anybody know if your suppose to use the pie symbol or the numbers when doing math

The length of BP is 14.4 meters.

To find the length of BP, we can use the property that states that when two chords intersect inside a circle, the product of the segment lengths on one chord is equal to the product of the segment lengths on the other chord.

Using this property, we can set up the equation:

AP * PC = BP * DP

Substituting the given values:

12 m * 6 m = BP * 5 m

Simplifying:

72 m^2 = BP * 5 m

To solve for BP, divide both sides of the equation by 5 m:

72 m^2 / 5 m = BP

Simplifying:

14.4 m = BP

Therefore, the length of BP is 14.4 meters.

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To evaluate the line integral F.dr using the given potential function o of the gradient field F and the curve C, we can use two methods: the first is to directly evaluate the integral using the parameterization of the curve and the second is to use the Fundamental Theorem of Calculus for Line Integrals.

In this case, we have the potential function o(x, y, z) = xy + xz + yz and the curve C given by r(t) = (t, 2t, 3t) for t between 0 and 1. Using the first method, we can substitute the parameterization of the curve into the integral F.dr and evaluate it directly. We have:

F.dr = (xy + xz + yz)(dx/dt, dy/dt, dz/dt)dt

= (2t^2 + 3t^2 + 6t^2)(1, 2, 3)dt

= (11t^2)(1, 2, 3)dt

Integrating this from 0 to 1, we get:

F.dr = ∫_0^1 (11t^2)(1, 2, 3)dt = (11/2, 11, 33/2)

Using the second method, we can apply the Fundamental Theorem of Calculus for Line Integrals, which states that the line integral of a conservative field along a curve C depends only on the endpoints of C and the values of a potential function at these endpoints. Since we have a gradient field F, it is conservative, and we can find the potential function o by integrating the components of F. We have:

Fx = y + z

Fy = x + z

Fz = x + y

Integrating the first component with respect to x, we get:

o(x, y, z) = ∫ (y + z)dx = xy + xz + h(y, z)

Taking the partial derivative of this expression with respect to y, we get:

∂o/∂y = x + ∂h/∂y = x + z

Comparing this with the second component of F, we get:

x + z = x + z

Therefore, h(y, z) = yz, and we have:

o(x, y, z) = xy + xz + yz

Using the potential function, we can evaluate the line integral F.dr by computing the difference of the potential function at the endpoints of the curve. We have:

F.dr = o(r(1)) - o(r(0))

= o(1, 2, 3) - o(0, 0, 0)

= (2 + 3 + 6) - (0 + 0 + 0)

= 11

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The net force is the vector sum given by ⟨27,−31,14⟩N

To determine the net force acting on the system with the given forces, we have to compute the vector sum of the forces. The vector sum of the forces is equal to the net force acting on the system.

Now let's find the net force:

Fnet = F1 + F2
F1 = ⟨11, -18, 31⟩N and, F2 = ⟨16, -13, -17⟩N

Fnet = F1 + F2

= ⟨11,−18,31⟩N+⟨16,−13,−17⟩N

= ⟨11+16,−18+(−13),31+(−17)⟩N
= ⟨11,−18,31⟩N+⟨16,−13,−17⟩N

= ⟨27,−31,14⟩N

Therefore, the net force acting on the system is ⟨27,−31,14⟩N.

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

Answer: p = (3.6 x 10^4)(0.03)^2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the real answer would be 1/1048576

The statement "The Taylor series centered at 0 (aka MacLaurin Series) for f(x) = \(x^{11}\) sin x has only even powers of x" is false.

The Taylor series centered at 0 (or MacLaurin series) for the function f(x) = \(x^{11}\) sin(x) includes terms with both even and odd powers of x. The general form of the Taylor series for this function is:

f(x) = f(0) + f'(0)x + f''(0)\(x^{2}\)/2! + f'''(0)\(x^{3}\)/3! + ...

The derivative of f(x) = \(x^{11}\) sin(x) involves both the derivative of \(x^{11}\) (which has only even powers) and the derivative of sin(x) (which has both even and odd powers). Therefore, when the Taylor series is expanded, terms with both even and odd powers of x will be present.

Hence, the statement is false.

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Answer:

64 mm²

Step-by-step explanation:

16 × 4 = 64

good luck, i hope this helps :)

Answer:

so if you do 16×4 you will get 64mm2

Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

Answer:

x = 8

Step-by-step explanation:

Recall that the interior angles of a triangle always add up to 180 degrees.

Therefore:  77 + 50 + 7X - 3 = 180, or:

                   77          + 7X - 3 = 130, or:

                                     7x      = 56

Dividing both sides by 7 yields x = 8

The correct option e) 94.29%, for the probability that among the next 166 responses there will be at most 43 correct answers.

If we use a normal distribution to simulate any binomial distribution with p = 0.24 for n = 166 results, then:

There should be 43 correct responses, or

μ = np = 166*0.24

μ = np = 34.86

The number of accurate responses has a standard deviation of

σ = √(np(1-p))

σ = √(34.86*0.76)

σ = 5.14

43 correct responses have a z-value;

z = (x - μ)/σ

z = (43 - 34.86)/5.14

z = 1.58

The likelihood that 43 accurate responses are provided is:

N(1.58) = 0.9429

Thus, the probability that among the next 166 responses there will be at most 43 correct answers is 94.29%.

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The complete question is-

Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.

a) 74.56870% b) 74.30203% c) 75.20203% d) 94.95%  e) 94.29%

Answer:

∠E

Step-by-step explanation:

∠E is between PE and EN

Answer:

Step-by-step explanation:

-2

Answer:

(-3,-3)

Step-by-step explanation:

I think I think

Answer:

-1

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

6/18, divide each side by 3 and you get 1/3

3) The resulting density function \(f_W(w)\) can be derived by evaluating the integral. However, the integral does not have a closed-form solution and requires numerical methods or specialized techniques to calculate.

1. To find the probability P(11) for the random variable X with the probability density function f(x) = xe^(-x), we need to calculate the definite integral of the density function over the interval [1, ∞):

P(11) = ∫[1, ∞) f(x) dx

P(11) = ∫[1, ∞) xe^(-x) dx

To solve this integral, we can use integration by parts or recognize that the integrand is the derivative of the Gamma function.

Using integration by parts, let u = x and dv = e^(-x) dx. Then du = dx and v = -e^(-x).

P(11) = -[x * e^(-x)] [1, ∞) + ∫[1, ∞) e^(-x) dx

P(11) = -[x * e^(-x)] [1, ∞) - e^(-x) [1, ∞)

Evaluating the expression at the upper limit (∞), we have:

P(11) = -[∞ * e^(-∞)] - e^(-∞)

Since e^(-∞) approaches zero, we can simplify the expression to:

P(11) = 0 - 0 = 0

Therefore, the probability P(11) for the given density function is 0.

2. For the random variables X and Y with the given distributions, we want to find the conditional probability P(X = 1 | Y ≥ 3).

By using Bayes' theorem, the conditional probability can be calculated as:

P(X = 1 | Y ≥ 3) = P(X = 1 ∩ Y ≥ 3) / P(Y ≥ 3)

Since X and Y are independent, the joint probability can be expressed as the product of their individual probabilities:

P(X = 1 ∩ Y ≥ 3) = P(X = 1) * P(Y ≥ 3)

P(X = 1 ∩ Y ≥ 3) = (1/2) * P(Y ≥ 3)

The exponential distribution with mean 2 has the cumulative distribution function (CDF) given by:

F_Y(y) = 1 - e^(-y/2)

To find P(Y ≥ 3), we can use the complement property of the CDF:

P(Y ≥ 3) = 1 - P(Y < 3) = 1 - F_Y(3)

P(Y ≥ 3) = 1 - (1 - e^(-3/2)) = e^(-3/2)

Substituting this into the previous expression, we have:

P(X = 1 ∩ Y ≥ 3) = (1/2) * e^(-3/2)

Finally, calculating the conditional probability:

P(X = 1 | Y ≥ 3) = P(X = 1 ∩ Y ≥ 3) / P(Y ≥ 3)

P(X = 1 | Y ≥ 3) = [(1/2) * e^(-3/2)] / e^(-3/2)

P(X = 1 | Y ≥ 3) = 1/2

Therefore, the conditional probability P(X = 1 | Y ≥ 3) is equal to 1/2.

3. To derive the density function \(f_W(w)\) for the random variable W = X + Y, where X is exponentially distributed with E(X) = 1 and Y is standard normally distributed with density ϕ(y) = (1/√(2π)) * e^(-y^2/2

), we can use the convolution of probability density functions.

The density function for the sum of two independent random variables can be obtained by convolving their individual density functions:

\(f_W(w)\) = ∫[-∞, ∞]\(f_X\)(w - y) *\(f_Y\)(y) dy

Since X is exponentially distributed with mean 1, its density function is \(f_X(x)\) = e^(-x) for x ≥ 0, and Y is standard normally distributed with density ϕ(y), we have:

\(f_W(w)\) = ∫[0, ∞] e^-(w-y) * e^(-y) * ϕ(y) dy

Simplifying the expression, we get:

\(f_W(w)\) = ∫[0, ∞] e^(-w) * e^(-y) * ϕ(y) dy

Since Y follows a standard normal distribution, the density function ϕ(y) is given as:

ϕ(y) = (1/√(2π)) * e^(-y^2/2)

Substituting this into the previous expression, we have:

\(f_W(w)\) = (1/√(2π)) * ∫[0, ∞] e^(-w) * e^(-y) * e^(-y^2/2) dy

Since X and Y are independent, their sum W = X + Y is a convolution of exponential and normal distributions.

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Answer:

Tim purchased 6 video games.

Step-by-step explanation:

Let's set the number of games Time purchased as x.

Due to each game costing $25, the total amount of money used on buying games would be ($25)x.

Hence, as the total amount of money used to buy both the console and the video games would be $350, the equation can be set as:

\(\$25x + \$200 = \$350\)

\(\$25x = \$(350 - 200)\)

\(x = \frac{\$150}{\$25}\)

\(x = 6\)

Therefore, Tim purchased 6 video games.

Hope this helped!

The lower bound of the 95% confidence interval for the population mean is given as follows:

53.51.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 30 - 1 = 29 df, is t = 2.0452.

The parameters are given as follows:

\(\overline{x} = 55, s = 4, n = 30\)

Hence the lower bound of the interval is given as follows:

\(55 - 2.0452 \times \frac{4}{\sqrt{30}} = 53.51\)

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Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Using the diagram and given measurements the area of the shaded potion is solved to be 46 cm^2

Area of the shaded portion is solved using the following factors

Entire area of the rectangle

= length *  width

= 42 * 21

= 882 cm^2

Area of the smaller rectangle

= length * width

= 28 * 15

= 420 cm^2

Area of the shaded portion

= Entire area of the rectangle  -  Area of the smaller rectangle

= 882 cm^2 - 420 cm^2

= 462 cm^2

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The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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Angle A is approximately 43.48 degrees, angle B is approximately 31.52 degrees, and side c is approximately 91.19 units in the oblique triangle with sides a = 60, b = 8, and angle C = 105 degrees.

To find angle A, we can use the Law of Sines, which states that the ratio of the sine of an angle to the length of the opposite side is the same for all angles in a triangle. The formula is:\(\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\) Plugging in the given values, we have:

\(\(\frac{60}{\sin(A)} = \frac{8}{\sin(B)} = \frac{c}{\sin(105^\circ)}\)\)

Solving for angle A, we can use the inverse sine function:

\(\(\sin(A) = \frac{60}{c} \times \sin(105^\circ)\)\(A = \sin^{-1} \left(\frac{60}{c} \times \sin(105^\circ)\right)\)\)

Similarly, to find angle B, we can use the fact that the sum of angles in a triangle is 180°:

\(\(A + B + C = 180^\circ\)\)

\(\(B = 180^\circ - A - C\)\)

Finally, to find side c, we can use the Law of Cosines, which relates the lengths of the sides and the cosine of one of the angles:

\(\(c^2 = a^2 + b^2 - 2ab \cos(C)\)\)

Plugging in the given values, we can solve for side c.

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490

472 <490<500

it fits the criteria

Answer:

Please should we solve the equation or the angle?

The random variable x has a uniform distribution, defined on [7,11], therefore the P is (C) 0.75

For a uniform distribution, the probability of a random variable X falling within a specific interval is calculated by dividing the length of the interval by the total length of the distribution. In this case, X has a uniform distribution defined on [7, 11].
To find P(8 ≤ X ≤ 11), we first determine the length of the interval: 11 - 8 = 3. Next, we find the total length of the distribution: 11 - 7 = 4. Now, we can calculate the probability:
P(8 ≤ X ≤ 11) = (length of interval) / (total length of distribution) = 3 / 4 = 0.75
Thus, the correct answer is C, 0.75.

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The Taylor polynomial error bound provides an upper bound on the error between a Taylor polynomial approximation and the actual function value within a given interval.

Specifically, it guarantees that the absolute value of the difference between the actual function value and the Taylor polynomial approximation is no more than the maximum value of the absolute value of the (n+1)th derivative of the function within that interval, multiplied by the maximum distance between the point of approximation and the center of the Taylor series expansion. In other words, the error bound guarantees that the error in using the Taylor polynomial approximation is no larger than a certain value, which can be computed using the given formula.

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The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.

As given in the question,

Given :  95% of the test takers score are below z.

z-score is given  by,

z=(x-μ)/σ

Mean of the score 'μ' = 500

Standard deviation of the score ' σ' = 100

Z = 95%

  = 0.95

P(z<Z) = 1-0.95

           = 0.05

The value of z which corresponds to 0.05 in the table is equal to 1.96.

Substitute all the values we get,

z=(x-μ)/σ

⇒1.96 = ( x - 500 ) / 100

Multiply by 100 both the sides we get,

⇒ 196 = ( x - 500 )

⇒ x = 696

Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.

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The equation is 0 + 59 = 17 which can help Aly calculate the number of more toy cars than trucks. which is the correct answer would be an option (C).

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

We have been given that Aly has 59 toy cars and 17 toy trucks.

To determine the equation can help Aly calculate number of more toy cars than trucks she has

We have to subtract 17 from both sides and add 0

0 + 59 = 17

0 + 59 - 17 = 42

Therefore, the equation is 0 + 59 = 17 which can help Aly calculate the number of more toy cars than trucks.

Hence, the correct answer would be option (C).

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Answer:

Step-by-step explanation:

\(a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}\)