If an unfair coin is tossed into the air and drops without interruption, its probability of landing on heads is 0.51 whereas the probability of landing on tails is 0.49. If the payoff for landing on heads is $0.99 and the payoff for landing on tails is $1.01 and it costs $1 to play each game, should you play?


1)Yes, because over the long run your expected value is greater than the lowest payoff

2)No, because over the long run your expected value is lower than the lowest payoff

3)Yes, because over the long run your expected value is greater than the cost to play

4)No, because over the long run your expected value is less than the cost to play

Answer:

  252

Step-by-step explanation:

The question is fully equivalent to asking how many subsets of length 5 there are of 10 objects (digits 0–9). That number is 10C5, where nCk is the number of ways to choose k objects from a list of 10. The value of that is ...

  nCk = n!/(k!(n-k)!)

There are 252 ways to choose 5 numbers from the digits 0-9:

  10C5 = 10!/(5!(10-5)!) = 10·9·8·7·6/(5·4·3·2·1) = 9·4·7 = 252

_____

The order of the selection doesn't matter, because the selected digits are always arranged in decreasing order to form a decreasing number.

Answer:

Could you please post a video or give more simple explanations to someone who does not have prior knowledge of such problems?

Step-by-step explanation:

Step-by-step explanation:

5 gallons 3 quarts +4 gallons 2 quarts

5.3

+

4.2

=9.5 gallons

Answer: 10 gallons and 1 quart.

Explanation: 5 gallons + 4 gallons = 9 gallons. 3 quarts + 2 quarts = 5 quarts, and 4 quarts make a gallon. So, 10 gallons and 1 quart.

Answer: B

Step-by-step explanation:

Answer:

[tex]x = 20\°[/tex]

Step-by-step explanation:

By definition we know that the sum of the internal angles of a triangle is always equal to 180 °

in this case we have a right triangle. We know that right triangles have an angle of 90 °.

So the sum of the three sides of this triangle must be equal to 180 °

So

[tex]2x + 10 + 2x + 90 = 180[/tex]

We solve the equation for the variable x.

[tex]4x +100 = 180\\4x = 180-100\\4x = 80[/tex]

[tex]x = 20\°[/tex]

Answer: x=20

Step-by-step explanation:

2x+10+2x+90=180

4x+100=180

4x=80

X=20

The angle of intersecting chords is found by adding the two arcs intercepted by the angle and dividing that by 2.

PRQ = (102 + 70) / 2

PRQ = 172 /2

PRQ = 86 degrees.

When two chords cross within a circle, the angle created is one-half the total of the arcs intercepted by the angle and its vertical angle. The measure of ∠PRQ is 86°.

When two chords cross within a circle, the angle created is one-half the total of the arcs intercepted by the angle and its vertical angle.

The measure of ∠PRQ is,

∠PRQ = (102°+70°)/2

∠PRQ = 172° / 2

∠PRQ = 86°

Hence, the measure of ∠PRQ is 86°.

Learn more about Angles of Intersecting Chords Theorem:

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Answer:

Each child in Maria's party got 6 crayons more that each child in Dante's party

Explanation:

1- In Dante's party:

192 crayons are equally split among 16 children

This means that:

Each child got [tex]\frac{192}{16} = 12[/tex] crayons

2- In Maria's party:

234 crayons are equally split among 13 children

This means that:

Each child got [tex]\frac{234}{13}=18[/tex] crayons

3- getting the difference:

Difference = 18 - 12 = 6 crayons

This means that:

Each child in Maria's party got 6 crayons more that each child in Dante's party

Hope this helps :)

Answer:

G(x)=(1/3x)^2

Step-by-step explanation:

Ap ex

Answer:

The value of x = 4.1 cm

Step-by-step explanation:

From the figure we can see a circle, with chord 15.6 cm

A right angled triangle with hypotenuse 8.8 cm

To find the value of x

By using Pythagorean theorem,

Base² + Height² = Hypotenuse²

Here Base  = x, Height = 15.6/2 = 7.8 cm and Hypotenuse = 8.8 cm

x² + 7.8² = 8.8²

x² = 8.8² - 7.8²

 = 77.4 - 60.84

 = 16.56

x = √16.56 = 4.07 ≈ 4.1 cm

Therefore the value of x = 4.1 cm

Answer:

Option 3. 1,000 times

Step-by-step explanation:

we know that

The value of digit 8 in 82.77 is equal to 80

The value of digit 8 in 20.18 is 0.08

so

Divide 80 by 0.08

80/0.08=1,000 times

The value of the digit 8 in 82.77 is greater than and the value of the digit 8 in 20.18 by 1000.

The value of each digit in 82.77 is:

8 = tens

2 = units

7 = tenth

7 = hundredth

The value of each digit in 20.18 is:

2 = tens

0 = units

1 = tenth

8 = hundredth

The value of 8 in 82.77 is tens(10) and the value of 8 in 20.18 is hundredth (0.01).

Difference in value = 10 / 0.01 = 1000

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PART A (1 in diagram)

Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.

1. The domain of the given function f(x) is the set {10, 20, 30}.

All we can say about

[tex] {f}^{ - 1} (x)[/tex]

is that, it has a range of {10, 20, 30}.

This is because the domain of a function becomes the range of its inverse function.

2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,

[tex] {f}^{ - 1} (x) [/tex]

will contain the point (0,3).

Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.

In simple terms the domain of the function becomes the range of the inverse function and vice versa.

3. If the first term in an arithmetic sequence is 2.

Then we have a=2.

If the twelfth term is 211, then

[tex]a + 11d = 211...(1)[/tex]

Put a=2 into this equation.

[tex]2 + 11d = 211[/tex]

Solve for d.

[tex]11d = 211 - 2[/tex]

[tex]11d = 209[/tex]

[tex]d = \frac{209}{11} = 19[/tex]

If

[tex]a_n = 135[/tex]

then

[tex]a + (n - 1)d = 135[/tex]

Substitute a=2 and d=19

[tex]2 + (n - 1)19 = 135[/tex]

[tex]19(n - 1) = 133[/tex]

[tex](n - 1) = \frac{133}{19} [/tex]

[tex]n - 1 = 7[/tex]

[tex]n = 7 + 1 = 8[/tex]

Therefore n=8

Answer:

  c)  0.0156

Step-by-step explanation:

The general term a[n] of a geometric sequence is given in terms of the first term a[1] and common ratio r as ...

  a[n] = a[1]r^(n-1)

The given sequence has an initial term of a[1]=8 and a common ratio of 4/8=1/2. Then the general term is ...

  a[n] = 8(1/2)^(n-1)

The 10th term is then ...

  a[10] = 8(1/2)^(10-1) = 8(1/2)^9 = 8/512

  a[10] = 0.015625 ≈ 0.0156

Answer:

[tex]\text{A.}\quad\dfrac{xz}{2}[/tex]

Step-by-step explanation:

[tex]\dfrac{x^2yz}{y^2}\times\dfrac{y}{2x}=\dfrac{x^2yzy}{2xy^2}=\dfrac{1}{2}\cdot\dfrac{x^2}{x}\cdot\dfrac{y^2}{y^2}\cdot\dfrac{z}{1}\\\\=\dfrac{xz}{2}[/tex]

Answer:

y = (3/4)x

Step-by-step explanation:

1)  Find the slope of the line.  As we go from ( -8,-6) to (12,9), x increases by 20 and y increases by 15.  Thus, the slope, m, is m = rise / run = 15/20 = 3/4

2) Recognize that the y-intercept is zero (0) because this is direct variation; the line goes thru the origin.

3) write the equation of the line:  y = mx + b becomes y = (3/4)x

[tex]\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-6)}{12-(-8)}\implies \cfrac{9+6}{12+8}\implies \cfrac{15}{20}\implies \cfrac{3}{4}[/tex]

[tex]\bf \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-(-6)=\cfrac{3}{4}[x-(-8)]\implies y+6=\cfrac{3}{4}(x+8) \\\\\\ y+6=\cfrac{3}{4}x+6\implies y=\cfrac{3}{4}x[/tex]

[tex]\displaystyle\\\sum_{n=1}^7(4n+2)[/tex]

For this case we have that by definition the distributive property establishes:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

We have the following expression:

[tex](y ^ 2 + y) (x ^ 4 + 3x ^ 3-2x ^ 3) =[/tex]

Applying the distributive property we have:

[tex]y ^ 2 (x ^ 4 + 3x ^ 3-2x ^ 3) + y (x ^ 4 + 3x ^ 3-2x ^ 3)[/tex]

So, the given example is an example of distributive property.

ANswer:

Option B

Answer:

C. Circumcenter

Step-by-step explanation:

Definitions:

Orthocenter is the point where the three "altitudes" of a triangle meet. An "altitude" is a line that goes through a vertex and is at right angles to the opposite side.

Incenter is the center of an inscribed circle (the circle that fits perfectly inside triangle, just touching all sides). It is where the "angle bisectors" (lines that split each angle in half) meet.

Circumcenter is the center of circumscribed circle.  It is where the "perpendicular bisectors" (lines that are at right angles to the midpoint of each side) meet.

Centroid (or center of mass) of a triangle is the point where the three medians of the triangle meet.

As you can see from the definitions, point P is circumcenter, because it is the point of perpendicular bisectors intersection.

Answer:

[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]

[tex]4x+3y=5[/tex]

Step-by-step explanation:

we have

[tex]y-11=-\frac{4}{3}(x+7)[/tex] -----> equation of the line into point slope form

step 1

Find the equation of the line into slope intercept form

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

where

m is the slope

b is the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]y-11=-\frac{4}{3}(0+7)[/tex]

[tex]y=-\frac{28}{3}+11[/tex]

[tex]y=\frac{5}{3}[/tex]

therefore

[tex]b=\frac{5}{3}[/tex]

substitute

[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]  ----> equation of the line into slope intercept form

step 2

Find the equation of the line in standard form

[tex]Ax+By=C[/tex]

we have

[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]

Multiply by 3 both sides

[tex]3y=-4x+5[/tex]

[tex]4x+3y=5[/tex] ---> equation of the line in standard form

Answer: C) 1/16

-1/2 • -1/2 • -1/2 • -1/2 =1/16

[tex]\left(-\dfrac{1}{2}\right)^{-4}=\left(-2\right)^{4}=16[/tex]

Answer:

The image of point P is (1 , -1)

Step-by-step explanation:

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

  anti-clockwise around the origin

* Lets solve the problem

∵ P = (-1 , -1)

∵ P is rotated about the origin 90° counterclockwise

- Lets use this rule:

  If point (x , y) rotated about the origin by angle 90° counterclockwise

  then Its image is (-y , x)

∵ x-coordinate of point P = -1

∴ y-coordinate of the image of point P is -1

∵ y-coordinate of point P is -1

∴ x-coordinate of the image of point P is 1

- Lets write the image of point P

∴ The image of point P is (1 , -1)

Answer:

A^2+B^2=C^2

Step-by-step explanation:

(A)^2+(B)^2+(A)+(B)+2Cos(a)=C^2

Answer:

with a ruler?

Without the equation for k(x), we can't definitively determine the formula for h(x). However, if we knew k(x), we'd divide it by g(x) (-3x in this case) to find h(x). For instance, if k(x) is 6x, h(x) will be -2.

To find the formula for h, we need to divide k(x) by g(x). The formula for the function k should be given in addition to the graph in order for us to solve this. Assuming that g(x) is indeed -3x, we would divide the formula for k(x) by -3x to find h(x). However, without the expression for k(x), we can't definitively select an option for h(x) from your list.

If k(x) was 6x, and g(x) was -3x, h(x) would be -2. You would find this by dividing k(x), which is 6x, by g(x), which is -3x; resulting in -2. So, for this example, option B would be correct.

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Answer:

Part A)

Part B)

Explanation:

1) The earnings are calculated multiplying the number of hours by the hourly rate.

2) The hourly rate of both Peter and Cindy is the same: $ 4.50 / hour

3) Let the variable used for computing the number of hours be h.

4) The number of hours Peter works every day is 3 hours, so, using the letter P to name Peter's earnings, the expression to calculate his earnings is:

5) Similarly, the expression to calculate Cindy's earnings would be:

Answering part A)

You have to write an inequality to compare Peter's and Cindy's earnings:

This is, the earnings of Peter are greater than the earnings of Cindy.

Part B),

You have to write an inequality to calculate Cindy's per-hour income so that she earns at least $ 14 a day.

Given: 2r ≥ 14

Divide both sides by 2: r ≥ 14 / 2

Simplify: r ≥ 7

That means that Cindy's per-hour income should be at least $7 and hour so that she earns $14 a day.

Answer:

  c. 85(.60) + 87(.15) + 68(.10) + X(.15) = 78; X = 47.67

Step-by-step explanation:

The weighted average is the sum of products of score and weight. Choice C has the percentage weights properly expressed as decimal values.

___

The other equations could work if the final score of 78 were weighted by the corresponding equivalent of 100%. (X is wrong in the other choices as well.)

__

The attachment shows the "work". Given that choice C is the only correct equation, we presumed that the value of X was correct. The equation solver confirms this. If you want to do it by hand, compute the sum of products, subtract that sum, then divide by 0.15.

  X = (78 -70.85)/.15 = 7.15/.15 = 47 2/3

Answer:

Steam boat = 20 Knots , Yacht = 40 Knots

Step-by-step explanation:

Let the distance travelled by both the boats be x

Case 1: Steamboat

Speed [tex]S_{s}=\frac{x}{5}[/tex]

Case 2 : Yacht

[tex]S_{y}=\frac{x}{2.5}[/tex]

[tex]S_{y}=\frac{2x}{5}[/tex]

Also given that speed of yacht is 20 more than that of steamboat

[tex]S_{y} -S_{s}=20[/tex]

Hence

[tex]\frac{2x}{5} - \frac{x}{5} = 20[/tex]

[tex]\frac{x}{5} = 20[/tex]

[tex]x = 100[/tex]

Hence the distance traveled is 100 naut miles

Hence

Speed of Steam boat = [tex]\frac{100}{5}[/tex]  = 20 Knots

Speed of Yacht = [tex]\frac{100}{2.50}[/tex]  = 40 Knots

The answer would be:

Let n be "a number"

22 + 4n

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

22+4x

Step-by-step explanation:

The number should be x as a letter symbol.

The sum should be add sign.

22+4x is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

c=100

Step-by-step explanation:

To complete the square, it would really help if the coefficient of x^2 is 1 which is so formula for c in this case is just (b/2)^2

So (-20/2)^2

simplifying gives

(-10)^2

100

c=100

Answer:

100

Step-by-step explanation:

The question is on making the equation a perfect square

Given ;

[tex]x^2 - 20x + c[/tex]

To get c;

[tex]c=(\frac{b}{2} )^2[/tex]

where ;

[tex]b= -20[/tex]

[tex]c= (\frac{-20}{2} )^2 = 10^2 = 100[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{-20t^5u^2v^3}{48t^7u^4v}\implies \cfrac{-20}{48}\cdot \cfrac{t^5u^2v^3}{t^7u^4v^1}\implies \cfrac{-5}{12}\cdot \cfrac{v^3v^{-1}}{t^7t^{-5}u^4u^{-2}}\implies \cfrac{-5}{12}\cdot \cfrac{v^{3-1}}{t^{7-5}u^{4-2}} \\\\\\ \cfrac{-5}{12}\cdot \cfrac{v^2}{t^2u^2}\implies \cfrac{-5v^2}{12t^2 u^2}[/tex]

Answer: It is not possible for Janet to have won 10 games.

Step-by-step explanation:

Let be "x" the number of games Janet won.

We know that Nadia has won twice the number of games Janet has and the sum of the games Nadia and Janet have won together is 24.

Then, we express this situation with this equation:

[tex]x+2x=24[/tex]

So, let's check if it is possible for Janet to have won 10 games. Substitute [tex]x=10[/tex] into the expression:

[tex]10+2(10)=24\\\\10+20=24\\\\30=24\ (This\ is\ not\ true)[/tex]

Therefore, it is not possible for Janet to have won 10 games.

Answer:

not possible

Step-by-step explanation:

Let be "x" the number of games Janet won.

We know that Nadia has won twice the number of games Janet has and the sum of the games Nadia and Janet have won together is 24.

Then, we express this situation with this equation:

So, let's check if it is possible for Janet to have won 10 games. Substitute  into the expression:

Therefore, it is not possible for Janet to have won 10 games.

Answer:

1/9

Step-by-step explanation:

There are a total of 21 marbles.  In the first draw, there are 7 blue marbles out of 21.  In the second draw, since he replaces the marble, there are still 7 blue marbles out of 21.  So the probability is:

P = (7/21)²

P = 1/9