find the value of 8 and 1/3

The maximum earning is v(r,b)

Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.

Then v(r,b) satisfies the recursion

and

The stopping rule is simple: Stop when v(r,b)=0.

To explain the recursion . . .

If r,b>0, and the player elects to play a card, then:

Thus, if r,b>0, electing to play a card yields the value f(r,b).

But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).

Implementing the recursion in Maple, the value of the game is

v(26,26)=41984711742427/15997372030584

v(26,26)  ≈2.624475549

and the optimal stopping strategy is as follows . . .

So, The maximum earning is v(r,b)

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The linear equation that gives the rule for this table is y = -5x + 15

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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Answer: Choice B

The function is exponential.

An exponential function that models the data is f(x) = \(\displaystyle \boldsymbol{6^x}\)

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

Explanation:

Focus on the f(x) column.

The jump from "1" to "6" is "times 6".

The same can be said from "6" to "36" and from "36" to "216"

This heavily implies we have an exponential function. The specific function is \(f(x) = 6^x\)

Plugging in x = 0 leads to y = 1, x = 1 leads to y = 6, and so on.

For the negative exponent, we have

\(6^{-1} = \frac{1}{6^1} = \frac{1}{6}\)

so x = -1 works as well.

Answer:

3 x - 2 y = 8

y = 3/2 x - 4     rearranging

y = m x + b       standard equation for line

m' = - 2/3    for perpendicular line    m m' = -1

y = - 2/3 x + b

b = y + 2/3 x = 2 + 2/3 * -3 = 0       substituting given values

y = 2/3 x       required line

Answer:

x > -2

Step-by-step explanation:

-3x+2<8

Subtract 2 from each side

-3x+2-2<8-2

-3x<6

Divide each side by -3, remembering to flip the inequality

-3x/-3 > 6/-3

x > -2

Hey there!☺

\(Answer:\boxed{x>-2}\)

\(Explanation:\)

\(-3x+2<8\)

Let's subtract 2 from both sides of the inequality.

\(-3x+2-2<8-2\\-3x<6\)

Now divide both sides by -3.

\(\frac{-3x}{-3}<\frac{6}{-3}\)

Simplify 6/-3. Also remember that dividing a positive with a negative will give us a negative.

\(6/-3=-2\)

\(x>-2\)

Hope this helps!

The solution of the inequality |x+3| < 2 is -5 < x < -1.

And the graph is given in the image below.

The correct option is C.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

To solve the inequality |x+3| < 2, we need to consider two cases:

Case 1: x+3 ≥ 0

In this case, the inequality simplifies to x+3 < 2, which gives us x < -1.

Case 2: x+3 < 0

In this case, the inequality simplifies to -(x+3) < 2, which gives us -x-3 < 2, or -x < 5, or x > -5.

Combining the results from both cases, we get the solution:

-5 < x < -1

To graph the solution, we draw an open circle at x=-3

(since the absolute value is less than 2, not less than or equal to), and shade the region between -5 and -1.

Therefore, the solution is -5 < x < -1.

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Answer:

1/2

Step-by-step explanation:

When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!

Answer:

1/2.

Step-by-step explanation:

Sine = opposite side / hypotenuse.

The side opposite 60 degrees has length√3 and the hypotenuse = 2.

By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)

= 1 unit.

So cos 60 = adjacent / hypotenuse = 1/2.

Answer:

the first option, LON and NOP

Step-by-step explanation:

adjacent angles are side by side and cannot overlap

Answer:

1) angle LOM and angle MON

2) A. angle LON and angle NOP

The sum of angles 3 and 4 is equal to 180 degrees, therefore: A: true; this would be enough information to say that the lines are definitely parallel.

When two lines are intersected by a transversal, and the same-side interior angles are supplementary, that is are equal to 180 degrees, then we can state that the two lines are parallel to each other based on the converse of the same-side-interior angles theorem.

Given the following information:

Angle 4 and angle 3 are same-side-interior angles, thus:

89 + 91 = 180°

This means that, the sum of angle 4 and 3 are supplementary. Lines g and h are therefore parallel to each other.

In summary, our answer would be: A: true; this would be enough information to say that the lines are definitely parallel.

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Answer:

true

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

\(540 + 6x = 810\)

Step 1 : Collect like terms

\(6x = 810 - 540\)

Step 2 : Simplify

\(6x = 270\)

Divide both sides of the equation by 6

\( \frac{6x}{6} = \frac{270}{6} \)

Step 4 : Simplify

\(x = 45\)

I hope it helps :)

Answer:

Well...X=45

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:540+6*x-(810)=0

Pull out like factors :-270 + 6x  =   6 • (x - 45)

Solve  :    x-45 = 0::

Add  45  to both sides of the equation:  x = 45

Answer:

5+5m=15

Step-by-step explanation:

Answer:

dont know sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the balls are drawn with replacement, the probability of drawing a black ball on any single draw is 7/15. The probability of drawing 6 black balls in succession is the product of the probabilities of each individual draw being a black ball. Therefore, the probability is:

(7/15)^6 ≈ 0.019

Rounding to three decimal places, the probability is 0.019.

Answer:

0.003

Step-by-step explanation:

The probability of drawing a black ball on any given draw is 7/15, since there are 7 black balls and 15 total balls in the urn. Because the balls are replaced after each draw, the probability of drawing a black ball on each of the 6 successive draws is (7/15) x (7/15) x (7/15) x (7/15) x (7/15) x (7/15) = (7/15)^6.

Therefore, the probability of drawing 6 black balls in succession is:(7/15)^6 = 0.0028 (rounded to three decimal places)

So the probability that all 6 balls drawn from the urn are black is approximately 0.003.

The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

What is Standard Deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; Hence, the higher the standard deviation, the more dispersed the data.

We know that:

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

where \(x_{i}\)  is the mean and n is the number of observations.

\(\text { Standard Deviation }=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}\)

98% Confidence interval:  

\(\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}\)

Putting the values, we get,  

\(t_{\text {critical }} \alpha_{0.02}\\=\pm 2.14535.07 \pm 2.145\left(\frac{6.02}{\sqrt{15}}\right)\\=35.07 \pm 3.33\\=(31.74,38.4)\)

Hence, The lower and upper values of the confidence interval of the population mean for the minutes spent getting to work is (31.74,38.4)

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Answer:

yes it is greater

Step-by-step explanation:

Answer:

If g(t) = t^2 - 5t, then G = t - 5

If f(t) = 2t + 4, then F = 2( t + 2) / t (over t)

If (g * f)(5), then 5gf

Step-by-step explanation:

Answer:

Héctor salió de su casa con 12 euros.

Step-by-step explanation:

Cuando Héctor gastó en la entrada de cine una tercera parte del dinero con el que salió de casa, tenemos:

\( C = \frac{1}{3}x \)    (1)

Cuando compró una bolsa de palomitas con la cuarta parte:

\( P = \frac{1}{4}x \)    (2)                                  

Entonces al sobrarle 5 euros y relacionando las ecuaciones (1) y (2) con el monto inicial:

\( x - C - P = 5 \)

\( x - \frac{1}{3}x - \frac{1}{4}x = 5 \)

\( x = 12 \)

Por lo tanto, Héctor salió de su casa con 12 euros.  

Espero que te sea de utilidad!    

Answer:

The equation of a line that passes through the point (-5,7) and has a slope of -2/5 would be y = -2/5x + 5

Step-by-step explanation:

In the math term y = mx + b, "m" represents slope. So you can just substitute it for -2/5. "b" represents the y-intercept. 5 is the only number that works, so you just substitute "b" for 5.

The correct option regarding the addition of vectors t and v is given as follows:

A. <-1, -11>.

The standard notation of a vector is given as follows:

<x,y>.

In which:

To add two vectors, we add the elements at the same component.

Then the addition of vectors t and v is given as follows:

t + v = <2, -10> + <-3, - 1> = <2 - 3, -10 -1> = <-1, -11>.

From the result obtained above, the correct option in the context of this problem is given by option A.

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below for Function A.

\((\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-8)}}} \implies \cfrac{4 +5}{10 +8} \implies \cfrac{ 9 }{ 18 } \implies \cfrac{1 }{ 2 }\impliedby \stackrel{\textit{slope of}}{A} \\\\[-0.35em] ~\dotfill\)

\(y = \stackrel{\stackrel{m}{\downarrow }}{5}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \stackrel{\textit{slope of}}{B} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{A}{\cfrac{1}{2}} ~~ < ~~ \stackrel{B}{5} \end{array}}~\hfill\)

The factors of 14 are the numbers that divide evenly into 14. The factors of 14 are 1, 2, 7, and 14.

The first factor of 14 is 1. Every number can be divided by 1, so 1 is a factor of every number. The second factor of 14 is 2. This is because 14 divided by 2 equals 7. The third factor of 14 is 7. Seven times two is equal to 14. The fourth factor of 14 is 14. This is because 14 divided by 14 is equal to 1.

Factors are important when solving math problems. They are also important when looking at patterns and sequences in math. Knowing the factors of a number can help to identify patterns and sequences, and can also help solve equations and inequalities. Knowing the factors of a number can also help to find the greatest common factor of two or more numbers.

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The perimeter of a rectangular table is 198 inches.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, a rectangular table is 64 inches long and 35 inches wide.

Now the perimeter of table is

2(64+35)

= 2×99

= 198 inches

Therefore, the perimeter of a rectangular table is 198 inches.

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Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to).  We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:  

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2:  The slope is 1/2.    [This is "m."]

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points.  I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b  

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line:  y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2).  This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line:  (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

Answer:

31

Step-by-step explanation:

Square both sides of the equation to get

x+5 = 36

x = 31

Answer:

D

Step-by-step explanation:

I'm not the greatest in this subject, but I think that it's D/If the roof leaks, then the ceiling gets damaged because it clearly says that in the statement. It could be all of them, though, but this is my answer. Hope it helps!

Answer:

D. If it rains, then the ceiling gets damaged.

Explanation:

So, if it rains, then the roof leaks, and if the roof leaks, then the ceiling gets damaged, is the exactly the structure of the syllogism law that permits to conclude if it rains, then the ceiling gets damaged.