A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0.5, 100 simulated proportions for samples of size 25 is shown in the dotplot. Using the dotplot, is there evidence that the proportion of times a spun dime lands on heads is greater than 0.5?
A) Yes, a proportion of 0.68 proves that the true proportion of heads is greater than 0.5.
B) Yes, a proportion of 0.68 only occurred once out of 100 simulated proportions; therefore, there is sufficient evidence that the true proportion of heads is greater than 0.5.
C) No, a proportion of 0.68 is only 0.18 more than 0.5; therefore, there is insufficient evidence that the true proportion of heads is greater than 0.5.
D) No, a proportion of 0.68 or more occurred 7 times out of 100 simulated proportions; therefore, there is insufficient evidence that the true proportion of heads is greater than 0.5.

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{20})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 1}(x-\stackrel{x_1}{4}) \\\\\\ y-20=x-4\implies {\Large \begin{array}{llll} y=x+16 \end{array}}\)

Value of equation T - 40 = 3 T equals to 43.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system. Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given

Equation

T - 40 = 3

Adding 40 on both sides,

T = 40 + 3

T = 43

Value of equation T - 40 = 3 is 43.

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The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668 (rounded to four decimal places).

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668(rounded to four decimal places).Here's how to calculate it:Given data mean μ = 9,000 and standard deviation σ = 1,000.To calculate the probability that a random light bulb lasts more than 10,500 hours, convert the problem to a standard normal distribution.

z = (10,500 - μ)/σ = (10,500 - 9,000)/1000 = 1.50

Here's the standard normal distribution curve with the shaded area representing the probability required: Standard normal distribution curve with the shaded area

Now, the area under the curve to the right of z = 1.5 is the probability that a randomly chosen light bulb will last more than 10,500 hours.

Using the Z table, we can look up the value corresponding to a z-score of 1.5. The table gives us a value of 0.9332.Now, the area to the left of z = 1.5 is 1 - 0.9332 = 0.0668, which is the probability that a randomly chosen light bulb lasts more than 10,500 hours, rounded to four decimal places.

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The temperature decreases by about 1.7° for each 1-degree increase north in latitude.

Given

Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian.

The table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude.

The first row is labeled latitude (degrees North) with entries 42, 45, 39, 35, 32, 41, 40, 33, 30.

The second row is labeled high temperature (degrees Fahrenheit) with entries 53, 51, 67, 63, 70, 58, 61, 67, 72.

The slope of a line in the two-dimensional Cartesian coordinate plane is usually represented by the letter m, and it is sometimes called the rate of change between two points.

Hence, the temperature decreases by about 1.7° for each 1-degree increase north in latitude.

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Answer:

b

Step-by-step explanation:

edge 2022

The measure of ∠6 is 54 degrees.

When parallel lines are cut by a transversal, angle relationship are formed. Therefore,

∠6 = 5x + 9 (vertically opposite angles)

∠6 = ∠2

Hence,

∠2 + 13x + 9 = 180

5x + 9  + 13x + 9 = 180

18x = 162

x = 162 / 18

x = 9

Hence,

∠6 = 5(9) + 9  54°

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Answer:

Werid I don’t know

Step-by-step explanation:

The height of the waterfall is approximately 309 yards.

To find the height of the waterfall, we can use trigonometry. The given information states that the distance from the point to the waterfall is 1000 yards, and the angle from the ground to the top of the waterfall is 17 degrees.

We can use the tangent function, which relates the height (opposite side) to the distance (adjacent side) and the angle:

tan(angle) = height / distance

Substituting the given values:

tan(17 degrees) = height / 1000 yards

To isolate the height, we can multiply both sides of the equation by 1000:

1000 * tan(17 degrees) = height

Using a calculator, we can calculate the value of the tangent of 17 degrees:

tan(17 degrees) ≈ 0.309

Substituting this value:

1000 * 0.309 = height

Therefore, the height of the waterfall is approximately 309 yards.

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The interpretation that the likelihood that the first question will be true is (a) Likely

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

From the question, we have the following parameters that can be used in our computation:

Probability value:-

The value of the probability and the notation are given as

P(true) = 0.8

As a general rule of probability, we have

Range of probability value = 0 to 1 (inclusive)

Unlikely = less than 0.5

Equally likely and unlikely = 0.5

Likely = greater than 0.5

Using the above as a guide, we have the following:

The value of P(true) = 0.8 is greater than 0.5

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To find the area under the curve y = 1.5 x^-2.5 from x = 8 to x = t, a) Area ≈ 0.2455 b) Area ≈ 0.0816 c) Area = 3(8)^-1.5 + C

we need to integrate the function with respect to x.

The integral of y = 1.5 x^-2.5 is:

∫ 1.5 x^-2.5 dx = -3x^-1.5 + C

where C is the constant of integration.

To evaluate the definite integral from x = 8 to x = t, we plug in the upper and lower limits of integration and subtract the values:

Area = [-3t^-1.5 + C] - [-3(8)^-1.5 + C]

Simplifying this expression, we get:

Area = -3t^-1.5 + 3(8)^-1.5

Now we can find the area for t = 10 and t = 100:

(a) t = 10:

Area = -3(10)^-1.5 + 3(8)^-1.5

Area ≈ 0.2455

(b) t = 100:

Area = -3(100)^-1.5 + 3(8)^-1.5

Area ≈ 0.0816

To find the total area under the curve for x ≤ 8, we need to integrate the function from 0 to 8:

∫ 1.5 x^-2.5 dx = -3x^-1.5 + C

Area = [-3(8)^-1.5 + C] - [-3(0)^-1.5 + C]

Area = 3(8)^-1.5 + C

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Answer:

No Solution, x is unable to be found

(i) The number of different divisions possible when 15 children divide themselves into teams of 5 each (Team A, B, and C) is 756.

(ii) If the teams are not distinguishable, the number of different divisions possible is 756 divided by 3!, which equals 126.

(i) To determine the number of different divisions when 15 children divide themselves into three teams of 5 each, we can calculate the number of combinations.

Since the order of the teams does not matter, we use the combination formula.

The formula is nCr = n! / (r! * (n - r)!), where n is the total number of children and r is the number of children per team.

Plugging in the values, we have 15C5 * 10C5 = (15! / (5! * 10!)) * (10! / (5! * 5!)) = 756.

(ii) If the teams are not distinguishable, we need to account for the fact that the order of the teams doesn't matter.

Each division would be counted multiple times if we considered the teams distinguishable. Since there are 3! (3 factorial) ways to arrange the teams, we divide the previous result by 3!, which gives us 756 / 3! = 126.

This accounts for the different arrangements of the same teams and gives us the number of distinct divisions.

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Answer:

La orquesta ahorraría S/ 18577 al comprar un piano digital en vez de un piano de cola.

Step-by-step explanation:

Para saber cuánto ahorraría la orquesta al comprar un piano digital en vez de un piano de cola, tienes que encontrar la diferencia entre el precio de ambos pianos restando el valor del piano digital del valor del piano de cola:

32476-13899= 18577

De acuerdo a esto, la respuesta es que la orquesta ahorraría S/ 18577 al comprar un piano digital en vez de un piano de cola.

Answer:

(C)  b = 0.

Step-by-step explanation:

Slope = (b - 5) / (3 - (-2)) = -1

(b - 5)/ 5 = -1

b - 5 = -5

b = -5 + 5 = 0.

Answer:Answer: B,E or 2nd answer and last

Step-by-step explanation: i did this test two week ago and made 100 own it good look to you

Step-by-step explanation:

Answer:

yo

Step-by-step explanation:

its B and E on edge

or

StartFraction 13 over 2 EndFraction divided by three-fourths

StartFraction 13 over 2 EndFraction (four-thirds)

To find the number that makes the ratio 8:9 equivalent, we need to first understand the concept of equivalent ratios.Therefore, 9 is the number that makes the ratio 8:9 equivalent.

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To calculate the residual for observation 6, we first need to find the forecast for observation 6. Based on the given information, the forecast for observation 6 is 34. Therefore, the residual for observation 6 would be:

Residual = Actual Demand - Forecast
Residual = 38 - 34
Residual = 4

So the residual for observation 6 is 4.
Hi! To find the residual for observation 6, we need to subtract the forecast (F) from the actual demand (A). In this case, the observation 6 values are:

Actual Demand (A): 38
Forecast (F): 28

Now, we'll calculate the residual:

Residual = Actual Demand (A) - Forecast (F)
Residual = 38 - 28
Residual = 10

So, the residual for observation 6 is 10.

The pool dimensions are approximately 12.22 by 21.22 feet.

To start, we know that the pool must be a 77 sq ft rectangle, so we can use the formula for the area of a rectangle (length x width = area) to solve for the dimensions.

77 = length x width

Next, we know that the fenced off plot is a 17 by 26 feet rectangle. We can use this information to set up an equation for the distance between the pool and the fence:

17 - 2x = length
26 - 2x = width

We also know that the fence should be twice as far away on the end where the lifeguard chair will be located, so we can set up another equation:

17 - 4x = length (on the side with the lifeguard chair)

Now we can substitute the expressions for length and width into the formula for the area of a rectangle:

77 = (17 - 2x)(26 - 2x)

Expanding the expression on the right side, we get:

77 = 442 - 86x + 4x^2

Rearranging and simplifying, we get a quadratic equation:

4x^2 - 86x + 365 = 0

Using the quadratic formula, we can solve for x:

x = (86 +/- sqrt(86^2 - 4(4)(365))) / (2(4))

x = (86 +/- sqrt(55284)) / 8

x = (86 +/- 234.85) / 8

x = 36.86 or 2.39

We can ignore the negative value, so x = 2.39 feet.

Now we can use the equations for length and width to solve for the dimensions of the pool:

length = 17 - 2x = 17 - 2(2.39) = 12.22 feet
width = 26 - 2x (except on the side with the lifeguard chair, where it is 4x) = 26 - 2(2.39) = 21.22 feet

So the pool dimensions are approximately 12.22 by 21.22 feet.

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Answer:

A, or 50.24 ft.

Step-by-step explanation:

Doing the equation above, we know the radius of the circle, which is 8 ft.

8ft times 2 is 16ft.

16ft times pi gives us (rounded) 50.24 ft.

Answer:

No it is not a rational number

Step-by-step explanation:

A rational number is a number that can be written in the form

p

q

, where

p

and

q

are integers and

q

≠

o

.

All fractions, both positive and negative, are rational numbers. A few examples are

4

5

,

−

7

8

,

13

4

,

and

−

20

3

The proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

If three out of every thirteen trick-or-treaters were dressed as cowboys, it means that the proportion of trick-or-treaters dressed as cowboys is 3/13.

To find the proportion of trick-or-treaters who were not dressed as cowboys.

we subtract the proportion dressed as cowboys from 1 (since the total proportion of trick-or-treaters must sum to 1).

Proportion not dressed as cowboys = 1 - Proportion dressed as cowboys

Proportion not dressed as cowboys = 1 - (3/13)

Proportion not dressed as cowboys = (13/13) - (3/13)

Proportion not dressed as cowboys = 10/13

Therefore, the proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

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Answer:

y=-8x-2

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

7(2x-3y)

Let x = 8 and y = -3

7(2*8-3 (-3))

Inside parentheses first

7(16+9)

Add inside the parentheses

7(25)

Multiply

175

The third Taylor polynomial, denoted as T3(x), for the function f(x) = 7sin(x)e^(-5x) based at b = 0 is:

T3(x) = f(0) + f'(0)(x-0) + f''(0)(x-0)^2/2! + f'''(0)(x-0)^3/3!

To find T3(x), we need to calculate the values of f(0), f'(0), f''(0), and f'''(0) and substitute them into the formula.

First, we find f(0) by evaluating the function at x = 0:

f(0) = 7sin(0)e^(-5*0) = 0

Next, we find f'(0) by taking the derivative of the function and evaluating it at x = 0:

f'(x) = 7cos(x)e^(-5x)

f'(0) = 7cos(0)e^(-5*0) = 7

Similarly, we find f''(0) by taking the second derivative and evaluating it at x = 0:

f''(x) = -7sin(x)e^(-5x) - 7cos(x)e^(-5x)

f''(0) = -7sin(0)e^(-50) - 7cos(0)e^(-50) = 0 - 7 = -7

Finally, we find f'''(0) by taking the third derivative and evaluating it at x = 0:

f'''(x) = -7cos(x)e^(-5x) + 35sin(x)e^(-5x) + 7sin(x)e^(-5x)

f'''(0) = -7cos(0)e^(-50) + 35sin(0)e^(-50) + 7sin(0)e^(-5*0) = -7 + 0 + 0 = -7

Substituting these values into the formula for T3(x), we get:

T3(x) = 0 + 7x + 0/2! + (-7)(x^3)/3!

Simplifying further, we have:

T3(x) = 7x - 7x^3/6

Therefore, the third Taylor polynomial, T3(x), for the function f(x) = 7sin(x)e^(-5x) based at b = 0 is 7x - 7x^3/6.

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For a two-dimensional potential flow, the potential is given by 1 r (x, y) = x (1 + arctan x² + (1+ y)², 2πT where the parameter A is a real number. Given potential function is;ϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πT

To find velocity components ux and uy, we need to take partial derivative of potential functionϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πTUsing the chain rule;    ∂ϕ/∂x = ∂ϕ/∂r * ∂r/∂x + ∂ϕ/∂θ * ∂θ/∂x                                                                                             = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT ∂ϕ/∂y = ∂ϕ/∂r * ∂r/∂y + ∂ϕ/∂θ * ∂θ/∂y                                                                                              = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πTNow, replace cosθ and sinθ with x/r and y/r respectively∂ϕ/∂x = x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT- y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [x²-y²]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT∂ϕ/∂y = y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT + x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [2xy]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT(2) To find stagnation point, we have to find (x,y) such that ux = uy = 0 and ϕ(x,y) is finite. Here, from (1) we get two equations;  x(1+arctan(x² + (1+y)²))/2πT= 0 and  x(1+arctan(x² + (1+y)²))/2πT + y(1+arctan(x² + (1+y)²))/2πT= 0For (1), either x=0 or arctan(x² + (1+y)²) = -1, but arctan(x² + (1+y)²) can't be negative so x=0. Thus, we get the condition y= -1  from (2)So, stagnation point is (0, -1).(3) For the far field, pressure is p, density is P. In potential flow, we have;  P = ρv²/2 + P0,  where P0 is constant pressure. Here, P0 = P and v = ∇ϕ   so, P = ρ[ (∂ϕ/∂x)² + (∂ϕ/∂y)² ]/2Using expressions of ∂ϕ/∂x and ∂ϕ/∂y obtained above, we can find pressure at (0,-2).(4) Given flow is around a cylinder. For flow around cylinder, stream function can be written as;   ψ(r,θ) = Ur sinθ (1-a²/r²)sinθTo find centre and radius of the cylinder, we find point where velocity is zero. We know that ψ is constant along any streamline. So, at the boundary of cylinder, ψ = ψ0, and at the centre of the cylinder, r=0.Using stream function, it is easy to show that ψ0= 0.So, at boundary of cylinder; U(1-a²/R²) = 0, where R is radius of cylinder, which gives R=aSimilarly, at centre; U=0To find the resulting force on the cylinder, we first have to find the lift and drag coefficients;  C_d = 2∫_0^π sin²θ dθ = π/2   and  C_l = 2∫_0^π sinθ cosθ dθ = 0We know that C_d = F_d/(1/2 ρ U²L) and C_l = F_l/(1/2 ρ U²L)where L is length of cylinder.So, F_d = π/2 (1/2 ρ U²L) and F_l= 0. Thus, the resulting force is F= (π/2) (1/2 ρ U²L) at an angle 90° to the flow direction.

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Using these values, we can write Bernoulli's equation as: P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

(1) To determine the expression for the velocity components ux and uy, we can use the relationship between velocity and potential in potential flow:

ux = ∂Φ/∂x

uy = ∂Φ/∂y

Taking the partial derivatives of the potential function Φ(x, y) with respect to x and y:

∂Φ/∂x = (1+arctan(x^2+(1+y)^2)) - x * (1/(1+x^2+(1+y)^2)) * (2x)

∂Φ/∂y = -x * (1/(1+x^2+(1+y)^2)) * 2(1+y)

Simplifying these expressions, we have:

ux = 1 + arctan(x^2+(1+y)^2) - 2x^2 / (1+x^2+(1+y)^2)

uy = -2xy / (1+x^2+(1+y)^2)

(2) To find the value of A such that the point (x, y) = (0,0) is a stagnation point, we need to find the conditions where both velocity components ux and uy are zero at that point. By substituting (x, y) = (0,0) into the expressions for ux and uy:

ux = 1 + arctan(0^2+(1+0)^2) - 2(0)^2 / (1+0^2+(1+0)^2) = 1 + arctan(1) - 0 = 1 + π/4

uy = -2(0)(0) / (1+0^2+(1+0)^2) = 0

For the point (x, y) = (0,0) to be a stagnation point, ux and uy must both be zero. Therefore, A must be chosen such that:

1 + π/4 = 0

A = -π/4

(3) To determine the pressure at the point (0, -2), we can use Bernoulli's equation for potential flow:

P + 1/2 * ρ * (ux^2 + uy^2) = constant

At the far field, where the velocity is assumed to be zero, the pressure is constant. Let's denote this constant pressure as P_far.

At the point (0, -2), the velocity components ux and uy are:

ux = 1 + arctan(0^2+(1-2)^2) - 2(0)^2 / (1+0^2+(1-2)^2) = 1 + arctan(5) - 0 = 1 + arctan(5)

uy = -2(0)(-2) / (1+0^2+(1-2)^2) = 4 / 3

Using these values, we can write Bernoulli's equation as:

P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

Solving for P at the point (0, -2), we have:

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

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Solution:

Note that:

Find the area by substituting the values in the expression.

Answer: Your answer is 5 5/9 ft²

Step-by-step explanation: I did the test Here's proof

Hope it helped :D

The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

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Answer:

x = 220°

Step-by-step explanation:

∠AEB = ∠ABE = (180 - 80) /2 = 50   (isosceles triangle property)

∠BED = 90

x = 360 - 90 - 50 =220  

The measure of angle x is 220°.  

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle. An isosceles triangle's third side, which is not equal to its other two sides, is referred to as its base. The two angles that are opposite the equal sides are identical to one another.

Given that ΔABE is an isosceles triangle.

The length of AB = AE

And angle ∠BAE = 80°

According to the isosceles triangle property,

⇒ ∠ABE = ∠AEB

⇒ ∠ABE = (180 - 80) /2 = 50

Since BCDE is a rectangle

So ∠BED = 90°

x = 360 - ∠BED  - ∠AEB

x = 360 - 90 - 50 =220  

x = 220°  

Hence, the measure of angle x is 220°.  

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