when playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$ on the number or to bet ​$ that the outcome is any one of the possibilities . the gambler knows that the expected value of the ​$ bet for a single number is . for the ​$ bet that the outcome is ​, there is a probability of of making a net profit of ​$ and a probability of losing ​$. a. find the expected value for the ​$ bet that the outcome is . b. which bet is​ better: a ​$ bet on the number or a ​$ bet that the outcome is any one of the numbers ​? ​why?

Answer:

[tex]\frac{9x^{2}}{y^{2}}[/tex]

Step-by-step explanation:

First you need to do what is inside the parenthesis

Dividing by a variable with the same base means the powers subtract so if we do this for x we get.

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

That brings us to

[tex](\frac{3xy^{-\frac{1}{2}}}{y^{-\frac{1}{2}}})^2[/tex]

Then we need to do a similar process for the y variable.

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

Which brings us to

[tex](\frac{3x}{y})^2[/tex]

From here we just need to square the top and the bottom of the fraction which brings us back to our final answer with

[tex]\frac{9x^2}{y^2}[/tex]

Answer:

[tex]\dfrac{9x^2}{y^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(\dfrac{3x^{\frac{1}{2}}y^{-\frac{1}{2}}}{x^{-\frac{1}{2}}y^{\frac{1}{2}}} \right)^2[/tex]

Separate the variables inside the parentheses:

[tex]\implies \left( 3 \cdot \dfrac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}} \cdot \dfrac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \left( 3 \cdot x^{(\frac{1}{2}-(-\frac{1}{2}))} \cdot y^{(-\frac{1}{2}-\frac{1}{2})}\right)^2[/tex]

[tex]\implies \left( 3 \cdot x^{1} \cdot y^{-1}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^2 \cdot x^{(1 \cdot 2)} \cdot y^{(-1 \cdot 2)}[/tex]

[tex]\implies 9x^2y^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{9x^2}{y^2}[/tex]

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Answer:

The slope is 1/4

Step-by-step explanation:

hope it helps

The inequality that represents the legal driving speeds, s, in kilometers per hour is 45 >= s <= 70.

It should be noted that an inequality is simply used in mathematics to show that the expression or equation aren't equal.

From the information, the highway has a minimum speed limit of 45 miles per hour and a maximum speed limit of 70 miles per hour.

Therefore, the inequality that represents the legal driving speeds is 45 >= s <= 70.

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Answer:

The answer would be 92.8 but since we're rounding it'll be 90

Step-by-step explanation:

Answer:

x = 21

Step-by-step explanation:

Given line a is parallel to line b we can form the following equation to find the value of x:

6x + 12 + 2x = 180 (because these are supplementary angles and their sum is equal to 180)

add like terms

8x + 12 = 180 subtract 12 from both sides

8x = 168 divide both sides by 8

x = 21

Answer: 5.184 ft

Step-by-step explanation:

Answer:

MK= 12.5

AngleJNK=117°

AngleJNM=63°

Step-by-step explanation:

Part A:

MN = 3x + 1

JL = 2x + 9

JL and MK are the diagonals

MN = 1/2 of MK

MK =2(3x +1)

MK = 6x + 2

Therefore, JL = MK

2x + 9 = 6x +2

Collect like terms

2x-6x = 2 - 9

-4x = - 7

x = 1.75

Substituting the value of x,

MK = 6(1.75) + 2

MK = 10.5 + 2

MK = 12.5

Part B

AngleJNK = (5x +2)°

AngleJNM = (3x-6)°

Sum of interior angles of a quadrilateral = 360

Therefore, 2(5x +2)° + 2(3x-6)° = 360

(10x + 4) + (6x - 12) = 360

Collect like terms

10x + 6x - 12 + 4=360

16x = 360 + 8

16x = 368

x = 368/16

x = 23

Substituting the value of x

For angleJNK = 5(23) +2 = 115+2 = 117°

For angleJNM = 3(23) - 6 = 69 - 6 = 63°

multiply ecerything that is in the brackets by 3

[tex]3(x) + 3(2) + 7 \\ = 3x + 6 + 7 \\ = 3x + 13[/tex]

ATTACHED IS THE SOLUTION

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line L above

[tex]\stackrel{\textit{slope for line L}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +5}{6 +1}\implies \cfrac{9}{7} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{9}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{9}}}[/tex]

so we're really looking for the equation of a line whose slope is -7/9 and that it passes through (9 , 3)

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{7}{9}}(x-\stackrel{x_1}{9}) \\\\\\ y-3=- \cfrac{7}{9}x+7\implies {\Large \begin{array}{llll} y=- \cfrac{7}{9}x+10 \end{array}}[/tex]

Solution:

If

The general form of the coordinates of an ordered pair is

From the given expression;

The x-coordinate is -7

The y-coordiates is -2

Hence, the corresponding ordered pair is

Tate and Nathan will leave $ 19.48 to the server to cover up the bill and the tip when they go out to dinner at Red Robin.

As given in the question,

Since Tate and Nathan both order burgers for $12.49 each,

Total amount payable is

$12.49 + $12.49= $24.98.

Now 18% tip is equal to

18% of $24.98

(18/100) × 24.98

= $4.4964

= $4.50 (rounded to nearest cent).

Total gross amount payable (including 18% tip) is

24.98 + 4.50 = $29.48.

Now subtracting the birthday coupon for $10.00 off,

the net amount payable in the bill is

29.48 - 10.00

= $ 19.48

= 19.48 cents

Therefore, after using the coupon, they will leave the server $19.48 to cover the bill and the tip.

The complete question is:

Tate and Nathan go out to dinner at Red Robin They both order burgers for $12.49 each. Tate has a birthday coupon for $10.00 off, but the boys want to leave an 18% tip before subtracting the cour

After using the coupon, how much money will they leave the server to cover the bill and the tip? Round to the nearest cent.

a. $14.49

b. $2768

c. $4.79

d.$19.48

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functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

A)

0= 2x + 10 - 1

-9 = 2x

-4.5 = x

B)

0= 8x + 64

-64 = 8x

-8 = x

C)

0 = 2x - 16 +1

0 = 2x -15

7.5 = x

D)

0 = 13x - 39

39 = 13x

3 = x

functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

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Answer: The area of a circle is 286.37cm².

Step-by-step explanation: The answer to this question can be solved by finding the value of the radius from the circumference and substituting it into the area.

Following are the steps to solve this problem:-

Step 1.  The circumference of the circle is 60cm.

The formula for the circumference of a circle is 2[tex]\pi \\[/tex]r.

Step 2. Calculating the value of radius (r) is 2[tex]\pi[/tex]r=60 cm.

                                                                2x 3.14xr =60cm.

                                                                r= 9.55cm

Step 3. Calculate the area of a circle by using the formula [tex]\pi[/tex]r²

Substituting the valur r( from step 2 ) in the formula

                                                  3.14x9.55x9.55= 286.37cm²

Thus, the answer is 286.37cm²

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The distance that is between the ball and the goal line after these five plays is D. 36 yards.

From the information, the Eagles gain 31 yards on a pass toward the goal line and on the next four plays, the Eagles lose 3, 5, 7, and 4 yards, respectively.

After the first day, the yards remaining will be:

= 48 - 31

= 17

Now, the total distance between the goal line and the ball will be:

= 17 + 3 + 5 + 7 + 4

= 36

Therefore, the total distance is 36 yards.

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Answer:

1

Step-by-step explanation:

60 Kilometers = 120 minutes

60 ÷ 120 = .5

.5 × 2 = 1

1 kilometer = 2 Minutes

On subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign −.

Given is to subtract "3a – 7b + 12c" from "-5a – 21b + 3c".

Assume that -

A = 3a – 7b + 12c

B = -5a – 21b + 3c

B - A = (-5a – 21b + 3c) - (3a – 7b + 12c)

B - A = -5a - 21b + 3c - 3a + 7b - 12c

B - A = -5a - 3a - 21b + 7b + 3c - 12c

B - A = - 8a - 14b - 9c

Therefore, on subtracting "3a – 7b + 12c" from "-5a – 21b + 3c" we get -

- 8a - 14b - 9c

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Step-by-step explanation:

2pi = 360°

=>

10pi = 5×2pi = 5×360 = 1800°

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{7}) \end{array}}[/tex]

Answer: wowwww LOL

Step-by-step explanation:

Thanks Mr Shady, the f r e e p o. i n t s are now mine.

The expression that shows how many inches tall Tess is t = i - 3.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, Tess is 3 inches shorter than Johnny. and Johnny is i inches tall. Since Tess is shorter, we will subtract.

Therefore, the expression will be:

t = i - 3

where t = Tess height.

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Answer:

u = 4

Step-by-step explanation:

32 = 5u + 3u = 8u ( divide both sides by 8 )

4 = u

Step-by-step explanation:

u=4 after you add or combine like terms , you then divide both sides by the same factor

Answer:

  Multiplying both sides of the equation by 35 eliminates the fractions

Step-by-step explanation:

You want to know how to eliminate the fractions from the equation n/5+3/7=2.

The multiplication property of equality allows you to multiply both sides of an equation by the same number without changing the value of the variable. To eliminate fractions, the number we choose can be the least common denominator of the fractions.

Fractions with denominators 5 and 7 will have a least common denominator of 5·7 = 35. Multiplying the equation by 35 gives ...

  35(n/5 +3/7) = 35(2)

  7n +15 = 70

Multiplying both sides of the equation by 35 eliminates the fractions.

__

Additional comment

The solution to this 2-step equation is ...

  n = (70 -15)/7 = 55/7 = 7 6/7

[tex]f(x) = 3 {x}^{2} - x + 5[/tex]

thus ;

[tex]f( - 3) = 3 \times ({ - 3})^{2} - ( - 3) + 5[/tex]

[tex]f( - 3) = 3 \times 9 + 3 + 5[/tex]

[tex]f( - 3) = 27 + 8[/tex]

[tex]f( - 3) = 35[/tex]

_____________________________________________

[tex]f(4) = 3 \times ({4})^{2} - (4) + 5[/tex]

[tex]f(4) = 3 \times 16 - 4 + 5[/tex]

[tex]f(4) = 48 + 1[/tex]

[tex]f(4) = 49[/tex]

_____________________________________________

So :

[tex]2f( - 3) = 2 \times 35 = 70[/tex]

And ,

[tex] - f(4) = - 49[/tex]

so :

[tex]2f( - 3) - f(4) = [/tex]

[tex]70 - 49 = [/tex]

[tex]21[/tex]

Answer:

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In the illustration above, a circle with a few lines intersecting at various locations is shown. So, if we split the circle in half, the resulting semicircle has a vertical angle of 180 degrees. Since ∠ROP = 125°, ∠POS = 55° is obtained by taking 180° away from 125°. ∠POS and ∠QOR are equivalent terms. Also, ∠ROP = ∠QOS.

What is lines intersecting?

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

the characteristics of intersecting lines

The intersecting lines (two or more) never cross over at more than one location.

Any angle may be used to intersect the lines in any direction. Always larger than 0° and less than 180°, this angle is generated.

A pair of vertical angles are created by two intersecting lines. The vertical angles have the same vertex and are opposing angles (which is the point of intersection).

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Answer:

? = 4.492385

About 4.5 pounds

Step-by-step explanation:

m = money spent

80 - 44.6 = m

m = 35.4

m / 7.88 = ?

? = 35.4 / 7.88

? = 4.492385

About 4.5 pounds

Answer:

She bought 5 pounds of coffee

Step-by-step explanation:

If you subtract 80-40.60 you would get 39.4/39.40 and since each pound was 7.88 you divided 39.40 and 7.88 and you would get 5

1. Noah reads 9 pages.

2. The price of one pizza is $9.

3. Lin shares her stickers is 9.

1.Given,

Elena read three times as many pages as Noah.

and, She read 27 pages.

Now, According to the question:

3x = 27

x = 27/3

x = 9

Hence, Noah reads 9 pages.

2. Given,

Diego paid $27 to have 3 pizzas delivered

and, $35 to have 4 pizzas delivered

In the question, In place of $ 35 should be $36

So, we take the $36

Now, Diego paid $27 to have 3 pizzas delivered

$36 to have 4 pizzas delivered

Let x be the price of 1 pizza

then, 4x = 36

x = 36/4

x = $9

Hence, The price of one pizza is $9.

3. Given,

Lin has 27 stickers.

and, She gives 3 stickers to each of her friends.

Now, 27 is divided by 3  = 9

Hence, Lin shares her stickers is 9.

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The coordinates of the midpoint between point E(2, -8) and point F(-12, -6) on segment EF is ( -5, -7 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point E(2, -8)

F(-12, -6)

Coordinates of midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 2 + (-12) )/2, ( (-8) + (-6) )/2 )

M = ( 2 - 12 )/2, ( -8 - 6 )/2 )

M = ( -10 )/2, ( -14 )/2 )

M = ( -5 ), ( -7 )

M = ( -5, -7 )

Therefore, the midpoint of line segment EF is ( -5, -7 ).

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The value of the given expression g = h+9/5 is 127.

So, g = h+9/5:

Insert the values in the expression as follows:

Therefore, the value of the given expression g = h+9/5 is 127.

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The correct question is given below:

Evaluate the expression when g = 30 and h = 14.

g = h+9/5