A coin flip: A fair coin is tossed three times. The outcomes of the three tosses are recorded. Round your answers to four decimal places if necessary. Part 1 of 3 Assuming the outcomes to be equally likely, find the probability that all three tosses are "Tails." The probability that all three tosses are "Tails" is ______ Part: 1/3 alo Part 2 of 3 Assuming the outcomes to be equally likely, find the probability that the tosses are all the same. The probablility that the tosses are the same is ____

Answer:

i think 5

Step-by-step explanation:

the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show

\(3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}\)

now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus

\(100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft\)

Cube 2 contains 64 cubes 1.

Given that,
A box was made in the form of a cube. If a second cubical box has inside dimensions four times those of the first box,

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Let the dimension of the former cube 1 be a.
And the dimension of the later cube 2 is 4a.
Now the,
Ratio = volume of cube 2 / volume of cube 1
Ratio = (4a)³ / a³
Ratio = 64 a³ / a³
Ratio = 64

Thus, cube 2 contains 64 cubes 1.

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Answer:

cheapt

Step-by-step explanation:

Answer:

The answer is 17 km due north.

Step-by-step explanation:

24 km due north subtracted by 7 km east

Put north because it was first (this was based on a rule).

The distance between the final position to the initial position will be 25 km.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Pierre walks 24 km due north and then 7 km due east. Then the distance between the final position to the initial position will be

H² = 24² + 7²

H² = 576 + 49

H² = 625

H² = 25²

H = 25 km

The distance between the final position to the initial position will be 25 km.

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Answer:

g(x) is shifted left by two units

Similar shapes have the same angles. These two triangles have no angles in common, so they're not similar.

We cannot verify if each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p when f(p) = 0.

To verify that if f(p) = 0, then each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p, we need to substitute p into each function and check if the result is equal to p.

g1(x) = (3+x-2x^2)^(1/4)

Let's substitute p into g1(x):

g1(p) = (3+p-2p^2)^(1/4)

To verify if g1(p) = p, we need to show that (3+p-2p^2)^(1/4) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g1(x) has a fixed point at p without further calculations or approximations.

g2(x) = (x+3-x^4/2)^(1/2)

Let's substitute p into g2(x):

g2(p) = (p+3-p^4/2)^(1/2)

To verify if g2(p) = p, we need to show that (p+3-p^4/2)^(1/2) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g2(x) has a fixed point at p without further calculations or approximations.

g3(x) = (x+3/x^2+2)^(1/2)

Let's substitute p into g3(x):

g3(p) = (p+3/p^2+2)^(1/2)

To verify if g3(p) = p, we need to show that (p+3/p^2+2)^(1/2) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g3(x) has a fixed point at p without further calculations or approximations.

g4(x) = (3x^4+2x^2+3)/(4x^3+4x-1)

Let's substitute p into g4(x):

g4(p) = (3p^4+2p^2+3)/(4p^3+4p-1)

To verify if g4(p) = p, we need to show that (3p^4+2p^2+3)/(4p^3+4p-1) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g4(x) has a fixed point at p without further calculations or approximations.

Therefore, based on algebraic manipulations alone, we cannot verify if each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p when f(p) = 0. Further calculations or approximations would be required to determine the fixed points of these functions.

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To sketch the curve\(y = x^3 + 6x^2 - 9x,\)we can follow these steps:

Find the critical points by taking the derivative of y and setting it equal to zero:

\(y' = 3x^2 + 12x - 9 = 0\)

Solving for x, we get x = -3 or x = 1.

Determine the behavior of the curve around the critical points using the second derivative test:

y'' = 6x + 12

At x = -3, y'' < 0, so this is a local maximum.

At x = 1, y'' > 0, so this is a local minimum.

Find the y-intercept by setting x = 0:

\(y = 0^3 + 6(0^2) - 9(0)\)= 0.

Find the x-intercepts by setting y = 0:

\(x(x^2 + 6x - 9) = 0\)

Using the quadratic formula, we get x = (-6 ± √72)/2, which simplifies to x = -3 ± 3√2. So the x-intercepts are approximately -6.24 and 0.24.

Determine the end behavior of the curve by looking at the highest order term in y, which is \(x^3\). As x goes to positive or negative infinity, y goes to positive or negative infinity, respectively.

Use the information from steps 1-5 to sketch the curve. We know that the curve passes through the y-intercept at (0,0), has x-intercepts at approximately (-6.24,0) and (0.24,0), and has a local maximum at (-3,0) and a local minimum at (1,-2). We also know that as x goes to positive or negative infinity, y goes to positive or negative infinity, respectively. Putting all of this information together, we can sketch the curve as follows:

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1) Option B, which states that the confidence interval size shrank from 0.99 to 0.90, is the right answer.

2) Option D is the best decision. Confidence interval: 0.88

1) Confidence intervals are ranges of estimates for unknown parameters in frequentist statistics. Confidence intervals are given a confidence level. The most common level is 95%, but other levels, such as 90% or 99%, may be used as well.

Therefore, option B is the correct choice, which states that the confidence interval size decreased from 0.99 to 0.90

2) Probability is another word for confidence in statistics. An estimate that falls between the upper and lower values of a confidence interval, such as one constructed with a 95% level of confidence, is 95 out of 100 times likely to be accurate.

It can be calculated as:

df=n-1=19

t critical value 0.12 (two tail) = 1.62797

M = 51.5

sM = √(6.842 / 20) = 1.53

μ = M ± Z (sM)

μ = 51.5 ± 1.62797 * 1.53

μ = 51.5 ± 2.49

therefore, CI { 49.01 and 53.99 }

The correct choice is option D. 0.88 confidence interval.

. move the slider all the way to the right to a confidence coefficient of 0.99. now move the slider to a confidence coefficient of 0.90. what happened to the size of the confidence interval during the move from 0.99 to 0.90? from 0.99 to 0.90 the confidence interval size became larger from 0.99 to 0.90 the confidence interval size became smaller from 0.99 to 0.90 the confidence interval size remained constant -select- 2. what level of confidence would you need have so that the value of the true population mean of training time was between 49.01 and 53.99 days? 0.93 0.97 0.85 0.88

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Answer:

b

Step-by-step explanation:

The final amount after 20 years, compounded quarterly is $6,353.98.

The final amount after 5 years, compounded continuously, is  $1,145.10.

we can use the formula for compound interest:

\(A = P(1 + r/n)^(^n^\times^t^)\)

where A is the final amount,

P is the principal (starting amount),

r is the annual interest rate, t is the time in years, and n is the number of times compounded per year.

Plugging in the given values, we get:

\(A = 3750(1 + 0.035/4)^(^4^\times^2^0^)\)

A = $6,353.98

Therefore, the final amount after 20 years, compounded quarterly, is approximately $6,353.98.

P= $1,000; r=2.8%, t= 5yrs compounded continuously ​

For the second problem, we can use the formula for continuous compounding:

\(A = Pe^(^r^t^)\)

\(A = 1000e^(^0^.^0^2^8^\times^5^)\)

A = $1,145.10

Therefore, the final amount after 5 years, compounded continuously, is  $1,145.10.

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Answer:

The next sequence is 243

The pattern is x 3

3 x 3 = 9

9 x 3 = 27

27 x 3 = 81

81 x 3 = 243

Step-by-step explanation:

You're welcome.

The quadratic equation whose roots are x = - 1 / 3 and x = 4 is equal to 3 · x² - 11 · x - 4.

Algebraically speaking, we can form an quadratic equation from the knowledge of two distinct roots and the use of the following expression:

y = (x - r₁) · (x - r₂)

If we know that r₁ = - 1 / 3 and r₂ = 4, then the quadratic equation is:

y = (x + 1 / 3) · (x - 4)

y = x² - (11 / 3) · x - 4 / 3

If we multiply each side by 3, then we find the following expression:

3 · y = 3 · x² - 11 · x - 4

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The variance of X is 0.09.

Formula used: Variance is the square of the standard deviation. T

he formula to calculate variance of a discrete random variable X is given by:

Var(X) = E[X²] - [E(X)]²Calculation:

P(B) = 0.2P(A)

= 0.5P(AB) =

0.1

By definition,

P(A U B) = P(A) + P(B) - P(AB)

⇒ P(A U B) = 0.5 + 0.2 - 0.1

⇒ P(A U B) = 0.6

Now,E[X] = E[1B + ?]

⇒ E[X] = E[1B] + E[?]

Since 1B can have two values 0 and 1.

So,E[1B] = 1*P(B) + 0*(1 - P(B))

= P(B)

= 0.2P(A/B)

= P(AB)/P(B)

⇒ P(A/B)

= 0.1/0.2

= 0.5

So, the conditional probability distribution of ? given B is:

P(?/B) = {0.5, 0.5}

⇒ E[?] = 0.5(0) + 0.5(1)

= 0.5⇒ E[X]

= 0.2 + 0.5

=0.7

Now,E[X²] = E[(1B + ?)²]

⇒ E[X²] = E[(1B)²] + 2E[1B?] + E[?]²

Now,(1B)² can take only 2 values 0 and 1.

So,E[(1B)²] = 0²P(B) + 1²(1 - P(B))= 0.8

Also,E[1B?] = E[1B]*E[?/B]⇒ E[1B?] = P(B)*E[?/B]= 0.2 * 0.5 = 0.1

Putting the values in the equation:E[X²] = 0.8 + 2(0.1) + (0.5)²= 1.21Finally,Var(X) = E[X²] - [E(X)]²= 1.21 - (0.7)²= 0.09

Therefore, the variance of X is 0.09.

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Answer:

A

Step-by-step explanation:

For a right triangle, one of tha angles must be 90degrees. For the given right angles, the measure of its acute angles are 30, 60 and 90degrees respectively

Triangle is a 2-D shape that has 3 sides and angles. Some of the types of triangle include:

For a right triangle, one of tha angles must be 90degrees. For the given right angles, the measure of its acute angles are 30, 60 and 90degrees respectively

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The sine function is given by:

Therefore:

Therefore, we can conclude the sine is positive in II quadrant.

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

The cosine function is given by:

therefore:

Therefore, we can conclude the cosine is negative in II quadrant

The factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Given

5x³ + 20x³ + 2x +8 is a polynomial.

The factor of the polynomial.

5x³ + 20x³ + 2x +8 is a polynomial.

Take common, we get

5x²(x + 4) + 2(x + 4)

(5x² + 2) (x + 4)

[(x√5)² - (i√2)](x + 4)

(√5x - i√2)(√5x + i√2)(x + 4)

Thus, the factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

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Answer:

> Option D, or (5x2 + 2) (x + 4), is the correct choice.

Step-by-step explanation:

> This is the only correct answer choice for this equation.

Answer: A6/ 2/3= 9

Step-by-step explanation:

We know that one tile is 2/3 ft long and we want to cover 6 ft (which is the given measure of the back of the shower).

To know the number of tiles needed, we will simply do cross multiplication as follows:

1 tile ...............> 2/3 ft

?? tiles ...........> 6 ft

Number of tiles = (6*1) / (2/3)

Number of tiles = 6 / (2/3)

Number of tiles = 9 tiles

Answer:

A). 6 ÷ 2/3 = 9

Step-by-step explanation:

Answer:

The answer is C: 13/99

Step-by-step explanation:

To find the answer, you can simply look at all of the multiple choice answers and start dividing the numerator by the denominator. When you find the answer choice that has a quotient of 0.13131313131313, you will know your right answer.

Answer:

The value of x, y and z is 5, 15 and 30 respectively.

Step-by-step explanation:

Let the first number be x, second number be y and third number be z

Here, The sum of three numbers is 50

x + y + z = 50 ...(1)

The second number is three times the first number

y = 3x ...(2)

The third number is twice the second number

z = 2y ...(3)

Here, we know that y = 3x from equation (2). So, put this value in equation (3)

z = 2y

z = 2(3x)

z = 6x ...(4)

Here, y = 3x and z = 6x then put this in equation (1)

x + y + z = 50

x + 3x + 6x = 50

10x = 50

10x/10 = 50/10

x = 5

Here, The value of x is 5

So,

y = 3x

y = 3(5) = 15

z = 6x = 6(5) = 30

Thus, The value of x, y and z is 5, 15 and 30 respectively.

x + y + z = 50

5 + 15 + 30 = 50

50 = 50

L.H.S = R.H.S

Hence Verified!

-TheUnknownScientist 72

The LP model aims to maximize profit, considering constraints such as production limits and resource availability. The graphical solution helps identify the optimal solution by comparing slopes of the objective function and constraint lines.

1. LP Model:

Let:

x = number of Razors produced

y = number of Zoomers produced

Objective function:

Maximize profit = 70x + 40y

Subject to the following constraints:

x + y ≤ 700 (Total bikes produced cannot exceed 700)

x ≤ 300 (Number of Razors produced cannot exceed 300)

2x + y ≤ 900 (Polymer constraint)

3x + 4y ≤ 2400 (Labor hours constraint)

x ≥ 0, y ≥ 0 (Non-negativity constraints)

2. Constraints and Feasible Region:

The constraints can be represented graphically as follows:

x + y ≤ 700 (dashed line)

x ≤ 300 (vertical line)

2x + y ≤ 900 (dotted line)

3x + 4y ≤ 2400 (solid line)

x ≥ 0, y ≥ 0 (non-negativity axes)

The feasible region is the region that satisfies all the constraints and lies within the non-negativity axes.

3. Graphical Solution:

By plotting the feasible region and drawing isoprofit lines (lines representing constant profit), we can identify the optimal solution. The isoprofit lines will have different slopes depending on the profit value.

4. Slope Comparison Method:

To confirm that the solution obtained graphically is optimal, we can compare the slopes of the objective function (profit) line with the slopes of the constraint lines at the optimal point. If the slope of the profit line is greater (in case of maximization) or smaller (in case of minimization) than the slopes of the constraint lines, the solution is optimal.

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72x + 436= -96x + 1108x

72x+436=1012x

436=1012x−72x

436=940x

436/940=x

109/235=x

x=109/235

Hope this helps have a blessed and wonderful day!

Answer:

x=4

Step-by-step explanation:

72x+436=-96x+1108

or,72x+96x=1108-436

or,168x=672

x=672/168

x=4

Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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The answer is: ∫(-1)dz = -z + C

To evaluate the indefinite integral of -1 with respect to z, we need to find the antiderivative of -1. The antiderivative of -1 is -z. Since it's an indefinite integral, we should also include the constant of integration, C. Therefore, the answer is:

∫(-1)dz = -z + C

The process of finding the antiderivative of a function is known as integration. An indefinite integral is an integral that does not have any specific limits of integration. It is represented by the symbol "∫" and does not have any numerical value until a constant of integration is added.

In this case, we are asked to evaluate the indefinite integral of -1 with respect to z. To find the antiderivative of -1, we need to find a function whose derivative is -1. This is because the derivative and antiderivative are inverse operations.

The antiderivative of -1 is -z because the derivative of -z with respect to z is -1.

∫(-1)dz = -z + C

Where C is the constant of integration. It is important to include the constant of integration when finding the antiderivative because any constant value will have a derivative of 0. Therefore, adding the constant of integration ensures that all possible antiderivatives of a function are accounted for.

The result of the indefinite integral, -z + C, represents the set of all functions whose derivative is -1.

To check the answer, we can take the derivative of -z + C with respect to z:

d/dz(-z + C) = -1 + 0 = -1

This confirms that -z + C is indeed an antiderivative of -1.

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Answer:

2

Step-by-step explanation:

you take 1 and add 1 to it... and bam... 2

Answer:

2

Step-by-step explanation:

1+1=2 because 2-1=1 :0

Six semicircles lie in the interior of a regular hexagon with a side length of 2 so that the diameters of the semicircles coincide with the sides of the hexagon. The zone of the shaded locale is around 10.3923 square units.

 We will approach this problem by first finding the region of the hexagon and after that subtracting the zones of the six semicircles from it. The zone of a customary hexagon with side length 2 can be found utilizing the equation:

Region of hexagon = (3√3/2) x side\(^{2}\)

Substituting the given esteem of side length, we get:

Area of hexagon = (3√3/2) x 2\(^{2}\) = 6√3

The range of a crescent is half the region of the comparing circle. So, the zone of each crescent is:

Range of semicircle = 1/2 x π x radius\(^{2}\) = 1/2 x π x 1^\(^{2}\)= π/2

There are six semicircles, so the whole range of the semicircles is:

Add up to the zone of semicircles = 6 x π/2 = 3π At long last, able to find the zone of the shaded locale by subtracting the region of the semicircles from the range of the hexagon:

Zone of shaded locale = Range of hexagon - Add up to a range of semicircles

= 6√3 - 3π

≈ 10.3923 thus, the zone of the shaded locale is around 10.3923 square units. 

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Step-by-step explanation:

x/y = y/z = z/x

x = y²/z = zy/x and y = z²/x

x = y²/z

putting this into the 3rd part of the original equation :

z/x = z/ y²/z = z²/y²

now using the y identity of the second part there :

y = z²/x

z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)

so,

x²/z² = z/x

x³/z³ = 1

x/z = 1

x = z

then

y/z = y/x = z/x (= 1)

and therefore,

y/x = z/x meaning

y = z (and therefore = x)

so,

x = y = z

The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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