We are throwing darts on a disk-shaped board of radius 5. We assume that the proposition of the dart is a uniformly chosen point in the disk. The board has a disk-shaped bullseye with radius 1. Suppose that we throw a dart 2000 times at the board. Estimate the probability that we hit the bullseye at least 100 times.

Answer:

The first table.

Step-by-step explanation:

1 cup = 1 * 16 = 16 tablespoons

2 = 2 * 16 = 32

3 = 3*16 = 48

4 = 4*16 = 64 and so on....

[tex] cos(A) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} [/tex]

The cos A will be b/c

Cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse

The steps are as follow:

AB = c

BC = a

AC = b

Cos A = Adjacent side to A / Hypoteneous

Cos A = AC / AB

Cos A = b / c

Therefore the value of Cos A in given figure will be b / c

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Answer:

0.015 and 3/200.

Step-by-step explanation:

1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.

0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.

Answer:

32P6  

Step-by-step explanation:

nPr

n=32

r=6

Answer:length 30, width 18

Step-by-step explanation:

60% +100%=160%

160% × 2 = 320 %

96/320 = 0.3 ×100 =30 ( length)

30 × 0.6 =18 (width)

Check: (18 + 30) 2 = 96

Answer:

20%?

Step-by-step explanation:

Answer:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

Step-by-step explanation:

The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

7 + 2 = 9 speedometers, which means that [tex]N = 9[/tex]

2 are not correctly calibrated, which means that [tex]k = 2[/tex]

3 are chosen, which means that [tex]n = 3[/tex]

Complete the probability distribution table.

Probability of each outcome.

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,9,3,2) = \frac{C_{2,0}*C_{7,3}}{C_{9,3}} = 0.4167[/tex]

[tex]P(X = 1) = h(1,9,3,2) = \frac{C_{2,1}*C_{7,2}}{C_{9,3}} = 0.5[/tex]

[tex]P(X = 2) = h(2,9,3,2) = \frac{C_{2,2}*C_{7,1}}{C_{9,3}} = 0.0833[/tex]

Only 2 defective, so [tex]P(X = 3) = 0[/tex]

Probability distribution table:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

Answer:

400 + .03(250,000) = $7900

Step-by-step explanation:

Answer:

h=2

Step-by-step explanation:

f is translated right 2 units (so h=2) and up 2 units (so k=2)

The value of h is 2.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

A function f(x) when translated horizontally leads to the function g(x) which is equal to g(x) = f(x ± k) where k is the units to which the function is translated.

And the vertical translation leads to the function g(x) = f(x) ± k, where k is the units to which the function is translated.

Here the original function is, f(x) = 3ˣ.

The point corresponding to x = 0 in f(x) is x = 2 in g(x).

That is (0, 1) is translated to (2, 3).

f(x) is horizontally translated to the right.

3ˣ translates to 3ˣ⁻².

Hence the value of h is 2.

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Answer:

x =[tex]x =(\frac{c}{4} )^{1/3} \\[/tex]

input 2  output 32

output 256 input 4

Step-by-step explanation:

Answer:

x = 1/2; y = 1/3

Step-by-step explanation:

2x + 3y = 2     Eq. 1

-6x + 12y = 1     Eq. 2

Eq. 1

2x + 3y = 2

2x = -3y + 2

x = -3/2 y + 1

Eq. 2

-6x + 12y = 1

De Eq. 1 sabemos que x = -3/2 y + 1

-6x + 12y = 1

-6(-3/2 y + 1) + 12y = 1

9y - 6 + 12y = 1

21y - 6 = 1

21y = 7

y = 7/21

y = 1/3

Eq. 1

2x + 3y = 2

2x + 3(1/3) = 2

2x + 1 = 2

2x = 1

x = 1/2

Respuesta: x = 1/2; y = 1/3

Answer:

8 batches

in workings show whats left over but not counted.

As a batch its a whole number as the multiplier will usually be the fraction

and fraction / fraction should always show fraction but the whole number given with a remainder can be shown if not a whole number.

Step-by-step explanation:

6 1/2 = 6.5

and ;

3/4 of a pound = 0.75  of 1 pound

6.5 / 0.75 = 8.7         or in full workings write = 8.6666.....7

8.7/ 1 = 8 batches with 0.7 or 0.66667 left over

Answer In fraction for exam question given in fraction  8.7 = 8  batches

with  7/10 left over.

Answer:

Step-by-step explanation:

Cos 2A = 2Cos² A - 1

             [tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]

Answer:

To create the graph of k(x) , the graph of f(x)   undergoes  a vertical stretching  by a factor of 9.

Step-by-step explanation:

We are given that

[tex]k(x)=9f(x)[/tex]

We have to Identify the transformation that occurs to create the graph of k(x).

To create the graph of k(x) we will multiply the function f(x) value by 9.

Let f(x) be any function

[tex]g(x)=a f(x)[/tex]

Where a>1

It means to obtain the graph  of g(x) the graph f(x)  has  undergone a vertical stretching  by a factor of a.

We have k=9>1

Therefore, to create the graph of k(x) , the graph of f(x) undergoes a vertical stretching  by a factor of 9.

[tex]\rightarrow\sf {5a}^{2} + {b(a}^{2} + 5) + {b}^{2} [/tex]

[tex]\rightarrow\sf {5a}^{2} + {b(a }^{2} + 5) + {b}^{2} \\ = \sf {5a}^{2} + {ba}^{2} + b \times 5 + {b}^{2} \\ = \large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\rightarrow\large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\color{red}{==========================}[/tex]

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

Answer:

The answer is 40 chocolates in the box in total

Answer:

sin²2θ. (cos θ sin θ). cos 2θ

Step-by-step explanation:

finding g'(x)

g'(x)

= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }

= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

= 4 (cosθsinθ)³{ cos²θ - sin²θ}

= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}

= sin²2θ. (cos θ sin θ). cos 2θ

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)

Answer:

Joe's wife must drive at a rate of 45km/hour.

Step-by-step explanation:

We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.

Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.

Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:

[tex]2.5+0.5t[/tex]

Where t represents the time in minutes after his wife left the house.

And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:

[tex]2.5+0.5(10)=7.5\text{ km}[/tex]

Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:

[tex]10s=7.5[/tex]

Solve for s:

[tex]\displaystye s=0.75\text{ km/min}[/tex]

Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.

Answer:

2 feet

Step-by-step explanation:

Displacement at 0 seconds is 0 feet.

Displacement at 2 seconds is 2 feet because it took them 2 seconds to walk 2 feet.

Answer: B

Step-by-step explanation:

The line [tex]y=2x+3[/tex] is dotted and shaded above.

Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.

This leaves B as the correct answer.

Answer:

Equation: f(x) = 2(x + 5)^2 + 2

Vertex: (-5, 2)

Step-by-step explanation:

The form the question wants us to write the quadratic function in is called "vertex form":

f(x) = a (x - h)^2 + k

a = the a in a standard quadratic equation (y = ax^2 + bx + c) or the coefficient of the x^2

h = x coordinate of the vertex

k = y coordinate of the vertex

To find the vertex, we are going to use the quadratic equation given:

2x^2 + 20x + 52

Comparing it to the standard quadratic equation (y = ax^2 + bx + c),

a = 2

b = 20

c = 52

Now we can start finding our vertex.

To find h, we are going to use this formula:

-b / 2a

We already know b = 20 & a = 2, so we can just substitute that into our formula:

- (20) / 2*2

Which equals:

-20/4 = -5

So h (or the x coordinate of the vertex) is equal to -5

Next we will find k, or the y coordinate of the vertex.

To do that, we are going to plug in -5 into 2x^2 + 20x + 52:

2(-5)^2 + 20(-5) + 52

2(25) -100 + 52

50 - 100 + 52

-50 + 52

2

k (or the y coordinate of the vertex) is equal to 2

The vertex is (-5, 2)

However, we still need to find our equation in vertex form.

We know a = 2, h = -5, & k = 2. Now we substitute these into our vertex form equation:

a(x - h)^2 + k

(2)(x - (-5))^2 + (2)

2(x + 5)^2 + 2

(Remember that the -5 cancels with the - in front of it, making it a positive 5)

The equation is f(x) = 2(x + 5)^2 + 2

Hope it helps (●'◡'●)

The answer for the first line segment : (-3,-7) (-4,0)

The answer for 2nd line segment is :(-3,8) (-9,-5)

Step-by-step explanation:

Let do line segment QR and ST. first.

Step 1: Find a line that contains a points that is perpendicular to the line of reflection

"A reflection of a pre image and new image is perpendicular to the line of reflection.

This means for points Q,S,T and R, there is a line that. contains one point that is perpendicular to the line of reflection.

A line that is perpendicular to the line of reflection is the negative reciprocal of the slope so this means all 4 lines must be on a different slopes but the slopes must be 1/2.

To simplify, things, here are the lines that will all 4 points be on

Step 2: Find a point where both the line and line of reflection intersect at.

Now we need to find a line where both the line of reflections and the 4 lines will intersect at separately.

Step 3: Find the endpoints given the midpoint and the originally endpoint.

A reflection per and new image is equidistant from the point of reflection. So we. an say that the point where the line intersect is the midpoint of the pre and new image.

Using this info,

Connect R prime and Q prime. And that the new line segments

Connects S prime and T prime and that the new line segments.

Answer:

Step-by-step explanation:

Answer:

Part 1)

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Step-by-step explanation:

Part 1)

We want to simplify the expression:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]

We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:

[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]

In scientific notation, the coefficient is always between 1 or 10.

So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:

[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]

(You can see that the 10s can cancel out, giving us our original expression.)

Simplify. Thus:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]

Therefore, as we can see:

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Reviewing their work, we can see that only Skyler's approach was incorrect.

729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.

Answer:

58.80

Step-by-step explanation:

84 x .7(70%) =58.80

Answer:

$23.3

Step-by-step explanation:

you can use ratios to solve this:

$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99

So, 6.99 divided by 0.3 = 23.3

so the original price is $23.3

Answer:

Step-by-step explanation:

The mean the the average of 5 numbers. If the next score is x, then the mean is:

Solve it for x:

It is given that,

The mean is the average of 5 numbers.

Then if the,

Next score is x the mean will be.

We can solve now,

→ (85 +78 +77 + 69 + x)/5 = 80

→ (309 + x)/5 = 80

→ 309 + x = 80 × 5

→ 309 + x = 400

→ x = 400 - 309

→ x = 91

Hence, the next score is 91.