have been similarity transformations.

Therefore, the statement "OBC DE because of the definition of similarity in terms of similarity transformations" is true.

For such more question on similarity

https://brainly.com/question/29789257

#SPJ2

Answer:

[tex]P (X = 140) = 0[/tex]

Step-by-step explanation:

We know that the heron wingspan follow a normal distribution with an mean of 125 cm.

In this case we seek to find

[tex]P (X = 140)[/tex]

If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.

Then by definition of continuous random variable we have to:

[tex]P (X = a) = 0[/tex] where a is a constant.

That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.

Finally we can conclude that

[tex]P (X = 140) = 0[/tex]

To find the proportion of herons with a wingspan of exactly 140cm, calculate the z-score using the given mean and standard deviation. Use the z-score to find the area under the normal curve and determine the proportion. The resulting area is approximately 0.8944 or 89.44%.

To find the proportion of herons with a wingspan of exactly 140cm, we need to calculate the z-score for 140cm using the formula:

z = (x - μ) / σ

where x is the value being analyzed, μ is the mean, and σ is the standard deviation. Plugging in the values:

z = (140 - 125) / 12 = 1.25

To find the proportion, we can use the z-table or calculator to find the area under the normal curve to the left of z = 1.25. The resulting area is approximately 0.8944 or 89.44%.

Answer: [tex]\dfrac{3}{10}[/tex]

Step-by-step explanation:

Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.

The factors of 15 = [tex]1,\ 3,\ 5[/tex]

Then ,the probability of obtaining a factor of 15 is given by :-

[tex]P(A)=\dfrac{3}{5}[/tex]

The probability of getting a tail :-

[tex]P(B)=\dfrac{1}{2}[/tex]

Since both the events are independent , thus

The probability of obtaining a factor of 15 and a tail is given by :-

[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]

Hence, the required probability : [tex]\dfrac{3}{10}[/tex]

The 60% of adults who like pizza was found by dividing the adults who like pizza ( 0.36) by the total adults ( 0.60): 0.36 / 0.6 = 0.6 = 60%

To find the percent of children that like pizza divide 0.29 by 0.40:

0.29 / 0.40 = 0.725 = 72.5%, which is about 70%

The answer would be C. A greater percentage of children (about 70%) prefer pizza.

The percentage of children that prefer pizza are about 70%, which is Option(c) .

A relative figure reflecting hundredth parts of any quantity is called a percentage.

Children who like pizza = 0.29

Total No. of children = 0.40

Percentage of children who like pizza = (0.29 / 0.40) * 100

Percentage = 72.5% (about 70%)

The percentage of children who like pizza are about 70%(Option - c)

Learn more about percentages on:

https://brainly.com/question/2236179

#SPJ2

Answer:

(14.7 , 16.9)

Step-by-step explanation:

it is given that [tex]\bar{x}=15.8[/tex] tons

σ=3.8 tons

n=49

at 95% confidence level α=1-.95=0.05

[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]

=1.96 ( from the standard table)

at 95% confidence level the coefficient interval for μ is

[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]

[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]

[tex]15.8\pm 1.1[/tex]

(14.7, 16.9)

Answer:

The determinant is 15.

Step-by-step explanation:

You need to calculate the determinant of the given matrix.

1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):

[tex]\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right][/tex]

2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):

[tex]\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right][/tex]

3. Expand along the row 2: (See attached picture).

We get that the answer is 15. The determinant is 15.

Answer:

The answer is 15

Step-by-step explanation:

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

f(x) = -3 sin (x-pi) +2

Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value

sin has a maximum of 1

f (min) = -3(1) +2 = -1

g(x) has a minimum at x =3  

g(minimum) = -1

h(x) = (x+7)^2 -1

        The smallest a squared value can be is zero

     = 0 -1

h(min) =-1

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

Just did this :)

Answer:

  C.  (-2, -8)

Step-by-step explanation:

The function reduces to ...

  f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2

At x=-2, the function would evaluate to ...

  f(-2) = -2 -6 = -8

but cannot, because there is a hole in the function definition at that point.

There is a hole at (-2, -8).

Answer:

Step-by-step explanation:

Answer:

downtown workers

Step-by-step explanation:

The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.

Thus, option "downtown workers" is correct.

The population of the survey would be the city residents.

The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.

#SPJ12

[tex](5ab)^{\tfrac{3}{2}}=\sqrt{(5ab)^3}=\sqrt{125a^2b^3}[/tex]

How many households is 463 households

Answer:

C

Step-by-step explanation:

Just got it right.

Answer:

Is there supposed to be a photo

Step-by-step explanation:

Check the picture below.

Answer:

15

Step-by-step explanation:

70 = 4 x (a + 2.5)

70 = 4a + 10

70-10 = 4a

60 ÷ 4 = a

15= a

Answer:

(140, 37)

Step-by-step explanation:

If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same.  The number of miles will also be the same at this cost.  That means we need cost functions for each.  x is the number of miles that is driven, our independent variable.  If A-1 charges .10 per mile, the expression is .1x.  If the flat fee is 23, regardless of how many miles you drive, you can expect to pay

y = .1x + 23

If EZ charges .05 per mile, the expression is .05x.  If the flat fee is 30, regardless of how many miles you drive, you can expect to pay

y = .05x + 30

If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.

.1x + 23 = .05x + 30 and

.05x = 7 so

x = 140 miles.

In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.

y = .1(140) + 23

y = 14 + 23

y = 37

The coordinate pair is (140 miles, $37)

This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.

Answer:

[tex]f: (0,1) \to \mathbb{R}[/tex]

[tex]f(x) = \sin(1/x)[/tex]

Step-by-step explanation:

f is continuous because is the composition of two continuous functions:

[tex]g(x) = \sin(x)[/tex] (it is continuous in the real numbers)

[tex]h(x) = 1/x[/tex] (it is continuous in the domain (0,1))

It is bounded because [tex]-1 \leq \sin(\theta) \leq 1[/tex]

And it is not uniformly continuous because we can take [tex]\varepsilon = 1[/tex] in the definition. Let [tex] \delta > 0[/tex] we will prove that there exist a pair [tex]x,y\in \mathbb{R}[/tex] such that [tex]|x-y|< \delta[/tex] and [tex]|f(x) -f(y)|> \varepsilon = 1[/tex].

Now, by the archimedean property we know that there exists a natural number N such that

[tex] \frac{1}{N} < 2\pi \delta[/tex]

[tex]\Rightarrow \frac{1}{2\pi N} < \delta[/tex].

Let's take [tex]x = \frac{1}{2\pi N + \pi/2}[/tex] and [tex]y = \frac{1}{2\pi N + 3\pi/2}[/tex]. We can see that

[tex]|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}<\frac{1}{2\pi N} <\delta[/tex]

And also:

[tex]|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon[/tex]

And we conclude the proof.

This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).

11x11 rectangle = 165cm^2 area.

2 circles of 2cm radius = 2*4pi = 8pi = 25.13

165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)

Answer:

139.9

Step-by-step explanation:

First find the area of the circles.

A = pi*r^2

So pi*2^2

2^2 = 4

4*pi = 12.57

Then divide 12.57 by 2 because its only half a circle.

12.57/2 = 6.285

Then multiply 6.285 by 4 since there are 4 half circles.

6.285*4 = 25.14

Now find the area of the square.

A = lw

A= 15*11

A = 165

Now subtract 165 and 25.14.

165 - 25.14 = 139.86

Now round 139.86 to the nearest tenth

So 139.9

Answer:

Step-by-step explanation:

Income less expenses

Answer:

15

Step-by-step explanation:

i got it right pls mark brainliest

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have:

[tex]f(x)=3x+6\to m_f=3[/tex]

From the table:

[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]

[tex]m_f=m_g=3[/tex]

Answer:

1st one

Step-by-step explanation:

Below is the formula for the circumference of a circle

C = 2πr

This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...

16.4/ 2  = 8.2

Plug what you know into the formula and solve...

π = 3.14

r = 8.2

C = 2(3.14)(8.2)

C = 6.28(8.2)

C = 51.496

In the question it asks to round to the nearest tenth like so...

51.5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

51.496 rounded to the nearest tenth is 51.5

Answer:

 =57.89%

Step-by-step explanation:

The total number of golf ball is 4+8+7 = 19

P (red or yellow) = number of red or yellow

                              ------------------------------------

                                total number of golf balls

                           = 4+7

                              -----

                              19

                         =11/19

Changing this to a percent means changing it to a decimal and multiplying by 100%

                        = .578947368 * 100%

                         =57.8947368%

Rounding to two decimal places

                         =57.89%

The probability of drawing a red or yellow golf ball from the box can be calculated by dividing the total number of red and yellow balls (11) by the total number of balls in the box (19), resulting in a probability of 11/19 or approximately 57.89%.

To calculate the probability of drawing a red or yellow golf ball from the box, we first need to figure out the total number of balls in the box. This is found by adding up the number of each color of balls: 4 red balls + 8 green balls + 7 yellow balls = 19 total balls.

Next, we consider the total number of red and yellow balls, which is 4 red + 7 yellow = 11.

To find the probability, we divide the number of desired outcomes (red or yellow balls) by the total number of outcomes (total balls). So, the probability is 11/19.

To express this as a percentage rounded to two decimal places, we can multiply the result by 100, which gives us approximately 57.89%. So, there is a 57.89% chance of drawing a red or yellow ball from the box.

https://brainly.com/question/32117953

#SPJ11

Answer:

  C.  y = Ae^(-(x-b)²/c)

Step-by-step explanation:

A is a model of exponential growth.

B is a model of exponential decay.

D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.

The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.

The model that the graph represent is C that is y = Ae^(-(x-b)²/c).

A is an exponential growth model.

B is an exponential decay model.

D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.

The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.

For such more question on graph

https://brainly.com/question/19040584

#SPJ2

Answer:

¼ yd

Step-by-step explanation:

2/5 - 3/20

1. Find the lowest common denominator of the two fractions.

The LCD of 5 and 20 is 20.

2. Give the fractions the same LCD

2/5 - 3/20 = 8/20 - 3/20

3. Subtract the numerators

Keep the same denominator.

8/20 - 3/20 = 5/20

4. Simplify the fraction

5/20 = ¼  

The beetle crawled ¼ yd further than the spider.

Answer:

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = Bh . . . . . where B is the base area and h is the height

The volume of a pyramid or cone is given by ...

  V = (1/3)Bh . . . . . where B is the base area and h is the height

The area of a square of side length s is ...

  A = s²

The area of a circle of radius r is ...

  A = πr²

___

Using these formulas, the volumes of these objects are ...

  cylinder: (9π in²)(10 in) = 90π in³

  square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³

  cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid

Answer:

12.5

Step-by-step explanation:

Answer:

  5/12

Step-by-step explanation:

The fraction that is girls is the ratio of girls to the total of boys and girls:

  girls/(boys+girls) = 5/(7+5) = 5/12

Answer:

its answer is -x^3+x^2+3x-1

Step-by-step explanation:

f(x) +g(x)

= 8-4x-x^3+x^2+7x-9

= -x^3+x^2+3x-1

Answer:

The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Step-by-step explanation:

The given functions are

[tex]f(x)=8-4x-x^3[/tex]

[tex]g(x)=x^2+7x-9[/tex]

We have to find the value of f(x)+g(x).

[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]

[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]

On combining like terms we get

[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]

On simplification we get

[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]

Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Answer:

The dimensions of enclosed area are 200 and 400/3 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 800 feet of fencing

- We will but it around a rectangular field

- We will divided the field into 2 identical smaller rectangular plots

 by placing a fence parallel to one of the field's shorter sides

- Assume that the long side of the rectangular field is a and the

 shorter side is b

∵ The length of the fence is the perimeter of the field

∵ We will fence 2 longer sides and 3 shorter sides

∴ 2a + 3b = 800

- Lets find b in terms of a

∵ 2a + 3b = 800 ⇒ subtract 2a from both sides

∴ 3b = 800 - 2a ⇒ divide both sides by 3

∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)

- Lets find the area of the field

∵ The area of the rectangle = length × width

∴ A = a × b

∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]

- To find the dimensions of maximum area differentiate the area with

  respect to a and equate it by 0

∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]

∵ [tex]\frac{dA}{da}=0[/tex]

∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides

∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3

∴ 800 = 4a ⇒ divide both sides by 4

∴ 200 = a

- Substitute the value of a in equation (1)

∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]

* The dimensions of enclosed area are 200 and 400/3 feet

Answer:

Option D RX=4 units

Step-by-step explanation:

we know that

In the right triangle RTS

The cosine of angle TRS is equal to

cos(TRS)=RT/RS

substitute

cos(TRS)=6/9 -----> equation A

In the right triangle RTX

The cosine of angle TRX is equal to

cos(TRX)=RX/RT

substitute

cos(TRX)=RX/6 -----> equation B

∠TRS=∠TRX -----> is the same angle

Match equation A and equation B

6/9=RX/6

RX=6*6/9=4 units