Compute the probability of the event E1 that Bob wins in a duel against Eve alone, assuming he shoots first. (Hint: Let x be the probability Bob wins in a duel against Eve alone, assuming he fires first. If Bob misses his first shot and then Eve misses her first shot, what is the probability Bob wins in terms of x

[tex]\\ \sf\longmapsto y=2x-x^2[/tex]

[tex]\\ \sf\longmapsto 2x-x^2=0[/tex]

[tex]\\ \sf\longmapsto x^2-2x=0[/tex]

[tex]\\ \sf\longmapsto x(x-2)=0[/tex]

[tex]\\ \sf\longmapsto x=0,2[/tex]

⇒ y=2x−x2

⇒ 2x - x² = 0

⇒ x² - 2x = 0

⇒ x ( x - 2 ) = 0

⇒ x = 0, 2

Answer:

7

6

3

1

1

because first they go down by three then one

Answer:

7

6

3

1

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(9) = |9 + 9| = |18| = 18

f(-4) = |-4 + 9| = |5| = 5

f(0) = |0 + 9| = |9| = 9

pretty boring examples as you're always taking the absolute value of a positive number.

what do you suppose f(-12) is???

f(-12) = |-12 + 9| = |-3| = 3

Answer:

  $0.25 per ream

Step-by-step explanation:

The costs per ream are ...

  X: $40/(8 reams) = $5/ream

  Y: $19/(4 reams) = $4.75/ream

The savings per ream is $5.00 -4.75 = $0.25 for the cheapest brand.

Answer: It depends on how many years a person lives.

Step-by-step explanation:

Answer:

i think it is 0.7 correct me if i am wrong i am in the 6th grade

Step-by-step explanation:

Answer:

y=3/4x

Step-by-step explanation:

From the origin (0,0) count the rise to the next point (3) and then the run (4) leaving you with 3/4 as your slope.

Hope that helps

Answer:

26.16

Step-by-step explanation:

Answer:

26.16

Step-by-step explanation:

20 percent of 130.8

= (20/100)*130.8

= (20*130.8)/100

= 2616/100 = 26.16

Answer:

8(w+4)=5

Step-by-step explanation:

Step-by-step explanation:

absolutely. there is no mathematical problem to solve.

just do what the instructions tell you.

that is an exercise for you to get a feeling what is what.

Answer:

The perimeter of the rectangle is 3.5 m or 350 cm.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Step-by-step explanation:

The share of stock is $88.33 worth now which is the value of a share of stock on the stock market decreased by 14%.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

The value of a share of stock on the stock market decreased by 14%. If it used to be worth $102.64 which is given in the question.

We have to determine the evaluation of 15% of 60.

⇒ 14% of $102.64

15%  is expressed as 15/100 in fractional form

⇒ (14/100)(102.64)

15/100  is expressed as 0.15 in decimal form

⇒ (0.14)(102.64)

Apply the multiplication operation, and we get

⇒ 14.31

Therefore, 14% of $102.64 would be $14.31.

The share of stock is worth now: $102.64 - $14.31 = $88.33.

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Answer:

point-slope form: y-y1=m(x-x1) -> m=slope, (x1, y1) = coordinates of a point

point = (-14,-17) -> x1=-14, y1=-17

slope = 1 -> m=1

y-(-17)=1*(x-(-14)

y+17=1(x+14)

you don't need the *1 but some teachers are picky about that

Answer:

y + 17 = 1 ⋅ ( x + 14 )

Step-by-step explanation:

i think... trust someone else because i'm not 100% sure..

Answer:

y=-6x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(0-1)

m=(5+1)/-1

m=6/-1

m=-6

y-y1=m(x-x1)

y-(-1)=-6(x-1)

y+1=-6(x-1)

y=-6x+6-1

y=-6x+5

Answer:

It is 21 first guy is no doubt correct.

Step-by-step explanation:

The expression results to 21.

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

1⁵+5²/25⁰-5¹

So, 1⁵ = 1

5² = 25

25⁰ = 1

5¹ = 5

Now, 1⁵+5²/25⁰-5¹

= 1+ 25 / 1 - 5

= 1 + 20

= 21

Hence, the expression results to 21.

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Answer:

x=12

Step-by-step explanation:

you need the x alone so you substract 3 from both sides.

Then you have, -x= -12

You need the x positive so you change the sign for it but as it is an equation you need to do the same thing on the other side, making both sides positive.

x=12

Answer:

-0.2

Step-by-step explanation:

pls give me brainliest if possible

Hi,

(2x + 3y)² - (2x - 3y)²

= [(2x)² + 2x*3y + (3y)²] - [(2x)² - 2x*3y + (3y)²]

= (4x² + 6xy + 9y²) - (4x² - 6xy + 9y²)

= 4x² + 6xy + 9y² - 4x² + 6xy - 9y²

= 12xy

I hope it helped ✅(◠‿◕)

Answer:

D:x=2

Step-by-step explanation:

Rest of the triangle is just a distraction. The distance from B to any point in the bysector is the same as the distance from C to the same point (you can look at BDF and CDF and notice they're congruent by SAS). at this point it's just solving

[tex]2x + 3 = 4x - 1 [/tex]

which has 2 as a solution

Answer:

Step-by-step explanation:

91 : 14 = q : 6

q = 91 * 6 : 14

q = 39

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

check

91 : 14 = 39 : 6

6.5 = 6.5

the answer is good

It would be 100,000. If it were anything above 150,000, then it would round up to 200,000.

Hope this helps ^^

Answer:

"To round a number to the nearest 100,000, check the ten thousands digit to decide whether to round up or round down. If the ten thousands are 50,000 or more, round up. If they are 49,999 or less, round down. 450,000 to the nearest 100,000 is 500,000."

CONTENT NOT FROM MY WORD!!!

Answer:

Approximately [tex]\text{$0.26$ radian}[/tex] every minute.

Step-by-step explanation:

Convert the unit of velocity (kilometers-per-hour) to meters-per-minute so as to match the unit of radius (meters) and angular velocity (per-minute.)

[tex]\begin{aligned}v &= 11\; \rm km \cdot h^{-1} \\ &= 11 \times \frac{1000\; \rm m}{1\; \rm km} \times \frac{1\; \rm h}{60\; \text{minute}} \\ &\approx 183.33\; {\rm m} \cdot\text{minute}^{-1}\end{aligned}[/tex].

Calculate the circumference of this circle:

[tex]\begin{aligned}c &= 2\,\pi\, r \\ &= 2 \, \pi \times 700\; \rm m \\ &\approx 4398.2\; \rm m\end{aligned}[/tex].

Find the time required (in minutes) for this vehicle to go around this circle:

[tex]\begin{aligned}\frac{4398.2\; \rm m}{183.33\; {\rm m} \cdot \text{minute}^{-1}} \approx 23.990\; \text{minute}\end{aligned}[/tex].

A full circle corresponds to an angle of [tex]2\, \pi \; \text{radian}[/tex] ([tex]360^{\circ}[/tex].) In other words, this vehicle would have turned [tex]2\, \pi \; \text{radian}\![/tex] in approximately [tex]23.990\; \text{minute}[/tex] if it travels at a constant speed. The rate at which this vehicle turn would be:

[tex]\begin{aligned}\frac{2\, \pi}{23.990\; \text{minute}} \approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

In general, for angular velocity [tex]\omega[/tex], radius [tex]r[/tex], and velocity [tex]v[/tex], [tex]v = \omega\, r[/tex]. After updating the units, the angular velocity of this vehicle (the rate at which it turns) may also be found as:

[tex]\begin{aligned}\omega &= \frac{v}{r} \\ &\approx \frac{183.33\; \rm m \cdot \text{minute}^{-1}}{700\; \rm m} \\ &\approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

Answer:

y= -1x+4

Step-by-step explanation:

-1/1 is simplified to -1

Answer:

The fraction 1/4 is a rational number.

It stands for the ratio between the integers 1 and 4.

Answer:

this is your answer

Step-by-step explanation:

this is your answer

Answer:

The perimeter of a circle is calculated with 2πr

The r stands for radius. The radius is half of the diameter.

So r=2.25

Plug it in 2π(2.25)

It was simplify to 4.5π

Which would simplify down to 14.14 miles rounding to the nearest hundredth.

Recall the definition of absolute value:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Then we have a few cases to consider:

• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to

[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]

• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get

[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]

• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then

[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]

but we already have this solution.

• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then

[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]

which we also already found.

answer

a.) y=2.5x

area=2.5x^2

b.)2560

Step-by-step explanation:

a.  The construct the expression for the area of the rectangle in terms of x is y=2.5x

b. The area should be 2,560.

Given that,

Based on the above information, the calculation is as follows:

a) The expression should be y = 2.5x

b) The area should be

[tex]=2.5x^2\\\\= 2.5(32)^2[/tex]  

= 2560

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Answer:

answer is 8

Step-by-step explanation:

2/3(x+7)=10

2x/3+14/3=10

2x/3=10-14/3==>30-14/3

2x/3=16/3

x=16/3*3/2

x=8