you have a fair coin and want to calculate the probability that if you flip the coin 20 times, you will get exactly 14 heads. what is the probability for this event?

a) The solution that is in the interval -2≤rs - 1 is x=0.5, which is the approximation of the solution correct to two decimal places.

b) The remaining zeros of f(x) are -8i.

a) Generally, One way to approximate the solution of this equation is to use the method of bisection. The bisection method starts by finding the midpoint of the interval in which the solution is known to exist, and then determining which half of the interval the solution must lie in. This process is repeated until a sufficiently accurate approximation of the solution is found.

Another way to approximate the solution is to use a numerical method like the Newton-Raphson method. The Newton-Raphson method starts with an initial approximation of the solution and then uses the derivative of the function to find a better approximation.

However, for the given polynomial equation, the solution can be directly found by factoring it, which will give the roots of the polynomial equation.

By factoring 8x³+3x²-7x+6=0, we can get (2x-3)(4x+1)(x-2) = 0

so the roots are x = -0.25, 0.5, and 2

b)

The remaining zeros of f(x) are -8i.

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Answer: Hello how are you doing?

Step-by-step explanation: How may I help you?

50

I attached a pic of my work.

so what I did was find the amount of the other sides of the triangle using their opposite congruent sides. aka, the bottom is 90, which means the top should also be 90. and 90-50 is 40, so the rest of that side (which is one side of the triangle) should be 40.

and then I used the pythagorean theorem, since it is a right triangle (indicated by the squares in the corners).

the theorem states that a^2 + b^2 = c^2

so just plug in the legs (a and b), and you should get the amount of segment AB (which is c)

The area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

Let w be the width of rectangular pen.

We have been given that a farmer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.

Since the perimeter is 2 times the length and width of rectangle.

Perimeter of a rectangle = 2 (Width + Length)

Upon substituting our given values in above formula we will get,

[tex]100 = 2(w + length)\\50 = w + length\\50-w = Length[/tex]

Area of a rectangle = Width x Length

[tex]Area of a rectangle = w (50-w)\\= 50w - w^{2}[/tex]

Let us represent area in terms of width of rectangle as:

[tex]A(w) = 50w - w^{2}[/tex]

Therefore, the area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

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The distance between Orlando and Jacksonville is approximately 230 miles.

What is the distance?

Distance refers to the measurement of the separation between two points in space. It can be thought of as the length of the path between two points, and it can be measured in various units such as meters, feet, miles, kilometers, etc.

The distance between Orlando and Jacksonville is approximately 230 miles (370 km) if you take the most direct route by car. The driving distance between Orlando and Jacksonville is around 4 hours and 30 minutes. It could vary depending on the route taken and traffic conditions.

Hence, the distance between Orlando and Jacksonville is approximately 230 miles.

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The price of one slice of pizza is $3.5, and the price of one drink is $3.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x be the price of one slice of pizza and y be the price of one drink.

The system of equations can be written as:

3x + 2y = 16.50

4x + 4y = 26

To find the price of one slice of pizza and the price of one drink, we can use the substitution or elimination method.

After solving the equation for x and y we get the values as:

x = 3.5 and y = 3

So, the price of one slice of pizza is $3.5, and the price of one drink is $3.

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Answer:

9.919742348374221

Step-by-step explanation:

(x+5)(x)=x^2+5x. (x^2+5x)/2; x=

9.919742348374221

The ice cream costs $3 for a small serving and $4 for a large serving.

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 3 small servings of ice cream and 1 large serving of ice cream for $13, and 2 small servings of ice cream and 1 large serving of ice cream for $10. We can set up two equations to represent the situation:

Let S and L represent the cost of small servings and large servings respectively

3S + L = 13 --- (1)

2S + L = 10 --- (2)

From (1):
L = 13 - 3S  --- (3)

Put (3) in (2):

2S + L = 10

2S + 13-3S = 10

-S + 13 = 10

S = 13-10

S = $3

Put S = 3 into (3):

L = 13 - 3S

L = 13 - 3(3)

L = 13 - 9

L = $4

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The length of the shortest path is 44.69cm.

To find the length of the shortest path, we need to calculate the distance between the two points on the rim of the conical cup where the spider and the fly are located. Since the cone is symmetric, we can find the distance by considering a cross-section of the cone through the center of the cup.

In this cross-section, the spider and the fly are located on a circumference of radius 18 cm (half of the diameter of the cone). The distance between the spider and the fly is one-third of this circumference, or (2pi18 cm)/3 = 12*pi cm.

However, since the cone is 24 cm deep, the shortest path between the spider and the fly is not a straight line, but a curved path along the surface of the cone. To find the length of this path, we need to use the Pythagorean theorem to find the distance between the two points on the surface of the cone.

The height of the cone is 24cm, and the distance between the two points on the circumference is 12pi cm. Using the Pythagorean theorem, we can calculate the length of the shortest path as the square root of (12pi)^2 + 24^2 = 12pi cm + 576 = √(144π^2+ 576)cm=44.69 cm.

So, the length of the shortest path is √(144*π^2+ 576)cm = 44.69cm

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We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.

The initial value is b.

A linear function is a graph with straight lines.

A unit rate exists for all linear functions (b).

Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.

Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.

Paul's idea has a linear function as its equation.

This leads us to the conclusion that linear functions can be used to represent each of the ideas.

Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

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Correct Question:

The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.

To calculate the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts, we need to calculate the point estimate and margin of error. The point estimate is the proportion of first-year students who stated they intend on majoring in liberal arts

(62/100 = 0.62).

The margin of error is 1.96 times the standard error

(SE = √(p(1-p)/n) = √(0.62(1-0.62)/100) = 0.04).

The lower bound of the 95% confidence interval is the point estimate minus the margin of error

(0.62 - 0.04 = 0.58).

The upper bound of the 95% confidence interval is the point estimate plus the margin of error

(0.62 + 0.04 = 0.66).

Therefore, the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.

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Number of seats allocated to state A = 12

Number of seats allocated to state B = 18

Number of seats allocated to state C =22

Number of seats allocated to state D = 38

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Percentage of Population of state A = 258/1858 x 100 = 13.88%

Now, Number of seats allocated to state A = 13.88% of 45

                                                                       = 12.492 = 12 (whole number)

Percentage of Population of state B = 377/1858 x 100 = 20.29%

Now, Number of seats allocated to state A = 20.29% of 90

                                                                       = 18.261 = 18 (whole number)

Percentage of Population of state C = 456/1858 x 100 = 24.54%

Now, Number of seats allocated to state A = 13.88% of 90

                                                                       = 22

Number of seats allocated to state D = 90-(12+18+22) = 38

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Step-by-step explanation:

1.

equilateral triangle. all sides and also all angles are equal.

the sum of all angles in a triangle is always 180°.

so,

6x = 180/3 = 60°

x = 10

2.

all 3 angles are equal, so, also all 3 sides are equal.

6x - 5 = 5x

x - 5 = 0

x = 5

3.

again, all 3 angles are equal.

3x = 180/3 = 60

x = 20

4.

the 2 sides are marked as equally long.

4x = 40

x = 10

5.

isoceles triangle with 60° angle in top, that means it is again an equilateral triangle.

3x + 8 = 4x - 4

8 = x - 4

12 = x

6.

again all angles are equal.

4x = 60

x = 15

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~10(\sqrt[7]{x}+9)\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~10(\sqrt[7]{y}+9)} \\\\\\ \cfrac{x}{10}=\sqrt[7]{y}+9\implies \cfrac{x}{10}-9=\sqrt[7]{y} \\\\\\ \left( \cfrac{x}{10}-9 \right)^7=(\sqrt[7]{y})^7 \implies \left( \cfrac{x}{10}-9 \right)^7=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

2 3/4 square yd

Step-by-step explanation:

3/1 x 11/12 = 2 3/4

Line is not parallel to line because no scaling from point can transform triangle into triangle.

Line is not parallel to line because there is no transformation that can send triangle to triangle. A transformation is a function that changes the location, size, or orientation of an object. A dilation of a shape is a transformation that changes its size, either making it larger or smaller, but does not change its orientation. To determine if two lines are parallel, one must consider if a dilation from a point can send one line to the other. In this case, there is no dilation from point that can send triangle to triangle, so line is not parallel to line.

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Therefore , the solution of the given problem of probability comes out to be  1/ ( 1+ y)x².

Evaluating the chance that a claim is true or that a particular event will happen is the focus of the mathematical field known as probability theory. A chance can be represented by any number between 0 and 1, with 1 denoting certainty and 0 typically expressing the possibility of occurrence. The possibility or possibility that a happening will occur is represented diagrammatically as probability. Figures 0 and 1, percentage ranging 0% - 100%, and some other characters can be used to represent probabilities. the percentage of times, out of all possible possibilities, that an incidence occurred within a good set with equally likely options.

Here,

Probability for X (for x≥0)

=> [tex]\int\limits^{ \infty}_{ 0}[/tex]x e⁻ˣ⁽¹⁺ⁿ⁾ dy

=> -e⁻ˣ   [tex]\int\limits^{ \infty}_{ 0}[/tex]de⁻ˣⁿ

=>e⁻ˣ

Probability for X exceed 3

=>   [tex]\int\limits^{ \infty}_{ 3}[/tex]f(x)dx

=>    [tex]\int\limits^{ \infty}_{ 3}[/tex]e⁻³dx

=> e⁻³

Probability for y ≥ 0

=>   [tex]\int\limits^{ \infty}_{ 3}[/tex]xe⁻ˣ⁽¹⁺ⁿ⁾ dy

=>  [tex]\int\limits^{ \infty}_{ 3}[/tex]x/1 + y d e⁻ˣ⁽¹⁺ⁿ⁾ = 1/ ( 1+ y)x²

Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².

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As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

The amount or magnitude of the difference between two points is what is referred to as distance. It should be noted that the distance traveled between two positions and the distance between them are not the same. The total length of a path connecting two points is known as the distance traveled. A body's actual journey distance is referred to as distance. A different name for it is path length. For instance, the length of the path if an object is going from point O to point P will be equal to OP = 360 m. A scalar quantity is the distance. Only magnitude exists.

given

We will stop for food at after traveling 8 miles from Point B, or 90 miles total.

= 760 miles 

As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

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The complete question is " . Diagram of a car traveling 90 miles . Our food stop will be at what miles after we start our trip from Point B. "

The last customer will be in the book store for 3.22 seconds.

The solution can be calculated using Little's Law, which states that the average number of people in a system equals the average arrival rate multiplied by the average time spent in the system.

Using this formula, we can calculate the time that the last customer will spend in the book store.

Little's Law: Average number in system = Average arrival rate x Average time in system

Average number in system = 29 customers/second x 3 seconds = 87 customers

Average time in system = 87 customers/27 customers/second = 3.22 seconds

Therefore, the last customer will be in the book store for 3.22 seconds.

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By using a trigonometric relation, we will see that the value of x on the right triangle is x = 53.4

We want to find the value of x on the given right triangle, which is one of the cathetus of the triangle (the adjacent cathetus of the shown angle).

We know one angle of 51°, and the opposite cathetus of that angle, which has a measure of 66 units.

Here we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the known values, we will get:

tan(51°) = 66/x

Solving that for x, we will get:

x = 66/tan(51°) = 53.4

The measure of the adjacent cathetus is 53.4 units.

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The answer in the correct number of significant figures is 30.5.

What is the significant figure?

Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

We have given,

6.221 × 7.11 − 13.7

first, we determine the product of 6.221 and 7.11 and round the value to a minimum number of significant figures which is "3"   since  7.11 has "3" significant figures and 6.221 has "4" significant figures

so Product = 6.221 × 7.11 = 44.2

now we do the subtraction and round the answer to a minimum decimal number

44.2 - 13.7

30.5  

Hence, the answer in the correct number of significant figures is 30.5.

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The product of x and y is: "1"

Step-by-step Solution:

Given: 16/9, x, 1, y  are in Geometric Progression (G.P)

Let the general terms of a Geometric Progression are: a, ar, ar², ar³

So, On comparing we get; a=16/9,

⇒ar² = 1

⇒ 16/9*r² = 1

⇒ r² = 9/16

⇒ r = 3/4

x = ar

⇒ (16/9)(3/4)

⇒x=4/3.

y = ar³

⇒(r)(ar^2) = (3/4)(1)

⇒y=3/4.

Now, to find the product of "x" and "y":

⇒x*y = 4/3 x 3/4

⇒1

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x = 60° - 35°

x = 25°

The measure of angle FGJ is 25°

All the values after squares are,

a) 2.3

b) 22.1

c) 65.6

d) 176.9

e) 396

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The numbers are,

a) 1.5

b) 4.7

c) 8.1

d) 13.3

e) 19.9

Now, Find all the squares as;

a) 1.5

⇒ 1.5² = 1.5 × 1.5

          = 2.25

          = 2.3

b) 4.7

⇒ 4.7² = 4.7 × 4.7

           = 22.09

           = 22.1

c) 8.1

⇒ 8.1²= 8.1 × 8.1

         = 65.61

         = 65.6

d) 13.3

⇒ 13.3² = 13.3 × 13.3

            = 176.89

            = 176.9

e) 19.9

⇒ 19.9² = 19.9 × 19.9

             = 396.01

             = 396

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The data points to use is based on two companies knowledge to accomplice.

Here in this question we have been given an example of our time in a school team in which you have to realize on data to convince a group about the recommendation.

Here we also know that when we were making any recommendation to convince a group we have to keep its positive wherever we response to a question about the time you had to convince someone to do something your way.

Here we have also know that you may be tempted so may be tempted to put a negative spin on situation.

So, in order to accomplish the we have to accomplice and will have knowledge two companies knowledge to accomplice

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Answer:

10cm

Step-by-step explanation:

Pythagoras

(6×6) + (8×8) = □×□

36 + 64 = 100

square root of 100 = 10

Answer:

Step-by-step explanation:

The condition for a triangle whose two sides are 6cm and 8cm is the triangle should be right angled triangle.

so by this condition,

            =>    (hypotenuse)^2 = (base)^2 + (perpendicular)^2

           =>      (hypotenuse)^2 =  (6)^2 + (8)^2

          =>        hypotenuse = 10 cm

so the thisrd side of triangle is 10cm.

Answer:

A) I think that the answer is: 1x+3y=4x+1y

But I am not 100% sure so.

B) I don't know sorry  

In accordance with the above assertion, the offered differential equation by variable separation is P = 1/ (k*e^t +1).

A differential equation in mathematics is one that has one or more negatively influencing variables. Dy/dx provides the function's derivative. The phrase describes an equation with several ways to connect the dependent variable to one or more regressors.

dP/dt = P - P^2

1/(P - P^2)dP = dt

∫1/(P - P^2)dP = ∫dt

t + c = 1/(P - P2)dP, where c would be a constant

Use the partial fractions method to calculate the integrated on the left. We wish to rewrite 1/(P-P2) in the pattern A/P+B/(1-P) for those constants A and B since P-P2 factors to P(1-P). We therefore have:

1/[P(1-P)] = A/P + B/(1-P)

A(1-P) + BP = 1

When P is 1, we have A(1-1)+B(1)=1, or B=1.

When P is 0, we have A(1-0)+B(0)=1, or A=1.

So, we can rewrite 1/(P-P^2) as 1/P+1/(1-P).

Whilst doing the entire on the ODE's left side, we have:

∫1/(P - P^2)dP

∫[1/P + 1/(1-P)]dP

∫(1/P)dP + ∫1/(1-P)dP

ln(P) + ∫1/(1-P)dP

Make a u-substitution to perform the second integral:

u = 1-P, du = -dP

ln(P) - ∫(1/u)du

ln(P) - ln(u)

ln(P) - ln(1-P)

ln[P/(1-P)]

Reconnecting that to the ODE yields the following:

ln[P/(1-P)] = t + c

e^ln[P/(1-P)] = e^(t + c)

P/(1-P) = e^t * e^c

P/(1-P) = ke^t, where k is a constant equal to e^c

P = (1-P)ke^t

P = ke^t - Pke^t

P + Pke^t = ke^t

P(1 + ke^t) = ke^t

P = ke^t / (1 + ke^t)

P = e^t / (1/k + e^t)

P = e^t / (d + e^t), where d is a constant equal to 1/k

So, the general solution to the ODE is P = e^t / (d + e^t), where d is a constant.

p*(1-p) = k*e^t ( we say that e^k is a constant)

1-p/p = k*e^t

P = 1/ (k*e^t +1)

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The complete question is-

Solve the given differential equation by separation of variables.

dP/dt = P - P²

The number of minutes per mile that Lin does ride will be 8 minutes per mile.

Lin rides at a speed of 6 miles / 48 minutes = 0.125 miles per minute. For us to convert this to minutes per mile, we have to take the reciprocal of this value, which is 1 / 0.125 = 8 minutes per mile.

To convert speed from miles per minute to minutes per mile, you can take the reciprocal of the value which means is the upside value and top. In this case, 0.125 miles per minute to minutes per mile is 8 minutes per mile.

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